Shawn C. Kimmel. Master of Science in Mechanical Engineering. Dr. Dennis W. Hong, Chair Dr. Alfred L. Wicks Dr. Robert L. West

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1 Considerations for and Implementations of Deliberative and Reactive Motion Planning Strategies for the Novel Actuated Rimless Spoke Wheel Robot IMPASS in the Two-Dimensional Sagittal Plane Shawn C. Kimmel Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Dr. Dennis W. Hong, Chair Dr. Alfred L. Wicks Dr. Robert L. West May 30, 2008 Blacksburg, Virginia Keywords: Spoke, Wheel, Deliberative, Reactive, Robot, IMPASS, Autonomous, RoMeLa, Rimless, Mobility, Motion, Planning Copyright 2008, Shawn C. Kimmel

2 Considerations for and Implementations of Deliberative and Reactive Motion Planning Strategies for the Novel Actuated Rimless Spoke Wheel Robot IMPASS in the Two-Dimensional Sagittal Plane Shawn C. Kimmel (ABSTRACT) IMPASS is a novel spoke-wheel robot invented by researchers at the Robotics and Mechanisms Lab (RoMeLa) at Virginia Tech. The robot is driven by a rimless spoke wheel which can alter the length of any given spoke in the hub. This form of novel locomotion combines the efficiency of a wheeled robot and the mobility of a legged robot, arriving at a very practical mobility platform. A highly mobile robot such as IMPASS could prove very valuable in applications where the terrain is complex and dangerous, such as search and rescue, reconnaissance, or anti-terror response. A prototype has been constructed that effectively demonstrates the actuated spoke wheel concept using two wheels containing six spokes each. Manually controlling the motion of two wheels and twelve spokes would be a daunting task for any operator. Due to this inherent complexity, automated motion control is a necessity for the IMPASS platform. The work presented here will discuss two different approaches to the motion planning problem for the two-dimensional sagittal plane. The first approach is deliberative in nature and depends on fairly accurate terrain sensing. The motion planning first decides on a set of contact points based on obstacle configurations and a Lagrangian interpolation of the terrain. A lower level motion planning component then executes the movements that guide the spoke ends to the contact points. The second motion planning approach is reactive in nature. Proprioceptive and tactile sensors are used to determine the robot s pose and immediate surroundings. These sensors directly affect the motion profile of the robot. The reactive approach follows much simpler logic, which theoretically will make it more robust. Motion planning strategies were tested in simulation and on the IMPASS prototype. Both strategies proved to be well suited for different applications. The deliberative control was very successful in a structured environment, whereas the reactive control was able to cross a wider variety of terrain. The results from the testing also provided some insight into variables introduced by the hardware. Future improvements to the motion planning control include accounting for these variables in the hardware and eventually developing three-dimensional motion planning algorithms based on the lessons learned from the two-dimension case. The author would like to thank the National Science Foundation (NSF) for their support of this project under grant No. IIS

3 Dedication I would like to dedicate this work to my mother, who is the definition of strength and perseverance. iii

4 Acknowledgments The last two years have been a most enjoyable scholarly journey which would have been impossible without the friendship and guidance of my advisor Dr. Dennis Hong. He is a very perceptive and patient mentor, from whom I have learned much. Dr. Hong has created an excellent research environment which reflects his love and dedication to the field of robotics and mechanisms. To the other professors on my committee, thank you for your support and guidance through my Masters experience. Dr. Wicks, thank you for the invaluable stories, and barbecues and pizza when hours got long. Dr. West, thank you for the enlightening conversations. I would also like to take this time to thank a professor not on my committee, for without his encouragement I would not be where I am: Dr. Reinholtz. Your passion for knowledge and life is contagious. My gratitude goes out to Jesse Hurdus, an unofficial member of my committee who I was able to bounce ideas at on a daily basis. Within the student community, I would like to acknowledge first and foremost the senior design projects who worked tirelessly to create prototypes of the IMPASS robot. Without them, this work would not be possible. In particular, I would like to acknowledge Eric Russell and Blake Jeans for their contributions to the IMPASS software in the Robot Driver, High Climbing, and Reactive Motion Planning components. It has been a pleasure and a privilege to be a part of the senior design teams. Thank you Sean Eggar for providing assistance in testing and building of the robots. Finally, I would like to thank my fellow graduate students in the Robotics and Mechanisms Lab (RoMeLa) at Virginia Tech. Especially, I would like to thank the lab members that worked on IMPASS with me: Ping Ren and Ya Wang. Thank you both for the discussions and brainstorming sessions. In addition to these two, I would like to thank the other individuals in RoMeLa who has helped me in one capacity or another: Brad, Eric, Derek, Gabe, Ivette, Joe, John, Karl, and Robert; the best of luck to you in your research/ careers. iv

5 Contents 1 Introduction 1 2 Background Leg-Wheel Hybrids Non-Integrated Leg-Wheel Hybrids Integrated Leg-Wheel Hybrids Motion Planning IMPASS s Kinematics Autonomous Robotic Control Platform Development Spoke Actuation Hub Design Hub Drive Train Body Design Step Transitions One-Point Contact Step Transitions Constant Angular Velocity of Hub Constant Switching Angle of Spoke Two-Point Contact Step Transitions Experimenting with Two-Point Contact Transitions v

6 5 Motion Planning Deliberative Motion Planning Representation of the Environment and the Robot Defining Motion of the Robot Initial Contact Point Selection (ICPS) Step Execution Experimenting with Deliberative ICPS Motion Planning Reactive Motion Planning Conclusion Future Work Bibliography 84 A Deliberative Motion Planning Simulations 87 vi

7 List of Figures 1.1 Potential uses for an actuated spoke wheel robot A prototype of the IMPASS actuated spoke wheel platform has been developed and used for motion planning research Development of motion planning algorithms was conducted in a custom built simulator Non-integrated leg-wheel hybrid robots High mobility planetary explorers that use non-integrated leg-wheel mechanisms Integrated leg-wheel hybrid robots The integrated leg-wheel hybrid, Scout, uses an umbrella mechanism with one degree of freedom to change the wheel diameter [1] Stop motion pictures of RHex climbing a set of stairs using Ned s Improved Ascending Algorithm (NIAA). Each picture depicts the state of the robot upon completion of one of the four stages. Shaded dots below each picture indicate legs in contact with ground [2] Mobility analysis of a single actuated spoke wheel describing degrees of freedom for different configurations [3] Geometry and coordinate system for a planar single actuated spoke wheel [3] Frame of reference for the kinematic model of the actuated spoke wheel [4] Shakey was the first robot to preform autonomous operations by acting on sensor input [5] The IMPASS prototype climbing a set of stairs with ease Potential mechanisms for spoke actuation vii

8 3.3 The first iteration of the chain belt and sprocket design for the spokes of IMPASS The final iteration of the chain belt and sprocket design for the spokes of IMPASS The hub driveshaft is connected to the hub by a plate pictured on the left. The three spoke motors attach to this hub plate. All the wires for the hub run through the center of the shaft Hub plates transmit torque through a set of teeth that mesh with the adjacent hub plate. The plates are held in compression by six screws that run through hollow shafts around the edges of the hubs The drive mechanism for the spokes is a belt and sprocket. Tension in the belt is maintained with two coupled idler sprockets The hub drivetrains share their axis of rotation, but can rotate independently. A 90 degree gear box allows the motors to be positioned further back, helping with placement of the CG The maximum torque experienced by the hub motors occurs when the robot is climbing with a spoke that is extended to full length and oriented horizontally. The free-body diagram for this case is shown This picture shows the new carbon fiber body for IMPASS side by side with the old aluminum frame body. The new body saves on weight and is more protective of the interior components The two-point contact gait shown rotating clockwise through a step. This gait constrains the position of the hub center to a circle for which the radius is the step length divided by 3. The bar in the center of the robot s spokes is the center of the circular path, (x c, z c ). [6] IMPASS in a two-point contact configuration, showing the velocity vector v and contact point vector d g The simulator was used to test algorithms before implementing them on the robot The transition case for θ = 30. The front spokes touch the ground before θ = 0 because of compliance in the spokes and backlash in the hub gear train IMPASS s switching angle can be described relative to the x-axis or the line normal to the ground link of the terrain. These switching angles are referred to as θ and θ 2 respectively viii

9 4.6 When in the two-point contact configuration, IMPASS s legs make a triangle with the ground link. The boundary conditions can be determined by the sum of the angles equal 180 and the value of β This graph plots the spoke lengths IMPASS against each other as θ 2 is changed in a 16 inch step. r A is the bottom axis and r B is at the left. The rectangular box represents the robots physical limitations. For this 16 inch step, IMPASS has a continuous range in the solution space [7] Shown is the spoke lengths for IMPASS as θ 2 is changed in a 20 inch step. r Bz peaks first, followed by r Az The maximum and minimum spoke lengths are shown as horizontal lines. The minimum θ 2 is found at the vertical line where both spoke lengths are within the bounds There are infinite configurations in which IMPASS can transition with the one-point contact gait. This shows various configurations that are particularly useful from a motion planning perspective These graphs plot the spoke lengths of IMPASS, r A and r B, for a given step length. r A is the bottom axis and r B is at the left. The curve is created by varying θ 2 from 30 to 90, which rotates the robot through the full two-point contact case. The dashed box represents the physical limitation for spoke lengths [7] IMPASS descending an obstacle with θ = The left graph shows r Az and r Bz with respect to θ for equal spoke lengths. The line that peaks first is r Bz. The filled in region represents the area where the Descending Potential (DP)> 0 (i.e. r Bz > r Bz ). The right graph shows the DP, which reaches its maximum value at θ = 2 π = For any combination of spoke lengths, the greatest DP will always be achieved with IMPASS at the ledge of an obstale and a vertical ground link. The circle shows the foot path as the robot rotates through all possible θ The left graph shows r Az at minimum spoke length and r Bz at maximum spoke length with respect to θ. The filled in region represents the area where the Descending Potential (DP)> 0 (i.e. r Bz > r Bz ). The right graph shows the DP, which reaches its maximum value at θ = 2 π = The transition case for θ = 60. The front spokes touch the ground before θ = 0 because of compliance in the spokes and backlash in the hub gear train This figure shows the Non-Adjacent Ascending Transition configuration chosen for climbing large obstacles. θ is set equal to zero such that the back spoke is vertical, minimizing the effect of compliance in the spokes ix

10 4.17 IMPASS climbing a 12 inch obstacle with the Adjacent Ascending Transition, θ = 0. The front spokes touch the ground before θ = 0 because of compliance in the spokes and backlash in the hub gear train IMPASS climbing a 18 inch obstacle with the Non-Adjacent Ascending Transition, θ = 0. The compliance of the spokes is noticeable in Figure 4.18(d) [8] The robot traversing moderate obstacles in the simulation environment with the Default Transition, θ = This graph plots the length of the back spoke against the length of the front spoke during a two-point contact step. A dashed box has been included which shows the maximum and minimum spoke lengths. This particular step length of 17 inches enters and leaves the solution space six distinct times The arcs seen in this figure shows the possible position of the hub center for three consecutive steps. The points at which the arcs intersect is where the transition must occur IMPASS walking in the two-point contact gait. The transitions are determined by the contact points The software interfaces for controlling IMPASS The architecture for the Initial Contact Point Selection (ICPS) implementation of the deliberative approach follows the sense-plan-act sequence. The ICPS method has three basic steps within the contact point planner: Critical Contact Region (CCR) identification and refinement, Critical Contact Point (CCP) determination, and Intermediary Contact Point (ICP) determination When navigating non-traversable segments, IMPASS must step in certain critical contact regions (CCR) before and after the obstacle. These regions are geometrically determined from the dimensions of the robot When navigating non-traversable segments, IMPASS must step in certain critical contact regions (CCR) before and after the obstacle. These regions are geometrically determined from the dimensions of the robot The critical contact regions (CCR) for obstacle i can include other nontraversable segments The working contact regions (WCR) for obstacle i can include other nontraversable segments. The WCR may be significantly reduced from the critical contact region (CCR) x

11 5.7 When challenged by certain obstacles, IMPASS will have multiple configurations available with which to traverse the obstacle. Some of these configurations will be more intelligent than others Working Contact Ranges (WCR) for multiple obstacles can be combined to reduce the number of steps required. This can reduce the WCR for future obstacles The first step in the ICP selection algorithm is to estimate the number of steps that will need to be taken. This is done by calculating an average step distance d gavg based on the average height of the robot between h CCPi and h CCPi To find the roots for the Lagrange polynomial, n 1 evenly spaced contact points are placed between CCP i and CCP i+1. These must be vertically adjusted by z k based on the difference in slope between the hub center line (z = m 1 x + z 1 ) and the contact point line (z = m 2 x + z 2 ) The vertically adjusted contact points (x k, z k ) are used as the roots for a Lagrange polynomial. The function is translated by h CCPi in the positive z direction to be used as a hub center path The first iteration of contact points for the Lagrange polynomial function, L(x), will most likely not converge on the end contact point, CCP i+1. Here the first iteration exceeds the physical limitations of the robot. According to algorithm 5.1.3, δz will be negative for every successive iteration until a solution is reached IMPASS is shown here reaching a solution for the ICP of a given terrain and bounding CCP It is possible to choose a hub center trajectory that is physically impossible. This will cause clipping, shown by the hashed line It is possible to choose a hub center trajectory that is physically impossible. This will cause clipping, shown by the hashed line A program is used to calculate IMPASS s footpaths. These paths are used to detect future collisions IMPASS traversing obstacles using the Deliberative ICPS Motion Planner. A perfect terrain model was fed into the software to eliminate extraneous variables IMPASS traversing a dynamic terrain (a beanbag) using the reactive algorithm based on inclinometer readings for the body position xi

12 A.1 IMPASS climbing a set of three six inch steps and down an eleven inch obstacle. The Default Transition is used throughout most of the simulation with the exception of the large negative obstacle. Here the Descending Transition is used A.2 IMPASS climbing a set of terrain features in simulation. CCR and CCP are shown as dots on the surface of the terrain xii

13 List of Tables 5.1 Terrain Classifier Message Experimental Motion Profile Message Improved Motion Profile Message xiii

14 Chapter 1 Introduction In the last decade, there has been a significant increase in the use of robots in real world applications. This usage will only increase in years to come, most likely at an accelerated rate. As the demand for robotic solutions expands, so will demands on the physical abilities of robots. Currently one of the biggest weaknesses in robotic technology is mobility. Wheeled robots tend to be efficient and capable of high speeds, but are often limited to relatively smooth terrain. Legged robots on the other hand are better equipped to deal with irregular terrain. Unfortunately, legged robots are inherently more complex, often resulting in slow and inefficient operation. Developing a highly mobile platform that is practical for real world applications has proven difficult. To achieve both mobility and speed, robots are being developed that include both the leg and wheel concept into a single mechanism. These mechanisms tend to be simpler than legged platforms, but far more mobile than wheeled platforms. Varying degrees of leg-wheel integration have been experimented with. Some of these robots exhibit many degrees of freedom while others are very simple. Existing leg-wheel hybrid platforms will be discussed, as well as certain control strategies for these robots that are relevant to the platform proposed in this paper. The platform proposed in this paper is IMPASS (Intelligent Mobility Platform with Active Spoke System), a highly mobile leg-wheel hybrid. This robotic platform is based around a rimless spoke wheel with individually actuated spokes. The spokes have the ability to increase or decrease their length during operation. This results in a robot capable of traversing a variety of terrains, including obstacles up to 2 3 times the nominal walking height. An illustration of some potential capabilities of the actuated spoke wheel platform are shown in Figure 1.1. The robot would be able to maintain a consistent height over unstructured terrains. Small obstacles and ditches could be easily stepped over, while larger ones climbed. Hazards such as water or vegetation could be kept below the undercarriage of the robot. A prototype has been developed at RoMeLa (Robotics and Mechanisms Lab) of Virginia 1

15 Shawn C. Kimmel Chapter 1. Introduction 2 Figure 1.1: Potential uses for an actuated spoke wheel robot. Tech, shown in Figure 1.2. This robot has two actuated spoke wheels and a body with a tail. Each wheel has six spokes radiating from the hub, which are actually composed of three longer spokes that run through the middle of the hub. As a mechanical design problem, IMPASS offers many challenges due to the inherent complexity of individually actuated spokes. Packaging the drive mechanisms for multiple spokes with all associated electronics inside a reasonably sized hub required several design iterations. The lessons learned from this design will be discussed in the platform development chapter. Manually controlling a robot with as many degrees of freedom as IMPASS would be a difficult task requiring a very skilled operator. This paper discusses approaches to automated motion control in the two-dimensional sagittal plane. The motion planning solutions fall into two categories: deliberative and reactive. Deliberative control involves sensing the environment, building a world model from sensor data, and calculating an optimal path within that world for the robot to travel. Reactive control has no planning component per se. It is a biologically inspired approach that focuses on sensor-actuator couplings and simple behavior profiles. Both of the approaches have characteristics that make them attractive for IMPASS. Deliberative control tends to produce more a efficient and intelligent response. Reactive control results in less polished response, but because of its simplicity it tends to be more robust in unstructured environments. The algorithms presented in this paper were tested using a custom simulation package and the IMPASS prototype. The simulator, shown in Figure 1.3, provided a means of checking geometry constraints and terrain collisions. Experiments on the robot allowed researchers to comprehend the physical interactions of the robot with its environment. Results from these experiments indicated that the theoretical motion planning algorithms tuned in simulation were initially inadequate. The main differences between reality and simulation were a product of the dynamic properties of the hardware. In particular the compliance of the spokes, gear train backlash, and rolling contact point of the feet affected motion of the robot. Motion algorithms were revised to incorporate many of these unforseen interactions, resulting in a

16 Shawn C. Kimmel Chapter 1. Introduction 3 Figure 1.2: A prototype of the IMPASS actuated spoke wheel platform has been developed and used for motion planning research. Figure 1.3: Development of motion planning algorithms was conducted in a custom built simulator. much more capable motion planner. With the revised motion planning algorithms, IMPASS is able to climb obstacles more than 1.5 times its nominal height and descend obstacles greater than the nominal walking height. The IMPASS platform is a valuable addition to the world of mobile robotics. Potential applications for this robot range from search and rescue to anti-terror response to planetary exploration. Future work that would greatly benefit IMPASS include a more complete perception suite, three-dimensional kinematic analysis, and eventually three-dimensional motion planning algorithms.

