Robust Trajectory Planning for a Multirotor against Disturbance based on Hamilton-Jacobi Reachability Analysis

Ensuring safety in trajectory planning of multirotor systems is an essential element for risk-free operation. Even if the generated trajectory is known to be safe in the planning phase, unknown disturbance during an actual operation can lead to a dangerous situation. This paper proposes safety-guaranteed receding horizon planning against unknown, but bounded, disturbances. We first characterize forward reachable set (FRS) of the system, the set of states after a certain duration considering all possible disturbances, using Hamilton-Jacobi (HJ) reachability analysis. To compute the FRSs in real-time, we conservatively approximate the true FRS and perform ellipsoidal parameterization on the FRSs. Using the FRSs, we can plan a robust trajectory that avoids risky regions and rapidly re-plan the trajectory when the system encounters sudden disturbance. The proposed method is validated through an experiment of avoiding obstacles in a wind.