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

TL;DR

This paper introduces a novel local optimization method for UAV trajectories that guarantees validity and asymptotic optimality in known environments, handling non-convex constraints effectively.

Contribution

It presents the first local UAV-trajectory generator that ensures trajectory validity and asymptotic optimality simultaneously, with automatic discretization refinement.

Findings

Guarantees constraint satisfaction during optimization

Converges to first-order stationary point with refinement

Demonstrates robustness in challenging environments

Abstract

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.