Mixed Iterative Algorithm For Solving Optimal Impulsive Time-Fixed Rendezvous Problem

In this paper, an iterative algorithm for solving impulsive fuel-optimal rendezvous in a linearized gravitational field is proposed. The developed algorithm combines the iterative approach presented by Lion and Handelsman with a polynomial solver based on homotopy continuation methods using algebraic formulation of optimality conditions introduced recently by Carter. This allows to overcome the problems of non-smoothness of the resulting trajectory of the primer vector faced by several authors, when applying the LionHandelsman approach. The algorithm is designed for a general keplerian ellipse-to-ellipse impulsive transfer, through the use of Yamanaka-Ankersen transition matrix. For each iteration, homotopy continuation technique is used to solve polynomial equations system induced by the optimality conditions for a fixed number of impulses. Numerical results obtained on academic as well as non academic test cases are analysed through simulations

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