针对共面轨道的单脉冲拦截多目标问题，提出了一种求解拦截二、三目标的数值方法。对于单脉冲拦截二目标问题，当脉冲时刻或拦截某目标时刻给定时，通过Gibbs三矢量定轨算法，将该问题转化为求解只包含2个自由变量的非线性方程问题，通过Newton-Raphson迭代算法实现求解；进一步，考虑脉冲时刻自由，通过数值优化可得到燃料最优解。对于单脉冲拦截三目标问题，基于Lambert解将其转化为求解只包含2个自由变量的非线性方程问题，并通过数值迭代求解。两个问题求解时的迭代初值均通过Pork-Chop图法搜索得到。数值算例验证了提出方法的正确性及有效性。
This paper proposes a numerical method to solve the coplanar two/three-target orbit interception problem with a single impulse.For the two-target interception problem, the impulse time or interception time for the one target is considered to be free.By using the Gibbs method for orbit determination from three position vectors, the problem is transformed into solving the nonlinear equations of only two free variables.Newton-Raphson iterations are adopted to solve the nonlinear equations.The optimal fuel solution is obtained for this problem by numerically optimizing the impulse time.By using the Lambert algorithm, the three-target interception problem is also transformed into solving the nonlinear equations of only two free variables.Numerical iteration is adopted to solve the equations.The initial guesses of both two/three-target interception problem are obtained by the Pork-chop plot method.Numerical examples are provided to verify the correctness and effectiveness of the proposed methods.
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