Randomized Path Planning for a Rigid Body Based on Hardware Accelerated Voronoi Sampling

Probabilistic roadmap methods have recently received considerable attention as a practical approach for motion planning in complex environments. These algorithms sample a number of con gurations in the free space and build a roadmap. Their performance varies as a function of the sampling strategies and relative con gurations of the obstacles. To improve the performance when the path of a robot has to pass through narrow passages, some researchers have proposed algorithms for sampling along or near the medial axis of the free space. However, their usage has been limited because of the practical complexity of computing the medial axis or the cost of computing such samples. In this paper, we present e cient algorithms for sampling near the medial axis and building roadmap graphs for a freeying rigid body. We use a recent algorithm for fast computation of discrete generalized Voronoi diagrams using graphics hardware [HCK99a]. We initially compute a bounded error discretized Voronoi diagram of the obstacles in the workspace and use it to generate samples in the free space. We use multi-level connection strategies and local planning algorithms to generate roadmap graphs. We also utilize the distance information provided by our Voronoi algorithm for fast proximity queries and sampling the con gurations. The resulting planner has been applied to a number of free ying rigid bodies in 2D (with 3-dof) and 3D (with 6-dof) and compared with the performance of earlier planners using a uniform sampling of the con guration space. Its performance varies with di erent environments and we obtain 25% to over 1000% speed-up.

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