17 Chapter 2 Background While the implementation of the hybrid leg-wheel on IMPASS is novel, the concept of combining legs and wheels has been around for decades. The goal of this hybrid architecture is to mesh the advantages from both legged and wheeled mechanisms without inheriting the limitations. The wheel is a very efficient and proven form of locomotion, but it lacks the ability to traverse a variety of terrain. Legs on the other hand provide a great deal of mobility, but at the cost of efficiency. Legs possess greater degrees of freedom than wheels and they are able to touch the ground at discrete contact points. Combining legs and wheels in robotic locomotion is an excellent way to broaden the range of practical applications. This paper provides a summary of existing robots that fit into the leg-wheel hybrid classification, and their range of applications. The motion planning for leg-wheel hybrid robots is a area of much research, since there are many different ways to mediate leg and wheel functionalities. Traversing obstacles is the most heavily researched area within motion planning, since mobility is the main advantage of the leg-wheel hybrid concept. IMPASS has more degrees of freedom than most leg-wheel hybrids giving it more flexibility, but also more complexity. Motion planning for various leg-wheel hybrids will be discussed, focusing on obstacle traversal. Autonomous control of any robot in unstructured terrain provides many challenges. First of all, accurate localization and terrain sensing can be difficult to achieve. Secondly, unforseen circumstances may arise requiring robust programming, for example loose terrain can shift resulting in the inability to execute a planned motion. Intelligent traversal of unstructured terrain can take the shape of deliberative planned maneuvers, reactive sensor-action couplings, or any combination of the two. Presented is an overview of various control methods for robots in unstructured terrains. 4

18 Shawn C. Kimmel Chapter 2. Background 5 (a) Chariot uses a mechanically separated leg-wheel mechanism and is designed for exploration in forestry applications [9]. (b) Workpartner is a service robot built on a leg-wheel hybrid platform [10]. Figure 2.1: Non-integrated leg-wheel hybrid robots. 2.1 Leg-Wheel Hybrids (c) PAW uses four wheeled appendages to traverse terrain by rolling, walking, or galloping [11]. The concept of combining legs and wheels for robot locomotion is not new. Many different configurations have been developed, some with much success. Applications of leg-wheel hybrids include planetary exploration, reconnaissance, search and rescue, and anti-terror response. The common thread among these applications is the need to operate in unstructured terrain that is too dangerous, dirty, or dull for humans to operate in. There are two basic classifications of leg-wheel hybrids that will be discussed in this section: non-integrated leg-wheels and integrated leg-wheels. Some robots use a combination of individually distinguishable legs and wheels to accomplish their locomotion, hereafter referred to as non-integrated hybrids. Other leg-wheel hybrids actually integrate the legs into the wheels structure to enable reconfiguring of the wheel. The non-integrated hybrids tend to be able to support more weight and move quicker across relatively flat terrain, whereas the integrated hybrids tend to be better at traversing rougher terrains with larger obstacles Non-Integrated Leg-Wheel Hybrids There are many examples of non-integrated leg-wheel robots. The Chariot robot developed in Tohoku University in Japan has mechanically separated wheels and legs, shown in Figure 2.1(a) [9]. Chariot s locomotion can take the form of rolling, walking, or a hybrid of the two. Uses for this robot include exploration of uncharted terrain, especially for forestry applications. PAW, shown in Figure 2.1(c), is another non-integrated leg-wheel hybrid. This robot has four appendages with a drivable wheel fixed to the end of each appendage [12]. Locomotion for this robot can take the form of rolling, bouncing, or galloping [11, 13]. A similar robot, the WorkPartner, was developed as a service robot for humans [10]. Shown in Figure 2.1(b),

19 Shawn C. Kimmel Chapter 2. Background 6 (a) JPL s Sample Return Rover (SRR) uses wheeled appendages for crossing unstructured terrain [15]. (b) JPL s Athlete uses wheeled appendages for crossing unstructured terrain [16]. Figure 2.2: High mobility planetary explorers that use non-integrated leg-wheel mechanisms. the WorkPartner robot has four appendages with drivable wheels attached to the ends. However, this robot can use each of the appendages very similar to legs when the wheels are stopped, achieving a walking gait [14]. JPL s Sample Return Rover (SRR), Figure 2.2(a), and Athlete, Figure 2.2(b), are robots that are capable of traversing rough terrain and have been designed for designed for planetary exploration [15]. Non-integrated leg-wheel hybrids demonstrate good efficiency while still providing a great deal of mobility. However, these designs must usually transition between rolling and walking stages. This transition is effectively alternating between continuous and discontinuous ground contact. To achieve a more fluid gait across rough terrain with equal or greater mobility, the legs can be integrated into the physical structure of a wheel Integrated Leg-Wheel Hybrids Integrated leg-wheel hybrids can take many forms. One important distinction is whether the wheel has a rim or not. There are an abundance of rimless leg-wheel hybrids, also called rimless spoke wheels, but not so many that retain the rim of the wheel. One robot developed at Delaware University successfully showed a single degree of freedom leg-wheel hybrid with a rim, shown in Figure 2.3(a) [17, 18]. The wheel inscribes a polyhedral that can expand with a single degree of freedom to change the wheel diameter. The advantage of a rimless leg-wheel is the ability to traverse the terrain at discrete contact points without the inefficiencies associated with the majority of legged robots. Discrete contact points prove to be effective for dealing with discontinuities in the terrain. One robot that has achieved excellent speed and mobility with rimless spoke wheels is Whegs seen in Figure 2.3(b). Developed at Case Western University, Whegs uses three pairs of wheels

20 Shawn C. Kimmel Chapter 2. Background 7 (a) The Expanding Wheel robot uses an inscribed polyhedral mechanism with one degree of freedom to change the wheel diameter [18]. (b) Whegs uses an alternating tripedal gait to cross terrain quickly. The robot can traverse obstacles of up to 1.5 times the spoke length [19]. Figure 2.3: Integrated leg-wheel hybrid robots. (c) RHex is a highly mobile legwheel hybrid with the capability of climbing 0.2 meter steps [20] with each wheel having three rigid spokes. It walks using a biologically inspired alternating tripedal gait, similar to that of many insects including cockroaches and ladybugs. When climbing obstacles the front two axles passively align using a compliant axel to help pull the up the body. The robot is able to climb obstacles of up to 1.5 times the spoke length and jumping version of the robot can jump up to 2.5 times the spoke length [21]. This platform is capable of high speeds, but has a relatively high impact gait. Another rimless spoke wheel robot similar to Whegs is a robot named RHex. Shown in Figure 2.3(c), RHex has three pairs of rimless spoke wheels with only one spoke per wheel. The semi-circular spoke shape has been optimized for traversing discontinuous terrain features [22]. The round shape of the foot allows the hip joint to remain close to the ground contact point, which minimizes motor torque requirements. The compliance of the spokes is a natural shock absorber and transfers energy from step to step. RHex can climb a variety of step sizes, reportedly up to 0.2 meters in height at a rate of 1.55 s/step. Both of the previously discussed robots, RHex and Whegs, only actuate the rotation of the leg-wheel. Adding degrees of freedom to the legs can add greater mobility and capability. Scout is a robot with a single degree of freedom spoke actuation mechanism. Scout has an umbrella like mechanism that changes the diameter of the wheel. This robot is shown in Figure 2.4 [1]. The above mentioned robots all have similarities to IMPASS in that they are integrated leg-wheel hybrids. What makes IMPASS unique is that it can independently actuate each spoke, with the capability of allowing any spoke to reach twice its nominal length. This adds a great deal of mobility allowing IMPASS to climb obstacles 2 3 times the nominal walking height- a larger step than any of the previously mentioned robots. It is a more complicated design, but as will be shown in this paper it is possible to create a robust mechanical platform

21 Shawn C. Kimmel Chapter 2. Background 8 Figure 2.4: The integrated leg-wheel hybrid, Scout, uses an umbrella mechanism with one degree of freedom to change the wheel diameter [1]. and motion planning algorithms that demonstrate the IMPASS concept. 2.2 Motion Planning Leg-wheel hybrid robots have been developed to improve upon the mobility of wheeled robots. By having the capability to traverse the ground with discontinuous contact points, the robots are able to overcome otherwise non-traversable segments of the terrain. Crossing complex terrain requires special consideration for the motion of the robot. Each robot is unique in its hybridization of legs and wheels. Therefore, the motion planning that best controls a leg-wheel hybrid robot tends to be unique. The motion planning for several robots that are similar to IMPASS will be discussed, as well as the lessons that can be applied to motion planning algorithms for IMPASS. Perhaps the most similar in shape to IMPASS of all the leg-wheel hybrids is the six spoked rimless wheel discussed in [23,24]. The six spoked rimless wheel has been proposed as a model for passive-dynamic biped gaits. When two six spoked hubs attached to the same axel rotate 30 degrees out of phase such that they alternate contact points, there are significant parallels with human walking. Work done with these rimless wheels has shown steady state passive rolling of the wheel down a slope. The wheel reaches an average speed and a steady state periodic motion when descending any slope [24]. The steady state is achieved when the kinetic energy gained from falling equals the energy lost in collision of a spoke. This model could be helpful in modeling IMPASS down a ramp. However, not much work has been done with obstacle traversal for these rimless spoke wheels. The period motion achieved by the unactuated rimless spoke wheel while descending a slope

22 Shawn C. Kimmel Chapter 2. Background 9 Figure 2.5: Stop motion pictures of RHex climbing a set of stairs using Ned s Improved Ascending Algorithm (NIAA). Each picture depicts the state of the robot upon completion of one of the four stages. Shaded dots below each picture indicate legs in contact with ground [2]. is something that IMPASS could also achieve if none of the spokes change length and the tail slid without friction behind the hubs. However, IMPASS has the advantage of being able to actuate the spokes. This added freedom can be used to minimize the collision losses discussed in [23] and create a smoother gait. Collision losses are reduced by extending the next contact spoke in advance to touch the ground before the robot gains excess vertical momentum. Smoother walking is accomplished by having the contacting spoke alter its length during a step, achieving a more consistent vertical velocity of the robot. The smooth decent for IMPASS will actually be closer to the descent of a wheel. The Whegs robot is a similar rimless spoke wheel with only three spokes per hub. The proposed gait for this robot is similar to the six spoked rimless wheel, in that the hubs alternate contacting the ground. The Whegs robot prototype with six wheels walks with an alternating tripedal gait. This gait works efficiently and effectively in terrain without large obstacles. However when the robot encounters a larger obstacle that it must climb onto, both front hubs must share the lifting burden on the front legs. To accomplish this, the Whegs robot was designed with passive-compliant axels that allow the front legs to align under heavy loads. The robot can then lift itself onto the obstacle and return to the regular alternating tripedal gait. This passive alignment of the hubs is an effective way to balance

23 Shawn C. Kimmel Chapter 2. Background 10 operation in different settings with minimal complexity. RHex is a very robust mobility platform that uses six rimless spoke wheels to traverse unstructured terrain. This platform has been shown to cross unobstructed terrain relatively quickly. RHex also has the ability to climb successive steps of up to 0.2 meters, which is relatively close to the nominal walking height. Climbing with a six hub robot requires delicate coordination of the spokes. In his thesis, Ned Moore describes an algorithm for climbing steps of various dimensions [2]. The three pairs of rimless spoke wheels operate in a back to front wave gait, with at least two pairs of hubs always in contact with the ground. The ascending algorithm is broken down into four phases with each phase being defined by a duration and a final position for each leg. Figure 2.5 shows the legs in contact with the ground at each phase of the climb. This approach would be useful for an IMPASS design with multiple pairs of hubs. The spoke wheeled robots already discussed have dealt with rotation control. The controls in these robots is mostly focused on the position of contact points and pose of the legs. Because IMPASS can independently actuate its spokes, the motion planning problem becomes more complex. The length of the spokes can be changed, which alters the current and future position of the body. One way of approaching motion planning for IMPASS is to focus on the position of the body, more specifically the center of gravity (CG). When focusing on the CG, the problem becomes how to resolve a path. There are a plethora of optimization techniques for cost based optimization. The Path Planning chapter will discuss some optimization techniques that can be applied to IMPASS. 2.3 IMPASS s Kinematics The kinematic analysis for IMPASS s novel spoke wheel mechanism are described previously in [3,4] by Laney. For the purposes of this paper, it will be assumed that the spokes for both hubs are aligned and synchronized. We will also assume that there is no slip at the contact points, allowing them to be modeled as revolute joints. For the given hardware design of six spokes separated by 60, the robot can contact the ground with one, two, or three spokes. Each configuration has different mobility characteristics. The mobility of each case can be determined using Grubler s equation, given by M = 3(n 1) 2f 1 f 2 (2.1) where M is the number of relative degrees of freedom of the hub with respect to the ground, n is the number of links, f 1 is the number of 1 degree of freedom (DOF) joints, and f 2 is the number of 2 DOF joints. From this equation, it can be determined that the one-point contact case has two DOF. This can be visualized by the hub rotating about the contact point while the spoke changes length. The two-point contact case has a single DOF, the

24 Shawn C. Kimmel Chapter 2. Background 11 Figure 2.6: Mobility analysis of a single actuated spoke wheel describing degrees of freedom for different configurations [3]. motion of which will be discussed in a later section. Finally, the three-point contact case has zero DOF. The mobility analysis for IMPASS is summed up in Figure 2.6. A more complete kinematic analysis which takes into account asynchronous spoke movement for the two hubs is presented in [6], where the robot is treated as a mechanism with variable topology (MVT). The geometry and coordinate system must be defined. Figure 2.8 depicts the variables and coordinates with which IMPASS is defined. β is the angle that separates the spokes, which for the current prototype is fixed at 60 degrees. The six spokes are actually three fixed length spokes, all measuring l, that travel through the center of the hub. Therefore, by defining the length of three spokes we know the length of all the spokes. The convention for defining the spoke lengths dictates that the back contact point spoke length from A to O is r A. The lengths for the two spokes counter clockwise from this contact spoke are referred to as r B and r C, in that order. The lengths of any remaining spokes can be calculated as l minus the effective length of the spoke located 180 degrees around the hub. The coordinate system for IMPASS is described in Figure 2.8. It first consists of a Newtonian frame attached to the terrain, referred to as the N -frame. This frame is denoted by the inertially fixed X and Z axis in Figure 2.8. There is also a path frame, P-frame, rotated about angle φ to align axis p1 in the direction the robot is heading. For the scope of this paper, the P-frame will always be aligned with the N -frame. The I -frame is an intermediate frame rotated about p2 (the contact point connecting line) by angle θ. The robot revolves about the plane defined by this frame. The W -frame is fixed to the wheels, and is created by rotating by the angle ψ about the I1 axis. ψ is non-zero when the left and right spokes are of unequal length (r A L r A R). Finally, the body frame, is fixed to the chassis of the robot and is rotated from the w2 axis by -θ. These frames of reference will be used to discuss the robot in the following chapters.

25 Shawn C. Kimmel Chapter 2. Background 12 Figure 2.7: Geometry and coordinate system for a planar single actuated spoke wheel [3]. Figure 2.8: Frame of reference for the kinematic model of the actuated spoke wheel [4].

26 Shawn C. Kimmel Chapter 2. Background Autonomous Robotic Control Control of autonomous robots has come a long way in the last four decades. The first control approach was the Deliberative Paradigm, in which the robot follows a sense-plan-act sequence. Shakey, developed at Stanford Research Institute, was the first robot to exhibit the Deliberative Paradigm [25]. Figure 2.9 shows Shakey in a typical testing environment. A robot takes in sensor data to build a world map and/or locate itself in that map. Decisions are then made based on the world map combined with a-priori knowledge of the environment. Finally, the robot executes the plan based on its actuation scheme. The Deliberative Paradigm has the advantage of being able to use a large amount of information to make decisions with. The Deliberative Paradigm has its limitations. It works well with a closed-world assumption where there are no unpredictable situations, and when large amounts of computing power are available. However, the closed-world assumption is not very practical for real world applications, and until recently computing power has come at a premium. In the search for a more robust solution, Rodney Brooks kicked off a fundamental shift in artificial intelligence (AI) theory in This shift was towards biologically inspired solutions. After all, some of the most simple creatures on earth are capable of preforming surprisingly complex tasks. At the most basic level, animals operate with reflexes that are essentially sense-act couplings. The Reactive Paradigm was born out of the biologically inspired sense-act coupling. This paradigm dictates that a change in sensor state can directly elicit a change in state of the robot. At a higher level, a change in the robot s state may be described as a behavior. For example, when a centipede is poked, it enters a defensive behavior in which it curls up into a spiral. So the question is begged: How are behaviors selected? In 1986, Brooks introduced the Subsumption Architecture in which multiple layers of behaviors are chosen from by a system of inhibition and suppression [26]. Brooks noticed that with careful tuning of the behavior network, emergent behaviors would arise giving the impression of a higher level of intelligence [27]. However, the Subsumption Architecture has limitations in its modularity. The lower layers function based on the activity of the higher layers, making it difficult to change either one independently. Another approach to behavior selection is Ron Arkin s potential fields method [28, 29]. In this approach, each behavior will simultaneously produce a vector that describes the desired motion for that behavior. For example, obstacle avoidance would produce a vector normal to any obstacle surfaces and goal achievement would direct the robot towards the goal. The vectors from all these behaviors are summed, resulting in the final vector to be carried out by the robot. Problems with potential fields include trap situations where the robot gets stuck, inability to pass between closely spaced obstacles, and oscillations down hallways or between obstacles [30].

