共面单脉冲拦截多目标问题

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.