Nonlinear Optimal Control of Space Docking and Rendezvous Problem

In this paper a nonlinear optimal control is suggested. Spacecraft intended to rendezvous and dock with the target is controlled by actuators to have a safe and stable course while satisfying requirements. The Nonlinear optimal controller is designed using nonlinear equations of relative position and attitude of spacecraft for circular and elliptical orbits with and without reaction wheels. Cost function of the optimal control problem is expressed in the form of nonlinear quadratic regulator and control constraints are applied to the problem to gain controls in the allowable domain which is produced by the wheels. For the sake of robustness to the uncertainties as one of the most important element of the control design, nonlinear optimal control is derived using state dependent Riccatti equation based on analytical method of eigen vectors of Hamiltonian matrix. Simulation results show that this nonlinear control method achieves a good performance for rendezvous and docking problem.