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针对近距离相对运动的轨道控制问题,提出用常值小推力完成最优转移的方法。基于C-W方程,推导了相对运动解析解的表达式,讨论了在无控条件下能够形成稳定绕飞构型的初始相对速度和相对位置的限制条件,以此限制条件作为终端条件,以伴星释放时近似为零的相对速度和相对位置为初始条件,建立了利用连续小推力实现的伴星释放最优控制问题的模型。选用了高斯伪谱法将最优控制问题离散化,转化成非线性规划问题并通过系列二次规划法完成求解。数值仿真算例表明,利用高斯伪谱法求解此问题可以有效地收敛到最优解。
Aiming at the orbital control problem of short-distance relative motion, a method of completing the optimal transfer with small thrust of constant value is proposed. Based on the CW equation, the expression of the analytic solution of relative motion is deduced. The constraints that can form the initial relative velocity and the relative position of the stable fly-fly-formation under uncontrolled conditions are discussed. The constraint condition is taken as the terminal condition, When the relative velocity and relative position of the approximate zero are initial conditions, a model of optimal control of the companion release released by continuous small thrust is established. Gaussian pseudospectral method was used to discretize the optimal control problem and transformed into a nonlinear programming problem and solved by a series of quadratic programming methods. The numerical simulation shows that using Gaussian pseudospectral method to solve this problem can effectively converge to the optimal solution.