Robust-RRT: Probabilistically-Complete Motion Planning for Uncertain Nonlinear Systems

Robust motion planning entails computing a global plan that is safe under all possible uncertainty realizations, be it in the system dynamics, robot’s initial position, or with respect to external disturbances. Current approaches for robust either lack theoretical guarantees, make restrictive assumptions on dynamics and distributions. In this paper, we address these limitations by proposing rapidly-exploring random-tree (Robust-RRT) algorithm, which integrates forward reachability analysis directly into sampling-based control trajectory synthesis. We prove Robust-RRT probabilistically complete (PC) nonlinear Lipschitz continuous dynamical systems bounded uncertainty. other words, eventually finds feasible realizations assuming such exists. Our applies even unstable admit only short-horizon plans; because explicitly consider time evolution of reachable sets along trajectories. To best our knowledge, most general PC proof planning, terms types uncertainties can handle. Considering an exact computation computationally expensive some systems, incorporate demonstrate planner nonlinear, underactuated, hybrid systems.