Low-thrust, gravity-assist trajectory optimization via pseudospectral method and automatic differentiation

An approach for low-thrust and gravity-assist trajectory optimization is presented in this paper based on automatic differentiation and pseudospectral method. The B-plane model is used to increase robustness of the trajectory optimization problem. A Gauss pseudospectral method is applied to the parameterization of the entire trajectory, which includes the search of launch date in the same calculation framework to avoid the slow convergence rate and poor precision caused by stochastic search algorithms. A sequential quadratic programming (SQP) method is adopted as the solver of the resulting large scale nonlinear programming (NLP) problem. Strategies of serial optimization and elastic constraints are proposed in order that the NLP problem converges rapidly. The derivatives required by the SQP method are obtained by automatic differentiation to ensure high accuracy and a rapid convergence rate. Taking the optimization of Earth-Venus-Mars low-thrust gravity-assist trajectory as an example, the results verify the correctness and validity of the proposed method.