A Second-Order Gradient Solver using a Homotopy Method for Space Trajectory Problems

Recent developments in low-thrust trajectory optimization methods have shown that second-order gradient techniques can be e cient. Robust second-order methods allow one to solve complex dynamical problems, accounting for perturbations, and path constraints, with high delity. Convergence of the method, however, requires a very good initial guess, or a lot of user experience. Based on a quadratic expansion of the Lagrangian for the optimal control problem, the proposed method uses well known homotopy and continuation techniques to simplify the need of a very good initial guess for the optimization problem. The continuation variable is assigned to a physical parameter to solve complex dynamical problems. The new algorithm demonstrate an increased robustness.