UAV Trajectory Optimization for Maximum Soaring in Windy Environment

Abstract

Optimal trajectory planning in a windy environment is a complex problem when airplane performance characteristics are considered. This paper introduces a novel form of Legendre pseudospectral optimization to solve boundary value problems in UAV trajectory planning. The proposed architecture applies Legendre–Gauss–Lobatto and Hamilton–Jacobi–Bellman equations to generate candidate pieces of trajectories with respect to the UAV dynamic constraints. Analytical performance-based solutions are also developed for sample cases to achieve an optimal criterion in trajectory planning. Moreover, the notion of wind soaring is exploited to use the beneficial effects of tailwind velocities in trajectory planning. Integral cost functions are handled by Gauss-type quadrature rules. Simulations demonstrate the efficiency of the pseudospectral method compared with other solvers, in eliminating the difficulties of boundary value problems by employing the boundary points in the interpolation equation. The effectiveness of the proposed approach is demonstrated through dynamic simulations.