Belief space planning in multirobot

Abstract

In multi-robot systems, maintaining belief consistency is essential for optimal performance during joint tasks. However, due to limited communication, robots may develop inconsistent beliefs over time, leading to suboptimal actions and degraded performance. This report ad- dresses the challenge of belief consistency through a comprehensive framework that integrates communication-aware cooperative belief space planning, efficient belief tracking, and communication optimization methods. We model the divergence in robot beliefs using the Partially Observable Markov Decision Process (POMDP) and derive an expression for the maximum communication interval t to ensure that the deviation from the optimal objective remains within a specified threshold. The divergence is further quantified using Hidden Markov Models (HMM), Baum-Welch learning, and KL divergence, enabling robust tracking of belief degradation over time. To improve efficiency, we propose two common methods for belief consistency: Disjoint Set Union (DSU): Robots communicate selectively with the leader of their set, reducing communication complexity. Matroid Method: A structured approach leveraging matroid theory to optimize communication costs while maintaining consistency. We provide detailed algorithms for these methods, analyze their time complexity, and compare their effectiveness in ensuring belief consistency under communication constraints. This work demonstrates how strategic communication planning can significantly reduce overhead while preserving the performance of multi-robot systems.