Motion Planning for Humanoid Robots: Highlights with HRP-2

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1 Motion Planning for Humanoid Robots: Highlights with HRP-2 Eiichi Yoshida 1,2 and Jean-Paul Laumond 2 AIST/IS-CNRS/ST2I Joint French-Japanese Robotics Laboratory (JRL) 1 Intelligent Systems Research Institute, National Institute 2 LAAS-CNRS, University of Toulouse of Advanced Industrial Science and Technology (AIST) 7, av. du Colonel Roche AIST Central 2, Umezono 1-1-1, Tsukuba, Japan Toulouse, France e.yoshida@aist.go.jp, jpl@laas.fr Abstract In this paper we outlook current state of the art in the emerging research field of motion planning for humanoid robots. We will first introduce related research activities in several aspects of motion planning for humanoid robots, which include integration of dynamics and other 3D motion planning for wholebody motion and various tasks. We also mention locomotion planning and local whole-body dynamic motion generation. We next present two related ongoing research projects conducted at JRL-France. The first part shows results 3D wholebody humanoid motion planning for simultaneous locomotion and dynamic manipulation. A two-stage planning method is adopted to generate for stable locomotion and task execution, by integrating geometric and kinematic motion planner and dynamic pattern generator. The second work provides a general framework of task-driven whole-body motion generation including stepping. In that research tasks are given to the IK solver to generate whole-body motions by taking account of monitored criteria and task priorities. A dynamic walking pattern generator provides the stepping motion that is combined with task achieving motion using the same IK solver. Finally we comment perspectives for future direction of motion planning for humanoid robots. I. MOTION PLANNING FOR HUMANOID INTRODUCTION Humanoid robots are expected to perform complicated tasks thanks to their high mobility and many degrees of freedom (DOF) including legs and arms. Their anthropomorphic configuration gives another advantage that they can easily adapt to machines or environments designed for humans. One of the key issues to fully exploit the capacity of humanoid robots is to develop a methodology that enables them to explore and execute various dynamic tasks, requiring dynamic and smooth whole-body motion including collision avoidance and locomotion, like object carrying tasks. In the field of motion planning, advancement in probabilistic methods has greatly improved planning of the threedimensional (3D) motion of mechanism including complicated geometry and many degrees of freedom. However, most of those methods are based on geometric and kinematic planning in configuration space whereas dynamic control is required for humanoid motion planning in workspace to execute tasks by keeping its balance. Concerning control issues of humanoid robots, stable motion pattern can be generated efficiently thanks to the progress in biped locomotion control theory, basically based on ZMP (zero moment point [1]) control. Staying at LAAS-CNRS as a co-director of JRL-France Planning of 3D humanoid motion for tasks in complex environments must definitely benefit from those two domains. Indeed, integration of dynamics into geometric and kinematic motion planner is a challenging topic. In this paper, we first outlook the recent research trend in motion planning for humanoids in Sections II and III for consideration dynamics and other related issues. Section IV and V show researches on locomotion planning and wholebody dynamic motion generation. After brief introduction of research activities at JRL-France in Section VI, we present two of our research results, a 3D motion planning for simultaneous locomotion and manipulation and whole-body motion generation including support polygon reshaping are presented in Sections VII and VIII. Section IX gives several perspectives. II. HUMANOID MOTION PLANNING WITH DYNAMICS As stated earlier, recent progress in motion planning research now allows us to solve a three-dimensional (3D) collision avoidance motion of robot with complex structure with many DOFs in cluttered environments. This evolution attributes mostly to development of efficient algorithms based on sampling-based planning method such as Rapidly-exploring Random Trees (RRT) [2], [3], Probabilistic RoadMap (PRM) [4] and all their variants (See [5], [6] for two recent overviews). It is natural to have an idea to extend this method for humanoid robots. In this case, the essential issue are to face the high number of of DOFs and to incorporate dynamics to geometric and kinematic motion planning scheme. In [7] Kuffner classified the possible methods into three classes to deal with dynamics. The first one is a two-stage approach. In the first stage, a path is generated by geometric and kinematic planning, which is validated by considering dynamics to transform it into a dynamically executable trajectory. The second method is based on state-space approach which attempts to include the derivative. This unified approach takes account of dynamic constraints implicitly during planning via state transition equations. The third is any hybrid methods combining those two methods or using sensor information. Although the state-state approach looks nice, this approach doubles the state space and has not really been applied to humanoid motion planning. Two-stage approach has therefore been investigated intensively these years.

