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Real-world environments are inherently uncertain, and to operate safely inthese environments robots must be able to plan around this uncertainty. In thecontext of motion planning, we desire systems that can maintain an acceptablelevel of safety as the robot moves, even when the exact locations of nearbyobstacles are not known. In this paper, we solve this chance-constrained motionplanning problem using a sequential convex optimization framework. To constrainthe risk of collision incurred by planned movements, we employ geometricobjects called $\epsilon$-shadows to compute upper bounds on the risk ofcollision between the robot and uncertain obstacles. We use these$\epsilon$-shadow-based estimates as constraints in a nonlinear trajectoryoptimization problem, which we then solve by iteratively linearizing thenon-convex risk constraints. This sequential optimization approach quicklyfinds trajectories that accomplish the desired motion while maintaining auser-specified limit on collision risk. Our method can be applied to robots andenvironments with arbitrary convex geometry; even in complex environments, itruns in less than a second and provides provable guarantees on the safety ofplanned trajectories, enabling fast, reactive, and safe robot motion inrealistic environments.

Provably Safe Trajectory Optimization in the Presence of Uncertain Convex Obstacles