Nonlinear Optimal Control of Relative Rotational and Translational Motion of Spacecraft Rendezvous

摘要

A nonlinear optimal control technique is utilized to address coupled relative rotational and translational motion in spacecraft rendezvous. A new formulation of relative rotational dynamic with momentum exchange devices is developed. For a complete description of the relative motion dynamic in the final proximity phase, a kinematically coupled model of relative position and attitude is derived. For the sake of safety of the maneuvers and achieving smooth paths, which are critical issues during proximity, accurate motion control is needed; as a result, the state-dependent Riccati equation control technique is used to address far-range rendezvous and final proximity to a target in an elliptical orbit under small bounded perturbations and parameter uncertainty. The resulting state-dependent algebraic Riccati equation is solved using eigenvectors of a Hamiltonian matrix to find nonlinear optimal control gains. The proposed direct and numerically stable Hamiltonian method decreases computational time and cost. Numerical simulation results show that with this control method acceptable robustness and stability can be achieved. (C) 2017 American Society of Civil Engineers.