Optimization for Multitarget, Multispacecraft Impulsive Rendezvous Considering J2 Perturbation

Optimization for active debris removal using multiple spacecraft is investigated. The main challenge is to determine the rendezvous sequences of the targets considering the perturbation, which is a large-scale dynamic combinatorial optimization problem. A framework to solve this problem is presented. First, a semi-analytical method of fast estimation for characteristic velocity is proposed to help construct the sequences. The -medoid method is applied to distribute all the targets to multiple spacecraft so that each spacecraft can remove as many targets as possible with limited propellant. Given a distribution of targets, the sequences for each spacecraft are searched separately; thus the original combinatorial optimization problem is split into multiple small-scale ones that can be efficiently solved by tree search algorithms. An evolutionary algorithm nested with a tree search algorithm is proposed to improve the distribution of the targets, so that the spacecraft can remove all the targets with a low cost. Then optimal sequences are further searched using an ant colony optimization algorithm, and the rendezvous epochs are refined by a nonlinear programming algorithm. The efficiency of these methods is demonstrated by two scenarios of active debris removal.