Real-Time Robust Receding Horizon Planning Using Hamilton-Jacobi Reachability Analysis

Safety guarantee prior to the deployment of robots can be difficult due to unexpected disturbances in runtime. This article presents a real-time receding-horizon robust trajectory planning algorithm for nonlinear closed-loop systems, which guarantees the safety of the system under unknown but bounded disturbances. We characterize the forward reachable sets (FRSs) of the system based on the Hamilton-Jacobi reachability analysis as a means for safety verification. For the online computation of the FRSs, we approximate nonlinear systems as LTV systems with linearization errors and compute ellipsoids that encompass the FRSs in continuous time. Using the proposed ellipsoidal approximation of the FRSs, we formulate a computationally tractable robust planning problem that can be solved online. Consequently, the proposed method enables real-time replanning of a reference trajectory with safety guarantees even when the system encounters unexpected disturbances in runtime. The flight experiment of obstacle avoidance in a windy environment validates the proposed robust planning algorithm.