Multi-Robot Collision Avoidance under Uncertainty with Probabilistic Safety Barrier Certificates

TL;DR

This paper introduces Probabilistic Safety Barrier Certificates (PrSBC) for multi-robot collision avoidance, providing a theoretically guaranteed, minimally invasive control method that accounts for measurement and motion uncertainties without assuming specific uncertainty models.

Contribution

It proposes a novel probabilistic safety barrier framework using Control Barrier Functions that offers formal safety guarantees under uncertainty for multi-robot systems.

Findings

Effective collision avoidance in uncertain environments demonstrated in simulations

Provides worst-case safety guarantees without specific uncertainty distribution assumptions

Minimal controller modifications ensure safety with quadratic programming

Abstract

Safety in terms of collision avoidance for multi-robot systems is a difficult challenge under uncertainty, non-determinism and lack of complete information. This paper aims to propose a collision avoidance method that accounts for both measurement uncertainty and motion uncertainty. In particular, we propose Probabilistic Safety Barrier Certificates (PrSBC) using Control Barrier Functions to define the space of admissible control actions that are probabilistically safe with formally provable theoretical guarantee. By formulating the chance constrained safety set into deterministic control constraints with PrSBC, the method entails minimally modifying an existing controller to determine an alternative safe controller via quadratic programming constrained to PrSBC constraints. The key advantage of the approach is that no assumptions about the form of uncertainty are required other than finite support, also enabling worst-case guarantees. We demonstrate effectiveness of the approach through experiments on realistic simulation environments.