Abstract. 1 Introduction. 2 Concept of the mobile experimental

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1 ISR / ROBOTIK 2010 Mobile Experimental Platform for the Development of Environmentally Interactive Control Algorithms towards the Implementation on a Walking Humanoid Robot Giulio Milighetti, Janko Petereit and Helge-Björn Kuntze Fraunhofer Institute of Optronics, System Technologies and Image Exploitation, Karlsruhe, Germany name.surname@iosb.fraunhofer.de Abstract In the framework of the long term Collaborative Research Center SFB 588 Humanoid Robots the robot ARMAR III has to manage different basic skills in a highly dynamic environment. They mainly take place in the area close to the robot and require especially its upper body including head, arms and hands. However, during the last project phase the development has been mainly focused on basic skills which have to be accomplished mainly in a wider range and require also walking capability (e.g. carrying a tray). In order to investigate in advance such new environmentally interactive control algorithms, an adequate development platform is required. The mobile experimental platform developed with this goal at Fraunhofer IOSB consists of an upper body including various existing robot components like torso, head, arms and hands, as well as a lower body represented by a mobile robot. A Stewart platform provides then the functionality of a human hip connecting upper and lower body. This hexapod structure is the central element of the proposed platform because it is responsible for a motion of the upper body, that emulates the oscillations of a human gangway. Therefore, the most important steps of its design process will be discussed in this paper. In order to demonstrate the feasibility of the platform, a case study optimizing the gaze control of a humanoid robot head will be presented. 1 Introduction In the last years a new generation of humanoid robots has been emerged in the public and private environment opening new scenarios in the robot market. Such a robot requires human-like capabilities in order to cooperate and interact with humans as well as to act autonomously in a time-varying and loosely structured environment. In order to properly develop this innovative technology the Deutsche Forschungsgemeinschaft (DFG) has established in 2001 the long-term Collaborative Research Center SFB 588 Humanoid Robots in which the various aspects of the multifaceted interaction between robots and humans are investigated. Within this framework, the Fraunhofer IOSB is responsible for the development of a modular and flexible supervisory control concept which allows the robot to cope with different basic skills. Typical multi-sensor controlled skills implemented up to now are e.g. the grasping of randomly positioned parts, the fitting of parts into holes (e.g. key into key hole), the balancing of instable parts on a tray or the lifting and carrying of objects by adherence [1, 2, 3]. Thanks to the significant results achieved in the entire SFB, at the current state of development the demonstrator AR- MAR III is able to cope successfully with different complex skills. They mainly take place in the area close to the robot and require especially its upper body including head, arms and hands. Typical capabilities in a kitchen environment are e.g. loading and unloading the dishwasher or serving drinks from the fridge [6, 7]. During the last project phase started in 2008 the development has been focused on basic skills which have to be accomplished mainly in a wider range and require also walking capabilities. Since the mechanics of the new legged robot will be developed within this last project phase, an adequate mobile platform is required for investigating in parallel new environmentally interactive control algorithms. The concept for the realization of such a platform and the development of one of its central components as well as first experimental results are presented in detail in this paper. 2 Concept of the mobile experimental platform The mobile experimental platform developed at Fraunhofer IOSB for investigating and validating different control concepts consists of an upper body including various existing robot components like torso, head, arms and hands, as well as a lower body represented by a commercially available mobile robot. A Stewart platform provides then the functionality of a human hip connecting upper and lower body (figure 1). The mobile robot is equipped with various sensors for SLAM and autonomous navigation as well as for 682

near range manipulation within an unknown dynamically changing environment (laser range finder, inertial measurement unit, stereo camera, time-of-flight camera,... ).

