Optimization of variable-specific-impulse gravity-assist trajectories via optimality-preserving transformation

Abstract

This paper concerns optimization of fuel-optimal multi-gravity-assist trajectories based on the solutions of single-leg transfers that utilize the practical solar electric propulsion with variable specific impulse. This paper studies the optimization of fuel-optimal trajectories with multiple gravity assists and variable specific impulse. The multi-gravity-assist trajectory is composed of multiple legs each of which is solved individually and combined to provide an initial guess for the multi-leg problem. The specific impulse is taken as a control variable involved in solving the optimal control problems. To reduce the strong nonlinearity of the multi-point boundary-value problem caused by multiple gravity assists, an affine transformation on the costate variables based on single-leg transfers that preserves the fuel optimality is stated and termed optimality-preserving transformation. Secondly, the optimality-preserving transformation is applied to reformulate the first-order necessary conditions for the multi-leg transfer. As a result, the solutions of the single-leg transfers can be directly used as the initial guesses for the shooting function of the multi-leg transfer. The stated optimality-preserving transformation is readily suitable to parallel computing. Additionally, the modified logarithmic homotopy method is specifically applied in variable-specific-impulse cases. The strategy combined with these two methods is efficient in optimizing the fuel-optimal multi-gravity-assist trajectories. The realistic variable-specific-impulse NASA's Evolutionary Xenon Thruster is employed in numerical simulations considering one, two, and three gravity assists cases. As a result, this proposed strategy is demonstrated to result in significant improvement of the calculation efficiency.