The Before, During, and After of Multi-Robot Deadlock

TL;DR

This paper analyzes the causes of deadlock in multi-robot systems using control barrier functions, characterizes deadlock configurations, and proposes a decentralized algorithm to resolve deadlocks and ensure robots reach their goals.

Contribution

It provides a geometric and duality-based analysis of deadlock in multi-robot control, and introduces a provably-correct decentralized deadlock resolution algorithm.

Findings

Deadlock occurs at the boundary of the safe set due to force equilibrium.

Deadlock configurations are characterized by specific geometric properties.

The proposed algorithm successfully resolves deadlocks in simulations and real robot experiments.

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 \textit{deadlock}, an equilibrium of system dynamics that causes the robots to stall before reaching their goals. In this paper, we analyze the closed-loop dynamics of robots using CBFs, to characterize controller parameters, initial conditions, and goal locations that invariably lead the system to deadlock. Using tools from duality theory, we derive geometric properties of robot configurations of an $N$ robot system once it is in deadlock and we justify them using the mechanics interpretation of KKT conditions. Our key deductions are that 1) system deadlock is characterized by a force-equilibrium on robots and 2) deadlock occurs to ensure safety when safety is on the brink of being violated. These deductions allow us to interpret deadlock as a subset of the state space, and we show that this set is non-empty and located on the boundary of the safe set. By exploiting these properties, we analyze the number of admissible robot configurations in deadlock and develop a provably-correct decentralized algorithm for deadlock resolution to safely deliver the robots to their goals. This algorithm is validated in simulations as well as experimentally on Khepera-IV robots.