Incremental low-discrepancy lattice methods for motion planning

We present deterministic sequences for use in sampling-based approaches to motion planning. They simultaneously combine the qualities found in many other sequences: i) the incremental and self-avoiding tendencies of pseudo-random sequences, ii) the lattice structure provided by multiresolution grids, and iii) low-discrepancy and low-dispersion measures of uniformity provided by quasi-random sequences. The resulting sequences can be considered as multiresolution grids in which points may be added one at a time, while satisfying the sampling qualities at each iteration. An efficient, recursive algorithm for generating the sequences is presented and implemented. Early experiments show promising performance by using the samples in search algorithms to solve motion planning problems.

[1]  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).

[2]  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).

[3]  Steven M. LaValle,et al.  Quasi-randomized path planning , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

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

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

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

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

[8]  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).

[9]  Jean-Claude Latombe,et al.  A Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking , 2001, ISRR.

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

[11]  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).

[12]  A. G. Sukharev.  Optimal strategies of the search for an extremum , 1971 .

[13]  Robert Bohlin,et al.  Path planning in practice; lazy evaluation on a multi-resolution grid , 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).

[14]  H. Weyl.  Über die Gleichverteilung von Zahlen mod. Eins , 1916 .

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

[16]  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).

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

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