Path planning for pushing a disk using compliance

We consider the path planning problem for a robot that pushes a disk shaped object in an environment among obstacles. Instead of only allowing the object to move through the free space, we also allow the object to slide along the boundaries of the environment using compliance, extending the possibilities for the robot to find a push path. We present an exact algorithm that, given a path for the object consisting of k sections, preprocesses the environment consisting of n non-intersecting line segments in O(n/sup 2/ log n) and reports a push path in O(kn log n) time or reports failure if no path exists. Under the weak assumption of low obstacle density, the query time is reduced to O((k + n) log n).

[1]  Ivan J. Balaban,et al.  An optimal algorithm for finding segments intersections , 1995, SCG '95.

[2]  Rajeev Motwani,et al.  Nonholonomic path planning for pushing a disk among obstacles , 1997, Proceedings of International Conference on Robotics and Automation.

[3]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[4]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[5]  Micha Sharir,et al.  Coordinated motion planning for two independent robots , 1991, SCG '88.

[6]  Vladlen Koltun.  Segment Intersection Searching Problems in General Settings , 2003, Discret. Comput. Geom..

[7]  Russell H. Taylor,et al.  Automatic Synthesis of Fine-Motion Strategies for Robots , 1984 .

[8]  Mark H. Overmars,et al.  Algorithms for fence design , 1998 .

[9]  Matthew T. Mason,et al.  An exploration of sensorless manipulation , 1986, IEEE J. Robotics Autom..

[10]  Kenneth Y. Goldberg,et al.  Orienting polygonal parts without sensors , 1993, Algorithmica.

[11]  Mark de Berg,et al.  Motion Planning in Environments with Low Obstacle Density , 1998, Discret. Comput. Geom..

[12]  Bruce Randall Donald.  The complexity of planar compliant motion planning under uncertainty , 1988, SCG '88.

[13]  Micha Sharir,et al.  Coordinated motion planning for two independent robots , 1991, SCG '88.

[14]  Matthew T. Mason,et al.  Mechanics of Robotic Manipulation , 2001 .

[15]  Vijay Kumar,et al.  Motion planning with uncertainty , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[16]  Kevin M. Lynch,et al.  Nonprehensile robotic manipulation: controllability and planning , 1996 .

[17]  Matthew T. Mason,et al.  Mechanics and Planning of Manipulator Pushing Operations , 1986 .

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

[19]  B. Aronov.  Motion Planning for Multiple Robots , 1999 .

[20]  M.T. Mason,et al.  Dynamic manipulation , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

[21]  Randy C. Brost,et al.  Automatic Grasp Planning in the Presence of Uncertainty , 1988, Int. J. Robotics Res..

[22]  Amy J. Briggs.  An efficient algorithm for one-step planar compliant motion planning with uncertainty , 1992, Algorithmica.

[23]  Amy J. Briggs.  An efficient algorithm for one-step planar complaint motion planning with uncertainty , 1989, SCG '89.

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

[25]  Kevin M. Lynch,et al.  Stable Pushing: Mechanics, Controllability, and Planning , 1995, Int. J. Robotics Res..

[26]  Oussama Khatib,et al.  Experiments on Manipulation with Dynamic Skills , 1995 .