Provably Safe Real-Time Receding Horizon Trajectory Planning for Linear Time-Invariant Systems

Abstract

Safe operation in spaces under uncertainty is crucial for robotic systems, especially for mobile robots. Assorted unknown quantities such as external force or estimation error can be considered disturbances. However, many robust trajectory planning algorithms that take effects of disturbances into account often accompany heavy computational load or are excessive conservatism. In this paper, we present a provably safe real-time receding horizon trajectory planning algorithm for linear time-invariant (LTI) systems. The proposed method ensures the same level of safety that other reachability-based robust planning algorithms provide, while not overestimating the reachable set. We verify the proposed framework through simulation with a six-degree-of-freedom system, in which the proposed method generates safe trajectories faster than 100 Hz.