27 Shawn C. Kimmel Chapter 2. Background 14 Figure 2.9: Shakey was the first robot to preform autonomous operations by acting on sensor input [5]. Both Deliberative and Reactive control paradigms have their limitations. To cope with these limitations, hybrid architectures exist that can combine the two control methods. One example is the Three Layer Architecture that has a controller, sequencer, and deliberator [31]. The deliberator takes care of intensive computations and path planning. The controller executes the commands from the deliberator as defined by the sequencer. The sequencer selects a transfer function (essentially a behavior) to apply information from the deliberator to the controller. The hybridization of control paradigms opens the doors for more advanced and robust operation of autonomous agents. Deliberative, behavioral, and hybrid control strategies can all be practical depending on the situation. Due to IMPASS s wide breadth of applications, one overarching approach may not be appropriate. This dilemma will be discussed in this paper.

28 Chapter 3 Platform Development IMPASS s actuated spoke wheel concept has been realized in a prototype built in the Robotics and Mechanisms Lab (RoMeLa) at Virginia Tech. Design iterations began in 2004, mainly focusing on number of hubs, number of spokes, and spoke actuation method. After these basic elements were finalized, the design focus shifted to packaging of the hubs and body design. The current prototype can be seen in Figure 3.1. The prototype has two actuated spoke wheels that rotate about the same axis, but are connected to independent drive trains to allow differential turning. A single pair of hubs was chosen as opposed to multiple pairs because multiple pairs introduce more complexity to the robot and do not significantly increase mobility. In order to be able to turn the hubs, a tail is required to provide a reaction force that opposes the natural tendency for the body to rotate freely. Each hub has six spokes, which are actually 3 long spokes that travel through the center of the hub. The spokes are fiberglass to give them compliance. The compliance helps carry momentum from one step to the next, and doubles as a shock absorber. The spokes are driven by a chain and sprocket through the center of the hub. Since the spokes cannot intersect, they are located in parallel planes that move successively further away from the body with each new spoke. Each spoke is equipped with an independent Portescap 17N servo motor controlled using an optical quadrature encoder, two magnetic reed switches, and an Allmotion EZSV10 motor controller. All of these components are packaged in the hub, measuring four inches in diameter and four inches in thickness. The hub is actuated by a hollow drive shaft connected to a Maxon RE30 servo motor through a 90 degree gear box. The hollow drive shaft carries the wires from the hub into a slip ring in the center of the body. The Maxon motors are controlled using feedback from a Maxon HEDL 5540 optical quadrature encoder, a linear cam limit switch, and a Solutions Cubed MOTM motor controller. Computing is done by a PC104 with a Pentium 4 processor running LabVIEW RealTime or tethering to an external computer. Power is provided by a stack of 15

29 Shawn C. Kimmel Chapter 3. Platform Development 16 Figure 3.1: The IMPASS prototype climbing a set of stairs with ease. 6 Lithium-Ion batteries. Placement of the components within the body of the robot is particularly important. The placement of the center of gravity (CG) is crucial when traversing obstacles. The current prototype is actually being outfitted with a moving CG that helps with ascending and descending large obstacles. The design for the moving CG involves shifting the weight of the batteries and computer, which are located on a cart that can drive along the length of IMPASS s tail. Each system in IMPASS has been carefully designed for robust execution of this novel locomotion in rugged environments. The sections below will go into detail of how the mechanisms were developed and what lessons were learned in the process. 3.1 Spoke Actuation The spoke actuation of IMPASS is what truly makes it unique. At the same time, this unique degree of freedom offers significant design challenges. The final design must be compact, yet include several independently actuated spokes. At the same time the spokes need to be compliant, which makes it difficult to connect the drivetrain to the spokes.

30 Shawn C. Kimmel Chapter 3. Platform Development 17 (a) Spool and Wire Actuation (b) 4-bar Linkage and Power Screw (c) Rack and Pinion Figure 3.2: Potential mechanisms for spoke actuation. When considering different methods for linearly actuating a spoke, there were three major design criteria. The mechanism needed to be light, able to lift a significant amount of weight, and able to move relatively quickly. An additional design goal was to make the spokes compliant, to help carry momentum while walking. Designing for compliant spokes was especially tough, since the spokes have to be part of the actuating mechanism in order to have maximum travel. As the spokes deformed, it could cause binding or loss of tension in the mechanism. For the size and power requirements of the robot, electric actuation makes more sense than hydraulic, pneumatic, or smart material actuation. There are three main mechanisms that operate electric actuators: screw drives, gear drives, and belt drives. Screw drives are composed of a screw and a nut, where one is rotated relative to the other via an electric motor. A common example of a screw drive is a manually raised car jack. Screw linear actuators are capable of handling large loads, but are slow moving. In the rest position, motor would essentially be at rest because of the contact friction of the screw. Two implementations of the screw drive were investigated. The first was a four bar linkage, shown in Figure 3.2(b). The spoke would be made of two separate linkages that would connect in the middle with spacing rods. By driving the base links relative to each other the spoke would change its length. Problems with this design are its complexity and in- and out-of-plane bending. A second implementation considered comes in the form of a spooled wire rather than a nut. This design, shown in Figure 3.2(a), would use a rod, preferably threaded, to spool a wire onto. The wire would be flexible, allowing compliance in the spokes. However, when the spokes bend, tension would be lost causing the wire to drift across the spool or bind. With tensioning members in the feet, perhaps this design would be possible but that would add undesired weight to the feet. In the end, it would be difficult to ensure that the wire would never drift. Screw drive mechanisms would be appropriate for a robot carrying a heavy payload where speed was not much of an issue. However, a robot that can move quickly across terrain with a robust drivetrain is more versatile. Gear driven linear actuators are a speedier option than the screw drive. A good example of a gear driven actuator is the rack and pinion used to steer a car. The rack and pinion

31 Shawn C. Kimmel Chapter 3. Platform Development 18 Figure 3.3: The first iteration of the chain belt and sprocket design for the spokes of IMPASS. mechanism is pictured in Figure 3.2(c). There are a couple of downsides to a gear drive for this application. One is that they tend to be heavier because the materials must be high strength to withstand the forces in the gear teeth. High strength materials are usually quite rigid, which would make it difficult to design a compliant spoke. With a rigid material, the shock from taking a step would jar the mechanism shortening its lifespan. One material was found that may be able to work in this application, Duracon. However this material was still relatively stiff. A belt drive is attractive because it is light weight, flexible, and can move quickly. A flat belt could potentially slip with the loads experienced by IMPASS. A chain belt solves this problem by introducing physical interference between the sprocket and the belt to prevent slip. Figure 3.3 shows the first iteration of the belt and sprocket design. This design uses a chain belt that runs along the length of the spokes and departs at the hub center to wrap around the drive sprocket. Using a flexible drive belt makes it difficult to maintain tension, especially with a compliant spoke. This can be solved in a number of ways. The method chosen for IMPASS was to use two idler sprockets next to the drive sprocket, and pulleys to guide the spoke through the hub center. The final design includes a chain belt and sprocket to actuate the spokes, where the belt is actually part of the spoke. Figure 3.4 shows the final design, which stacks three chain and sprocket mechanisms in parallel. Tension is maintained on the chain by two coupled idler sprockets on either side of the drive sprocket. The coupling of the idler sprockets prevents any relative rotation, which ensures the belt will always be in tension between the two sprockets. The spokes are driven by Portescap 17N E1 motors mounted to the inside of the hub, as shown in Figure 3.5. The drive mechanisms for the three spokes are

32 Shawn C. Kimmel Chapter 3. Platform Development 19 (a) Cut-away isometric view (b) Cut-away side view Figure 3.4: The final iteration of the chain belt and sprocket design for the spokes of IMPASS. Figure 3.5: The hub driveshaft is connected to the hub by a plate pictured on the left. The three spoke motors attach to this hub plate. All the wires for the hub run through the center of the shaft. stacked in parallel. Locating the motors on the inside of the hub is ideal because of space constraints, but makes it challenging to provide torque to outside spokes. To do this, the drive shafts for the outer spokes must pass through the plane of the inside spokes. To save space, the hub plates that separate adjacent drive mechanism are shared. Therefore, each plate must have holes that support the drive shafts, idler shafts, and pulley shafts for the surrounding drive mechanisms. Figure 3.4(b) shows the pattern of holes that was carefully crafted to allow passage and support of these shafts. Hub plates were made in house using a CNC machine to ensure precision placement of the holes. Fitting the spoke drive trains inside of the hub was just one of the challenges faced in designing the IMPASS spoke wheel. The next section discusses other challenges to the hub design.

33 Shawn C. Kimmel Chapter 3. Platform Development Hub Design Once the design for three spoke drivetrains was determined, there were several other considerations that had to go into the design of the hub. Weight of the hub was an issue, so material had to be chosen such that it was light but could handle the stress. Because the material needed to be light, transmission of torque through the hub was a design challenge. In addition to material and torque transmission considerations, packaging all the components in a small footprint also posed a challenge. The list of components includes all of the mechanical components already mentioned and electronics for controlling the spokes. The first ever IMPASS hub was built of aluminum plating with aluminum spokes. The CAD model of this design is shown is Figure 3.3. It was easily strong enough to handle the stresses of operation, but weighed over ten pounds. Providing the torque to drive this large and heavy hub would require a large amount of power, and possibly a generator on board for long missions. To reduce power consumption, the weight of the robot needed to be reduced. The latest version of the hub was made from nylon, which is light, rigid, and machines fairly well. Holding the plates in compression are six screws that run through hollow threaded nylon shafts built into the hub plates. The problem with these shafts is that they could not take much torque. To remedy this problem, the plates had teeth built into them that meshed with the adjacent plate. These teeth are shown in Figure 3.6. The teeth double as a layer of protection for the mechanical components, shielding them from outside objects. In addition to the mechanical components, the hub also must contain the electronics necessary to drive the spokes. The current design includes a motor controller, encoder and two limit switches for each spoke. The motor controllers, Allmotion model EZSV10, were chosen for their small footprint. The encoders, US Digital model E4P, can be seen on the outside of the hub in Figure 3.7, and are connected to the drive shafts, which are extended to go all the way through the hub. Reed limit switches are attached to the rim of the hub, and magnets have been added to each foot. Limit switches are used to initialize and calibrate the position of the spokes and prevent any software failures from driving the feet into the hub. The original design called for compliant spokes. Since the degree of compliance was not known, the spokes were designed to be interchangeable. To accomplish this, the belt is tensioned and held in place by the feet. When the feet are removed, the spokes can be easily removed and replace with another material. The main material that has been tested with is fiberglass. The current prototype houses the drive trains, motor controllers, encoders, and limit switches for three spokes (effectively six spokes), all in a 4 inch diameter, 4 inch deep cylinder. This satisfied the goal of a compact hub with multiple independently actuated spokes.

34 Shawn C. Kimmel Chapter 3. Platform Development 21 Figure 3.6: Hub plates transmit torque through a set of teeth that mesh with the adjacent hub plate. The plates are held in compression by six screws that run through hollow shafts around the edges of the hubs. Figure 3.7: The drive mechanism for the spokes is a belt and sprocket. Tension in the belt is maintained with two coupled idler sprockets.

35 Shawn C. Kimmel Chapter 3. Platform Development 22 Figure 3.8: The hub drivetrains share their axis of rotation, but can rotate independently. A 90 degree gear box allows the motors to be positioned further back, helping with placement of the CG. 3.3 Hub Drive Train Located in the body of IMPASS is the hub drive train, which provides the torque to propel the robot from step to step. Not much torque is needed for the average step, however climbing up large steps can require a significant amount of torque. To provide this high torque load while maintaining accurate position control, we use a Maxon RE30 motor with a Maxon HEDL 5540 encoder. The motors are controlled by a Solutions Cubed motor controller, model MOTM2, which provides position and velocity control. A 230:1 gear reduction was required on this motor for IMPASS to be able to climb its maximum theoretical obstacle height of 38.1 inches (calculated based on 22 inch maximum spoke length). This gearing ratio is obtained by a 90 gearbox and a gear head on the Maxon motor. Using the 90 gearbox also allows the motors to be placed more towards the rear of the robot, which helps keep the CG more towards the rear. The next section will discuss CG placement in more detail. One significant problem encountered in the design of the hub drivetrain was passing the bundle of wires required for spoke operation. Normally a wheel does not need wires to operate. Since the wheels rotate relative to the body, the wires would bind up if they could not rotate relative to the electronics inside the body. A slip ring was used to allow the hub wires to freely rotate. To get the wires from the slip ring in the body to the hub, wires had to be passed through the driveshaft or along a notch in the drive shaft. The current prototype has had much success with passing the wires through a hollow driveshaft, which is mounted to the back plate of the hub. The first iteration of the driveshaft mounted to the center of the hub plate and required disassembly of the hub to remove. Mounting and removing the hub to the driveshaft was made easier by including a large plate with the driveshaft that mounted to the outside rim of the hub. A connector was placed on the hub side of the driveshaft that was small enough to slide through the hollow in the shaft. This makes for

36 Shawn C. Kimmel Chapter 3. Platform Development 23 Figure 3.9: The maximum torque experienced by the hub motors occurs when the robot is climbing with a spoke that is extended to full length and oriented horizontally. The free-body diagram for this case is shown. easy disassembly of the drivetrain. The wires come out of the body side of the driveshaft into the slip ring, and finally to the computer. The computer, along with other essential components within the body are covered in the next section. 3.4 Body Design The robot is capable of being controlled by a PC-104 board running LabVIEW RealTime or by an external computer via a tether. Power for computing and motors can also come via two routes. Built-in Lithium-ion batteries provide a local source of power. A stack of 12 batteries that displaces about 56 cubic inches is capable of running the robot for around 2 hours, depending on the terrain. The power can also be provided via a tether. Location of the electronic components was carefully considered, because the center of gravity (CG) of the robot is important. There is no single perfect location for the CG. Due to the versatile nature of IMPASS s terrain traversal, it is sometimes desired to have the CG at the back of the support polygon and other times at the front. During the initiation of a climb or decent, the desired position of the CG is at the back of the tail. For the climbing case, the torque on the hub motor is less when the CG is located further back. This can be seen by analyzing the free-body diagram in Figure 3.9 which shows IMPASS in the climbing configuration. The reaction force on the front spoke, F spoke is described by the equation F spoke = mga 2(A + B + C) (3.1)

37 Shawn C. Kimmel Chapter 3. Platform Development 24 Figure 3.10: This picture shows the new carbon fiber body for IMPASS side by side with the old aluminum frame body. The new body saves on weight and is more protective of the interior components. where m is the mass of the robot, g is the acceleration of gravity, and A, B, and C are the lengths of the segments shown in Figure 3.9. The torque on the hub motor, T hub, is given by T hub = F spoke L (3.2) where L is the length of the extended spoke. By making the value of A smaller, we can reduce the torque necessary for climbing the obstacle. Therefore, a CG located towards the back of the tail is advantageous in this configuration. However, once the hub has climbed upon the obstacle and torque is again at normal levels, the robot must pull the tail up over the obstacle. Here a CG located in the tail makes it difficult to complete the ascent of the obstacle. For descending obstacles, the ideal CG location is different than the ascending case. At the initiation of the step, it is more desirable to have keep the weight back in the tail for stability reasons. When stepping down, the support polygon for IMPASS shrinks significantly as the hub center passes over the feet contact points. The size of an obstacle that can be downclimbed is directly affected by the location of the CG. Once the hub has descended and it is time to bring the tail down, the best location for the CG is up at the front of the robot. This minimizes the impact of the tail on the ground. The product of the robot s weight and the moment arm between the foot contact point and the CG directly determines the amount of torque that acts on the body as soon as the tail leaves the edge of the obstacle. As can be seen, the appropriate location of the CG depends on the situation. To deal with this conflict, the CG can either be centrally located or be relocatable. In the current body, the CG is located centrally which allows for climbing of obstacles up to approximately half the of maximum theoretical obstacle height. However, a new body is under construction that will mount the computer and Lithium-ion batteries on a track. By moving these components

38 Shawn C. Kimmel Chapter 3. Platform Development 25 along the track, the CG can be repositioned. The shell of the new body design is shown in Figure Another important feature of the robot is the shape of the tail. When following behind the body over obstacles, the tail must not get stuck. Additionally, when coming down obstacles the tail should lower as smoothly as possible. An attractive shape for the tail is a curve that is convex with respect to the ground. This design encourages continuous contact of the tail with the ground and helps prevent catching on sharp terrain features. The front edge of the tail s convex curve provides an angle of contact with obstacles that promotes less force in the direction normal to the front face of the obstacle. This results in less friction with the terrain features. The back side of the curve provides a smooth transition when down-climbing obstacles. The IMPASS prototype demonstrates that the proposed method of locomotion is mechanically feasible. Using a belt and sprocket drive train integrated into the spoke, it is possible to get a large range of linear spoke movement at high speeds without tensioning problems. The hub is compact in size and effectively contains six actuated spokes and associate electronics. The hub drivetrain provides adequate torque to climb the maximum theoretical height of 2 3 times the nominal walking height. Location of the CG is central, as to moderate the advantages associated with the different stages of climbing and descending obstacles. A tail design has been conceived and implemented which has characteristics that promote constant contact with the ground. Here the hardware has been presented for a highly mobile robotic platform. In the next chapter, we will investigate the best ways for the robot to take steps across a variety of terrains.

