This paper describes a novel homotopy method to compute fuel-optimal trajectories starting from a time-optimal solution. The time-optimal problem is proposed to serve as a gateway for solving the minimum thrust problem. Homotopy is used to link the original low-thrust fuel-optimal problem with the minimum thrust problem. Two new variables are introduced in the dynamic model. The first is a logarithm of mass variable and the second is an acceleration magnitude variable. The analytic expression of the logarithm of mass co-state is solved. For the time-optimal problem, initial co-state of logarithm of mass can be expressed by thrust magnitude and transfer time. Then, the number of unknown initial co-states decreased. The effectiveness and optimality of the proposed method is validated through simulations of two rendezvous missions.

中文翻译：

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连接时间最优和燃料最优轨迹的同伦方法

本文描述了一种新的同伦方法，用于从时间最优解开始计算燃料最优轨迹。提出时间最优问题作为解决最小推力问题的途径。同伦用于将原始低推力燃料优化问题与最小推力问题联系起来。动态模型中引入了两个新变量。第一个是质量变量的对数，第二个是加速度幅度变量。求解了质量共态对数的解析表达式。对于时间最优问题，质量对数的初始共态可以用推力大小和传递时间来表示。然后，未知初始共态的数量减少。通过对两个交会任务的模拟，验证了所提出方法的有效性和最优性。