Behavior-based Arm Control for an Autonomous Bucket Excavator

Transcription

1 Behavior-based Arm Control for an Autonomous Bucket Excavator Sergey Pluzhnikov, Daniel Schmidt, Jochen Hirth, and Karsten Berns Robotics Research Lab, Dept. of Computer Science, University of Kaiserslautern, Gottlieb-Daimler-Straße, Kaiserslautern Abstract. The paper at hand presents a novel, biologically inspired approach to numerically solve the inverse kinematics problem of arbitrary kinematic chains without instability problems and with low computational complexity. The kinematic chain of the robot arm is transferred to a network of behavior-based joint controllers, which try to deliver the best control value to solve the global problem. By means of controlling a wheeled excavator robot arm, the capabilities of this approach to work for redundant structures with the desired precision are shown. 1 Introduction Autonomous and assistive systems become more and more important for both, industrial products as well as academical research. These systems can operate in areas polluted by toxic waste or radiation without any risk for humans. One of the projects in this field involves the development of a fully autonomous bucket excavator. A key functionality of such a system is autonomous landscaping according to a specified target state. This paper presents the scientific system idea in comparison to classical inverse kinematics solvers and proves its capability to control complex machines by implementing it to control the arm of an autonomous 18 t bucket excavator (see figure 1). Using this implementation several experiments to determine the quality have been realized. A crucial aspect for the realization of this task as well as an interesting functionality to support the human operator is to control the movement of the bucket by simply specifying its target position and orientation in 3D-space. To solve this problem, traditional approaches like inverse kinematics can be adopted from industrial robotics. Unfortunately these approaches require time consuming processing (typically complex numeric solvers) and detailed knowledge of the environment in order to calculate the trajectories for every single joint. Since the perception of the environment in outdoor scenarios is a very difficult task as the situation dynamically changes and because of disturbances that will appear on the real construction field, more robust and flexible approaches to control the excavator s bucket are required. Looking to the area of autonomous robotics lead to so called biologically motivated solutions. For recent years behavior-based control approaches have been developed and investigated for the realization of flexible and robust control system. Based on these considerations a behavior-based system to control the TCP (Tool Center Point) of a kinematic chain has been developed. The first idea of such a system has been implemented for the control of the arms and the body of the robot Work Partner [1]. This

2 Fig. 1. The autonomous bucket excavator fulfilling an automated dumping task. idea has been refined to control the focused point of the humanoid robot ROMAN [2]. Based on these ideas, a general control system capable of modelling various kinematic chains has been developed. The most widely used methods in this field are analytical and numerical solvers. A good overview of these methods is given in [3]. Generally speaking, both types of methods have serious drawbacks. They are based on division of joint structure of an object into kinematic units for which analytical solutions can be derived and partition an inverse kinematics problem into subproblems for each of these units. Analytical methods are generally more efficient and reliable than their numerical counterparts, but require special kinematic structures. Such methods in most cases are not applicable to redundant robots. Numerical solvers take a system of equations describing kinematic constraints and search for a solution with various approximation methods. Usually such methods require much computational power as inverse matrix calculations is required and provide unacceptable results in regions close to singularities. Moreover, convergence of such methods depends on initial guess made at the beginning of the task solving. One more drawback of traditional inverse kinematics algorithms is that they can break down or become unacceptably slow for highly redundant systems. Trying to overcome these difficulties, many alternative solutions were proposed. For example, in [4] a method based on neural networks is described. It is applied to a manipulator with 3 degrees of freedom. According to the paper, the method produced reasonable results, but tool orientation was not considered and the result was influenced by initial guess greatly. Another option is to use a behavior-based approach. An example of such solver for a human arm with 7 DOF is presented in [5]. The author does not provide a general algorithm; his solution is applicable only to arm kinematics as it fully exploits specific features of such kinematic configuration.

