Adaptive nonlinear control for spacecraft with coupled translational and attitude dynamics

In this paper, we address a tracking control problem for the coupled translational and attitude motion of a spacecraft. Specifically, a nonlinear adaptive control law is developed to ensure global asymptotic tracking of the desired translational and attitude trajectories in the presence of unknown mass and inertia parameters of spacecraft. Using the vectrix formalism the translational and attitude dynamics of spacecraft is modeled, where the mutual coupling in the translational and attitude motion induced by their gravitational interaction is duly accounted. The four-parameter quaternion representation is employed to describe the attitude kinematics of spacecraft in order to enable large orientation maneuvers. Based on the structure of the resulting system dynamics, the filtered translational and attitude tracking error dynamics are developed, which facilitate the transformation of second-order translational and attitude motion error dynamics as first-order equations, thus providing a considerable simplification in control law synthesis/analysis. With the aid of two linear operators, the open-loop filtered tracking error dynamics is parameterized such that the unknown mass and inertia parameters of spacecraft are isolated and can be estimated on-line. Using a Lyapunov framework, nonlinear control and adaptation laws are designed that ensure the global asymptotic convergence of the translational and attitude position tracking errors, despite the presence of unknown mass and inertia parameters of spacecraft. In addition, the form of the filtered tracking error reveals the convergence of translational and attitude velocity tracking errors of spacecraft. An illustrative numerical simulation is presented to demonstrate the effectiveness of the proposed control design methodology for the coupled translational and attitude motion control of spacecraft.