  Safety is a core challenge of autonomous robot motion planning, especially in
the presence of dynamic and uncertain obstacles. Many recent results use
learning and deep learning-based motion planners and prediction modules to
predict multiple possible obstacle trajectories and generate obstacle-aware ego
robot plans. However, planners that ignore the inherent uncertainties in such
predictions incur collision risks and lack formal safety guarantees. In this
paper, we present a computationally efficient safety filtering solution to
reduce the collision risk of ego robot motion plans using multiple samples of
obstacle trajectory predictions. The proposed approach reformulates the
collision avoidance problem by computing safe halfspaces based on obstacle
sample trajectories using distributionally robust optimization (DRO)
techniques. The safe halfspaces are used in a model predictive control
(MPC)-like safety filter to apply corrections to the reference ego trajectory
thereby promoting safer planning. The efficacy and computational efficiency of
our approach are demonstrated through numerical simulations.