3 Fig. 2. Schematic view and a model of the boom of the bucket excavator. 1 - Torso joint, 2 - Boom joint, 3 - Dipper arm joint, 4 - Stick joint, 5 - Bucket pitch joint, 6 - Bucket roll joint, 7 - Tool center point (TCP) In this paper a behavior-based inverse kinematics solver is introduced. It works within the ib2c-framework 1 presented in [6]. The solver has been simulated with 6-DOF bucket excavator (see figure 2) as a part of the AMoBA (Autonomer Mobilbagger - Autonomous Mobile Excavator) project whose long term goal is to make a real bucket excavator fully autonomous to perform landscaping tasks on a planned excavation site. The input parameters for the whole inverse kinematics are the position (x, y, z) and the orientation (Roll, Pitch, Yaw) relative to the center point at the bottom of the bucket excavator. The outputs of the task are 6 values of joint angles. The proposed solution does not involve complex algebraic calculations and singular configurations do not affect its performance. Another positive ability is that the solver could be easily expanded to systems with higher number of joints without greatly increasing the amount of computations. 2 Concept Unlike traditional inverse kinematics solvers suggested, the approach at hand does not presume centralized solution of the task. Instead every joint has a controller deciding in 1 integrated Behavior-based Control

4 Fig. 3. State machine of the designed inverse kinematics solver. i - iteration counter; i max - maximum number of iterations; new_desired_pose - a flag set when desired pose is changed, reset in Start solving state. which direction a joint should rotate in order to solve the global task of moving the tool to the desired point with desired orientation. In general, these controllers do not know whether the task is solvable, the position of the other joints, and how these joints move. The inverse kinematics task is solved incrementally according to the following procedure (see figure 3). When a new desired pose of TCP is set by a higher-level controller, the behavior network becomes active. At this moment it acquires the data about the current joint angles and switches to solving mode. During each iteration, all the joint controllers calculate a relatively small (approximately 1 4 ) step in the desired direction, then the steps of all joints are internally simulated and a new virtual position of the TCP is calculated. The joint controllers use this virtual position as new input and generate values for the next step. One supervising module compares the desired TCP pose and simulated virtual TCP pose. If the poses are close to each other, in position and orientation, the inverse kinematics task is considered as solved and the last calculated values of joint angles are provided as output of the solver. Afterwards, the solver remains inactive until a new desired TCP pose is provided as an input. Alternatively, if the task has not been solved in a reasonable number of iterations, the values that pro-

5 vided the closest TCP pose compared to the desired pose are given as the result. In this case the solver does not stop working and continues the search for a better solution. 3 Implementation The whole algorithm was implemented as a behavior-based network described in the following. The basic component of the proposed system is the so-called behaviorbased module of the ib2c-framework (figure 4). A behavior-based module is characterized by the triples: B = ( f a, f r,f) (1) e s ı B = ( f a, f r,f) u a r Fig. 4. The basic behavior module and the behavior fusion module both provide the same standardized inputs and outputs. where f a represents the activity function, f r means the target rating function, and F is the transfer function of the behavior. Depending on the input signals of a behavior, the stimulation s, the inhibition ı, and the input vector e, these functions calculate the output signals, activity a, target rating r, and the output vector u. The characteristic functions of a behavior as well as the input and output signals are defined as follows: Stimulation s: All behaviors receive their stimulation from other parts of the control system. The co-domain of the stimulation is [0,1], where s = 0 means no stimulation and s = 1 means full stimulation, values in between refer to a partially stimulated behavior. The stimulation of a behavior can be seen as the intended relevance of this behavior in the current situation. For some applications it is usefull to stimulate a behavior module permanently. This is indicated by a black triangle at the stimulation iput of the depicted module. Inhibition ı: A behavior can be inhibited by several other behaviors. The inhibition i of a behavior is defined as: i = max i j, where n denotes the number of inhibiting j=0,...,n 1 behaviors. The inhibition has the inverse effect of stimulation, i = 0 refers to no inhibition and i = 1 refers to full inhibition.