39 Chapter 4 Step Transitions Unlike many other mobile robots, IMPASS has the flexibility to choose the way it transitions from one step to another. This capability stems from the ability to change the length of the spokes, and therefore create different geometries. This flexibility provides IMPASS with the ability to consider many factors including efficiency, smoothness of motion, terrain clearance, or stability. There are technically infinite ways to leave a current step and enter the next, but certain configurations are more attractive. Transitions discussed in this chapter focus on considerations for continuous motion profiles, orientation of the spokes, and capability to traverse obstacles. For the purposes of this paper, obstacles are defined as a segment of terrain which is nontraversable to IMPASS. Positive obstacles are ones that exhibit a positive vertical displacement in the direction that the robot is moving. Negative obstacles exhibit a negative vertical displacement in the direction that the robot is moving. This definition will be expanded in the Motion Planning chapter, but for the discussions in this chapter the current definition will suffice. The stability of the robot is determined by two factors, the center of gravity (CG) location and the support polygon. The CG of the robot can be described by (x CG, z CG ). The support polygon is the outline that is formed by the the contact points. For the one-point contact gait, the support polygon will be formed by three points, the tail and one spoke from each wheel. For the two-point contact gait, the support polygon includes five points which include the tail and two spokes from each wheel. This paper considers static stability, which is achieved when the vertical projection of the support polygon includes the CG. For two dimensional sagittal plane analysis, the support polygon is one dimensional. As long as the horizontal component of the CG, x CG, is located between the front-most and rear-most contact points, the robot is considered stable. The one-point and two-point contact gaits each have unique considerations that define their step transitions. Therefore, both gaits will be discussed in their own section. The step 26

40 Shawn C. Kimmel Chapter 4. Step Transitions 27 (a) (b) (c) Figure 4.1: The two-point contact gait shown rotating clockwise through a step. This gait constrains the position of the hub center to a circle for which the radius is the step length divided by 3. The bar in the center of the robot s spokes is the center of the circular path, (x c, z c ). [6]. transitions presented here will be used to help refine the control space for path planning algorithms. 4.1 One-Point Contact Step Transitions The one-point contact gait for IMPASS exhibits excellent mobility. This gait can be used to position the hub anywhere in the two dimensional sagittal plane within the robot s physical limitations. The tradeoff for this flexibility is stability. With only three points contacting ground (one on the tail, and one spoke from each hub), the robot would enter an unstable case if one contact point were to temporarily loose contact with the ground. Additionally, the support polygon for the robot is reduced in this gait, making the placement of the CG more important. This section will look at step transitions that can compensate for stability concerns, as well as maximize the benefits of the one-point contact gait. Any stable one-point contact transition requires that two feet contact the ground from each hub. Therefore, the robot must obey the kinematics of the two-point contact case at the instant of the transition. The two-point contact case has one DOF, which constrains the position of the hub center to a range of motion that forms a circle, shown in Figure 4.1. This circle is described by a center point (x c, z c ) with radius r c based on the contact points (x 1, z 1 ) and (x 2, z 2 ). The properties of the circle can be calculated by the equations x c = x 1 + d g 3 cos(30 + α g ) (4.1)

41 Shawn C. Kimmel Chapter 4. Step Transitions 28 Figure 4.2: IMPASS in a two-point contact configuration, showing the velocity vector v and contact point vector d g. z c = z 1 + d g 3 sin(30 + α g ) (4.2) r c = d g 3 (4.3) where (x 1, z 1 ) is the back spoke contact point, d g is the vector that connects the back spoke contact point to the front spoke contact point, and α g is the pitch of vector d g. The two values d g and α g are shown in Figure 4.2 and defined by the equations d g = (x 2 x 1 ) 2 + (z 2 z 1 ) 2 (4.4) α g = arctan( z 2 z 1 x 2 x 1 ) (4.5) Various configurations for IMPASS in the two-point contact gait are shown in Figure 4.1. During a one-point contact transition, the robot must be in a state that is consistent with the geometry of the two-point contact gait. This section discusses various approaches to onepoint contact transitions based on the geometry of the robot within the two-point contact circle.

42 Shawn C. Kimmel Chapter 4. Step Transitions Constant Angular Velocity of Hub One of the most important considerations in motion planning is providing a continuous motion profile to the actuators. Motors cannot make discrete changes, so it is desirable to command a continuous motion function. For IMPASS, this applies mainly to the contacting spokes and the hub rotation. With respect to one-point contact step transitions, the spokes are not much of a consideration since they are either coming into contact with the ground or leaving the ground. Therefore they are only constrained on one side of the transition. However, the rotation of the hub must be considered since it describes motion of both previous and future steps simultaneously. This section discusses solving for transitions such that the angular velocity for the hub is constant. At the instant before transition, the hub s angular velocity, ω A is described by ω A = v A Sinρ A r A (4.6) where r A is the vector describing the rear spoke, v A is the hub velocity, and ρ A is the angle between the spoke and velocity vectors. These variables are shown in Figure 4.2. At the instant after transition, the hub s angular velocity is a function of the new contact spoke, r B, the velocity for that spoke, v B, and the relative angle ρ B. Setting the angular velocities for the front and back spokes equal results in the equation v A Sinρ A r A = v B Sinρ B r B (4.7) In a previous paper, Laney discusses the constant ω case for purely horizontal velocity on a horizontal terrain. His paper showed that the switching angle that gives a constant ω is always 30 degrees [3], where the switching angle is defined as θ shown in Figure 2.8. In reality the terrain IMPASS will be traversing will not be horizontal. Also there will be a vertical component to the velocity as the robot adjusts to the terrain. The results from Laney s paper can be generalized to give the following property If d g v, Then constant ω occurs at θ = 30 α (4.8) Vectors d g and v can be chosen in motion planning such that they are parallel. Using this property provides the path planner with a simple correlation between the velocity and contact point vectors. It also makes for an easy calculation to find the switching angle.however, this transition method lacks flexibility. To have access to a wider range of transitions, the velocity and contact point vectors must be decoupled, i.e. they need not be parallel. The spoke and velocity vectors still must be chosen such that ω A is equivalent to ω B. To

43 Shawn C. Kimmel Chapter 4. Step Transitions 30 prevent any significant jerk on the robot, an instantaneous change in the velocity vector will not be allowed. Therefore, v A and v B are set equal, simplifying the problem. Additionally, the vectors r A and r B are kinematically linked by the two-point contact arrangement. This linkage provides us with the relation that ρ A is 60 greater than ρ B. Here a new angle ρ v d is introduced in Figure 4.2 which describes the difference in slope between d g and v. Angles ρ A and ρ B can be written in terms of ρ v d and the switching angle θ shown by ρ A = ρ v d + θ + 90 (4.9) ρ B = ρ v d + θ + 30 (4.10) Using the assumptions above, we arrive at a reduced form of Equation 4.7 in the form 0 = r A r B Sin(ρ v d + θ + 90 ) Sin(ρ v d + θ + 30 ) (4.11) It is immediately apparent that the magnitude of the velocity vector is not important, only the orientation. Equation 4.11 allows motion planning to choose the velocity vector and contact points independently of each other. The switching angle is still a factor in the decision of what values to choose for d g and v because the position of the robot depends on the switching angle. In fact, there is an interdependence between θ, d g, and v that motion planning must consider for any transition. The constant ω approach to solving one-point contact transitions is attractive because it provides a second-order continuous motion function for the hub motors. Additionally, by setting v A and v B equal, we are preventing the robot from experiencing any significant shock during transition. This method is beneficial for the motors, but has shortcomings in the types of terrain it can handle. The next section will discuss transitions that have more advanced mobility capabilities. Experiments with Constant Angular Velocity Transitions The Constant Angular Velocity Transition for the one-point contact gait was tuned initially in a custom built simulator. The simulation environment was created using LabVIEW with the IMAQ toolkit. Motion messages are received by the simulator component and used to create a visual representation of the robot and the terrain as shown in Figure 4.3. This software made it possible to detect any flaws in the motion planning algorithms when applied to an ideal robot and terrain. Of course, ideal conditions rarely exist in the real world. To truly validate an algorithm, it must be tested on hardware. The software architecture was designed such that a motion

44 Shawn C. Kimmel Chapter 4. Step Transitions 31 (a) Starting at θ = 30 (b) Middle of step (c) Transition at θ = 30 Figure 4.3: The simulator was used to test algorithms before implementing them on the robot. (a) Starting at θ = 0 (b) Front feet first touch the ground, θ < 30 (c) Transition complete, θ = 30 Figure 4.4: The transition case for θ = 30. The front spokes touch the ground before θ = 0 because of compliance in the spokes and backlash in the hub gear train. command was communicated using a standard protocol. This made the the jump from simulation to hardware easy. Since the motion planner is independent of the hardware, a robot driver software component had to be written as the go between for motion commands and the actuators. The simulation testing of the motion algorithms showed proper execution of the constant angular velocity transition. However, when the algorithm was implemented on the robot there were distinct differences. These differences were due to certain physical and mechanical properties of the robot. The Constant Angular Velocity Transition was tested on horizontal ground. The tests are shown in Figure 4.4. The front spoke contacts the ground prematurely, seen in Figure 4.4(b). As a result, the robot violated the no-slip condition in order to finally reach the correct transition geometry in Figure 4.4(c). The discrepancy between the analytical and experimental results was caused by certain properties of the hardware. Deviation from the theoretical findings due to hardware was expected to some degree. There were two major reasons that the robot contacted the ground early. The first reason is that there is noticeable backlash in the hub gear train, which is magnified by the fact it is attached to a long spoke. Angular position of the hub is measured upstream of the gear train, right at the motor. This makes accurate positioning for the hub itself impossible. When the hub center passes over the contact spokes, the gears switch to the other face of their teeth making the robot pitch forward Initialization and calibration for position of the hub can be done on either side of the gear

45 Shawn C. Kimmel Chapter 4. Step Transitions 32 train backlash. For transitions, it is best to initialize position such that the hub is rotated as far forward as possible relative to the body during initialization. This causes the position of the hub to be inaccurate when leaving a transition, but this is less critical than entering a transition. The second factor driving the early ground contact is the compliance of the spokes. The spoke does not radiate in a straight line from the hub when under load. Therefore the rotation of the hub relative to the body is not indicative of the the true rotation of the robot about the contact point, as it has been modeled in the software. As the load on the spoke shifts, the degree of bending changes. This variable deflection would need to be taken into account to achieve an accurate value of hub rotation about the contact point. The two factors just discussed cause an over-rotation of the hub. The result of this overrotation is that the front spoke contacts the ground before it is supposed to. We then find IMPASS in a two-point contact configuration with the spokes not in their final geometry. To reach the final geometry, one or more of the spokes must slip because the two-point contact kinematics could not be followed. In experiments, we found that both front and back spokes could slip depending on the step. Determining which spoke would slip requires an understanding of the friction forces. In a two-point contact stance with the tail contacting the ground, we have a statically indeterminate system. The normal forces at the contact points depend on the stiffness of the members. The tail is very stiff, while the stiffness in the spokes varies significantly with their orientation and length. Depending on where the front spoke touches the ground with respect to the desired contact point, the stiffness can significantly vary. With the current transition, the spoke is contacting the ground before the desired contact point, making it shorter and more vertical than planned; therefore it is more stiff. Because of the increased stiffness in the front spoke for the experimental transition, there is more friction to prevent slip. The back spoke would then be more likely to slip. If either of the two spokes were to slip, it is preferred that the front spoke slips. The back contact point is the reference for future steps. If this contact point is moved the robot will loose accurate localization, potentially causing a foot to be misplaced on a critical terrain feature. There are two basic solutions that can prevent the over-rotation of the hub resulting in slip of the back contact point. One is to build a model to predict actual hub position based on mechanical and physical properties of the robot. The second method is to plan the gait such that the front contact point will slip instead of the back contact point. If a better position estimate for the hub was available, the motion planning software would be able to touch the front spoke to the ground at the ideal point. To get an accurate value for the rotation about the contact point, a model of the gear train backlash and spoke compliance would need to be built. Such a model is not included in the scope of this paper, but would be an attractive option for future research. A fairly simple software solution was devised to prevent slip of the back spoke by always

46 Shawn C. Kimmel Chapter 4. Step Transitions 33 Figure 4.5: IMPASS s switching angle can be described relative to the x-axis or the line normal to the ground link of the terrain. These switching angles are referred to as θ and θ 2 respectively. slipping the front spoke. By extending the front spoke past its desired transition length in advance of the transition, it will prematurely contact the ground beyond the desired contact point and prevent the over-rotation of the hub. Adding additional support spokes helps increase accuracy of position readings by reversing the gear train backlash and reducing compliance in the back spoke. The difference between this spoke pre-extension and the current algorithm is that the front spoke is always longer and at a shallower angle than the back spoke. The back spoke does not slip because there is more normal force acting on it. While this solution violates the no-slip criteria, it does produce a practical solution to the mechanical problems encountered with this transition Constant Switching Angle of Spoke While a constant motion profile is beneficial, it is not necessary. There are other factors that are just as important to the robot which can be accomplished via other configurations. One possible way to define a step transition is by the angle that the back contact spoke makes with the z-axis of the inertially fixed N -frame, θ. Another, very similar way is to choose a switching angle relative to the ground link. The switching angle based on the ground link will be called θ 2. Both switching angles are shown in Figure 4.5. θ 2 is related to θ by the equation

47 Shawn C. Kimmel Chapter 4. Step Transitions 34 (a) Minimum physical switching angle (b) Isosceles triangle (c) Maximum physical switching angle Figure 4.6: When in the two-point contact configuration, IMPASS s legs make a triangle with the ground link. The boundary conditions can be determined by the sum of the angles equal 180 and the value of β. θ 2 = θ α (4.12) Both methods, using a constant θ or θ 2, will be discussed in this chapter. First we will investigate the boundary conditions for the switching angle. The boundaries for θ 2 are explicitly defined as ( 90 + β) < θ 2 < 90 (4.13) whereas the boundary conditions for θ depend on the ground link angle α. To define the boundary for θ we simply use Equation 4.12 and the boundaries for θ 2 given in Equation Equation 4.12 was derived from simple geometry. A triangle is formed in the two-point contact case. This triangle includes the two spokes in contact with the ground and the ground link, as seen in Figure 4.9. The interior angles of the triangle must sum to 180, so subtracting β from this sum gives us the total range of motion for the spokes. For the robot proposed in this paper, β is equal to 60 so the maximum theoretical range is 120. The theoretical range assumes that the spokes can be any length. In reality, the spokes have physical limitations on their lengths, specifically 3.5 inches minimum and 21.5 inches maximum for the IMPASS prototype. With these limitations, the full 120 range of motion cannot be realized. This is explained in Figures 4.6(a) and 4.6(c). A graphical representation of the leg length constraint is shown in Figure 4.7. The curve plots the back spoke length, r A, versus the front spoke length, r A, for a fixed step distance, d g, of 16 inches across the full range of theoretical switching angles, 30 < θ 2 < 90. The dashed rectangle shows the physical limitations of the spoke lengths. If the step distance were to increase much more what is shown in this figure, the curve would no longer have a single continuous segment within the box. Without a continuous curve, the robot would not be able to exist in all configurations at that step length. Using this analysis tool, it has been determined that the maximum step distance that allows the robot to rotate continuously from the minimum

48 Shawn C. Kimmel Chapter 4. Step Transitions r B r A Figure 4.7: This graph plots the spoke lengths IMPASS against each other as θ 2 is changed in a 16 inch step. r A is the bottom axis and r B is at the left. The rectangular box represents the robots physical limitations. For this 16 inch step, IMPASS has a continuous range in the solution space [7]. angle to the maximum angle is inches. If the step distance is increased past inches, then portions of the curve will still be within the solution space. These extreme conditions are not very useful for the two-point contact gait, but can still be used for one-point contact transitions. First we must find the physical boundaries for the switching angle. The minimum θ 2 is achieved when r A is at a minimum and r B is at a maximum, which is the top left corner of the dashed box. The maximum θ 2 is found in the opposite configuration in the bottom right corner of the dashed box. The stepping distance for the minimum and maximum angles can be found using the analysis tool in Figure 4.7. Both extremes occur at a step length of 20 inches. The minimum and maximum angles can be solved for using this step distance. Figure 4.8 illustrates the back and front spoke lengths as a function of θ 2. Horizontal lines show the physical limitations of the spoke lengths. A vertical line is used to show the minimum angle thatthe robot can switch at, which is is θ 2 = 8.7. The maximum switching angle will occur at the same rotation from the horizontal x-axis, but on the opposite side of the robot. The actual range of switching angles for IMPASS is therefore < θ 2 < Now that the boundaries for switching angles have been defined, we can look at the advantages offered by various configurations. The switching angles have been separated into categories based on their performance characteristics. These categories are shown in the list below.

49 Shawn C. Kimmel Chapter 4. Step Transitions 36 Figure 4.8: Shown is the spoke lengths for IMPASS as θ 2 is changed in a 20 inch step. r Bz peaks first, followed by r Az The maximum and minimum spoke lengths are shown as horizontal lines. The minimum θ 2 is found at the vertical line where both spoke lengths are within the bounds. A. Equivalent Spoke Length Transition, θ 2 = 30 B. Descending Transition, θ = 60 C. Ascending Transition, θ = 0 for Adjacent and Non-Adjacent Spokes D. Default Transition, θ = 30 Each of these transition configurations will be discussed individually. Testing was conducted on the robot for each type of transition. There were some interactions with the physical and mechanical properties of the robot that resulted in unexpected phenomenon. Some of these were easy to fix, while others would require some more advanced modeling. These problems and solutions will be discussed for each transition. A: Equivalent Spoke Length Transition, θ 2 = 30 The most versatile switching angle for IMPASS is θ 2 = 30. In this configuration IMPASS is capable of making the largest and smallest steps across flat terrain. This is graphically shown in Figure The point on the curve that corresponds to θ 2 = 30 is always located on the line of unity slope that goes through (0, 0). As long as the maximum and minimum spoke lengths are universal for all spokes on the hub (i.e. the solution space is a square), the line of unity slope will go through the bottom left and top right corners of the constraint region. The Figure 4.10 shows that maximum and minimum step length occur in these corners.

