Abstract
This paper describes a new exact and efficient collision checker for testing single straight-line segments in c-space or sequences of such segments. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multi-robot systems. Unlike the commonly used fixed-resolution method, the new checker does not require manual tuning of the resolution parameter and cannot fail to find existing collisions. To achieve this, it automatically and dynamically adjusts the required local c-space resolution by relating distances and path lengths in workspace. Several additional techniques are presented in this paper to further increase the checker’s efficiency in PRM planners and scenarios with high geometric complexity. Extensive experiments, first on segments randomly generated in c-space, next as part of an existing PRM planner, and finally as part of a path smoother/optimizer have shown that the new checker is faster than the common resolution-based approach (with suitable resolution).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. M. Amato, O. B. Bayazit, L. K. Dale, C. Jones, and D. Vallejo. OBPRM: An obstacle-based PRM for 3d workspaces. In Proc. of the Workshop on Algorithmic Foundations of Robotics (WAFR’98), pages 155–168, March 1998.
J. Barraquand, L. Kavraki, J. C. Latombe, T.Y. Li, R. Motwani, and P. Ragha-van. A random sampling scheme for path planning. Inernational Journal of Robotics Research, 16 (6): 759–774, 1996.
J. Bäsch, L. Guibas, and J. Hershberger. Data structures for mobile data. In SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms), 1997.
R. Bohlin and L. Kavraki. Path planning using lazy PRM. In Proc. of the Int. Conf. on Robot. & Autom. (ICRA), pages 521–528, 2000.
S. Cameron. A study of the clash detection problem in robotics. In Proc. IEEE Int. Conf. on Robotics & Automation, volume 1, pages 488–493, 1985.
S. A. Cameron. Collision detection by four-dimensional intersection testing. IEEE Trans. Robotics Automat., 6: 291–302, June 1990.
J. F. Canny. Collision detection for moving polyhedra. IEEE Trans. Patt. Anal. Mach. Intell, 8 (2): 200–209, Mar 1986.
J. D. Cohen, M. C. Lin, D. Manocha, and M. Ponamgi. I-COLLIDE: An interactive and exact collision detection system for large-scale environments. In Sym. on Interactive 3D Graphics, pages 189–196, 218, 1995.
L. Dale, G. Song, and N. Amato. Faster, more effective connection for probabilistic roadmaps. Technical Report TR00–005, Department of Computer Science, Texas A&M University, 20, 2000.
A. Foisy and V. Hayward. A safe swept volume method for collision detection. In The Sixth International Symposium of Robotics Research, pages 61–68, Pittsburgh (PE), Oct. 1993.
S. Gottschalk, M. C. Lin, and D. Manocha. OBBTree: A hierarchical structure for rapid interference detection. Comp. Graphics, 30 (Annual Conf. Series): 171–180, 1996.
D. Hsu, J. C. Latombe, and R. Motwani. Path planning in expansive configuration spaces. International Journal of Computational Geometry and Applications, 9 (4&5): 495–512, 1999.
P. Jiménez, F. Thomas, and C. Torras. 3D collision detection: A survey. Computers and Graphics, 25 (2): 269–285, 2001.
L. E. Kavraki, P. Svestka, J. C. Latombe, and M. Overmars. Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation, 12 (4): 566–580, 1996.
E. Larsen, S. Gottschalk, M. C. Lin, and D. Manocha. Fast distance queries with rectangular swept sphere volumes. In IEEE Conf. on Rob. and Auto., 2000.
M. Lin, D. Manocha, J. Cohen, and S. Gottschalk. Collision detection: Algorithms and applications. In J. P. Laumond and M. Overmars, editors, Algorithms for Robotic Motion and Manipulation: WAFR 1996, pages 129–142. A. K. Peters, 1996.
M. C. Lin and J. F. Canny. A fast algorithm for incremental distance calculation. In IEEE Int. Conf. on Rob. and Auto., pages 1008–1014, 1991.
M. C. Lin and S. Gottschalk. Collision detection between geometric models: a survey. In IMA Conference on Mathematics of Surfaces, volume 1, pages 602–608, San Diego (CA), 1998.
B. Mirtich. V-clip: Fast and robust polyhedral collision detection. ACM Transactions on Graphics, 17 (3): 177–208, July 1998.
Ch. Nielsen and L. E. Kavraki. A two-level fuzzy PRM for manipulation planning. In Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Japan, 2000.
S. Quinlan. Efficient distance computation between non-convex objects. In IEEE Intern. Conf. on Rob. and Auto., pages 3324–3329, 1994.
G. Sanchez and J. C. Latombe. A single-query bi-directional probabilistic roadmap planner with lazy collision checking. In Int. Symposium on Robotics Research (ISRR’01), Lome, Victoria, Australia, 2001.
A. Schweikard. Polynomial time collision detection for manipulator paths specified by joint motions. IEEE Trans. Rob. Autom., 7 (6): 865–870, 1991.
G. Van der Bergen. Efficient collision detection of complex deformable models using AABB trees. Journal of Graphic Tools, 2 (4): 1–13, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schwarzer, F., Saha, M., Latombe, JC. (2004). Exact Collision Checking of Robot Paths. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-45058-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07341-0
Online ISBN: 978-3-540-45058-0
eBook Packages: Springer Book Archive