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Generating locally optimal UAV-trajectories is challenging due to thenon-convex constraints of collision avoidance and actuation limits. We presentthe first local, optimization-based UAV-trajectory generator thatsimultaneously guarantees the validity and asymptotic optimality for knownenvironments. \textit{Validity:} Given a feasible initial guess, our algorithmguarantees the satisfaction of all constraints throughout the process ofoptimization. \textit{Asymptotic Optimality:} We use an asymptotic exactpiecewise approximation of the trajectory with an automatically adjustableresolution of its discretization. The trajectory converges under refinement tothe first-order stationary point of the exact non-convex programming problem.Our method has additional practical advantages including joint optimality interms of trajectory and time-allocation, and robustness to challengingenvironments as demonstrated in our experiments.

Robust & Asymptotically Locally Optimal UAV-Trajectory Generation Based on Spline Subdivision