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 possible control actions that are probabilistically safe with theoretical guarantee. By formulating the chance-constrained safety set into deterministic control constraints with PrSBC, the safety controllers can be computed by minimally modifying the existing unconstrained controller via a quadratic program subject to the 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 the effectiveness of the approach through experiments on realistic simulation environment.
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