Quaternion-based adaptive attitude control of asteroid-orbiting spacecraft via immersion and invariance

Abstract

The design of an attitude control system for an asteroid-orbiting satellite via immersion and invariance is the subject of this paper. It is assumed that the asteroid is rotating with a constant rate, and that the inertia parameters of the satellite and the coefficients in the spherical harmonic gravitational potential of the asteroid are not known. The objective is to regulate the quaternion trajectory of the satellite orbiting in an equatorial orbit. Based on the immersion and invariance (I&I) theory, a noncertainty-equivalence adaptive (NCEA) attitude control law is derived. For the design, a backstepping design process involving two steps is used, and filtered signals are constructed to overcome the difficulty in solving certain matrix inequalities of the I&I methodology. The control law includes a stabilizer and an identifier - designed separately. Unlike the classical certainty-equivalence adaptive (CEA) systems, here the estimated parameters include not only the signals obtained from an integral type update law, but also judiciously chosen nonlinear algebraic signals that yield stronger stability properties. By the Lyapunov stability analysis, it is shown that the quaternion trajectories of the disturbance input-free closed-loop system asymptotically converge to the equilibrium point. The control law is effective in regulating the attitude to the equilibrium point with minimal rotation of spacecraft. Also, for the model with disturbance input, uniform ultimate boundedness of system trajectories is established. Simulation results for the attitude control of spacecraft in orbit around asteroid 433 Eros are presented for illustration. These results show that the spacecraft achieves nadir pointing attitude despite uncertainties in the system dynamics.