6 Activation ι: The activation of a behavior represents the relevance of a behavior for handling the current situation. It is calculated depending on the stimulation s and the inhibition i, with ι = s (1 i). The co-domain of the activation is [0,1], where 1 refers to full activation and 0 to no activation. Activity a: The activity a [0, 1] of a behavior represents its influence on the current robot behavior. An activity of 1 represents a fully active behavior whereas an activity of 0 represents a completely inactive behavior. The activity of a behavior is used to stimulate other behaviors. Furthermore so-called derived activities have been introduced. They offer the possibility to transfer only a part of the activity to other behaviors. That way more fine-grained stimulation can be realized. The activity a and the derived activities a are calculated by the activity function f a. They are defined as follows: f a : R m [0,1] [0,1] [0,1] q, f a ( e,ι) = a = (a, a) T (2) where with a = ( a 0,a 1,...,a q 1 ) T (3) a i a i {0,1,...,q 1} (4) Target Rating r: The target rating r [0,1] of a behavior indicated the behavior s satisfaction. A target rating of 0 refers to a satisfied behavior, a target rating of 1 to a completely unsatisfied one. In contrast to the activity the target rating does not depend on the activation. Therefore, it can be used to indicate whether a behavior would become active in case of activation. In case of the Exclusive Behavior (introduced below), this information is used to coordinate multiple behaviors. The target rating is calculated by the target rating function f r, which is defined as f r : R m [0,1], f r ( e) = r (5) Transfer Function F: The transfer function represents the intelligence of a behavior. It can be implemented in a way that it depends on internal variables representing a certain state of the behavior. That way, not only reactive sensor responses but also deliberative behaviors can be implemented. The transfer function calculates the output vector u R n of a behavior depending on the input vector e R m and the behavior s activation ι. Typically the input vector consists of sensor information and behavior signals of other behaviors. The output vector on the other hand provides control data for the actuators or for other behaviors. A typical application for behavior-based approaches is the modelling of complex control networks by combining and coordinating multiple rather simple behavior modules. Therefore, ib2c provides the so called Fusion Behavior modules. Such a Fusion Behavior is implemented as a specialized behavior module, which receives the output vectors as well as the behavior signals of the behavior modules to be coordinated and generates a combined output vector depending on the fusion function.

7 Fig. 5. Modular structure of the inverse kinematics solver. It contains four elements which deliver their sensor values (yellow) and control values (red) via specific interface channels. These ib2c elements are used to build up the structure of the solver, which is depicted in figure 5. The core element of the solver is the group Boom Behavioral Network which contains a set of identical joint controllers per joint. During each iteration they calculate the desired delta joint value. According to kinematic structure of the bucket excavator, four joints work in the same plane. This can lead to negative consequences, as all the joints, unaware of each other, may move towards the same direction and, therefore, lead to a too large global step. To prevent this, inhibition connections are used. It means that if, for example, a joint which is close to the end of kinematic chain moves, the other joints rotating in the same plane are inhibited and their activity is reduced for one iteration. The inhibition signals should propagate from the end of the kinematic chain to its beginning across all the joints, moving in the same plane. Each joint controller has two parts which work simultaneously. Its structure is represented in figure 6. One is trying to reach the desired position (Increase/Decrease Angle to Reach Position), another adjusts the desired orientation (Increase/Decrease Angle to Reach Orientation) of the TCP. Their results are combined by a fusion behavior with weighted fusion function, which creates the control values by summing up the input values and dividing them by two. The relation, how big the role of the positioning part is compared to the role of the orientation part, is defined by a special coefficient K w. If K w = 1, only the positioning part is important and the output of orientation part is disregarded. At the value K w = 0 the opposite happens. If 0 < K w < 1, both parts are considered, but with different importance. The joints at the end of kinematic chain deal with the orientation of the TCP, the further a joint is from end of kinematic chain, the more position-oriented it is.

8 Fig. 6. Internal structure of a joint controller. The modules and the structure used by both parts are identical. Each of them consists of two identical behavior modules whose output is consolidated by a fusion behavior which delivers the highest input value as a control value (maximum fusion). One of these behaviors tries to rotate the joint in positive direction, the other one in negative one. Each of the four behavior modules, composing a joint controller, has a clear and simple structure. It receives the actual joint angle and the x and y coordinates of the actual and desired TCP points within the local 2D joint rotation plane as an input. Each behavior tries move the actual point to the desired point by rotation of the corresponding joint. The maximum increment of the angle for a step is limited. Additionally it depends on how close the actual and desired points are to each other. The latter one allows to decrease the maximal step size in a region close to the desired pose and increase accuracy. The Direct Kinematics Transform module (see figure 5) provides the input for the joint controllers. The module contains a model of kinematic chain in Denavit-Hartenberg [7] notation and updates it with the values of joint angles provided to its input. After the chain is updated, the module provides data for both parts of joint controllers responsible for positioning and orientation of TCP correspondingly. For the positioning part, the module translates the coordinates of actual and desired positions of the TCP into the coordinate frames connected to corresponding joints. The resulting x and y coordinates serve as input for the joint controllers. For the orientation part, coordinate frames representing actual and desired orientation of TCP are translated to corresponding joint coordinate frames. The frames are represented as 3 3 rotation matrices. Each column of the rotation matrix represents coordinates of 3 basis vectors i, j, k of corresponding coordinate system. A joint can perform rotation only around 1 axis and cannot adjust all the 3 vectors simultaneously. Therefore, only those vectors that can be affected most should be chosen. As the rotation around the z-axis can change only x and y coordinates of basis vectors, the basis vectors with the least z-coordinates should be picked which that means that they lie in the XY -plane of the joint at most. As both, the actual (a) and desired (d) TCP orientations have to be considered at the same time, the final selection of output coordinates is made on basis