2 Fig. 2. Non-gaited humanoid locomotion [14] Fig. 1. Balanced reaching motion generated in [8] Kuffner and his colleagues initiated this area and have been actively working on this topic. They proposed a method to generate collision-free dynamically-stable humanoid motion using RRT [8] through a two-stage method (Fig. 1). In this method first statically stable configurations are pre-computed and the random planner makes a search to find a collision-free path from initial to final configurations. After the planning, the path is then transformed into minimum-jerk trajectory and smoothed by verifying dynamic ZMP constraints. If the collision is detected the trajectory is slowed down towards the statically stable configurations. In this research, support state (double or single support) does not change and locomotion is not included. In our research we developed a framework in order to generate 3D collision-free motions that take account of both the locomotion and task including dynamics [9]. We will provide some detailed description of this method in section VII. III. MOTION PLANNING FOR HUMANOID OTHER ISSUES There are a number of other topics where motion planning is concerned for humanoid robots. Probabilistic planning method can take advantage of its efficiency for many DOFs for various types of problem. Kagami et al. [10] proposed a motion planner for humanoid arm trajectory using RRT based on stereo vision. As a humanoid robot has a many links, it is important to detect rapidly if the desired motion can be executed safely. For this purpose self-collision avoidance are addressed [11], [12]. Not only collision avoidance but also motion planning taking advantage of contact is now being investigated. Hauser et al. [14] proposed planning of non-gaited locomotion of humanoid to go through a rough terrain using locomotion by supporting its body with hands and feet (Fig. 2). Escande et al. [13] presented a method of planning support contact points so that the humanoid robot can accomplish tasks that require multiple contacts, like taking a distant object on the table by supporting its body by one hand. Manipulation planning is another interesting topic. Stilman studied a method for navigation among movable obstacles that allows the humanoid to reach the goal by displacing interfering obstacles [15]. Okada et al. developed a software framework for high level motion generation for the robot to move in a daily-life environment including 3D geometric model based action/motion planner and runtime modules contains 3D visual processor, force manipulation controller and walking controller [16]. IV. LOCOMOTION PLANNING It is an important issue how the locomotion is planned for humanoid robots. Research on bipedal walking has a long history and now walking pattern generators have been proposed (for example, [17], [18], [19], [20]) based on ZMP control whose reliability has been verified through hardware experimentations. Kagami et al. and Gutmann et al. proposed on-line foot step planning methods using the environment model built by observation for human-size H7 robot [21] and smaller QRIO robot [22] (Fig. 3). Kuffner et al proposed a footstep planner to determine the footprints in rough terrain [23]. Humanoid robots can also make use of its many DOF to go around various environments by changing its locomotion modes. Fig. 3. On-line path-planning for navigation on rough-terrain [22]

3 A method was first proposed by Shiller et al to allow a digital actor go through narrow spaces by switching walking and crawling locomotion using the environment model which is given a priori [25]. Kanehiro et al. proposed a method that allows the humanoid robot to go through constrained spaces by switching between various predefined locomotion styles (normal biped walking, walking with twisting its waist, side stepping, walking with bending knees deeply and crawling), using a simulated 3D view [26] (Fig. 4) and 3D grid map builder [27]. V. WHOLE-BODY DYNAMIC MOTION GENERATION Finally, the generation of whole-body dynamic motion is closely related to motion planning. Whereas the motion planning takes charge of global plan from initial to goal configurations, a whole-body motion generation concerns how to make valid local motions by taking account of several constraints. So it is important in order to create feasible dynamic trajectories from motions that have been provided by the global motion planner. Khatib and his colleagues have been working on dynamic motion generation for humanoid robots by using task specification in operational space approach [28]. In their work a hierarchical controller synthesizes whole-body motion based on prioritized behavioral primitives including postures and other tasks in a reactive manner. Kajita et al. proposed a resolved momentum control to achieve specified momentum by whole-body motion [29]. Mansard et al. [30] proposed a task sequencing scheme to achieve several tasks including walking and reaching at the same time. We have also developed a taskdriven support polygon reshaping [31] that enables a wholebody tasks as introduced later in section VIII. There are several task-specific whole-body motions that have been