A general method for C-space evaluation and its application to articulated robots

A general method to obtain the obstacle representation in the robot configuration space is presented. The method is based on a solid mathematical formalism that has as a key element a mathematical expression to evaluate the C-obstacle representation. The use of the proposed method and the choice of a suitable coordinate system, in the workspace as well as in the configuration space, lead to the fact that the obstacle representation in the configuration space could be seen as a convolution of two functions that describe the robot and the obstacles, respectively. The computational load can then be reduced drastically if convolution properties are applied. The method is directly applicable to mobile and articulated robots without any kind of adaptation or restriction of the shape of the elements that constitute the robot and the shape of the obstacles. Hence, its utilization is quite suitable to motion planning and control problems.

[1]  J. Michael McCarthy,et al.  An algebraic formulation of configuration-space obstacles for spatial robots , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

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

[3]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[4]  P. Vega,et al.  Fast Procedure to Obstacle Representation in the Configuration Space for Mobile Robots , 1998 .

[5]  Belén Curto,et al.  Mathematical formalism for the fast evaluation of the configuration space , 1997, Proceedings 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA'97. 'Towards New Computational Principles for Robotics and Automation'.

[6]  Micha Sharir,et al.  Efficient algorithms for planning purely translational collision-free motion in two and three dimensions , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[7]  J. Michael McCarthy,et al.  Parameterized descriptions of the joint space obstacles for a 5R closed chain robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[8]  Lydia E. Kavraki.  Computation of configuration-space obstacles using the fast Fourier transform , 1995, IEEE Trans. Robotics Autom..

[9]  Wyatt S. Newman,et al.  Rapid computation of configuration space obstacles , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[10]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[11]  Leonidas J. Guibas,et al.  A kinetic framework for computational geometry , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[12]  B. Donald.  Motion Planning with Six Degrees of Freedom , 1984 .

[13]  J. Michael McCarthy,et al.  Equations for boundaries of joint obstacles for planar robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[14]  Anthony A. Maciejewski,et al.  Path planning and the topology of configuration space , 1993, IEEE Trans. Robotics Autom..

[15]  L. Gouzenes.  Strategies for Solving Collision-free Trajectories Problems for Mobile and Manipulator Robots , 1984 .

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

[17]  Randy C. Brost,et al.  Computing metric and topological properties of configuration-space obstacles , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[18]  Bernard Faverjon.  Object level programming of industrial robots , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[19]  Belén Curto,et al.  A Theoretical Approach to Potential Fields within the Configuration Space Using Green's Functions , 2001 .

[20]  R. Theron,et al.  Evaluation of the configuration space of robots upon a distributed computing system , 2001, 2001 European Control Conference (ECC).

[21]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[22]  Tomás Lozano-Pérez,et al.  Parallel robot motion planning , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[23]  Wyatt S. Newman,et al.  What is This? Downloaded from , 1991 .

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

[25]  Vladimir J. Lumelsky.  Effect of kinematics on motion planning for planar robot arms moving amidst unknown obstacles , 1987, IEEE J. Robotics Autom..