Modern robotics often involves multiple embodied agents operating within a shared environment. Path planning in these cases is considerably more challenging than in single-agent scenarios. Although standard Sampling-based Algorithms (SBAs) can be used to search for solutions in the robots' joint space, this approach quickly becomes computationally intractable as the number of agents increases. To address this issue, we integrate the concept of factorization into sampling-based algorithms, which requires only minimal modifications to existing methods. During the search for a solution we can decouple (i.e., factorize) different subsets of agents into independent lower-dimensional search spaces once we certify that their future solutions will be independent of each other using a factorization heuristic. Consequently, we progressively construct a lean hypergraph where certain (hyper-)edges split the agents to independent subgraphs. In the best case, this approach can reduce the growth in dimensionality of the search space from exponential to linear in the number of agents. On average, fewer samples are needed to find high-quality solutions while preserving the optimality, completeness, and anytime properties of SBAs. We present a general implementation of a factorized SBA, derive an analytical gain in terms of sample complexity for PRM*, and showcase empirical results for RRG.

翻译：现代机器人学通常涉及在共享环境中运行的多个具身智能体。在这些情况下，路径规划比单智能体场景更具挑战性。虽然标准的基于采样的算法（SBAs）可应用于搜索机器人在联合空间中的解，但随着智能体数量增加，这种方法在计算上会迅速变得不可行。为解决此问题，我们将因式分解概念集成到基于采样的算法中，该方法仅需对现有方法进行最小修改。在寻找解的过程中，一旦我们使用因式分解启发式方法确认未来解将相互独立，便可解耦（即因式分解）不同智能体子集，使其进入独立的低维搜索空间。因此，我们逐步构建一个精简超图，其中某些（超）边将智能体划分为独立的子图。在最佳情况下，该方法可将搜索空间维度的增长从关于智能体数量的指数级降至线性级。平均而言，在保持SBAs的最优性、完备性和任意时刻性质的同时，所需样本更少以获得高质量解。我们提出了一种因式分解SBA的通用实现，推导了PRM*在样本复杂度方面的分析增益，并展示了RRG的实验结果。