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-dimensional robot, we generally build a graph structure called a roadmap, a discrete approximation of a complex continuous C-space, to reason about connectivity. Checking collision-free connectivity in the roadmap requires expensive edge-evaluation computations, and thus, reducing the number of evaluations has become a significant research objective. However, in practice, we often face infeasible problems: those in which there is no collision-free path in the roadmap between the start and the goal locations. Existing studies often overlook the possibility of infeasibility, becoming highly inefficient by performing many edge evaluations. In this work, we address this oversight in scenarios where a prior roadmap is available; that is, the edges of the roadmap contain the probability of being a collision-free edge learned from past experience. To this end, we propose an algorithm called iterative path and cut finding (IPC) that iteratively searches for a path and a cut in a prior roadmap to detect infeasibility while reducing expensive edge evaluations as much as possible. We further improve the efficiency of IPC by introducing a second algorithm, iterative decomposition and path and cut finding (IDPC), that leverages the fact that cut-finding algorithms partition the roadmap into smaller subgraphs. We analyze the theoretical properties of IPC and IDPC, such as completeness and computational complexity, and evaluate their performance in terms of completion time and the number of edge evaluations in large-scale simulations.

翻译：运动规划在配置空间（C-space）中寻求无碰撞路径，该空间表示环境中机器人所有可能的构型。由于为高维机器人显式构建C-space具有挑战性，我们通常构建一种称为路图的图结构——即复杂连续C-space的离散近似——来推理连通性。在路图中检查无碰撞连通性需要昂贵的边评估计算，因此减少评估次数已成为重要研究目标。然而在实践中，我们常面临不可行问题：即路图中起始位置与目标位置之间不存在无碰撞路径。现有研究常忽略不可行性可能，导致在大量边评估中效率低下。本文针对存在先验路图的场景解决这一疏漏——即路图的边包含从历史经验中学习到的无碰撞概率。为此，我们提出迭代路径与割集寻找（IPC）算法，通过在先验路图中迭代搜索路径和割集来检测不可行性，同时尽可能减少昂贵的边评估。为进一步提升效率，我们引入第二种算法——迭代分解与路径割集寻找（IDPC），该算法利用割集寻找算法将路图划分为更小子图的性质。我们分析了IPC和IDPC的理论特性（如完备性和计算复杂度），并在大规模仿真中从完成时间和边评估次数两方面评估其性能。