Factorization of Multi-Agent Sampling-Based Motion Planning
This addresses the scalability problem in multi-robot systems for robotics applications, offering a novel method for a known bottleneck.
The paper tackles the computational intractability of multi-agent motion planning in robotics by integrating factorization into sampling-based algorithms, reducing the search space dimensionality growth from exponential to linear in the number of agents and requiring fewer samples on average while preserving optimality and completeness.
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.