Approximator of multi-impulse near-circular transfers for multi-rendezvous sequence optimization

To find the optimal rendezvous time and order of each target in a multi-rendezvous mission, it’s nessassory to evaluate Δ v between different targets with different departure times and transfer durations. To improve the efficiency of Δ v evaluation, this paper proposes an analytical method for assessing the optimality of a given double-impulse trajectory by leveraging relative dynamic equations based on orbital differences. Furthermore, a gradient-based nonlinear programming algorithm is established for the rapid optimization of three-impulsive trajectory when the double-impulse trajectory is suboptimal. The methodology is validated through various case studies, encompassing both low-Earth-orbits and asteroid orbits. The results indicate that our optimality checks align with the prime vector theory while demanding fewer computations. Additionally, the three-impulsive solutions rapidly obtained via our nonlinear programming algorithm are consistent with those obtained from multi-impulse evolutionary optimization models. A multi-target rendezvous optimization case also proves its applicability to optimization of multi-rendezvous missions.