  In this paper, we present a decentralized and communication-free collision
avoidance approach for multi-robot systems that accounts for both robot
localization and sensing uncertainties. The approach relies on the computation
of an uncertainty-aware safe region for each robot to navigate among other
robots and static obstacles in the environment, under the assumption of
Gaussian-distributed uncertainty. In particular, at each time step, we
construct a chance-constrained buffered uncertainty-aware Voronoi cell (B-UAVC)
for each robot given a specified collision probability threshold. Probabilistic
collision avoidance is achieved by constraining the motion of each robot to be
within its corresponding B-UAVC, i.e. the collision probability between the
robots and obstacles remains below the specified threshold. The proposed
approach is decentralized, communication-free, scalable with the number of
robots and robust to robots' localization and sensing uncertainties. We applied
the approach to single-integrator, double-integrator, differential-drive
robots, and robots with general nonlinear dynamics. Extensive simulations and
experiments with a team of ground vehicles, quadrotors, and heterogeneous robot
teams are performed to analyze and validate the proposed approach.