9 of the following criteria: arg min( i d z + i a z, j d z + j a z, k d z + k a z ) The x and y coordinates of corresponding coordinate vectors serve as input for the joint controllers. The main purpose of Behavioral Network Enable Switch module depicted in figure 5 is estimation whether the desired pose of TCP is achieved. It generates the activation signal for the behavioral network which is active since the moment when the new desired pose is introduced till the task has been solved. It also generates Reset and Store current position signals for the Output MUX module. This module decides when and which signals should be provided as output of the solver and what signals Direct Kinematics Transform module receives as input. The decision if it is closer or not is made based on two ratings for orientation and for position. In this particular implementation the orientation rating has priority as it is important for an excavator not to lose the content of the bucket. 4 Experiments To evaluate the developed system, several experiments to determine the quality have been realized. figure 7 presents the deviation of the TCP from the given target position. In this test scenario a sequence of different target positions, which were several meters apart, was given. It can be seen that every time a new target position is provided there is a high deviation which is decreased over time. It is remarkable that after a while the errors are always below 5 cm. Fig. 7. Deviation of the TCP from the given target position. The peaks are caused by the new target positions. The vertical axis depicts the deviation in meters, the horizontal axis depicts the time.

10 The proposed inverse kinematics solver was tested with the simulation model of the bucket excavator and demonstrated adequate good results. It was used together with a trajectory planner that divided the whole trajectory into small steps so the smooth movement of the excavator could be achieved. figure 7 represents the error of the task solution during performing a complex trajectory consisting of 6000 steps which included simultaneous changes of bucket pitch angle and x and z coordinates of TCP. Each point on horizontal axis represents one point in time when the trajectory planner provided new input to the inverse kinematics solver. At this moment the so far found solution of previous task was estimated and the corresponding errors are represented along the vertical axis (in cm for x and z coordinates and in radians for pitch angle). The overall accuracy of the solver was set to 5 cm for position and to 0.09 rad (5.2 ) for roll, pitch and yaw. When the error violates those bounds on the graph it means that the solution has not been found within the period between calculation of 2 consecutive points by the trajectory planner. Increasing this period or running the solver quicker improves the overall performance. The number of iterations needed to solve a task depends on how much the actual and desired poses differ. For situations when this difference is not too big the solution is usually found within 10 till 30 iterations. 5 Conclusion and Future Work The advantage of the proposed solver is that it does not require great computational power: the solving process does not involve calculations of Jacobians or matrix inversions; the most complex operation is matrix multiplication, which is also performed predetermined number of times per step. Therefore, even for robots with redundant kinematic structure the solver does not have problems with singularities and redundant configurations that may arise while using numerical inverse kinematics solvers. Another positive ability is that the solver could be easily expanded to systems with bigger number of joints without great increase in amount of computations. Moreover, in future the whole solver may be implemented as a library component configurable for desired kinematic chain with arbitrary number of joints. The drawback of such solver is that it has a heuristic nature which means that not always the solution is found even if the desired pose is reachable. This effect may become more evident in systems with complex kinematics. Also the solver lacks time determinism as the number of iterations needed for solving a task may differ significantly depending on the task. One more difficulty arises in the fine tuning of the solver. Each joint controller has 5 parameters (not including joint limits) affecting overall performance and determination of optimal solution may be quite complicated. Formalizing how the parameter values should be defined could be also a matter for future research. Another important characteristic of the behavior-based control is the ability to specifically suppress the movement of one joint controller. As the others are still active, the overall task solving process still continues. This will make complex obstacle avoidance during movements possible or allow for working with less joints if hardware breakdowns occur.

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