MV-FAC: Mean–Variance Value Function Factorization for Multi-Robot Mean–Standard Deviation Moving Target Search

Abstract

This paper studies a risk-sensitive formulation of the multi-robot search problem, termed multi-robot mean-standard deviation search (MuRMSS), in which a team of robots cooperatively search for a moving target by minimizing a linear combination of the mean and standard deviation of search time. However, the standard deviation term is inherently non-additive, making it difficult to estimate, incompatible with canonical multi-robot search algorithms, and preventing consistent decomposition into individual robot utilities, which is essential for scalable multi-robot cooperation. In view of these challenges, we propose MV-FAC, which comprises a mean-variance temporal-difference module that jointly learns the mean and variance of search time, a factorization module that decomposes them into individual utilities, and a decentralized policy optimization module that minimizes each robot’s individual mean-std objective. We further establish and prove the mean-std individual global minimization (MS-IGM) theorem, thereby ensuring consistency between individual- and team-level objectives. Extensive simulation studies on standard multi-robot search benchmarks demonstrate that MV-FAC achieves the best overall mean-std search-time performance. We also validate MV-FAC's practicality by deploying it on a physical multi-robot system for moving target search in a real-world building environment.