Multi-modal Motion Planning in Non-expansive Spaces

Motion planning problems encountered in manipulation and legged locomotion have a distinctive multi-modal structure, where the space of feasible configurations consists of intersecting submanifolds, often of different dimensionalities. Such a feasible space does not possess expansiveness, a property that characterizes whether planning queries can be solved efficiently with traditional probabilistic roadmap (PRM) planners. In this paper we present a new PRM-based multi-modal planning algorithm for problems where the number of intersecting manifolds is finite. We also analyze the completeness properties of this algorithm. More specifically, we show that the algorithm converges quickly when each submanifold is individually expansive and establish a bound on the expected running time in that case. We also present an incremental variant of the algorithm that has the same convergence properties, but works better for problems with a large number of submanifolds by considering subsets of submanifolds likely to contain a solution path. These algorithms are demonstrated in geometric examples and in a legged locomotion planner.

[1]  Timothy Bretl,et al.  Motion Planning for Legged Robots on Varied Terrain , 2008, Int. J. Robotics Res..

[2]  Lydia E. Kavraki,et al.  A two level fuzzy PRM for manipulation planning , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[3]  Mike Stilman,et al.  Navigation among movable obstacles , 2007 .

[4]  Jean-Claude Latombe,et al.  On Delaying Collision Checking in PRM Planning: Application to Multi-Robot Coordination , 2002, Int. J. Robotics Res..

[5]  Lydia E. Kavraki,et al.  On finding narrow passages with probabilistic roadmap planners , 1998 .

[6]  Dinesh Manocha,et al.  Path Planning among Movable Obstacles: A Probabilistically Complete Approach , 2008, WAFR.

[7]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[8]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .

[9]  Jean-Claude Latombe,et al.  Kinodynamic motion planning amidst moving obstacles , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[10]  Kostas E. Bekris,et al.  Probabilistic Roadmaps of Trees for Parallel Computation of Multiple Query Roadmaps , 2003, ISRR.

[11]  Siddhartha Chaudhuri,et al.  Smoothed analysis of probabilistic roadmaps , 2007, Comput. Geom..

[12]  Jeffrey J. Biesiadecki,et al.  Athlete: A cargo handling and manipulation robot for the moon , 2007, J. Field Robotics.

[13]  Thierry Siméon,et al.  A probabilistic algorithm for manipulation planning under continuous grasps and placements , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  Jean-Claude Latombe,et al.  On the Probabilistic Foundations of Probabilistic Roadmap Planning , 2006, Int. J. Robotics Res..

[15]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

[16]  Thierry Siméon,et al.  Sampling-Based Motion Planning under Kinematic Loop-Closure Constraints , 2004, WAFR.

[17]  Rajeev Motwani,et al.  Path Planning in Expansive Configuration Spaces , 1999, Int. J. Comput. Geom. Appl..

[18]  Rajeev Motwani,et al.  Path planning in expansive configuration spaces , 1997, Proceedings of International Conference on Robotics and Automation.

[19]  Victor Ng-Thow-Hing,et al.  Randomized multi-modal motion planning for a humanoid robot manipulation task , 2011, Int. J. Robotics Res..

[20]  Rachid Alami,et al.  Two manipulation planning algorithms , 1995 .

[21]  Jean-Claude Latombe,et al.  On multi-arm manipulation planning , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[22]  Timothy Bretl,et al.  Motion Planning for a Six-Legged Lunar Robot , 2006, WAFR.

[23]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[24]  Jean-Claude Latombe,et al.  Randomized Kinodynamic Motion Planning with Moving Obstacles , 2002, Int. J. Robotics Res..

[25]  Timothy Bretl,et al.  Non-gaited humanoid locomotion planning , 2005, 5th IEEE-RAS International Conference on Humanoid Robots, 2005..

[26]  J. Latombe,et al.  Randomized Query Processing in Robot Motion Planning , 1998 .

[27]  Lydia E. Kavraki,et al.  Randomized Query Processing in Robot Path Planning , 1998, J. Comput. Syst. Sci..

[28]  Mark H. Overmars,et al.  An Effective Framework for Path Planning Amidst Movable Obstacles , 2006, WAFR.

[29]  Timothy Bretl,et al.  Learning-Assisted Multi-Step Planning , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[30]  Mark H. Overmars,et al.  The Gaussian sampling strategy for probabilistic roadmap planners , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[31]  Howie Choset,et al.  Principles of Robot Motion: Theory, Algorithms, and Implementation ERRATA!!!! 1 , 2007 .

[32]  Timothy Bretl,et al.  Multi-Step Motion Planning for Free-Climbing Robots , 2004, WAFR.

[33]  Brian H. Wilcox,et al.  Athlete: A cargo handling and manipulation robot for the moon: Research Articles , 2007 .

[34]  Lydia E. Kavraki,et al.  A probabilistic roadmap approach for systems with closed kinematic chains , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).