  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.