intensively investigated: pushing [32], [33], [34], and lifting [35], and pivoting [36]. Currently, many researchers are intensively working to integrate those recent developments with global motion planner. Fig. 5 shows an example of planning of pivoting manipulation to move a bulky object to final position. VI. RESEARCH IN JRL USING HUMANOID PLATFORM One of the main research areas in JRL-France at LAAS- CNRS has been also motion planning for humanoid robots using software and hardware platforms HRP-2 [37] and OpenHRP [38]. We have also been working on human-robot Fig. 4. Passing narrow space by changing locomotion style [26] Fig. 5. Planning result of pivoting with HRP-2 humanoid robot holding the box. Arm configurations are calculated using inverse kinematics from fixed contact points on the box. interaction, software architecture and control issues. Introduction of projects in JRL-France in French is found in a web page [39]. In the following two sections, we present our work on whole-body motion planning for humanoid robots. In the first part, a two-stage iterative planning framework is introduced where geometric motion planner and dynamic pattern generator interact by exchanging the trajectory, to obtain 3D whole-body dynamic motions simultaneous tasks including locomotion, in complex environments. The second part describes a task-driven motion generation method that allows a humanoid robot to make whole-body motions including support polygon reshaping to achieve the given tasks. VII. 3D MOTION PLANNING FOR SIMULTANEOUS MANIPULATION AND LOCOMOTION We have proposed a two-stage planning framework [9] based on the geometrical and kinematic planning technique [40] whose output is validated by dynamic motion pattern generator [19]. Using proposed planning framework, we could obtain 3D whole-body humanoid motions for execution of dynamic task in complex environment. The main contribution of our approach is to cover both manipulation and locomotion tasks in a single unified framework. A. Two-stage planning method Fig. 6 illustrates the two-stage planning method we have proposed. At the first stage of motion planning (upper part in Fig. 6), the geometric and kinematic motion planner takes charge of generating collision-free walking path described by the position and orientation (X, Θ) of the waist for a bounding box approximating the humanoid robot, as well as the upper body motion expressed by joint angles (q u ) to achieve desired tasks. Here we assume that robot moves on a flat plane with obstacles. Then at the second stage, those outputs is given to the dynamic pattern generator [19] (lower part in Fig. 6) of humanoid robots to transform the input planar path into a dynamically executable motion described by waist position and orientation (X d, Θ d ) and joint angles of whole body (q) at sampling time of 5[ms] by taking account of dynamic

4 Start / goal position Environment Input Motion planner / reshaper Robot Waist position & orientation X, Θ Upper body motion q u Dynamic pattern generator Waist position & orientation Fig. 6. X d, Θ d Motion planning Task y Joint angles q Dynamic motion generation Dynamic humanoid motion Collision or Too near? Output Collision checker Two-stage motion planning framework balance based on ZMP. However, the generated dynamic motion often differs from the geometrically and kinematically planned path, which may cause unpredicted collision. Then the planner goes back to the first stage to reshape the previous path based on randomized method to avoid possible collision. This refining process is repeated until the planner obtains a collision-free and dynamically stable 3D whole-body motion to realize locomotion and task execution. If no solution is found, then a new walking plan is searched. n q For local reshaping, we apply a method based on a motion editing method in graphics animation (see [41] for survey). By using this method in workspace for path reshaping, this allows the planner to generate smoother path by deforming a segment of path, not each configuration. The proposed method is characterized by integration of motion planner and dynamic pattern generator to deal with 3D whole-body motion to achieve collision avoidance, task execution and locomotion at the same time. We assume that the geometric and physical information of environment or object is known beforehand to plan the robot s motion prior to task execution. In the next section we address the improvement of quality of reshaped motion. B. Results The proposed method has been applied to a 3D collisionfree motion planning for tasks involving locomotion and manipulation. In this problem, the humanoid robot should carry a bar of 2m with two disks at its edges from the initial Fig. 8(a) to goal Fig. 8(b) position in a constrained environment with composed of two lamps and a tall table. Since the distance between the two lamps is shorter than the bar length, the bar should pass through with an angle. At the beginning of the motion, the computed trajectory for the bar makes the robot move to the left, then walk forward with a certain angle to path through the gap (Fig. 8c-e). Here the motion of the upper part of the robot is computed using a generalized inverse kinematics algorithm with two tasks (left hand to the bar and right hand to bar) the chest is moved consequently to complete both tasks. This example also shows that the complete geometry of the object has been considered in the collision-detection and path (a) Initial position (b) Goal position (c) (d) (e) (f) (g) Fig. 7. Simulation of 3D collision-free motion for bar-carrying task

