  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.
