  Safe navigation is a fundamental challenge in multi-robot systems due to the
uncertainty surrounding the future trajectory of the robots that act as
obstacles for each other. In this work, we propose a principled data-driven
approach where each robot repeatedly solves a finite horizon optimization
problem subject to collision avoidance constraints with latter being formulated
as distributionally robust conditional value-at-risk (CVaR) of the distance
between the agent and a polyhedral obstacle geometry. Specifically, the CVaR
constraints are required to hold for all distributions that are close to the
empirical distribution constructed from observed samples of prediction error
collected during execution. The generality of the approach allows us to
robustify against prediction errors that arise under commonly imposed
assumptions in both distributed and decentralized settings. We derive tractable
finite-dimensional approximations of this class of constraints by leveraging
convex and minmax duality results for Wasserstein distributionally robust
optimization problems. The effectiveness of the proposed approach is
illustrated in a multi-drone navigation setting implemented in Gazebo platform.
