I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Randomized query processing in robot path planning
Journal of Computer and System Sciences
On finding narrow passages with probabilistic roadmap planners
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
OBPRM: an obstacle-based PRM for 3D workspaces
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Proceedings of the sixth ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
On the Probabilistic Foundations of Probabilistic Roadmap Planning
International Journal of Robotics Research
Sampling-based path planning for geometrically-constrained objects
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Roadmap composition for multi-arm systems path planning
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Detecting narrow passages in configuration spaces via spectra of probabilistic roadmaps
Proceedings of the 2010 ACM Symposium on Applied Computing
A Connectivity-Based Method for Enhancing Sampling in Probabilistic Roadmap Planners
Journal of Intelligent and Robotic Systems
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Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method--small-step retraction--that helps PRM planners find paths through such passages. This method consists of slightly "fattening" robot's free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual free space. Fattened free space is not explicitly computed. Instead, the geometric models of workspace objects (robot links and/or obstacles) are "thinned" around their medial axis. A robot configuration lies in fattened free space if the thinned objects do not collide at this configuration. Two repair strategies are proposed. The "optimist" strategy waits until a complete path has been found in fattened free space before repairing it. Instead, the "pessimist" strategy repairs the roadmap as it is being built. The former is usually very fast, but may fail in some pathological cases. The latter is more reliable, but not as fast. A simple combination of the two strategies yields an integrated planner that is both fast and reliable. This planner was implemented as an extension of a pre-existing single-query PRM planner. Comparative tests show that it is significantly faster (sometimes by several orders of magnitude) than the pre-existing planner.