Deadlock Analysis and Resolution for Multi-robot Systems

Abstract

Collision avoidance for multirobot systems is a well studied problem. Recently, control barrier functions (CBFs) have been proposed for synthesizing controllers that guarantee collision avoidance and goal stabilization for multiple robots. However, it has been noted that reactive control synthesis methods (such as CBFs) are prone to deadlock, an equilibrium of system dynamics that causes robots to come to a standstill before reaching their goals. In this paper, we formally derive characteristics of deadlock in a multirobot system that uses CBFs. We propose a novel approach to analyze deadlocks resulting from optimization based controllers (CBFs) by borrowing tools from duality theory and graph enumeration. Our key insight is that system deadlock is characterized by a force-equilibrium on robots and we show how complexity of deadlock analysis increases approximately exponentially with the number of robots. This analysis allows us to interpret deadlock as a subset of the state space, and we prove that this set is non-empty, bounded and located on the boundary of the safety set. Finally, we use these properties to develop a provably correct decentralized algorithm for deadlock resolution which ensures that robots converge to their goals while avoiding collisions. We show simulation results of the resolution algorithm for two and three robots and experimentally validate this algorithm on Khepera-IV robots.