2 near range manipulation within an unknown dynamically changing environment (laser range finder, inertial measurement unit, stereo camera, time-of-flight camera,... ). Its purpose is to realize the translational motions in the walking direction by means of an almost constant velocity. Combining this primary motion with some hip oscillations, almost any trajectory of the human body can be emulated. In order to generate this overlaid motion, an hexapod kinematics has been chosen. Advantages of such a structure are beside its positioning accuracy, the big allowed payloads and its high stiffness and stability. These characteristics together with its compact form make a Stewart platform the ideal structure for the intended application. In order to have a platform with optimal characteristics for the specified task, a tailored parallel kinematics has been developed. The most important steps of this design process will be discussed in section 3. The trajectory data used for the realization of realistic human gaits are acquired by means of a motion capturing system at the Institute for Sports and Sports Science (IFSS) of the Karlsruhe Institute of Technology (KIT) within a different sub-project of SFB 588. By moving the upper base of the Stewart platform with a trajectory that emulates the motion of the human hip, the body components installed on the top of it are subject to the same disturbances that arise during a real human walking and the developed control algorithm can be evaluated under realistic conditions. A first validation of the platform functionality will be presented on the basis of a case study in paragraph 4. 3 Mechatronic design of a dedicated Stewart platform The intended application of the Stewart platform imposes specific requirements on the design process. On the one hand we strive for a large working range and great dexterity to simulate the wide spectrum of human gait motion, on the other hand the platform has to be able to cope with high payloads. As shown later these are two contradictory criteria which form a multi-objective optimization problem. For symmetry reasons we decided for a kinematic arrangement where the six legs each one consisting of a linear actuator are pairwise connected to base and platform using high precision universal joints. In order to obtain reasonable overall platform dimensions we choose actuators with a minimal length of 384 mm and a maximal stroke of 200 mm in advance. With this setup in mind there are only four design parameters left to determine. These are (cf. figure 2) the base radius r B, the platform radius r P, the base pairing angle ϕ B and the platform pairing angle ϕ P. (a) base (b) platform Figure 2: Sketch of the hexapod s base and platform 3.1 Optimization of the working space In the first part of the design process we concentrate on the maximization of working space and dexterity. In [4] a method for constructing a Stewart platform with optimal dexterity in a given local point has been proposed. As movements near the zero position are very common, we adopt that position as point of interest. This yields to the following two constraints on the design parameters: ϕ B + ϕ P < 120 r P < r B 2r P (crossing legs) Figure 1: Concept of a mobile experimental test and development platform for legged humanoid robots Additionally we want to assure a great dexterity over a wide range of the working space. In order to get a measure for the dexterity we use the inverse kinematics to compute the volume of the working space for a given required rotation θ of the platform. For this purpose we define the coordinates of the center of the platform to be member of the working space W(θ) if a rotation of the platform using Euler angles (i.e. a rotation by θ around the x-, y-, or z-axis or any combination of these) leads to a valid leg configuration. 683

3 With the known platform position q, platform rotation R and joint vectors b i and p i for i = 1,..., 6 according to figure 3 the inverse kinematics are given by s i = R p i + q i b i, (1) l i = s i, i {1,..., 6}. (2) Figure 4: Volume of the working space with max. rotation θ = 5 (blue) and 15 (red) without consideration of force constraints Figure 3: Sketch for computation of inverse kinematics For the practical computation of the working space volume we sampled the space around the zero position and performed the calculation of the leg lengths for each discrete position. If l min l i l max holds for all i {1,..., 6} the volume of the associated tiny cube is added to the working space volume. We computed the volume for different sets of design parameters to get an overview on the influence of the individual parameters. Once again we discretized the parameter space and simulated the working space for all combinations of the following parameter values: r B {200 mm, 250 mm, 300 mm}, r P {150 mm, 200 mm, 250 mm, 300 mm}, ϕ B {5, 15, 25, 35, 45, 55 }, ϕ P {5, 15, 25, 35, 45 }, θ {5, 15 }. The result is shown in figure 4. The volume was computed for a total number of 360 parameter sets. The plot depicts the volume for each combinatorial step. Thus, the computation process results in four nested loops: The outer loop cycles through the different values of r B, the next one through r P, the one after that through ϕ B and the most inner one through ϕ P. Consequently, in figure 4 the values of ϕ P repeat every 5 steps, the values of ϕ B every 30 steps and the values of r P every 120 steps. As seen from the plot a maximization of the working space volume is achieved for r B = r P and ϕ B and ϕ P as near to 60 as possible. Furthermore, the minimal required possible rotation angle θ has a drastic influence on the size of the volume: Increasing θ from 5 to 15 makes the volume decrease by more than 70%. 3.2 Introduction of further constraints The computations of the working space in the previous section were all made on the assumption of a massless platform. However, for a real mechanism the forces due to the self-weight of platform and actuators and due to the potential payload as well as further mechanical constraints must be taken into account. Therefore, the computation of the working space has been extended to respect those constraints. The restrictive mechanical criterion is the fact that the installed universal joints only allow for an angle of max. 45. This constraint can be integrated very easily using vector arithmetics. The second and most important, but yet more complicated to calculate, criterion is the maximum force which each actuator must exert to carry the platform and a potential additional payload. The rest of this chapter develops (on the basis of [5]) the equations for the occurring forces in the actuators. If not stated otherwise, all vectors are given with respect to the platform coordinate system. Referring to figure 3 we can write s i = p i P b i = p i R B b i + R B q, where R denotes the rotation matrix, which expresses {P } in the coordinates of {B}. By normalizing the leg vector and computing the momentum (3) s i = s i s i (4) m i = p i s i (5) we get the new vector [ ] si u i = = [ s m ix i s iy s iz m ix m iy ] m iz (6) which contains the so called Plücker coordinates. 684

