Factorization of Multi-Agent Sampling-Based Motion Planning

TL;DR

This paper introduces a factorization approach to multi-agent sampling-based motion planning that reduces computational complexity by decoupling agents into independent subproblems, maintaining optimality and completeness.

Contribution

The paper presents a novel factorization method for sampling-based algorithms that significantly reduces search space dimensionality in multi-agent motion planning.

Findings

Reduces search space growth from exponential to linear in the number of agents.

Fewer samples are needed to find high-quality solutions.

Maintains optimality, completeness, and anytime properties of SBAs.

Abstract

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.