Robust & Asymptotically Locally Optimal UAV-Trajectory Generation Based on Spline Subdivision
This addresses trajectory planning for UAVs, offering a novel approach with theoretical guarantees, though it appears incremental in the context of existing optimization methods.
The paper tackles the challenge of generating locally optimal UAV trajectories under non-convex constraints like collision avoidance and actuation limits, presenting an optimization-based method that guarantees validity and asymptotic optimality, with experimental demonstrations of robustness in challenging environments.
Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees the validity and asymptotic optimality for known environments. \textit{Validity:} Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization. \textit{Asymptotic Optimality:} We use an asymptotic exact piecewise approximation of the trajectory with an automatically adjustable resolution of its discretization. The trajectory converges under refinement to the first-order stationary point of the exact non-convex programming problem. Our method has additional practical advantages including joint optimality in terms of trajectory and time-allocation, and robustness to challenging environments as demonstrated in our experiments.