Abstract
Applications such as robot programming, design for manufacturing, animation of digital actors, rationale drug design, and surgical planning, require computing paths in high-dimensional geometric spaces, a provably hard problem. Recently, a general path-planning approach based on a parallelizable random sampling scheme has emerged as an effective approach to solve this problem. In this approach, the path planner captures the connectivity of a space F by building a probabilistic roadmap, a network of simple paths connecting points picked at random in F. This paper combines results previously presented in separate papers. It describes a basic probabilistic roadmap planner that is easily parallelizable, and it analyzes the performance of this planner as a function of how well F satisfies geometric properties called ∈-goodness, expansiveness, and path clearance. While ∈-goodness allows us to study how well a probabilistic roadmap covers F, expansiveness and path clearance allow us to compare the connectivity of the roadmap to that of F.
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Hsu, D., Latombe, JC., Motwani, R., Kavraki, L.E. (1999). Capturing the Connectivity of High-Dimensional Geometric Spaces by Parallelizable Random Sampling Techniques. In: Pardalos, P.M., Rajasekaran, S. (eds) Advances in Randomized Parallel Computing. Combinatorial Optimization, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3282-4_8
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DOI: https://doi.org/10.1007/978-1-4613-3282-4_8
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