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：运动规划旨在构型空间(C-space)中寻找无碰撞路径，该空间表示环境中机器人的所有可能构型。由于高维机器人的C-space难以显式构建，我们通常构建称为路图的图结构（即复杂连续C-space的离散近似）来推理连通性。在路图中检测无碰撞连通性需要昂贵的边评估计算，因此减少评估次数成为重要研究方向。然而实际中，我们常面临不可行问题：路图中起始位置与目标位置之间不存在无碰撞路径。现有研究常忽视不可行性，导致因执行过多边评估而效率低下。本文针对存在先验路图的场景解决这一问题——路图的边包含从先前经验中习得的无碰撞概率。为此，我们提出迭代路径与割集搜索(IPC)算法，通过在先验路图中迭代搜索路径与割集来检测不可行性，同时尽可能减少昂贵的边评估计算。我们进一步通过引入第二种算法——迭代分解与路径割集搜索(IDPC)来提升IPC效率，该算法利用割集搜索将路图分解为更小子图的特性。我们分析了IPC和IDPC的完备性与计算复杂度等理论性质，并在大规模仿真中从完成时间与边评估次数两个维度评估其性能。