Optimal Multi-Objective Linearized Impulsive Rendezvous

The multi-objective optimization of linearized impulsive rendezvous is investigated in this paper and this optimization includes the minimum characteristic velocity, the minimum time of flight, and the maximum safety performance index, of which the trajectory safety performance index is defined as the minimum relative distance between a chaser and a target in the chaser's free-flying path. A theoretical model for calculating this safety performance index is provided. The three-objective optimization model is proposed based on the Clohessy-Wiltshire system, wherein a generalized inverse matrix solution for linear equations is applied to avoid handling the terminal equality constraints. The multi-objective nondominated sorting genetic algorithm is employed to obtain the Pareto solution set. The proposed approach is evaluated using the -V-bar homing and +V-bar homing rendezvous missions. It is shown that tradeoffs between time of flight, fuel cost, and passive trajectory safety for rendezvous trajectory is quickly demonstrated by the approach. By identifying multiple solutions, the approach can produce a variety of missions to meet different needs.

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