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Juan Burgos, Jory Denny, Nancy M. Amato, "Improving Roadmap Quality through Connected Component Expansion," Technical Report, TR13-003, Texas A&M University, Apr 2013.
Technical Report(ps, pdf, abstract)

Motion planning is the problem of computing valid paths through an environment. However, because computing exact solutions is intractable, sampling-based algorithms, such as Probabilistic RoadMaps (PRMs), have gained popularity. PRMs compute an approximate mapping of the planning space by sacrificing completeness in favor of efficiency. However, these algorithms have certain bottlenecks that hinder performance which causes difficulty mapping narrow or crowded regions, and the cost of nearest-neighbor queries, which is the asymptotic bottleneck of these algorithms. Thus, roadmaps may fail to efficiently capture the connectivity of the planning space. In this paper, we present a set of connected component (CC) expansion algorithms, each with different biases (random expand, expand to the nearest CC, expand away from the host CC, and expand along the medial-axis) and expansion node selection policies (random, farthest from CC's centroid, and difficult nodes), that create a linked-chain of configurations designed to enable efficient connection of CCs. Given an a priori roadmap quality requirement in terms of roadmap connectivity, we show that when our expansion methods augment PRMs, we reach the required roadmap connectivity in less time.