50 Shawn C. Kimmel Chapter 4. Step Transitions 37 (a) Equivalent Spoke Length (b) Descending (c) Adjacent Spoke Ascending (d) Non-Adjacent Spoke Ascending (e) Default Figure 4.9: There are infinite configurations in which IMPASS can transition with the onepoint contact gait. This shows various configurations that are particularly useful from a motion planning perspective.

51 Shawn C. Kimmel Chapter 4. Step Transitions r B r B r A r A (a) Minimum Step Distance (b) Maximum Step Distance Figure 4.10: These graphs plot the spoke lengths of IMPASS, r A and r B, for a given step length. r A is the bottom axis and r B is at the left. The curve is created by varying θ 2 from 30 to 90, which rotates the robot through the full two-point contact case. The dashed box represents the physical limitation for spoke lengths [7]. With this switching angle, IMPASS is exactly halfway between the minimum and maximum switching angle. The stability is dependent on the ground link angle α, and therefore will vary from step to step. As α becomes more negative or the step distance d g becomes larger, this transition becomes less stable. Additionally the stability depends on the terrain previous to the obstacle. For example, the robot would be much less stable if the front of the robot had just descended a negative obstacle and the tail was still on the obstacle. An in depth stability analysis will not be covered in this paper, but would be a good area for future research. As discussed the the Constant Angular Velocity transition section, it is easy to choose a velocity vector parallel to the ground link. If these two vectors are chosen to be parallel, the Equivalent Spoke Length Transition will have a constant ω. It becomes apparent that there are cases of overlap between the transition classifications. These dual identity cases will inherit the benefits of both of the transition classifications that describe it. The strength of the Equivalent Spoke Length transition lies it its flexibility to reach a wide range of step lengths. This can be useful in situations when large areas of terrain are considered non-traversable, forcing contact points to be spaced far apart. Also, when IMPASS encounters sudden terrain changes that require path planning adaptations within a limited space, the Equivalent Spoke Length transition allows for small steps to make those adaptations. It may seem logical that the Equivalent Spoke Length Transition would be good for obstacle traversal, but future sections will show that other transitions exist that are better

52 Shawn C. Kimmel Chapter 4. Step Transitions 39 Figure 4.11: IMPASS descending an obstacle with θ = 60. suited for obstacles. However, before other transitions are discussed, the simulation and experimentation for this transition will be presented. Experiments with Equivalent Spoke Length Transition Simulation and experiments on IMPASS using the Equivalent Spoke Length Transition were conducted on horizontal terrain. These tests had the same findings described in the experimenting with Constant Angular Velocity Transitions. The simulator showed proper execution of the steps. However, the hub gear train backlash and spoke compliance caused problems with accurately measuring the hub rotation. This resulted in premature contact of the front spoke with the ground. As a result of the premature contact, the back spoke contact point had issues with slip. Slip is a problem for an path planning that depends on accurate positioning of the feet. This is the case for deliberative motion planning. However, the reactive approach does not necessarily require accurate foot positioning. Ascending obstacles did not have any problems with back spoke slip, since the back spoke was always more stiff and located closer to the CG. However, descending obstacles did prove to have problems with back spoke slipping. The software solution mentioned in the Constant Angular Velocity Transition section worked to prevent back spoke slipping. B: Descending Transition, θ = 60 The switching angle for a step determines the orientation of the contact spokes during the transition. When θ equals 30, the back and front spoke have the same vertical displacement per unit length. As the switching angle is increased greater than 30, the forward spoke is able to achieve a greater vertical displacement than the back spoke. This concept is presented in Figure 4.11, which shows IMPASS with θ = 60 with equal lengths for the front and back spokes. The front spoke is clearly able to achieve a greater vertical displacement in the N -frame.

53 Shawn C. Kimmel Chapter 4. Step Transitions 40 r z, inches DP, inches Θ Θ 20 5 Figure 4.12: The left graph shows r Az and r Bz with respect to θ for equal spoke lengths. The line that peaks first is r Bz. The filled in region represents the area where the Descending Potential (DP)> 0 (i.e. r Bz > r Bz ). The right graph shows the DP, which reaches its maximum value at θ = 2 π = The aforementioned bias in vertical displacement facilitates easier transitions to terrain that is below the height of the current contact point, i.e. negative obstacles. Here, a metric is introduced called descending potential or DP, which describes the ability of the robot to traverse negative terrain features. This metric is calculated by the equation [ π ] DP (θ) = r Bz r A z = r B Cos 3 θ r A Cos[θ] (4.14) The first term gives the vertical rise of the front spoke, and the second term gives the rise of the back spoke. According to this metric the switching angle with the greatest DP is achieved when both spokes are at maximum length and the ground link is vertical, such that θ = 120 and α = 90. The DP metric for this configuration is shown in Figure Implementation of this maximum DP case would lead to a precarious configuration. With both spokes at maximum length and θ = 120, the hub center will be in front of the contact points by 3 times the spoke length. Placement of the CG will need to be extremely far back 2 for a stable stance. To be realistic, this configuration can only exist with a moving center of gravity, which is possible but not necessary. In addition to CG issues, this configuration does not contact the bottom of the back foot. The back foot is essentially used as a hook to hold onto the top of the obstacle. The safety of the robot becomes a concern here. If the back foot slips before the front foot can contact, the robot could roll off the obstacle potentially damaging components or falling onto its back or side becoming immobilized. Without a moving CG or a guaranteed foot hold for the back foot, the maximum DP configuration is not practical. Since neither of these issues have been solved for the current prototype, a different configuration had to be used. In the interest of making a solution that is appropriate for any robot with a centrally located CG, the exact location of the CG is not used. θ is constrained to less than 90 so that the contact spoke will have normal contact with the ground. The back spoke length is fixed at its minimum length. This way the

54 Shawn C. Kimmel Chapter 4. Step Transitions 41 Figure 4.13: For any combination of spoke lengths, the greatest DP will always be achieved with IMPASS at the ledge of an obstale and a vertical ground link. The circle shows the foot path as the robot rotates through all possible θ. furthest that the hub center can overhang the obstacle is the minimum spoke length. The front spoke is fixed at its maximum value to provide the largest difference in r B and r A that is possible. This will maximize the value of the DP. Applying these constraints freezes IMPASS in an position in the two-point contact case that can be described as θ 2 = With the back spoke at the minimum length and the front spoke at the maximum length, the robot is capable of a step length of 20 inches. Therefore, the robot is capable of descending 20 inches. This is shown in Figure The first graph shows the vertical component of each spoke with respect to θ. The second graph shows the actual DP metric, peaking at 20 inches with θ = Again, the resulting orientation of the robot is with a vertical contact point vector. This brings to light the relationship that for any combination of spoke lengths, the orientation with the greatest DP will always be when α = 90. Logically this can be determined by picturing a circle around the back contact point with radius equal to the step distance. The lowest point on the circle will always be located straight down. Using an α of 90 gives the greatest DP, but it is not very practical. A vertical contact point vector requires the back spoke to be precariously perched at the edge. This configuration also requires the back spoke to be stuck in the bottom corner of the obstacle, which can only happen with a perfectly vertical obstacle. To address these issues, a factor of safety can be added that places the back spoke away from the edge and the front spoke forward. With these factors of safety, θ = 60 becomes an attractive switching angle. Setting θ to 60 allows the front spoke to be vertical, which is desirable with compliant spokes. The spoke will flex minimally in the vertical orientation, providing the most reliable spoke length. This switching angle suffers a DP loss of only 0.25 inches compared to other angles, while gaining

55 Shawn C. Kimmel Chapter 4. Step Transitions 42 r x, inches DP, inches Θ Θ 10 5 Figure 4.14: The left graph shows r Az at minimum spoke length and r Bz at maximum spoke length with respect to θ. The filled in region represents the area where the Descending Potential (DP)> 0 (i.e. r Bz > r Bz ). The right graph shows the DP, which reaches its maximum value at θ = 2 π = a comfortable horizontal distance of 2.5 inches between the contact points. The horizontal distance can be split into 1.25 inches of clearance from the obstacle for both contact points. If the robot needs to descend a height of less than inches, it would be better to increase the rear spoke length than change the angle. This will give the hub more ground clearance and decrease the change in angular velocity between the two steps. Maintaining the 60 switching angle provides consistency and keeps the front spoke vertical, which are both beneficial. Experiments with Descending Transition Testing the Descending Transition was very exciting because the robot was attempting to statically descend a significant distance in a single step. Fortunately, testing in the simulation environment was sufficient for development of functional software. Running the code on the robot for the first time went without a single accident. Figure 4.15(c) shows the robot successfully transitioning down from an obstacle using the θ = 60 transition. Entering the Descending Transition went relatively smoothly compared to the Constant Angular Velocity and Equivalent Spoke Length Transitions. The problems encountered in the other transitions, i.e. hub gear train backlash and spoke compliance, had been magnified by large spoke lengths. When descending an obstacle, the back spoke is so short that these factors were less pronounced. However, it was found in initial experiments that the front spoke did not extend all the way to the ground. The robot rotated to about 70 before touching the ground. This may have been due to some measurement error or some compliance in the spokes. This problem was easily fixed by virtually increasing the height of the obstacle so that the robot would extend the front spoke further. For the 12 inch obstacle shown in Figure 4.15, the robot was actually told that the height of the obstacle was 14 inches.

56 Shawn C. Kimmel Chapter 4. Step Transitions 43 (a) Starting at top of obstacle (b) Hanging over obstacle (c) Transition initiated θ = 60 (d) Transition complete (e) Next transition Figure 4.15: The transition case for θ = 60. The front spokes touch the ground before θ = 0 because of compliance in the spokes and backlash in the hub gear train.

57 Shawn C. Kimmel Chapter 4. Step Transitions 44 An additional problem was encountered following the transition. Right after the Descending Transition finished, the back spoke is almost at full length entering the next transition, shown by Figure 4.15(d). In the experiment, soon after the Descending Transition was complete the hub rotated through almost 20 freely- taking up the hub gear train backlash and bending the spoke. If the CG had not been far enough back, the robot could have easily flipped over at this point. The effect of the placement of the CG on descending and ascending capabilities was discussed in the Platform Development chapter, but did not include the dynamic aspects found in this experiment. The robot could be statically stable for the entirety of the step, but still fall forward from the momentum created during the free hub rotation. Even with a robot that will not fall because of a rear located CG, the peak torque required by the motors to stop the robot s momentum is particularly high. At this point in the experiment, the current draw from the robot almost doubled. Unfortunately, there are no easy software solutions to circumvent the free rotation described in this experiment. One potential option is to try and reverse the motors when the backlash is being absorbed to catch the robot s fall earlier. This would be very difficult to time, but could potentially help the problem. The motor reversal was not investigated for this paper, but could be a good update in future software revisions. C: Ascending Transition, Adjacent and Non-Adjacent Spokes, θ = 0 Ascending an obstacle has many geometric similarities to the descending case, but is fundamentally different in that there is less focus on stability and more on torque. One constraint that was imposed on the descending case will be removed for the ascending case. The referenced constraint is that the spokes must contact the ground on the bottom of the foot as opposed to the side. Here we allow the robot to use the front spoke partially as a hook to pull itself onto the obstacle. Removing the normal contact constraint also opens up the possibility of using non-adjacent spokes to climb. This gives two transitions, the Adjacent Ascending Transition and the Non-Adjacent Ascending Transition. Adjacent spokes are defined as two spokes that are separated by angle β around the hub. By using non-adjacent spokes, we can greatly increases the size of obstacles that can be climbed. In order to ensure that the foot would be able to stick, the edges were coated with a silicone based non-skid substance. The first case that was investigated was transitioning over an obstacle with the bottom of the front spoke touching the ground. Here we can draw lessons from the descending case. The maximum ascending potential, AP, is obtained at θ = 60 with a vertical ground link. This is 180 degrees from the location of the maximum DP. The equation for AP is essentially the negative of the DP, given by

58 Shawn C. Kimmel Chapter 4. Step Transitions 45 [ π ] AP (θ) = r Az r B z = r A Cos[θ] r B Cos 3 θ (4.15) The maximum AP configuration does not meet the criteria that the bottom of the feet must touch the ground. Therefore, we are limited to θ > 30. As discussed in the Descending Transition section, a vertical spoke provides greater stiffness and more reliable support. We will therefore consider θ = 0 for the Adjacent Spoke Ascending Transition. This switching angle allows a maximum obstacle height of inches, which is the same height that the robot can descend with the Descending Transition. For obstacles over inches, the robot must use the side of the front spoke as opposed to the bottom of the foot. The feet have been shaped to be able to hook terrain features and have been outfitted with a non-skid surface. However, this ascending case is likely to experience some slip on the front foot contact point as the robot climbs. Again here we find that the maximum climbing height is achieved with a vertical ground link, as was the case for the descending transitions. Using the Non-Adjacent Spoke Transition, the robot is able to theoretically climb 2 3 times the nominal walking height. Here the nominal walking height is defined as half the overall spoke length. The theoretical height is not achievable for several reasons stemming from the implementation of platform. For one, the full length of a spoke cannot be used on one side of the hub. The feet cannot travel into the hub. The full length of the spoke, L, is 25 inches, while the maximum spoke length,l max is 21.5 inches. In addition to the spoke length constraint, we must take into account the front spoke must be extended beyond the obstacle to hook the edge. The magnitude of the vector between the hub center and the contact point, r B, will end up being less than the spoke length needed to hook the obstacle. The distance that the front spoke must be extended past the contact point will be named l hook. The value of l hook must be determined conservatively since a slip while climbing could cause a great deal of impact to the robot. In the experimentation section, the value of l hook for the current IMPASS prototype will be discussed. Due to the physical constraints listed in the previous paragraph, the maximum climbing height is reduced. The AP with θ = 30 is AP = (l max l hook )2 3 (4.16) When l hook is taken into account, 30 is no longer the maximum possible obstacle height. This switching angle forces both r A and r B to be the same length, which is l max l hook. Really, only r B must be set to l max l hook. A larger obstacle height can be reached if r A is set to l max. Using the law of cosines we can determine the maximum possible height AP 2 = l 2 max + (l max l hook ) 2 2(l max )(l max l hook )Sin(2β) (4.17)

59 Shawn C. Kimmel Chapter 4. Step Transitions 46 Figure 4.16: This figure shows the Non-Adjacent Ascending Transition configuration chosen for climbing large obstacles. θ is set equal to zero such that the back spoke is vertical, minimizing the effect of compliance in the spokes. where 2β is the angle between the non-adjacent spokes. While this gives a maximum climbing height for the ideal condition, we must consider that in reality the robot will not encounter ideal obstacles and will have trouble with exact foot placement in the bottom corner of the obstacle. Additionally, one factor not mentioned above is the material properties of the spokes. Due to the compliance in the spokes, the rear spoke will become shorter under load further reducing the maximum climbing height. The amount of compliance in the rear spoke can be minimized while allowing for easy foot placement of the back spoke by using θ = 0. This climbing configuration positions IMPASS with the back spoke vertically. This will minimize bending of the compliant material in the rear spoke. Figure 4.16 shows the geometry for this configuration. The height that the robot can climb, AP, using this transition is described by the equation AP = r A + Sin(30)( r B + l hook ) (4.18) In this section we have discussed two configurations for the Ascending Transition. The first is the Adjacent Ascending Transition, which ensures that all spokes will contact the ground with the bottom of their feet. The Non-Adjacent Ascending Transition on the other hand and uses the side of the front spoke to pull the robot onto the obstacle. The Non-Adjacent Ascending Transition is capable of climbing obstacles much higher than the Adjacent Ascending Transition. Both Ascending Transition configurations use a switching angle of θ = 0 because it minimizes the compliance in the back spoke and allows the robot to stand back from the obstacle. Experiments with Ascending Transition As with the other transitions, the Ascending Transitions were run first in simulation. The results from these tests indicated that the algorithms were ready for implementation on the robot. Running these algorithms on the robot was not only going to be a test for the software, but also for the hardware. The Non-

60 Shawn C. Kimmel Chapter 4. Step Transitions 47 (a) Starting at θ = 0 (b) Raising the body (c) Front spokes initiate contact with the obstacle (d) Back feet leave the ground (e) IMPASS pulls itself onto the obstacle (f) On top of the obstacle Figure 4.17: IMPASS climbing a 12 inch obstacle with the Adjacent Ascending Transition, θ = 0. The front spokes touch the ground before θ = 0 because of compliance in the spokes and backlash in the hub gear train. Adjacent Ascending Transition provides the ultimate test of the hub drivetrain s available torque. The first experiment was run on the Ascending Adjacent Spoke Transition, which is shown in Figure The experiment was a success; IMPASS is capable of stepping onto an obstacle with this transition. The height of the obstacle traversed was 12 inches- IMPASS s nominal walking height. One notable difference between simulation and physical testing was that the switching angle was slightly less than 0 in the physical testing. This is most likely due to a hub positioning error in the motion planning software. As the body changes angle with respect to the terrain, the Motion Planner must apply a correction to the hub position read from the encoder to achieve the absolute inclination of the body. The simulator s model for the body was not extremely accurate, which most likely caused a false correction value to be sent during the climb. This correction error, in addition to hub gear train backlash and spoke compliance, is the reason that the robot transitioned a little early. The Ascending Non-Adjacent Transition was tested on an obstacle 18 inches high. The robot successfully climbed the obstacle. Perhaps the most impressive part of the climb is when the back spokes leave the ground an the robot s weight is supported on the edges of the front spoke feet. The non-skid substance applied to the sides of the feet were able to provide enough friction to hold most of the weight of a 15 pound robot. The robot could then proceed to pull itself onto the obstacle and continue walking. One important finding from the experiments was the minimum distance that the spoke needed to be extended beyond the lip of the obstacle. It was found that the robot s front spoke would always slide back to approximately 2 inches past the lip. It was at this position

61 Shawn C. Kimmel Chapter 4. Step Transitions 48 (a) Starting at θ = 0 (b) Raising the body (c) Front feet initiate contact with the ground (d) Back feet leave the ground (e) IMPASS pulls itself onto the obstacle (f) On top of the obstacle Figure 4.18: IMPASS climbing a 18 inch obstacle with the Non-Adjacent Ascending Transition, θ = 0. The compliance of the spokes is noticeable in Figure 4.18(d) [8]. the feet could get enough traction on the ground to support the bodies weight. From this we can conclude that the experimental minimum of l hook is 2 inches. It is more prudent to place the spoke somewhat beyond the minimum l hook value and let the spoke slide down the obstacle edge into climbing position. An observation that would be useful for reactive programming was noticed during these experiments. If the front spoke of the robot overshoots the obstacle, it will slide back until it reaches a fairly consistent length of 2 to 3 inches past the lip of the obstacle. A climbing behavior could be created that would fully extend the front spoke before coming down onto a suspected obstacle. The robot would climb with consistent performance.

