Fast UAV Trajectory Optimization using Bilevel Optimization with Analytical Gradients

We present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier subproblems. With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem. The challenge of obtaining the gradient of the timing variables is solved by sensitivity analysis of parametric NLPs. The exact analytic gradient is computed from the dual solution as a by-product, whereas existing finite-difference techniques require additional optimization. The bilevel optimization framework efficiently optimizes both timing and state variables which is demonstrated on generating trajectories for an unmanned aerial vehicle. Numerical experiments demonstrate that bilevel optimization converges significantly more reliably than a standard NLP solver, and analytical gradients outperform finite differences in terms of computation speed and accuracy. Physical experiments demonstrate its real-time applicability for reactive target tracking tasks.