Simultaneous Spatial and Temporal Assignment for Fast UAV Trajectory Optimization using Bilevel Optimization

TL;DR

This paper introduces a fast UAV trajectory planning framework using bilevel optimization, which efficiently updates spatial and temporal parameters by reformulating the problem to reduce computation time and improve scalability.

Contribution

The proposed method reformulates the bilevel optimization by moving safety constraints to the upper level, enabling linear scaling of computation time with safety set count.

Findings

Computation time scales linearly with safety sets.

The method significantly reduces planning time compared to state-of-the-art.

Validated through simulations demonstrating efficiency and scalability.

Abstract

In this paper, we propose a framework for fast trajectory planning for unmanned aerial vehicles (UAVs). Our framework is reformulated from an existing bilevel optimization, in which the lower-level problem solves for the optimal trajectory with a fixed time allocation, whereas the upper-level problem updates the time allocation using analytical gradients. The lower-level problem incorporates the safety-set constraints (in the form of inequality constraints) and is cast as a convex quadratic program (QP). Our formulation modifies the lower-level QP by excluding the inequality constraints for the safety sets, which significantly reduces the computation time. The safety-set constraints are moved to the upper-level problem, where the feasible waypoints are updated together with the time allocation using analytical gradients enabled by the OptNet. We validate our approach in simulations, where our method's computation time scales linearly with respect to the number of safety sets, in contrast to the state-of-the-art that scales exponentially.