Optimal Terrain Following Trajectory Regeneration Using Linear Gauss Pseudo-Spectral Method

A numerical method for two-dimensional terrain following optimal trajectory regeneration is proposed in this paper, which corrects the planned optimal trajectory to avoid collision with previously unknown obstacles. The neighboring extremal problem is established near the optimal terrain following trajectory, which can be regarded as a two-point boundary-value problem (TPBVP) and solved using Linear Gauss Pseudo-Spectral (LGP) method. Compared with the classical backward sweep method for solving TPBVPs, LGP method is much faster in obtaining approximate results. Numerical simulations are provided to validate the effectiveness and demonstrate the features of the problem.