62 Shawn C. Kimmel Chapter 4. Step Transitions 49 D: Default Transition, θ = 30 The previous two sections have discussed ascending and descending configurations. However, many obstacles that IMPASS encounters will be fairly small in size, not requiring any gait adaptation. The gait that best balances moderate obstacles, both positive and negative, is a constant θ = 30. In this configuration, the slope of both front and back contact spokes is the same. That means that the robot can achieve equal AP and DP during any step. The maximum height change that can be traversed in the Default Transition, AP = DP is AP = DP = l max Sin(60 ) l min Sin(60 ) (4.19) Having such flexible height change characteristics is very valuable. Sensor data can change at a moments notice, springing a positive or negative obstacle into the robot s path that requires changes to the current step. With the Default Transition, the robot is equally ready for a height change in any direction. This transition also has good stability characteristics. The hub can only extend past the back contact point by distance l max at full height. For the current robot, the Default Transition 2 is always stable. In general for a centrally located CG, this transition should be static for most, if not all, of its operating range. In unstructured terrain, where future contact points are not guaranteed to be stable, it is very beneficial to have a stable switching angle. Say the front foot stepped on a piece of loose rubble, the back spoke would have to recover the robot s stability. With a switching angle greater than θ = 30 stability becomes a serious concern. On the other hand, as θ is reduced from 30, the DP is decreased. Having a good DP value for the standard transition is critical, since it is more likely that a negative obstacle won t be detected than a positive one. An perception suite on a low lying robot will have trouble detecting negative obstacles from any significant distance. The Default Transition provides a good balance of the characteristics that make up a good standard walking transition. In this configuration, the robot is equally able to ascend or descend obstacles. This transition has good stability characteristics. On the current prototype, the Default Transition is stable across the entire operating range. While maintaining this stability, the robot is still able to descend fairly large obstacles that may appear late due to perception difficulties. The Default Transition has the right properties to be used throughout much of IMPASS s operation. Experiments with the Default Transition The results from experimenting with this transition showed the same results as the Constant Angular Velocity Transition and the Equivalent Spoke Length Transition. The robot in its physical form is not ideal like the simulator. Examples of the robot running with θ = 30 in simulation are shown in Figure 4.19.

63 Shawn C. Kimmel Chapter 4. Step Transitions 50 (a) Starting at θ = 30 (b) Approaching obstacle (c) Transition over obstacle (d) Next transition Figure 4.19: The robot traversing moderate obstacles in the simulation environment with the Default Transition, θ = 30. Physical problems including gear train backlash and spoke compliance led to issues with the accuracy of the the hub rotation measurement. The robot tended to over-rotate at the end of a step causing early contact with the ground. This caused some problems with foot slip, forcing future contact points to be offset. This transition worked well for climbing moderate obstacles, but would have trouble with large obstacles. For these we must look at other transitions. 4.2 Two-Point Contact Step Transitions On terrain that is more unstable, the two-point contact gait is preferable. In this situation the robot will have five points of contact (two feet from each hub and the tail) and a larger support polygon. The downside is that the kinematics of this gait constrained the motion to one DOF. Motion planning therefore become much less flexible. Planning ahead to accommodate future steps is of the utmost importance. Figure 4.20 shows the solution space for a given step length. It is very possible for the robot to enter a step in which it cannot rotate continuously through the full range of motion. For the dimensions of the current IMPASS, the maximum step distance at which the robot can rotate continuously through its range of motion is 16.5 inches. Any step distance above this value should be avoided unless it is only being used specifically for a short range of motion. One particular time that this could apply is in preparing for obstacle traversal. Unlike with the one-point contact transitions, which can occur in a number of configurations, the two-point contact transitions are completely constrained by the contact points that have been chosen. Figure 4.21 shows the possible trajectories of the hub center for three consecutive steps. Transitions between these steps must occur at the intersection of the arcs to obey the two-point contact kinematics. Since the two-point contact transitions have no flexibility once contact points are chosen,

64 Shawn C. Kimmel Chapter 4. Step Transitions r B r A Figure 4.20: This graph plots the length of the back spoke against the length of the front spoke during a two-point contact step. A dashed box has been included which shows the maximum and minimum spoke lengths. This particular step length of 17 inches enters and leaves the solution space six distinct times. Figure 4.21: The arcs seen in this figure shows the possible position of the hub center for three consecutive steps. The points at which the arcs intersect is where the transition must occur.

65 Shawn C. Kimmel Chapter 4. Step Transitions 52 (a) Starting at θ = 60 (b) (c) Equivalent Spoke Lengths (d) (e) (f) Switching at θ = 60 Figure 4.22: IMPASS walking in the two-point contact gait. The transitions are determined by the contact points. the transition geometry from one step to the next simply requires finding the intersection of the arcs and placing the next spoke down at that time Experimenting with Two-Point Contact Transitions The two-point contact transitions were tested in the simulator. Frame captures from the simulation are seen in in Figure The motion commands for the two-point contact are the same as the one-point contact, so the same robot driver could be used. IMPASS took its first two-point contact steps, looking just as it had in simulation. The physical conditions that facilitated problems in the one-point contact gait did not effect the two-point contact gait. Because the robot could distribute its weight over more members, the spokes were less compliant and the hub gear train backlash was not freely released. The two-point contact case closely mirrors the theoretical results.

66 Chapter 5 Motion Planning Manual control of all the spokes on IMPASS during a maneuver would be a daunting task for any operator. For IMPASS to be practical for real world applications, automated motion planning of the spokes is absolutely necessary. Instead of manual control, a user friendly software interface was developed, shown in Figure 5.1. This software provides the user with indicators of the motions and intensions of the robot. Currently, the user only needs to input a START command and a Desired Forward Velocity. Due to the many degrees of freedom that IMPASS possesses, there are infinite solutions to the motion planning problem. Research has uncovered many avenues that arrive at an acceptable solution, but there are a few methods that particularly stand out. This paper will discuss the various motion planning methods that have been devised. For the scope of this paper, motion planning will be defined as the manner in which the robot transitions from one stance to another stance, where the second stance can be, and often is, with different ground contact points. This motion planning component would answer to a higher level supervisory program, such as a way-point follower for autonomous operation or directional control from a human operator. (a) Supervisory Control (b) Motion Planner (c) Simulator Design Module Figure 5.1: The software interfaces for controlling IMPASS. 53

67 Shawn C. Kimmel Chapter 5. Motion Planning 54 As discussed in the background chapter, there are a couple of ways to approach the AI problem of autonomous navigation. Assuming sensor data is fairly accurate, the deliberative approach to path planning makes a lot of sense for IMPASS. This approach allows the robot to build a map of the terrain. With this information, IMPASS can plan an optimal path based on its hierarchy of needs. Again, this all hinges on a fairly reliable perception suite. In reality, however, sensor data is never perfect. There is a significant amount of filtering and processing required to provide accurate data for a world map, and redundant sensors are often used, further complicating the situation. To reduce the cost of extra sensors and the unreliability of perception data, the reactive approach to navigation can be implemented. This approach dictates a close coupling between sensor data and actions. The robot would be equipped with simple sensors such as inclinometers, tactile sensors, and torque sensors. IMPASS s actions would be dictated by a set of predefined behaviors selected based on the situational data. This approach tends to suffer much less from sensor noise and unplanned encounters, but lacks the optimality provided by the deliberative approach. The deliberative and reactive based methods of operating IMPASS will both be discussed in more depth in this chapter. 5.1 Deliberative Motion Planning In this section, we will delve into the aspects of motion planning from a deliberative standpoint. During development of the software, it was assumed that an accurate world map would be provided by a perception component. However, this world map need not be accurate for more than a few steps, since the motion planning software will re-plan frequently. The kinematic properties of IMPASS predicate an interdependence between the path of the robot body and the ground contact points. For the two-point contact gait, the robot body path and contact points are directly linked due to the one DOF mobility of the system. However for the one-point contact gait, one does not uniquely define the other. In this section we will focus on the one-point contact gait because its flexility makes it an attractive option. The problem of deliberative path planning can be approached from two angles. We can start by either determining the body path first or the contact points first. Initial Contact Point Selection (ICPS) focuses on choosing optimal foot contact points that ensure the best chance of success. For example, IMPASS would avoid dangerous areas of the terrain and maximize stability. On the other hand, Initial Body Path Selection (IBPS) allows the robot to determine an optimal body path catered towards particular goals, such as minimizing impacts experienced by a payload. While ICPS and IBPS are used to focus on particular motion planning goals, they are both capable of considering secondary goals. For example, with the ICPS method, once contact points are chosen there is still a great deal of freedom in choosing the body path of the robot

68 Shawn C. Kimmel Chapter 5. Motion Planning 55 Figure 5.2: The architecture for the Initial Contact Point Selection (ICPS) implementation of the deliberative approach follows the sense-plan-act sequence. The ICPS method has three basic steps within the contact point planner: Critical Contact Region (CCR) identification and refinement, Critical Contact Point (CCP) determination, and Intermediary Contact Point (ICP) determination. to minimize payload accelerations. For the IBPS, once the body path is chosen, selection of contact points is still flexible. Selection of a motion planning approach for a given application would be based on factors such as terrain type and the robot s hierarchy of needs. In this paper, we will focus on an implementation of the ICPS approach. The architecture is shown in Figure 5.2. The ICPS approach is broken down into two types of planning, contact point selection and step execution. Contact point selection sets up the transitions that the robot will need to take. Step execution determines how to get from transition to transition. Before the ICPS implementation can be discussed, we must first define the representation of the robot s position and motion, and the terrain within the motion planning software Representation of the Environment and the Robot Before the robot can make any decisions on what action to take, it must first acquire terrain and localization information. Both sets of information must be communicated in a modular manner that can be useful to multiple decision making components. Here we discuss the representation of the terrain and the robot. The terrain is represented as discrete segments of the surface in the two dimensional sagittal plane. Here we are assuming that the left and right hubs will encounter identical terrain. Estimating the terrain as discrete segments allows for easy separation of the terrain into traversable and non-traversable sections. The resolution of the terrain segments can also

69 Shawn C. Kimmel Chapter 5. Motion Planning 56 Table 5.1: Terrain Classifier Message. Message Fields Variable Contact Point (Inches) (x i, z i ) Traversable? (Boolean) T rav i Non-Adjacent Spoke Required? (Boolean) Climb i be tuned to accommodate different terrains. More irregular terrains would use a higher resolution. For the algorithms discussed in the deliberative portion of this paper, it has been assumed that the length of the terrain segments is greater than the length of the foot contact area. This allows the contact points to be mapped onto a single terrain segment. It was also assumed that the terrain could be expressed as a function of x, i.e. there are no overhanging terrain features. Even if overhanging terrain features existed, there is no apparent advantage to stepping under the overhang. Therefore, the overhang would be modeled as a vertical wall. Vertical walls are modeled as almost vertical, with a very slight x distance added to keep the terrain a function of x. This section is not focused on the computation of the terrain profile, but rather what form it is passed in, and how it is handled by the motion planning software. The IMPASS software architecture is set up such that a perception component compiles sensor data and provides an array of terrain points. These points are in the form (x i, z i ). The array of terrain segments is then fed into a platform specific software component that processes the terrain information. This component is called the Terrain Classifier. Each terrain segment is defined as traversable or non-traversable based on the slope of the segment and a friction model of the robot s feet. If a segment is non-traversable, it is also tagged with a rating that defines whether the robot can walk over it with adjacent spokes or if climbing is necessary with the Ascending Non-Adjacent Spoke Transition. The Terrain Classifier then outputs a message in the form described in Table 5.1. Here the Traversable? and Non- Adjacent Spoke Required? fields apply to the segment between terrain points (x i, z i ) and (x i+1, z i+1 ). This output is much more useful to the Motion Planner than just the terrain array. Robot localization is based on the inertially fixed coordinate system. The pose of the robot is completely defined by the following variables α ˆ (x c, z c ) = Hub center position with respect to the inertially fixed coordinate system ˆ α = Inclination of the body ˆ θ = Rotation of the hub (Absolute, with 0 being at the beginning of a mission). ˆ θ = Rotational velocity of the hub

70 Shawn C. Kimmel Chapter 5. Motion Planning 57 Table 5.2: Experimental Motion Profile Message. Message Fields Variable Absolute Angular Position of Hub (Radians) θ Length of Spoke 1 (Inches) l 1 Length of Spoke 2 (Inches) l 2 Length of Spoke 3 (Inches) l 3 ˆ R 1, R 2, R 3 = Lengths of three adjacent spokes ˆ R 1, R 2, R 3 = Linear velocities of three adjacent spokes With this information, the robot can be positioned with respect to the terrain Defining Motion of the Robot In addition to common protocol for the inputs to motion planning, we must have a convention for the outputs of motion planning. Motion planning must communicate its intended motion to the Robot Driver component. For the experiments referenced in this paper, the robot was controlled using position control. The motion planner outputs a four part message defined in Table 5.2. Only three spoke lengths are needed since each hub only has three motors controlling the spokes. The values l 1, l 2, and l 3 are attached to specific spokes throughout operation. This means the motion planner must keep track of the orientation of the spokes continuously. It was found during experimentation that position control resulted in a somewhat jerky motion. The communication rate with the motor controllers was not high enough to get continuous motion. Solving this problem requires a new motion profile message. There were insufficient resources available to re-design the Motion Planner around a new communication profile during the tenure of my research. However, an improved protocol is suggested for future research. There are several descriptors that help to constrain IMPASS s motion. Some of these that are particularly useful include: ˆ Foot trajectories ˆ Spoke lengths and velocities ˆ Hub center trajectory and rotation

71 Shawn C. Kimmel Chapter 5. Motion Planning 58 Table 5.3: Improved Motion Profile Message. Message Fields Variable Absolute Angular Position of Hub (Radians) θ Angular Velocity of Hub (Radians/Sec) ω Length of Spoke 1 (Inches) l 1 Velocity of Spoke 1 (Inches/Sec) v 1 Length of Spoke 2 (Inches) l 2 Velocity of Spoke 2 (Inches/Sec) v 2 Length of Spoke 3 (Inches) l 3 Velocity of Spoke 3 (Inches/Sec) v 3 ˆ Center of gravity trajectory The motion of IMPASS can be defined by many combinations of these descriptors. Depending on the approach to the motion planning solution, certain combinations become more or less convenient. To keep things modular, a standard convention is chosen that is convenient for the Robot Driver. The Robot Driver is responsible for actuating four pairs of motors. One pair of motors control the hub rotation for both hubs, and three pairs of motors control the spoke lengths for each hub. Therefore, a convenient representation of IMPASS s pose would include motion profiles for each of these motors. By adding a desired velocity to the previous motion profile command in Table 5.2, the motion profile paints a more complete picture of how the robot should be moved. This position at velocity profile is shown in Table 5.3. Position at velocity control should provide the Robot Driver with sufficient information to produce smooth motion Initial Contact Point Selection (ICPS) Any robot traveling in unstructured terrain will encounter hazards. These hazards can come in various shapes and sizes. Many mobile robots attempt to avoid terrain hazards by steering around them. IMPASS has the advantage of being able to intelligently step over hazards by choosing suitable contact points. Examples of hazards IMPASS could avoid in this manner are terrain instabilities, sharp points, and obstacle ledges. This section discusses the approaches to motion planning from a contact point selection point of view. There are three steps the motion planning software runs through to choose contact points: Critical Contact Region (CCR) identification and refinement, Critical Contact Point (CCP) determination, and Intermediary Contact Point (ICP) determination. The goals of this

72 Shawn C. Kimmel Chapter 5. Motion Planning 59 software are first and foremost to avoid non-traversable terrain, secondly to undergo minimal vertical displacement, and thirdly to maintain a walking height as close to the nominal walking height as possible to enable maximum adaptability to sudden changes in terrain. Critical Contact Region (CCR) Identification and Refinement The main focus of this research is the advanced mobility capabilities of the actuated spoke wheel design. Therefore, the foremost concern with IMPASS is surmounting obstacles. Here we define an obstacle based on the Terrain Classifier message: an obstacle is any set of consecutive non-traversable segments preceded and followed by a traversable segment. A positive obstacle is one in which the terrain after the obstacle is more positive in the z axis, and a negative obstacle is one in which the terrain after the obstacle is more negative in the z axis. In order for IMPASS to traverse an obstacle, there is a certain region preceding and following the obstacle in which the robot is required to step in order to climb the obstacle. These ranges, hereto referred to as Critical Contact Regions (CCR), are determined by the physical dimensions of the robot. Figure 5.3 shows the CCR for a given positive obstacle. Preceding the obstacle is CCR1 i, and following the obstacle is CCR2 i, where i is the index of the first non-traversable segment in the obstacle. The points in the two-dimensional sagittal plane for a pair of CCR associated with an obstacle are as follows: ˆ (x CCRa, z CCRa ) = furthest back point from which IMPASS can still pass the obstacle ˆ (x CCRb, z CCRb ) = closest point preceding the obstacle from which IMPASS can make a step past the obstacle ˆ (x CCRc, z CCRc ) = closest point on the far side of the obstacle to which IMPASS can step from the front side of the obstacle ˆ (x CCRd, z CCRd ) = furthest forward point to which IMPASS can step from a foothold preceding the obstacle The robot transitions which determine the CCR in Figure 5.3 are not the only configurations that solve for CCR of obstacles. Depending on the terrain before and after the obstacle, as well as the dimensions of the obstacle, non-adjacent or adjacent spokes may reach the more extreme point. For example, we need three configurations to determine the CCR for the obstacle in Figure 5.4. The height of the obstacle in Figure 5.3 prevents the non-adjacent spoke from reaching a far point on top of the obstacle because the hub and middle foot would collide with the terrain. There will be times when obstacles will be located in close proximity to each other. Just such a case is shown in Figure 5.5. Here the CCR will span other non-traversable segments,

73 Shawn C. Kimmel Chapter 5. Motion Planning 60 Figure 5.3: When navigating non-traversable segments, IMPASS must step in certain critical contact regions (CCR) before and after the obstacle. These regions are geometrically determined from the dimensions of the robot. Figure 5.4: When navigating non-traversable segments, IMPASS must step in certain critical contact regions (CCR) before and after the obstacle. These regions are geometrically determined from the dimensions of the robot.