4 3.2.1 Balance of forces F I + F G + F ext + F i = 0. (7) As we are only interested in the stationary forces we set the inertial forces F I to zero. The force of gravity F G may be computed to F G = m P g with g = R B g (8) with the known mass m P which is the sum of platform selfweight and applied payload. The weight of the legs causes an external force F ext. We use κ to denote the relative position of a leg s center of gravity (for κ = 0 it is located at the lower end, for κ = 1 at the upper end). A choice of κ = 0.5 corresponds to a homogeneous mass distribution along the leg direction. A leg s force of gravity causes a torque F G,leg = m leg R B g (9) τ i = κ s i F G,leg (10) on the joint which connects the leg to the platform. Using this the resulting forces acting at the platform can be computed to which leads to F legi = τ i s i τ i s i τ i s i (11) F ext = F legi. (12) The sum in equation (7) can be written as the matrix product F i = S f, (13) with S = [ s 1 s 2 s 3 s 4 s 5 s 6 ] consisting of the legs unit vectors and (14) f = [ f 1 f 2 f 3 f 4 f 5 f 6 ] (15) consisting of the forces exerted by the linear actuators. By utilizing the previously developed equations, the balance of forces (7) can be rewritten as S f = m P g F legi. (16) Torque balance The torque balance can be written analogous to the balance of forces: C I + C ext + C i = 0. (17) Once again we choose C I = 0. The external torque is caused by the weight of the legs C ext = p i F legi. (18) The sum in equation (17) can be expressed in terms of the matrix product C i = M f (19) with M = [ m 1 m 2 m 3 m 4 m 5 m 6 ] (20) being the matrix of the normalized leg moments and f being the same exerted forces as in equation (15). The equations (18) and (19) can be used to write (17) as M f = p i F legi. (21) Solving the linear system Finally, the equations (16) and (21) can be combined to form the following system of linear equations: s 1x s 6x s 1y s 6y s 1z s 6z m 1x m 6x m 1y m 6y m 1z } {{ m 6z } U [ S M] f = f 1 f 2 f 3 f 4 f 5 f 6 m P g 6 F legi 6 p i F legi m P g 6 F legi = 6. p i F legi (22) As both the matrix of Plücker coordinates U and the right side are entirely known, the system (22) can easily be solved for the unknown vector of exerted forces f Working space volume with constraints Using the same approach as in section 3.1 we extend the criteria for a point to be in the working space with two further constraints. Now we require each point of the working space to meet the three requirements 685

l min l i l max f i f max arccos(s i s zeroposi ) 45 for all i {1,..., 6}. The results are shown in figure 5 for an exemplary payload of 5 kg and a maximum allowed actuator force of 70 N.

