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Motion planning seeks a collision-free path in a configuration space(C-space), representing all possible robot configurations in the environment.As it is challenging to construct a C-space explicitly for a high-dimensionalrobot, we generally build a graph structure called a roadmap, a discreteapproximation of a complex continuous C-space, to reason about connectivity.Checking collision-free connectivity in the roadmap requires expensiveedge-evaluation computations, and thus, reducing the number of evaluations hasbecome a significant research objective. However, in practice, we often faceinfeasible problems: those in which there is no collision-free path in theroadmap between the start and the goal locations. Existing studies oftenoverlook the possibility of infeasibility, becoming highly inefficient byperforming many edge evaluations.  In this work, we address this oversight in scenarios where a prior roadmap isavailable; that is, the edges of the roadmap contain the probability of being acollision-free edge learned from past experience. To this end, we propose analgorithm called iterative path and cut finding (IPC) that iteratively searchesfor a path and a cut in a prior roadmap to detect infeasibility while reducingexpensive edge evaluations as much as possible. We further improve theefficiency of IPC by introducing a second algorithm, iterative decompositionand path and cut finding (IDPC), that leverages the fact that cut-findingalgorithms partition the roadmap into smaller subgraphs. We analyze thetheoretical properties of IPC and IDPC, such as completeness and computationalcomplexity, and evaluate their performance in terms of completion time and thenumber of edge evaluations in large-scale simulations.

Motion Planning (In)feasibility Detection using a Prior Roadmap via Path and Cut Search