Dynamics and adaptive control for spacecraft relative motion with disturbances and parametric uncertainties

Abstract

In this dissertation, a nonlinear relative motion dynamics model in the presences of disturbances and parametric uncertainties is derived for high precision relative motion of the 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. The dynamic differential equations proposed in this dissertation could be used to design a general, elliptical orbit for satellites in an LEO formation, accurately and without any approximation. To minimize fuel cost while keeping the desired relative orbit, a relative $J_2$ -invariant dynamic model is also designed. The relative $J_2$ -invariant dynamic model for the desired elliptical reference orbit was designed with the mean orbital elements and the differences in the mean orbital elements, using the matching method based on the direction cosine matrix, in terms of Euler angles. This designed $J_2$ -invariant relative dynamics can be used to establish the relative position, velocity, and acceleration directly and easily. For space-craft 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. The update laws in this control law are used to estimate the parametric uncertainties and bounds of randomly bounded external disturbances. Thus, this proposed control law can deal with unmatched uncertainties to achieve the desired states without requiring prior knowledge of the bounds of uncertainty. 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.