Building and navigating a network of local minima

We present a novel method that constructs and navigates a network of local minima of potential fields defined over multidimensional spaces. Though motivated by problems of motion planning for robotic manipulators, similar techniques have been proposed for use in other domains such as molecular chemistry and drug design. The method is based on building a roadmap of paths connecting local minima of a potential function. The novel approach consists of an up-hill search strategy used to climb out of local minima and find new nearby local minima, without doubling back on previous local minima. With this up-hill search strategy, one can find local minima otherwise difficult to encounter, and one can focus the search to specific local minima and specific directions from those local minima. The construction of the roadmap can be done in parallel with very little communication. We present extensive simulation results. © 2001 John Wiley & Sons, Inc.

[1]  Vipin Kumar,et al.  A parallel formulation of informed randomized search for robot motion planning problems , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[2]  Henning Tolle,et al.  Collision-free Real-time Path-planning In Time Varying Environment , 1992, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems.

[3]  Vladimir J. Lumelsky,et al.  Real-time collision avoidance in teleoperated whole-sensitive robot arm manipulators , 1993, IEEE Trans. Syst. Man Cybern..

[4]  Vipin Kumar,et al.  Toward Real-Time Motion Planning , 1994 .

[5]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[6]  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).

[7]  Vipin Kumar,et al.  Parallel search algorithms for robot motion planning , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[8]  T. Laliberte,et al.  Efficient algorithms for the trajectory planning of redundant manipulators with obstacle avoidance , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[9]  Dominik Henrich,et al.  A review of parallel processing approaches to motion planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[10]  Jean-Claude Latombe,et al.  Numerical potential field techniques for robot path planning , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[11]  J. Navarro-Pedreño.  Numerical Methods for Least Squares Problems , 1996 .

[12]  P. Langley.  Systematic and nonsystematic search strategies , 1992 .

[13]  Lydia E. Kavraki,et al.  A framework for using the workspace medial axis in PRM planners , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[14]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[15]  Lydia E. Kavraki,et al.  Randomized preprocessing of configuration for fast path planning , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[16]  David B. Leake.  Artiicial Intelligence , 2001 .

[17]  J. Latombe,et al.  Probabilistic Roadm Aps for Path Planning in High-dimensional Connguration Spaces , 1997 .

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

[19]  Åke Björck,et al.  Numerical methods for least square problems , 1996 .

[20]  Pierre Bessière,et al.  The Ariadne's Clew Algorithm , 1993, J. Artif. Intell. Res..

[21]  Angel P. del Pobil,et al.  Practical Motion Planning in Robotics: Current Approaches and Future Directions , 1998 .

[22]  Narendra Ahuja,et al.  Gross motion planning—a survey , 1992, CSUR.

[23]  M. Boden.  Arti cial Intelligence and Natural Man , 1977 .

[24]  Nancy M. Amato,et al.  Probabilistic roadmap methods are embarrassingly parallel , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).