5 l min l i l max f i f max arccos(s i s zeroposi ) 45 for all i {1,..., 6}. The results are shown in figure 5 for an exemplary payload of 5 kg and a maximum allowed actuator force of 70 N. Thus, as there is a trade-off between the two design goals (maximizing the working space volume and possible payload), one has to choose an optimal parameter set according to the priorities with regard to the desired application. We decided to shift the focus slightly to the maximization of the payload capability. After iteratively refining the working space volume computations we decided for a base radius r B = 220 mm, a platform radius r P = 150 mm and a base and platform angle r B = r P = 25 which leads to a sufficient setup for the dedicated application. Figure 6 shows a three dimensional plot of the working space for the selected mechanical configuration for a required minimum rotation by θ = 5. 4 Case study: Gaze control of a humanoid robot head Figure 5: Volume of the working range with max. rotation θ = 5 (blue) and 15 (red) and active force constraints In order to demonstrate the feasibility of the experimental Stewart platform a case study will now be discussed. Considered will be the vision controlled manipulation of a dynamically moving object (e.g. a cup) as exemplary shown in figure 7. During the first phase of such a task the robot has to fix its gaze on the target despite the presence of disturbing motion due to the walking system. The enormous influence of the force constraints lets the volume of the working space degrade to approx. 2 dm 3 if a possible rotation by 15 is required. Contrary to the unconstrained case now an optimal design parameter set consists of a platform radius r P which is significantly smaller than the base radius r B. Furthermore, small angles ϕ B and ϕ P allow for a higher payload. Figure 7: ARMAR III grasping a cup 4.1 Experimental set-up Figure 6: 3D volume of the working space of the selected kinematics For testing, evaluating and optimizing different gaze control algorithms the ARMAR III head [8] has been mounted on the Stewart platform (figure 8). Goal is to achieve a robust tracking of a moving target while both robot and object are moving arbitrarily. The translational motion of the hip has been extracted from the data of a human gait at a velocity of 1.2 m/s and transferred to the upper basis 686

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7 References [1] Milighetti, Giulio and Kuntze, Helge-Björn Multi- Sensor Robot Control for Humanoid Two-Arms- Skills, Robotik 2006, Munich, Germany. [2] Milighetti, Giulio and Kuntze, Helge-Björn On the robot based surface finishing of moving unknown parts by means of a new slip and force control concept, IEEE International Conference on Robotics and Automation 2007 (ICRA 07), Rome, Italy. [3] Milighetti, Giulio and Kuntze, Helge-Björn Vision Controlled Grasping Using a Smart Hand, Workshop on Cognitive Vision, Humanoids 2008, Daejeon, Korea. Figure 12: Comparison between position and velocity control of the robot head 5 Conclusion A mobile experimental platform has been presented, which provides the opportunity to investigate different environmentally interactive control algorithms and basic skills for a walking humanoid robot. The motion of the human hip during a gangway has been emulated through a Stewart platform connecting lower and upper body. In order to develop an hexapod with convenient working space and adequate payload for this specific task, a tailored parallel kinematics has been developed. The design process takes into account both geometrical and force constraints. For demonstrating the feasibility of the platform a case study has been presented, in which the gaze control of the AR- MAR III head has been investigated and optimized. Acknowledgment The authors gratefully acknowledge that the research project presented in this paper has been supported by the Deutsche Forschungsgemeinschaft (DFG). [4] Pittens, Kenneth H. and Podhoreski, Ron P. A Family of Stewart Platforms with Optimal Dexterity, Journal of Robotic Systems 10, pp , [5] Fichter, E. F. A Stewart Platform-Based Manipulator: General Theory and Practical Construction, The International Journal of Robotic Research 5, pp , [6] Vahrenkamp, N. and Wieland, S. and Azad, P. and Gonzalez, D. and Asfour T. and Dillmann, R. Visual Servoing for Humanoid Grasping and Manipulation Tasks 8th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2008), Daejeon, Korea. [7] Prats, M. and Wieland, S. and Asfour, T. and Pobil, A. P. del and Dillmann, R. Compliant Interaction in Household Environments by the Armar-III Humanoid Robot 8th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2008), Daejeon, Korea. [8] Asfour, T. and Welke, K. and Azad, P. and Ude, A. and Dillmann, R. The Karlsruhe Humanoid Head 8th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2008), Daejeon, Korea. 688

Humanoid Manipulation

Humanoid Manipulation Tamim Asfour Institute for Anthropomatics, Computer Science Department, Humanoids and Intelligence Systems Lab (Prof. Dillmann) wwwiaim.ira.uka.de www.sfb588.uni-karlsruhe.de KIT