On the Probabilistic Foundations of Probabilistic Roadmap Planning

Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot’s configuration space affect the performance of a PRM planner? These questions have received little attention to date. This paper tries to fill this gap and identify promising directions to improve future planners. It introduces the probabilistic foundations of PRM planning and examines previous work in this context. It shows that the success of PRM planning depends mainly and critically on favorable “visibility” properties of a robot’s configuration space. A promising direction for speeding up PRM planners is to infer partial knowledge of such properties from both workspace geometry and information gathered during roadmap construction, and to use this knowledge to adapt the probability measure for sampling. This paper also shows that the choice of the sampling source—pseudo-random or deterministic—has small impact on a PRM planner’s performance, compared with that of the sampling measure. These conclusions are supported by both theoretical and empirical results.

[1]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[2]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[3]  C. Branden,et al.  Introduction to protein structure , 1991 .

[4]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[5]  Umesh V. Vazirani,et al.  An Introduction to Computational Learning Theory , 1994 .

[6]  Lydia E. Kavraki,et al.  Randomized query processing in robot path planning (Extended Abstract). , 1995, Symposium on the Theory of Computing.

[7]  Lydia E. Kavraki,et al.  Randomized query processing in robot path planning , 1995, STOC '95.

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

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

[10]  Lydia E. Kavraki,et al.  Analysis of probabilistic roadmaps for path planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[11]  P. Svestka.  On probabilistic completeness and expected complexity for probabilistic path planning , 1996 .

[12]  Joseph O'Rourke,et al.  Handbook of Discrete and Computational Geometry, Second Edition , 1997 .

[13]  Gregory S. Chirikjian,et al.  Useful metrics for modular robot motion planning , 1997, IEEE Trans. Robotics Autom..

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

[15]  Craig D. McGray,et al.  The self-reconfiguring robotic molecule: design and control algorithms , 1998 .

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

[17]  Lydia E. Kavraki,et al.  Robotics: The Algorithmic Perspective : WAFR 1998 , 1998 .

[18]  Craig D. McGray,et al.  The self-reconfiguring robotic molecule , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[19]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[20]  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).

[21]  Arancha Casal,et al.  Self-reconfiguration planning for a class of modular robots , 1999, Optics East.

[22]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

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

[24]  Leonidas J. Guibas,et al.  A probabilistic roadmap planner for flexible objects with a workspace medial-axis-based sampling approach , 1999, Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No.99CH36289).

[25]  Dinesh Manocha,et al.  Interactive motion planning using hardware-accelerated computation of generalized Voronoi diagrams , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[26]  Lydia E. Kavraki,et al.  Path planning using lazy PRM , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[27]  Thierry Siméon,et al.  Visibility-based probabilistic roadmaps for motion planning , 2000, Adv. Robotics.

[28]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[29]  Dinesh Manocha,et al.  A Voronoi-based hybrid motion planner , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

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

[31]  Pekka Isto,et al.  Constructing probabilistic roadmaps with powerful local planning and path optimization , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[32]  Julian V. Noble,et al.  The full Monte , 2002, Comput. Sci. Eng..

[33]  Mark H. Overmars,et al.  A Comparative Study of Probabilistic Roadmap Planners , 2002, WAFR.

[34]  Steven M. LaValle,et al.  Efficient nearest neighbor searching for motion planning , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

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

[36]  Seth Hutchinson,et al.  Using manipulability to bias sampling during the construction of probabilistic roadmaps , 2003, IEEE Trans. Robotics Autom..

[37]  Dan HalperinS.  Hybrid Motion Planning: Coordinating Two Discs Moving Among Polygonal Obstacles in the Plane , 2002 .

[38]  David Hsu,et al.  The bridge test for sampling narrow passages with probabilistic roadmap planners , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

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

[40]  Steven M. LaValle,et al.  Incremental low-discrepancy lattice methods for motion planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[41]  Steven M. LaValle,et al.  On the Relationship between Classical Grid Search and Probabilistic Roadmaps , 2004, Int. J. Robotics Res..

[42]  Lydia E. Kavraki,et al.  Measure theoretic analysis of probabilistic path planning , 2004, IEEE Transactions on Robotics and Automation.

[43]  Jean-Daniel Boissonnat,et al.  Algorithmic Foundations of Robotics V, Selected Contributions of the Fifth International Workshop on the Algorithmic Foundations of Robotics, WAFR 2002, Nice, France, December 15-17, 2002 , 2004, WAFR.

[44]  Andrew M. Ladd,et al.  Measure Theoretic Analysis of , 2004 .

[45]  Lydia Tapia,et al.  A Machine Learning Approach for Feature-Sensitive Motion Planning , 2004, WAFR.

[46]  D. Spielman,et al.  Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time , 2004 .

[47]  David Hsu,et al.  Workspace importance sampling for probabilistic roadmap planning , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[48]  Oliver Brock,et al.  Adapting the sampling distribution in PRM planners based on an approximated medial axis , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[49]  Piotr Indyk,et al.  Nearest Neighbors in High-Dimensional Spaces , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[50]  Dinesh Manocha,et al.  Collision and Proximity Queries , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[51]  Oliver Brock,et al.  Toward Optimal Configuration Space Sampling , 2005, Robotics: Science and Systems.

[52]  Gildardo Sánchez-Ante,et al.  Hybrid PRM Sampling with a Cost-Sensitive Adaptive Strategy , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[53]  Oliver Brock,et al.  Sampling-Based Motion Planning Using Predictive Models , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

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

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

[56]  Yu-Chi Chang,et al.  Finding Narrow Passages with Probabilistic Roadmaps: The Small-Step Retraction Method , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[57]  Mark H. Overmars,et al.  Reachability Analysis of Sampling Based Planners , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[58]  Mark H. Overmars,et al.  Using Workspace Information as a Guide to Non-uniform Sampling in Probabilistic Roadmap Planners , 2005, Int. J. Robotics Res..

[59]  Mark H. Overmars,et al.  Creating small roadmaps for solving motion planning problems , 2005 .

[60]  Nancy M. Amato,et al.  Metrics for analyzing the evolution of C-space models , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[61]  Ho-Lun Cheng,et al.  Multi-level free-space dilation for sampling narrow passages in PRM planning , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[62]  Simon Parsons,et al.  Principles of Robot Motion: Theory, Algorithms and Implementations by Howie Choset, Kevin M. Lynch, Seth Hutchinson, George Kantor, Wolfram Burgard, Lydia E. Kavraki and Sebastian Thrun, 603 pp., $60.00, ISBN 0-262-033275 , 2007, The Knowledge Engineering Review.

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