Robust orbital transfer for low earth orbit spacecraft with small-thrust

This paper studies the problem of robust orbital control for low earth orbit (LEO) spacecraft rendezvous subjects to the parameter uncertainties, the constraints of small-thrust and guaranteed cost during the orbital transfer process. In particular, the rendezvous process is divided into in-plane motion and out-plane motion based on C-W equations, and the relative motion models with parameter uncertainties are established. By considering the property of null controllable with vanishing energy (NCVE), the problem of orbital transfer control with small thrust and bounded control cost is proposed. A new Lyapunov approach is introduced, and the controller design problem is cast into a convex optimization problem subjects to linear matrix inequality (LMI) constraints. With the obtained controller, the orbit transfer process can be accomplished with small thrust and the control cost has an upper bound simultaneously. Different possible initial states of the transfer orbit are also analyzed for the controller design. An illustrative example is provided to show the effectiveness of the proposed control design method, and the different performances caused by different initial states of the transfer orbit are illustrated.