5 (a) (b) (c) (d) (e) (f) (g) (h) Fig. 8. Experiment of 3D collision-free motion for bar-carrying task at JRL-France planning procedure and no bounding box has been used (see Fig. 7f) where the concave part of the disk and the bar is close to the lamp. At the end of the motion (Fig. 7g), the tall table is avoided. The complete trajectory execution time is around 28 sec. The simulation has been done with KineoWorks and OpenHRP dynamic simulator. Fig. 8 shows the real execution of the robotic platform HRP-2 #14 at LAAS-CNRS. VIII. WHOLE-BODY TASKS INCLUDING SUPPORT POLYGON RESHAPING We here address the following problem of how to reposition the humanoid body when performing reaching or grasping tasks for a target far away. The proposed method is based on reshaping the support polygon of the humanoid robot to increase its workarea by coupling generalized inverse kinematics and dynamic walking pattern generator. While using inverse kinematics, the global motion is guaranteed to be dynamically stable. Such a property is a direct consequence of the zero moment point (ZMP) control provided by the pattern generator we use. Fig. 9 illustrates the proposed motion generation framework with an example of a reaching task. Priorities are given to the target task as well as to other tasks such as the position of center of mass. We employ generalized inverse kinematics to generate a whole-body motion for those tasks based on the given priorities [42]. During the motion, several constraints are monitored which are expressed by such measures as manipulability for whole-body, end-effector errors from target, or joint limits. If the task cannot be achieved because those monitored constraints are not satisfied, a reshaping planner of support polygon is activated automatically to increase accessible space of the robot, keeping the inverse kinematics working to achieve the tasks. The reshaping is performed based on geometric planning to deform the support polygon in the direction Task: reaching end-effector Task Priority: End-effector Center of mass Generalized IK Gaze... Constraints: Manipulability End-effector error... [Task not accomplished] Generalized IK + Whole-body motion Support polygon reshaping Dynamic pattern generation Fig. 9. A general framework for task-driven whole-body motion including support polygon reshaping required by the specified task. Thanks to the usage of freefloating base, the changes in support phase can be easily integrated in the computation. As a result, the stepping motion is generated using a biped walking pattern generator [19] and the blended whole-body motion including the target task is recalculated. Our contribution is to consider the possibility of reshaping the support polygon by stepping to increase the accessible space of the end-effectors in the 3D space. Our approach makes use of the whole body in the 3 directions of the 3D space. Moreover, in spite of our reasoning being based on inverse kinematics and simple geometric support polygon reshaping, our method guarantees that the motion is dynamically stable. This property is a consequence of the pattern generator [19] we use to generate the stepping behavior.

6 A. Method Overview The support polygon reshaping integrates two important components, the generalized inverse kinematics and dynamic walking pattern generator. The former provides a general way to deal with the whole-body motion generation to perform the prioritized tasks. The latter takes charge of the stepping motion to change the foot placements. Figure 10 shows an overview of the method. The task is specified in the workspace as ẋ j with priority j from which the generalized IK solver computes the whole-body motion as joint angles q of the robot. Meanwhile, several criteria such as manipulability or joint limits are monitored if they do not prevent the desired whole-body motion. As long as the criteria are satisfied, the computation of whole-body motion continues until the target of the task is achieved. If the task cannot be achieved due to unsatisfied criteria, the support polygon planner is triggered in order to Input prioritized tasks - Foot placement - CoM position - Reaching target - Gaze direction Motion output Not solved Generalized IK solver Task. Joint angles. Fig. 10. Yes Criteria Monitor - Manipulability - Joint limits - Task error -... Satisfied? No Support polygon planner Solution? Yes Walking pattern generator Method overview No Foot placement CoM motion. extend reachable space. A geometric module determines the direction and position of the deformation of support polygon so that the incomplete task is fulfilled. The position of a foot is then derived to generate the motion of CoM ẋ CoM by using a dynamic walking pattern generator [19]. Using this CoM motion, the