Dual-quaternion-based adaptive motion tracking of spacecraft with reduced control effort

The position and attitude tracking of a rigid spacecraft is approached with coupled six-degrees-of-freedom dynamics described by dual quaternions. By taking advantage of the compact, nonlinear, integrated relative motion dynamics, a simple proportional-derivative (PD) controller is designed at first in the absence of modeling uncertainties. The presence of unknown mass and inertia as well as unknown constant disturbances is then taken into account. An adaptive controller is developed by combining the PD controller with an adaptive algorithm, which provides estimations of unknown parameters and disturbances. Both controllers ensure almost global asymptotic convergence of the relative pose tracking error. In addition, the proposed methods are not only computationally efficient but can also reduce the control energy consumption, since the gyroscopic terms involved in the system dynamics are preserved, rather than being cancelled by feedback. Numerical simulations demonstrate the effectiveness of the proposed methods.