Steps toward derandomizing RRTs

We present two new motion planning algorithms, based on the rapidly exploring random tree (RRT) family of algorithms. These algorithms represent the first work in the direction of derandomizing RRTs; this is a very challenging problem due to the way randomization is used in RRTs. In RRTs, randomization is used to create Voronoi bias, which causes the search trees to rapidly explore the state space. Our algorithms take steps to increase the Voronoi bias and to retain this property without the use of randomization. Studying these and related algorithms would improve our understanding of how efficient exploration can be accomplished, and would hopefully lead to improved planners. We give experimental results that illustrate how the new algorithms explore the state space and how they compare with existing RRT algorithms.

[1]  Henryk Wozniakowski,et al.  Information-based complexity , 1987, Nature.

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

[3]  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).

[4]  Ming C. Lin,et al.  Constraint-Based Motion Planning Using Voronoi Diagrams , 2002, WAFR.

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

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

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

[8]  Jean-Claude Latombe,et al.  Robot Motion Planning: A Distributed Representation Approach , 1991, Int. J. Robotics Res..

[9]  Steven M. LaValle,et al.  RRT-connect: An efficient approach to single-query path planning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[10]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[11]  H. Woxniakowski.  Information-Based Complexity , 1988 .

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

[13]  Bruce Randall Donald,et al.  Algorithmic and Computational Robotics: New Directions , 2001 .

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

[15]  Steven M. LaValle,et al.  Current Issues in Sampling-Based Motion Planning , 2005, ISRR.

[16]  P. Bessière,et al.  The Ariadne's Clew Algorithm , 1998, J. Artif. Intell. Res..

[17]  Yong Yu,et al.  On sensor-based roadmap: a framework for motion planning for a manipulator arm in unknown environments , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[18]  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).

[19]  Nancy M. Amato,et al.  MAPRM: a probabilistic roadmap planner with sampling on the medial axis of the free space , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[20]  D. Mount.  ANN Programming Manual , 1998 .

[21]  J. Halton.  On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[22]  Nancy M. Amato,et al.  A randomized roadmap method for path and manipulation planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[23]  Dinesh Manocha,et al.  Interactive navigation in complex environments using path planning , 2003, I3D '03.

[24]  Dinesh Manocha,et al.  Randomized Path Planning for a Rigid Body Based on Hardware Accelerated Voronoi Sampling , 1999 .

[25]  Fred J. Hickernell,et al.  Randomized Halton sequences , 2000 .

[26]  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.

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

[28]  Steven M. LaValle,et al.  Incrementally reducing dispersion by increasing Voronoi bias in RRTs , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.