74 Shawn C. Kimmel Chapter 5. Motion Planning 61 as long as the step is still possible. However, the points that define the CCR are expanded to define the boundaries of the other obstacles. All points in CCR1 i previous to (x CCRb, z CCRb ) are named (x CCRak, z CCRak ) where k = 1 is the boundary of CCR1 i and k increases as the points move towards the obstacle. For CCR2 i, all the points after (x CCRc, z CCRc ) are named (x CCRdk, z CCRdk ) where k = 1 is the boundary of CCR2 i and k increases as the points move towards the obstacle. CCR are calculated very similarly for positive and negative obstacles. calculating CCR for a positive obstacle is as follows The method for 1 Determine (x CCRc, z CCRc ): The end point of the non-traversable segments (edge of obstacle) is equal to (x CCRc, z CCRc ). 2 Determine (x CCRa, z CCRa ): Draw a circle of radius l m ax 3 (the maximum step distance of a non-adjacent spoke step) around point (x CCRc, z CCRc ) and find the furthest point back on the terrain which it contacts. Beginning here, iteratively search forward in the terrain for the first valid IMPASS configuration that connect the current search point to (x CCRc, z CCRc ). 3 Determine (x CCRb, z CCRb ): Because we have assumed that the terrain can be expressed as a function of x, we can conclude that the beginning point of the non-traversable segment that start the obstacle is equivalent to (x CCRb, z CCRb ). 4 Determine (x CCRd, z CCRd ): We must investigate two possible points for (x CCRd, z CCRd ), one for an adjacent spoke step and one for a non-adjacent spoke step. The adjacent spoke step point is found by drawing a circle of length l max (maximum step distance of an adjacent spoke step) around point (x CCRb, z CCRb ); beginning at the most forward point, we iteratively search backward in the terrain for the first valid IMPASS configuration that connects the current search point to (x CCRb, z CCRb ). The non-adjacent spoke step point is then located by iteratively moving forward from the point just found and checking for valid steps between (x CCRa, z CCRa ) and (x CCRb, z CCRb ) with the nonadjacent spoke configuration. If a distance of l max 3 from (xccrb, z CCRb ) is reached, the search is stopped and the adjacent spoke step point is taken as (x CCRd, z CCRd ). The valid step check mentioned in the list was developed as a fairly simple lower level program that checks through IMPASS s known configurations for a geometrically possible step without terrain interference. Stability is absent from this analysis. This is to keep the software more modular. With a moving CG being considered for future robots, stability could require a more involved analysis. The stability will be taken into account later in the contact point selection process. The method for determining the CCR for a negative obstacle is only slightly different from the positive obstacle determination. The steps are as follows 1 Determine (x CCRb, z CCRb ): The begining point of the non-traversable segments (edge of obstacle) is equal to (x CCRb, z CCRb ).

75 Shawn C. Kimmel Chapter 5. Motion Planning 62 (a) (b) Figure 5.5: The critical contact regions (CCR) for obstacle i can include other nontraversable segments.

76 Shawn C. Kimmel Chapter 5. Motion Planning 63 2 Determine (x CCRd, z CCRd ): Draw a circle of radius l max 3 (the maximum step distance of a non-adjacent spoke step) around point (x CCRb, z CCRb ) and find the furthest point forward on the terrain which it contacts. Beginning here, iteratively search backwards in the terrain for the first valid IMPASS configuration that connect the current search point to (x CCRb, z CCRb ). 3 Determine (x CCRc, z CCRc ): Because we have assumed that the terrain can be expressed as a function of x, we can conclude that the end point of the last non-traversable segment in the obstacle is equivalent to (x CCRc, z CCRc ). 4 Determine (x CCRa, z CCRa ): We must investigate two possible points for (x CCRa, z CCRa ), one for an adjacent spoke step and one for a non-adjacent spoke step. The adjacent spoke step point is found by drawing a circle of length l max (maximum step distance of an adjacent spoke step) around point (x CCRc, z CCRc ); beginning at the furthest back point, we iteratively search forward in the terrain for the first valid IMPASS configuration that connects the current search point to (x CCRc, z CCRc ). The non-adjacent spoke step point is then located by iteratively moving back from the point just found and checking for valid steps between (x CCRc, z CCRc ) and (x CCRd, z CCRd ) with the nonadjacent spoke configuration. If a distance of l m ax 3 from (x CCRc, z CCRc ) is reached, the search is stopped and the adjacent spoke step point is taken as (x CCRd, z CCRd ). Essentially the difference between the positive and negative CCR is that they are mirror images if flipped over a vertical axis. This is reflected in the determination of the CCR. Now that the full range of points which can be used to traverse an obstacle is known, we will develop a Working Contact Range (WCR) which reduces the CCR to a range of points that are practical for the robot. The WCR reduces the CCR in 2 ways. First, all unstable transitions are thrown out. Second, the WCR eliminates contact points within a distance of l obsmin from the beginning or end of any non-traversable segment. Both of these constraints refine the potential contact regions to something the robot can actually be expected to execute. Figure 5.6 shows the terrain from Figure 5.5 reduced from CCR to WCR. The non-adjacent step is unstable in most configurations for the current prototype. This significantly reduces the WCR. A l obsmin of 2 inches is used, further reducing the WCR. We now have arrived at a set of practical contact range that account for the robot s physical capabilities. Critical Contact Point (CCP) Determination Once the WCR have been determined, we can determine where best to put the contact points. Here is where IMPASS can capitalize on the deliberative approach. Figure 5.7 shows an obstacle which could be traversed two different ways, one of which is significantly more

77 Shawn C. Kimmel Chapter 5. Motion Planning 64 (a) (b) Figure 5.6: The working contact regions (WCR) for obstacle i can include other nontraversable segments. The WCR may be significantly reduced from the critical contact region (CCR).

78 Shawn C. Kimmel Chapter 5. Motion Planning 65 Figure 5.7: When challenged by certain obstacles, IMPASS will have multiple configurations available with which to traverse the obstacle. Some of these configurations will be more intelligent than others. efficient than the other. The algorithm used for choosing contact points will determine the apparent intelligence of the robot. The first step in determining CCPs is to further refine the WCRs. Specifically, combining and removing WCRs. For example, the dark IMPASS in Figure 5.7 has removed WCRs from adjacent obstacles and the greyed IMPASS has combined WCRs. The purpose of combining WCRs is to eliminate unnecessary steps. The combined segments can then be searched for possible omissions. First, the software combines all the overlaps. In this analysis, each traversable segment is evaluated independently of the WCR it is associated with. For example, (x CCRa1, z CCRa1 ) to (x CCRa2, z CCRa2 ) from Figure 5.6(b) is independent from (x CCRa3, z CCRa3 ) to (x CCRb, z CCRb ). All traversable segments are added to a new array of segments. Whenever two segments have an overlap, the common range to both is accepted as the new segment. The combining of segments must be done from the beginning of the terrain to the back. The reason being that as traversable ranges are combined and therefore shrunk, it will change the WCR on the other side of the obstacle. This concept is shown in Figure 5.8. The combination occurs from the from the current position in the terrain array to the furthest away because it is assumed that the quality of perception data will degrade with distance. This should minimize motion planning mistakes based on poor perception data. The new array is called the combined working contact region (CWCR) array. Once the WCRs have been combined, the motion planning can begin to search for contact regions that can be bypassed. Here, as with the combining of contact regions, we start

79 Shawn C. Kimmel Chapter 5. Motion Planning 66 Figure 5.8: Working Contact Ranges (WCR) for multiple obstacles can be combined to reduce the number of steps required. This can reduce the WCR for future obstacles. at the beginning of the terrain array where perception data will be more accurate. Any non-adjacent range in the CWCR array that can be connected by a geometrically valid and stable step will result in the exclusion of the intermediary contact regions. Using the methods of combining and bypassing contact point regions, we have filtered out WCRs that would have otherwise impeded efficient operation. This final step to reform the contact regions gives us our finalized contact region (FCR) array. The algorithm used for contact point selection is designed to maximize the success rate of the robot. Most importantly, this involves successful traversal of obstacles. The worst case scenario is slipping off the ledge of an obstacle. Therefore, contact points must be chosen that step well beyond the top of an obstacle, for both positive and negative obstacles. To aid in this, the contact points below obstacles can be chosen close to the obstacle wall. These concepts are applied to a algorithm that builds contact points as it steps through the FCR array. The evaluations are as follows: 1 If the contact range is in a depression, meaning it has a negative obstacle behind and a positive obstacle in front, the contact point is chosen at the middle of the range. 2 Else if the contact range has a positive obstacle in front, the contact point is chosen at the front of the range 3 Else if the contact range has a negative obstacle behind, the contact point is chosen at the rear of the range 4 Else choose the contact point in the middle of the range The result of this algorithm is an array of contact points that provide a means of traversing the obstacles. To complete the information for these contact points, each must have a

80 Shawn C. Kimmel Chapter 5. Motion Planning 67 transition associated with it. Here, we consider the groundwork laid in the transitions chapter. There are four basic transitions we will use: Non-Adjacent Ascending Transition, Adjacent Ascending Transition, Descending Transition, and Default Transition. The Non- Adjacent Ascending Transition is used whenever the Adjacent Ascending Transition is not sufficient. The ascending and descending transitions are used for obstacles above a height h obs1. To recap, the ascending and descending transitions use a switching angle of θ = 0 and θ = 60 respectively. The Default Transition uses a constant switching angle of θ = 30 for any obstacle of lesser height than h obs1. For the experiments performed on the Deliberative Motion Planning, a value of 9 inches was used for h obs1. Applying the transition determination criteria finalizes the critical contact point array. The next step is to determine the contact points in between non-adjacent critical contact points. Intermediary Contact Point (ICP) Determination The primary goal of contact point selection, which is to successfully traverse the obstacles in the terrain, has been satisfied by the process presented in the CCP Determination section. With the selection of the ICPs, we can now factor in the secondary goal of minimizing height change and keeping the height relative to the terrain close to the nominal walking height. These two goals can compete, which the ICP determination method takes into account. Each pair of CCPs that cannot be connected with a valid step must have at least one transition in between. The first step in finding those intermediary contact points is to determine the height of the robot s hub center at the the bordering CCPs. The hub center points are (x 0,i, z 0,i ) and (x 0,i+1, z 0,i+1 ). Calculating a height requires a reference. It is not important what reference is used, just that it is consistently used to calculate all heights. Here we will use the z coordinate for the back contact point, CCP i. The heights of the back and front CCPs are given as h CCPi and h CCPi+1 respectively. These heights are averaged to find h CCPi avg. The ICP algorithm strives for linear interpolation of the hub center position. However, this is a difficult proposition with uneven terrain. The ICP algorithm accounts for the contours of the terrain by adapting the desired hub center position found using linear interpolation. To describe the features in the terrain, we will map a Lagrangian interpolation of the terrain onto the linear interpolation of the hub center path. The degree of the Lagrangian polynomial is determined by the estimated number of steps that will be taken. The initial estimation for the number of steps is determined using an average step length taken at height h CCPi avg, defined as d gavg. These variables are shown in Figure 5.9. The distance between CCP i and CCP i+1 is divided by d gavg. This number is then rounded according to h CCPi avg. If h CCPi avg is larger than the nominal walking height then we round up, otherwise it is rounded down. The resulting value n is the number of steps. The process of calculating n is summarized in the equation

81 Shawn C. Kimmel Chapter 5. Motion Planning 68 Figure 5.9: The first step in the ICP selection algorithm is to estimate the number of steps that will need to be taken. This is done by calculating an average step distance d gavg based on the average height of the robot between h CCPi and h CCPi+1. n = CCP i CCP i+1 Rounded up if h CCPi avg > h nominal otherwise round down. (5.1) d gavg The roots of the Lagrangian polynomial are determined by vertically projecting n 1 evenly spaced points along the terrain between CCP i and CCP i+1. The distance that separates these contact points is d g avg. All together this gives n + 1 roots for the polynomial. Before the Lagrange polynomial is solved, the roots must be mapped onto the linear interpolation of the hub center path. This is done by applying a z axis correction factor, z, according to the slope of two lines: the hub center linear interpolation and the contact point linear interpolation. The lines are described by equations O i O i+1 : z = m 1 x + z 1 (5.2) CP P i CCP i+1 : z = m 2 x + z 2 (5.3) For the purposes of this analysis, we translate the O i O i+1 line down to CCP i, making z 1 and z 2 equal. CCP i is set as the origin of a temporary coordinate system to make the z intercepts zero. These two lines are illustrated in Figure z is calculated by z(x k ) = (m 1 m 2 )x k (5.4) Applying the correction gives a new set of coordinates, where x is unchanged and the new z coordinate for root k, given as z k, is calculated by the equation

82 Shawn C. Kimmel Chapter 5. Motion Planning 69 Figure 5.10: To find the roots for the Lagrange polynomial, n 1 evenly spaced contact points are placed between CCP i and CCP i+1. These must be vertically adjusted by z k based on the difference in slope between the hub center line (z = m 1 x + z 1 ) and the contact point line (z = m 2 x + z 2 ) Figure 5.11: The vertically adjusted contact points (x k, z k ) are used as the roots for a Lagrange polynomial. The function is translated by h CCPi in the positive z direction to be used as a hub center path.

83 Shawn C. Kimmel Chapter 5. Motion Planning 70 z k(x k ) = z(x k ) + z k (5.5) In determining the Lagrange polynomial, we must first solve for the Lagrange basis polynomials given by the equation l k (x) = n j=0,j k x x j x k x j (5.6) These basis polynomials can then be combined to give the Lagrange polynomial using the following equation L(x) = n z k l k (x) (5.7) k=0 we then translate the Lagrange polynomial to the hub centers, simplify to a n degree polynomial in the form L(x) = a n x n + a n 1 x n a 0 + h CCPi (5.8) Figure 5.11 shows both the original and translated Lagrange polynomial function. The Lagrange equation is not necessarily an accurate representation of the terrain, it is instead a particular representation of the terrain that focuses on terrain features in the proximity of the ICPs. We don t care so much about the terrain in between contact points since we have already determined it is traversable, and therefore without drastic elevation changes. This is an advantage of the rimless spoke wheel design. Now that we have a desired hub center path, the next step is to iteratively solve for the contact points. The solver starts with the initial contact point, CCP i, and uses the geometry of the θ = 30 configuration to determine the set of contact points along the terrain that correspond to the given L(x). Figure 5.12 demonstrates the set of contact points for a given terrain and L(x). The contact points are named (x k, z k ) where k is 0 for the first contact point and is incremented by one for each subsequent contact point. The contact points are found until one is equivalent to CCP i+1 or goes beyond it. The end contact point will rarely line up with CCP i+1 on the first run. To converge on a solution in which the final contact point aligns with CCP i+1, a vertical adjustment, δz, is applied to L(x). The algorithm that is applied for determining δz after each run is 1 If any of the steps are out of range for the θ = 30 configuration, then a δz that brings the robot back into its physical range will be permanently applied. For example, if a step is too high, then δz will be negative for all subsequent iterations.

