Probabilistic Multi-Robot Collision Avoidance Using Chance-Constrained Safety Barrier Certificates

This paper introduces Chance-Constrained Safety Barrier Certificates (CC-SBC) for decentralized collision avoidance of multi-robot systems that account for uncertainty in robot state estimation. The work builds upon the previously proposed Safety Barrier Certificates (SBC) approach. We present a probabilistic formulation by introducing CC-SBC, a chance-constrained set that defines a probabilistic safe control space for each robot in the system. The CC-SBC chance constraints are then reformulated into a set of deterministic quadratic constraints, which allows the robot to find a safe controller by solving a quadratically constrained quadratic program (QCQP). We validate through simulations that the proposed approach can achieve safe navigation of a team of robots taking into account the robots' state estimation uncertainties.