Planning Paths for a Flexible Surface Patch

This paper presents a probabilistic planner capable of finding paths for a flexible surface patch. The planner is based on the probabilistic roadmap approach to path planning while the surface patch is modeled as a low degree Bezier surface. We assume that we are dealing with an elastic part and define an approximate energy model for the part. The energy function penalizes excessive shear and bending of the part and we assume that low-energy configurations correspond to reversible elastic deformations of the part. The planner captures the connectivity of a space by building a roadmap, a network of simple paths connecting configurations selected in the space using randomized techniques. We report on the implementation of our planner and show experimental results with examples where the surface patch is required to move through a small hole in its workspace. Our work is a first step towards considering the physical properties of parts when planning paths.

[1]  Sidney F Borg,et al.  Fundamentals of Engineering Elasticity , 1962 .

[2]  Jean-Paul Laumond,et al.  Feasible Trajectories for Mobile Robots with Kinematic and Environment Constraints , 1986, IAS.

[3]  Demetri Terzopoulos,et al.  Energy Constraints on Deformable Models: Recovering Shape and Non-Rigid Motion , 1987, AAAI.

[4]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[5]  Demetri Terzopoulos,et al.  Physically based models with rigid and deformable components , 1988, IEEE Computer Graphics and Applications.

[6]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[7]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[8]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[9]  Andrew P. Witkin,et al.  Fast animation and control of nonrigid structures , 1990, SIGGRAPH.

[10]  Sidney F. Borg,et al.  Fundamentals of Engineering Elasticity: (Revised 2nd Printing) , 1990 .

[11]  George Celniker,et al.  Deformable curve and surface finite-elements for free-form shape design , 1991, SIGGRAPH.

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

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

[14]  Randall H. Wilson,et al.  On geometric assembly planning , 1992 .

[15]  D. Baraff.  Dynamic simulation of nonpenetrating rigid bodies , 1992 .

[16]  David Baraff,et al.  Dynamic Simulation of Non-penetrating Rigid Bodies , 1992 .

[17]  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.

[18]  Richard M. Murray,et al.  A motion planner for nonholonomic mobile robots , 1994, IEEE Trans. Robotics Autom..

[19]  Tsai-Yen Li,et al.  Assembly maintainability study with motion planning , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[20]  Yunhui Liu,et al.  Modeling and cooperation of two-arm robotic system manipulating a deformable object , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[21]  Joel W. Burdick,et al.  Gait kinematics for a serpentine robot , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[22]  James K. Mills,et al.  Multi-robot control for flexible fixtureless assembly of flexible sheet metal auto body parts , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

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

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

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

[26]  Hirofumi Nakagaki,et al.  Study of deformation and insertion tasks of a flexible wire , 1997, Proceedings of International Conference on Robotics and Automation.

[27]  Jean-Claude Latombelatombe.  Ing of Connguration Space for Fast Path Planning , 2007 .