84 Shawn C. Kimmel Chapter 5. Motion Planning 71 Figure 5.12: The first iteration of contact points for the Lagrange polynomial function, L(x), will most likely not converge on the end contact point, CCP i+1. Here the first iteration exceeds the physical limitations of the robot. According to algorithm 5.1.3, δz will be negative for every successive iteration until a solution is reached. Figure 5.13: IMPASS is shown here reaching a solution for the ICP of a given terrain and bounding CCP. 2 If the conclusion of the iteration is reached and has not converged, and the robot has not broken a physical constraint at any time during any iteration, then we direct δz based on the proximity of CCP i+1 to the last two contact points. If the last contact point is closer to CCP i+1 then a negative δz is applied. Otherwise a positive δz is applied. 3 The solution is reached such that CCP i+1 aligns with the last contact point. The solution for the terrain given in Figure 5.12 is given in Figure The set of contact points produced by this solver are the ICPs for a given section of traversable terrain. Applying this solver to the rest of the non-adjacent CCP gaps will give a complete contact point array in which each pair of contact points is adjacent. Additionally, each pair of adjacent contact points has been assigned one of four transition configurations:

85 Shawn C. Kimmel Chapter 5. Motion Planning 72 high climb, ascending, descending, or moderate obstacle transition. This completes the contact point selection process. The robot has a separate motion planning component that handles the execution of the steps. This will be discussed in the next section Step Execution Once contact points have been found, the robot must determine how to get from point to point. The step executer uses a path planning algorithm to accomplish this. Since the hub center position for each step has been determined by the contact point planner, the step executer solves a hub center trajectory for the robot. There are many mathematical approaches to solving a path for multiple points, so we must first consider the factors that surround this problem. On a platform which is traversing unstructured terrain, look-ahead distance is a consideration. It is beneficial to plan ahead, but it is inevitable that the perception data will be updated on a regular basis, causing the contact points and path of the robot to be replanned on a regular basis. Therefore, we do not need a large look-ahead distance. A second consideration is physical constraints. Even though it is known that each transition configuration is geometrically possible, it would be possible to plan a hub center path that exceeds the geometric constraints of the robot. If a step execution algorithm allows for solutions outside of the physical constraints of the robot, then clipping will occur. This concept is presented in Figure In this section we discuss the initial path planner developed for IMPASS and outlines the implementation of an improved path planner. The first path planner developed for IMPASS, which was implemented in robot experimentation, is linear interpolation between adjacent hub center points. This algorithm has a single point look ahead distance which would be good for short range sensors. It is possible for clipping to occur, so a check is preformed to ensure that no motor commands are sent that cannot be realized. An example of the linear hub trajectory can be seen in Figure 4.4. A clear benefit of this method is that it is very computationally simple. The downside is that there is no smoothing between steps. A new path planner is proposed to help with this smoothing. A potential improvement to the path planner would use a Lagrange polynomial to connect the hub center positions for multiple steps with a high order polynomial. This implementation would be very similar to the contact point selection process described in the ICP Determination section. The first root of the polynomial would be the previous hub center position. The robot would have a look-ahead distance of n steps, with the hub center from each step being a new root. Using Equations 5.6 and 5.7 we arrive at a polynomial which describes a desired hub center path. This implementation has not been tested, but would almost certainly provide a smoother hub center trajectory than the linear interpolation.

86 Shawn C. Kimmel Chapter 5. Motion Planning 73 Figure 5.14: It is possible to choose a hub center trajectory that is physically impossible. This will cause clipping, shown by the hashed line. Non-Contact Spokes Up until this point, we have only discussed the motion planning of the contacting spokes. Unfortunately, we cannot forget about the non-contact spokes. The main consideration here is terrain interference. An simple obstacle avoidance technique is described in this section which keeps the non-contact spokes from running into terrain features. Behaviorally, the obstacle avoidance can be classified as a subsumption architecture. There are two behaviors, standard spoke motion and obstacle avoidance. If an imminent collision warning is triggered, then the obstacle avoidance behavior takes over. The standard spoke motion behavior simply uses a constant velocity to go from one position to another. Once the spoke leaves the ground, the length is referred to as l nc1, and the opposite side of the same spoke is L l nc1, as shown in Figure The name for the length of the given spoke changes to l nc2 as soon as the next spoke leaves the ground. Finally, when the opposite end of the given spoke touches the ground it is referred to as l nc3. The standard spoke motion behavior changes the position of the spoke from l nc1 to l nc3 with a constant velocity. The obstacle avoidance behavior is triggered by an imminent collision warning. This warning is determined by a software component that calculates the foot paths of non-contacting spokes. The simulator can be used to display these foot paths, shown in Figure If a future collision is detected, the path of the spoke will be adapted to keep a certain

87 Shawn C. Kimmel Chapter 5. Motion Planning 74 Figure 5.15: It is possible to choose a hub center trajectory that is physically impossible. This will cause clipping, shown by the hashed line. (a) Foot paths for flat terrain. (b) Foot paths for obstructed terrain: Without Collision Avoidance (c) Foot paths for obstructed terrain: With Collision Avoidance Figure 5.16: A program is used to calculate IMPASS s footpaths. These paths are used to detect future collisions.

88 Shawn C. Kimmel Chapter 5. Motion Planning 75 distance, l colavoid, from the terrain. For the software tested in the simulator, shown in Figure 5.16(c), a distance of 1 inch was used. This same distance was used in the experiments discussed in the next chapter Experimenting with Deliberative ICPS Motion Planning Deliberative motion planning software was tested in two phases. The first phase was in simulation. A custom built simulator was developed for analysis of IMPASS in the twodimensional sagittal plane. The second phase of testing was conducted on the prototype. There were unforseen interactions with the hardware and the motion planning for the prototype. Finally, this section concludes with what adjustments could be made to the motion planning algorithms. Testing in simulation provided feedback on two critical aspects of motion planning. First, the simulator showed the hub rotation and position of all the spokes. Simultaneously controlling multiple spokes and keeping track of them throughout operation was an initial challenge which the simulator helped with. Any glitches in position control could be detected with the visual interface. Secondly, terrain interference could be checked for in the simulator by putting in the test track geometry. The current obstacle avoidance software was tuned using this method. See Figure 5.16 for a visual of the simulator s assistance with obstacle avoidance. The finalized deliberative software showed good results in simulation and also provided insight into the limitations. A couple of examples of simulation tests can be found in the Appendix in Figures A.1 and A.2. It can be seen that the chosen contact points allow for effective traversal of the terrain. Where CCR overlap, the software was able to combine the regions thereby minimizing unnecessary steps. One major limitation of the software is the foot trajectory planning. Since the obstacle avoidance of the feet is in the lower level motion planning, it is unable to plan ahead for obstacles. The result is that the collision avoidance will sometimes require a very quick moment of the spoke that is outside of the physical capabilities. One solution is to place a foot trajectory planner in the higher level motion planner. This will add computation time, but as long as this is not deemed to be too slow the foot trajectory planner could add significant value to the robot. After checking the software in simulation, it was implemented on the robot. Figure 5.17 shows a test for the robot on uneven terrain. To truly test the motion planning software, perfect terrain information was read in. It would be hard to track errors in the perception software, and be sure it was not motion planning s error. It was already known that gear train backlash in the hub drivetrain and spoke compliance caused problems with the motion planning software- this was expected. The solutions to this problem have been discussed in the experimental results for the Transitions chapter. One new problem did surface during this multiple step test. It was found that the robot s

89 Shawn C. Kimmel Chapter 5. Motion Planning 76 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) Figure 5.17: IMPASS traversing obstacles using the Deliberative ICPS Motion Planner. A perfect terrain model was fed into the software to eliminate extraneous variables.

90 Shawn C. Kimmel Chapter 5. Motion Planning 77 contact points could not be modeled as point contacts. The foot actually rolls over the terrain surface, gaining ground that is not accounted for in the motion planning software. This can be seen in Figure 5.17(j), where the robot s spoke runs into the terrain feature. Here, the foot placement is supposed to be 3 inches in front of the obstacle, but instead ends up right against the wall. Figure 5.17(k) shows the foot in the corner preceding the obstacle. Future software revisions of the motion planning component should include a model of this rolling contact point. This mainly effects the contact point planner. In Figure 5.17 the robot was about 3.5 inches past the expected position after 7 steps, giving us a forward creep of about half an inch per step. 5.2 Reactive Motion Planning The downside to the deliberative motion planning approach is that it is dependent on reliable and complete sensor data. Should bad or incomplete sensor data be used to make a decision, the deliberative approach could fail. The reactive approach provides a more simple and robust method of motion planning. Here we discuss implementations that focus on a close link between sensors and actions that produce failure resistent code. For a robot with as many degrees of freedom as IMPASS, there are inevitably many ways to implement the reactive paradigm. A reactive approach is closely tied to the sensors that are being used. Attractive sensors for using on a reactive IMPASS are an inclinometer, tactile sensors for the feet, and torque sensors. The inclinometer can be used to provide a general idea of the slope of the terrain. The binary functionality of tactile sensors makes them attractive for just about any reactive robots. Torque sensors can be used to detect whether the robot has encountered an obstacle and is climbing. Currently the robot is equipped with an inclinometer, but not tactile or torque sensors. Equipping the feet with tactile sensors is a challenge because of wiring. With the spokes moving through the hub center, there is no conventional solution to communicating an electrical or mechanical signal between the feet and the hub. Wireless technology may be able to provide a telemetry solution, but this has yet to be investigated. Torque sensors could be added within the body. However, getting accurate indication of collisions from these devices may be difficult. The first algorithm presented here is completely based on the inclinometer readings. It was developed by Eric Russell, a member of the IMPASS senior design team. The algorithm is based around the Equivalent Spoke Length Transition. On flat ground this is described by θ = 30. As the terrain increases in pitch, θ is reduced by the terrain angle α. The same is true for a descending terrain. This algorithm can be described by the equation: θ = 30 α (5.9)

91 Shawn C. Kimmel Chapter 5. Motion Planning 78 This algorithm also uses a different non-contact spoke velocity curve. The spoke is extended past its desired length, L l nc3, and then retracted to its desired length as the robot nears the contact point. This allows IMPASS to be stable when a descent is ahead, but cannot be detected. Since there is no active terrain sensing, it does not matter if the feet slip. Figure 5.18 shows this algorithm implemented on the robot. In the pictures, IMPASS is traversing a bean bag. This dynamic terrain would be very difficult for the deliberative motion planning, but poses no problem for the reactive motion planning. Both deliberative and reactive approaches have their strong points. The deliberative is stronger is a more structured, static environment. However, for unstructured and dynamic environments, the reactive motion planning is clearly superior. There is still much more development that can go into developing algorithms for both approaches. This paper has presented a couple of algorithms that are successful and have been implemented on the IMPASS prototype. As the IMPASS platform is further developed, these algorithms can be used in the testing of other hardware and software features.

92 Shawn C. Kimmel Chapter 5. Motion Planning 79 (a) (b) (c) (d) (e) (f) (g) (h) Figure 5.18: IMPASS traversing a dynamic terrain (a beanbag) using the reactive algorithm based on inclinometer readings for the body position.

93 Chapter 6 Conclusion In the field of mobile robotics, it has proven difficult to design a simple, yet highly mobile robot. Wheeled robots have the advantage of being very simple and efficient. However they have trouble in unstructured terrains where the height of the ground can change suddenly. Leg-wheel robots are more mobile than wheeled robots because of increased DOF and discrete contact points. The downside to legged robots is that they require more complex mechanisms to realize their high mobility. The advantages of wheels and legs can be combined into a single mechanism to create a simple and highly mobile platform. IMPASS is a leg-wheel hybrid robot with good mobility characteristics and a simple actuation concept. The IMPASS mobility platform is a rimless wheel with individually actuated spokes. Each spoke is capable of changing its length, allowing IMPASS to coordinate motion over complex terrains. The discrete contact points of the spokes allow IMPASS to step over obstacles significantly larger than the nominal walking height. In this paper, we discussed the hardware development that has resulted in the construction of a functional IMPASS prototype. The prototype has two rimless wheels with six spokes each supporting a body and tail. The spokes travel through the hub center effectively acting as two spokes separated by 180. This design only requires three spokes total for each wheel. The spokes are compliant, providing built-in shock absorbtion and allowing kinetic energy to be passed from step to step. A chain belt and sprocket mechanism is used to actuate the spokes. Both wheels are driven by motors inside of the body. All of the actuators are controlled by an on-board PC-104 computer running Labview. The robot is capable of gracefully traversing obstacles over 1.5 times the nominal walking height and descending obstacles greater than the nominal walking height. The prototype has proven an excellent test bed for development of intelligence software. IMPASS is not a practical platform without some form of automated motion planning. Controlling each independent degree of freedom of the system in coordinated motion is a 80

94 Shawn C. Kimmel Chapter 6. Conclusion 81 task most appropriate for a computer. Two gaits are possible with the IMPASS platform. Each is described by the number of feet in contact with the ground during a step. IMPASS has a one-point contact gait and two-point contact gait. Of these, the one-point contact is more attractive as a mobility platform because it has two DOF as opposed to the single DOF possessed by the two-point contact. This paper has laid the ground work for intelligent motion control, and discusses two very different philosophies in developing the motion control software. Preceding any discussion of motion planning, we first seek understand the transitions that the robot undergoes from step to step. Transitions can be described by the angle that the back spoke makes with the z-axis, given as θ. There are infinite number of angles that the robot can switch at. Climbing and descending large obstacles is best done with angles of 0 and 60 respectively, because the extended spoke is oriented vertically. The compliance in the spokes is least prevalent with vertically oriented spokes. There are two configurations in which IMPASS can climb, one using an adjacent spoke and the other with a non-adjacent spoke. In the non-adjacent spoke configuration, the forward spoke is used to actually pull IMPASS up onto the obstacle. This configuration can be used to climb much higher obstacles that the adjacent spoke climbing case. For normal walking, we have chosen a switching angle of 30 because it can achieve a future contact point that is either higher or lower with equal ability. Using these transitions assists IMPASS in determining an intelligent method for traversing terrain. The two philosophies that can be used to approach the motion planning problem are the deliberative approach and the reactive approach. Using the deliberative approach involves the construction of a world model. Decisions are made based on this world model and any a-priori knowledge, allowing a fairly comprehensive path planning solution. On the other hand, a much simpler approach is reactive in nature- meaning that the actuator control is closely linked to the sensor inputs. There are two basic methods of deliberative motion planning for IMPASS, Initial Contact Point Selection (ICPS) and Initial Body Path Selection (IBPS). This research focuses on the ICPS method. Contact point selection can be broken down into three steps, Critical Contact Region (CCR) identification and refinement, Critical Contact Point (CCP) determination, and Intermediary Contact Point (ICP) determination. The CCR step determines where the robot must step to traverse obstacles; the CCP step determines where in those ranges is most ideal for IMPASS; and finally the ICP step calculates the best way to get from one obstacle to the next. Each pair of adjacent contact points is assigned a transition configuration (i.e. ascending, descending, or default). Once contact points have been selected, a body path is chosen for the robot that moves it from one transition state to another. Motion planning must also consider the the non-contact spokes in that they must avoid any terrain interference. To this end, collision avoidance software has been developed that plans the foot trajectories. When a future collision is detected, the spoke path is altered to maintain a safe distance (one inch for the current prototype). The deliberative motion planning was tested with obstacles and ramps using ideal sensor data. The approach proved to be effective

95 Shawn C. Kimmel Chapter 6. Conclusion 82 in simulation but in reality was unable to account for the distance that the robot advances each step as the foot rolls over the ground. With minor modifications, this algorithm could be effective in a physical environment. Deliberative planning is dependent on reliable and complete sensor data. While this assumption may be sufficient for the two-dimensional sagittal plane, it is a much more difficult problem in unstructured three-dimensional environments. The reactive approach to motion planning focuses on direct sensor data rather than a world map. For IMPASS, this can include, but is not limited to, inclination of the body, touch sensors on the feet, and torque sensors on the hubs. Information from these sensors can be directly tied to simple motion planning behaviors. The algorithm discussed in this chapter uses inclinometer data to plan steps using the Equivalent Leg Length transition. This approach has proven effective over obstacles less than the nominal walking height of the robot and dynamic terrain. However, it is not yet capable of handling larger obstacles. The considerations for motion planning in the two-dimensional sagittal plane have been discussed. Also, implementations of the deliberative and reactive approaches to motion planning have been presented with their associated advantages and limitations. There is considerably more research that can be done with the IMPASS platform in light of the findings from this thesis. 6.1 Future Work As this paper has shown, IMPASS is an excellent mobility platform. There is still much work that can be done to further understand the full capabilities of this robot. This paper has covered the considerations for motion planning, but has only shown two implementations. For the deliberative approach, the ICPS method has been fairly well covered. An adjustment needs to be made that accounts for the forward creep of the feet during a step. Also a model of the spoke compliance and hub gear train backlash would provide for more accurate execution of the motion. The other deliberative approach, the IBPS method, has still yet to be delved into. This method could be very valuable for payload impact management. There is still much work that can be done with reactive motion planning paradigms. Currently the robot can climb moderate obstacles. Once the robot is outfitted with tactile and hub torque sensors, new algorithms can be tested that will advance the mobility of the robot with reactive software. All the experiments conducted for the deliberative software were done with ideal terrain information. IMPASS is not yet capable of Simultaneous Localization and Mapping (SLAM). This is a difficult problem on any mobile robot in an unstructured terrain. Currently a Laser Range Finder (LFR) and cameras are outfitted on the robot. These sensors can be integrated into a reliable perception suite using current SLAM techniques.

96 Shawn C. Kimmel Chapter 6. Conclusion 83 Lastly, there is a whole range of research topics for IMPASS in three dimensions. The motion planning and perception problems in particular become far more complicated with the addition of a third dimension. However, three-dimensional operation is where IMPASS must succeed to become a practical mobility platform for real world applications. It remains to be seen whether the deliberative or reactive approach will prevail for this robot, or whether a hybridization of the two will be the answer. With effective motion planning and perception, the applications for this platform are endless. The world would greatly benefit from such work.

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100 Appendix A Deliberative Motion Planning Simulations 87

101 88 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) Figure A.1: IMPASS climbing a set of three six inch steps and down an eleven inch obstacle. The Default Transition is used throughout most of the simulation with the exception of the large negative obstacle. Here the Descending Transition is used.