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.

本文涉及基于单腿转移的解决方案的燃料最优多重力辅助轨迹的优化，该解决方案利用具有可变比冲的实际太阳能推进力。本文研究了具有多重重力辅助和可变比冲的燃料最优轨迹的优化。多重力辅助轨迹由多条腿组成，每条腿分别求解并组合起来，为多腿问题提供初步的猜测。将特定的脉冲作为解决最佳控制问题所涉及的控制变量。为了减少由多重重力辅助引起的多点边值问题的强烈非线性，提出了一种基于单腿转移的肋骨变量变量的仿射变换，该变换可保留燃料的最优性，并称为最优性保持性变换。其次，采用最优保存变换来重新定义多分支转移的一阶必要条件。结果，单腿转移的解决方案可以直接用作多腿转移的拍摄功能的初始猜测。所述的保持最优性的变换很容易适用于并行计算。此外，改进的对数同伦方法专门用于可变比冲量情况。结合这两种方法的策略可有效地优化燃料最佳多重力辅助轨迹。现实的特定于变量的脉冲NASA' 考虑到一种，两种和三种重力辅助情况，在数值模拟中采用了进化型氙气推进器。结果，证明了该提出的策略可导致计算效率的显着提高。