original task is then redefined as the whole-body motion including stepping that is recalculated using the same generalized IK solver. The generalized IK solver benefits from the redundancy of the mechanism to choose the solution that best solves the task according to some constraints. Among these works, inverse kinematics algorithms that project tasks with lower priority into the null space of the Jacobian of the higher priority tasks have been widely studied (e.g., [42], [43], [44], [45]). B. Results We have conducted experiments of the generated motion using a humanoid platform HRP-2 for front and sideways reaching tasks that requires stepping as shown in Figs. 11 and 12. As can be seen clearly in Fig. 11(c) and Fig. 12(c), the robot successfully performed the desired reaching task through whole-body motion that unifies reaching task and stepping motion by keeping dynamic balance. Note that the tasks of keeping gaze direction towards the end-effector target position are taken into account in this experiment. Fig. 13 shows the manipulability measure of the arm during the forward reaching task illustrated in Fig. 11. Without reshaping, the arm approaches singular configuration where the manipulability becomes lower than the threshold at 2.6[s] and the computation keeping the same support polygon is discarded. In Figs. 14, the time development of x (front) positions of ZMP measured from the ankle force sensors are plotted for the sideways reaching motion. The dotted and solid lines are the planned and measured trajectories respectively. The shaded areas in those graphs depict the transition of the projected support polygon area. We can see the simulation results to the experimental results. We can also observe that the ZMP goes out of the initial support polygon after stepping, which demonstrates the necessity of support polygon reshaping. (a) (b) (c) (d) (e) Fig. 11. Experimentation of front reaching task. Putting weight on the right foot in (b), the robot goes through a posture that is not statically stable (c) to finish stepping in (c). The final goal of the end effector is achieved at (e). The gaze direction is always maintained in the direction of the end-effector goal.

7 (a) (b) (c) (d) (e) Fig. 12. Experimentation of sideways reaching task. Putting weight on the right foot in (b), the robot goes through a posture that is not statically stable (c) to finish stepping in (c). The final goal of the end effector is achieved at (e). Notice that the robot makes a whole-body motion including reaching task, stepping and keeping the gaze. arm manipulability 1.50e e e e e e-04 reshaping no reshaping 0.00e time [s] Fig. 13. Manipulability for front reaching. Without support polygon reshaping, the manipulability measure decreases below the threshold. Although it also decreases with reshaping, the manipulability increases in the course of stepping motion. 0.4 x [m] Projected support polygon area ZMP x (exp) ZMP x (ref) time [sec] Fig. 14. Experimental and simulation results of transition of x component of ZMP for front reaching motion. The shaded area expresses the transition of the projection of support polygon in x axis. IX. PERSPECTIVES This paper has surveyed researches on motion planning for humanoid robots. We have presented researches on several important topics such as 3D motion planning, other planning for tasks, locomotion planning and local whole-body motion generation. Then we have presented the ongoing studies in JRL-France on methods for 3D motion planning for simultaneous locomotion and manipulation and support polygon reshaping for dynamic motion of humanoid robot. As future directions, first the integration of perception into motion planning is a critical issue [16], [47]. Many of presented researches assume that the model of the environment is completely known. Challenging research topics include how to adapt the planned motion during dynamically updated environment and how to deal with uncertainty for humanoid motion. The second issue is consideration of dynamics into planning. Main approaches in current research, including ours, are twostage methods that first kinematically plan then smooth or modify it through dynamic motion generator. How to incorporate motion planning and complex whole-body dynamics will be an active research topic for coming years. ACKNOWLEDGMENTS The authors thank to Claudia Esteves, Oussama Kanoun, Mathieu Poirier, Rachid Alami, Takeshi Sakaguchi and Kazuhito Yokoi for their devoted participation in discussions and experimentations. REFERENCES [1] M. Vukobratović and B. Borovac, Zero-Moment Point - Thirty-five Years of its Life, Int. J. Humanoid Robotics, 1-1, , [2] S. LaValle and J. Kuffner: Rapidly-Exploring Random Trees: Progress and Prospects, In Algorithmic and Computational Robotics: New Directions, , A K Peters, [3] D. Hsu, J.C. Latombe and R. Motwani Path Planning in Expansive Configuration Spaces Int. J. Computational Geometry and Applications, 4, , [4] L. Kavraki, P. Svestka, J.-C. Latombe and M. Overmars. Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces IEEE Trans. on Robotics and Automation, 12-4, , 1996.

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