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To operate reactively in uncertain environments, robots need to be able toquickly estimate the risk that they will collide with their environment. Thisability is important for both planning (to ensure that plans maintainacceptable levels of safety) and execution (to provide real-time warnings whenrisk exceeds some threshold). Existing methods for estimating this risk areoften limited to models with simplified geometry (e.g. point robots); othershandle complex geometry but are too slow for many applications. In this paper,we present two algorithms for quickly computing upper bounds on the risk ofcollision between a robot and uncertain obstacles by searching for certificateregions that capture collision probability mass while avoiding the robot. Thesealgorithms come with strong theoretical guarantees that the true risk does notexceed the estimated value, support arbitrary geometry via convexdecomposition, and provide fast query times ($<200\mu$s) in representativescenarios. We characterize the performance of these algorithms in environmentsof varying complexity, demonstrating at least an order of magnitude speedupover existing techniques.

Fast Certification of Collision Probability Bounds with Uncertain Convex Obstacles