Optimal Rendezvous Sequence for LEO Debris Capture

The purpose of this study is to exploit the effect of Earth’s non-sphericity perturbation, particularly due to the J2 term, in order to optimize the capture sequence of potential orbital debris. In LEO, such cause of disturbance is prevailing over the others, and it acts by affecting the longitude of the ascending node (Ω), the argument of perigee (ω ) and, accordingly, the true anomaly (ν). The goal of optimizing the ΔV is achieved by taking advantage of the rate of variation of Ω and ω, and compensating for the ΔΩ and Δω, present between the orbital transfer vehicle (chaser) and the debris to be captured (target). Obviously, the perturbation will lead to favourable variations of the orbital parameters only for some combinations of Ω and ω. Yet the presence of a debris population with random distribution of Ω and ω, makes this application particularly suited to the problem. The single maneuver has been modeled with a 4-impulse time fixed rendez-vous and the optimization problem has been addressed by implementing a hybrid evolutionary algorithm, which adopts, in parallel, three different strategies, namely, Genetic Algorithm, Differential Evolution and Particle Swarm Optimization.