Dynamics and Adaptive Control for Spacecraft Relative Motion with Disturbances and Parametric Uncertainties

A nonlinear relative motion dynamics model in the presence of disturbances and parametric uncertainties is presented for the high precision relative motion of a spacecraft. The disturbances include the Earth's oblateness, atmospheric drag, and thrust error. The parametric uncertainties in the atmospheric drag coefficients and thrust alignments are considered. To minimize fuel cost Delta V while keeping the desired relative orbit, a relative J(2)-invariant dynamics model is also designed. For spacecraft relative motion tracking maneuver, an adaptive backstepping sliding mode control law under limited low thrust is developed. This control law combines the advantages of adaptive backstepping and sliding mode control, where knowledge of the upper bounds of parametric uncertainties and disturbances are not required. Within the Lyapunov framework, the proposed control law is proved to guarantee global asymptotic convergence to the desired states. Numerical simulation results show the effectiveness of the nonlinear relative motion dynamics model and proposed control law.