Anti-Unwinding Immersion and Invariance Adaptive Attitude Control of Rigid Spacecraft with Inertia Uncertainties

A modular anti-unwinding dynamic scaling-based immersion and invariance (I&I) adaptive control is devised for rigid spacecraft attitude with inertia uncertainties. It is shown that the parametric regressor matrix cannot be integrable in the attitude dynamics, which results in a nonanalytical solution to the partial differential equations in the I&I controller design. First, in order to overcome the integrability obstacle, the proposed method provides a general and simple matrix reconstruction to make the regressor matrix integrable. Second and foremost, by virtue of a novel modified scaling factor involving saturation function, this paper shows that this method does not require any prior knowledge of the spacecraft inertia matrix and can be conducted without a scaling factor in the controller implementation, which achieves a simpler controller structure and lower dimensional dynamic extension. Moreover, the unwinding problem typically arising in attitude quaternion dynamics is addressed just by the initial value of the attitude quaternion. Finally, numerical simulations are carried out to demonstrate the effectiveness and anti-unwinding characteristic of the proposed controller.