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

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