Optimal planning of LEO active debris removal based on hybrid optimal control theory

Abstract

The mission planning of Low Earth Orbit (LEO) active debris removal problem is studied in this paper. Specifically, the Servicing Spacecraft (SSc) and several debris exist on near-circular near-coplanar LEOs. The SSc should repeatedly rendezvous with the debris, and de-orbit them until all debris are removed. Considering the long-duration effect of J2 perturbation, a linear dynamics model is used for each rendezvous. The purpose of this paper is to find the optimal service sequence and rendezvous path with minimum total rendezvous cost (Δv) for the whole mission, and some complex constraints (communication time window constraint, terminal state constraint, and time distribution constraint) should be satisfied meanwhile. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed, as well as the solution method. The proposed approach is demonstrated by a typical active debris removal problem. Numerical experiments show that (1) the model and solution method proposed in this paper can effectively address the planning problem of LEO debris removal; (2) the communication time window constraint and the J2 perturbation have considerable influences on the optimization results; and (3) under the same configuration, some suboptimal sequences are equivalent to the optimal one since their difference in Δv cost is very small.