最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间，针对平动点航天器编队重构的均衡耗能最优轨迹规划问题，提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解，并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域；同时，不需要对协态初值准确猜测，避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟，结果表明，本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标，具有一定的应用价值。

Optimal trajectory planning method and its application in balanced energy reconfiguration of spacecraft formation near the libration point

Because balanced-energy spacecraft formation can increase the lifetime of the entire spacecraft formation,aiming at the optimal trajectory planning for balanced-energy reconfiguration of spacecraft formation near the libration point,a novel algorithm based on the approximation of three types of variable (state,co-state and control) is proposed for solving nonlinear optimal control problem.By employing the Lagrange interpolation of the three variables,the nonlinear optimal control problem is transformed into a system of nonlinear equations.Furthermore,the explicit form of the Jacobi matrix is derived to increase the computational efficiency of the nonlinear equations.On one hand,the proposed method satisfies the necessary condition of optimal control theory; on the other hand,no initial guesses of costate variables are required,and it also avoids the solving of a large scale nonlinear planning problem.Numerical simulations about the case of the fixed center spacecraft and the case of no center spacecraft have been discussed.The results show that the proposed method can achieve the objective of balanced-energy reconfiguration of spacecraft formation