Immersion and invariance based adaptive attitude control of asteroid-orbiting spacecraft using modified Rodrigues parameters

Abstract

The attitude control of an asteroid-orbiting spacecraft based on immersion and invariance (I&I) theory is the subject of this paper. It is assumed that the moment of inertia matrix and the gravitational parameters are not known. The objective is to attain nadir pointing attitude on an elliptic orbit. First, based on the I&I principle, an adaptive attitude control system using the Modified Rodrigues Parameters (MRPs) is derived. Through the Lyapunov stability analysis, the asymptotic convergence of the MRP trajectories to the origin is established. Interestingly, in contrast to traditional adaptive systems, the trajectories of the closed-loop system converge to an attractive manifold in an extended state space. Then, for the purpose of comparison, this MRPs-based control law and a quaternions-based control system (also designed using the I&I principle) are simulated for the attitude control of the spacecraft in eccentric orbits around asteroid 433 Eros. It is observed that while each I&I-based control law can accomplish precise attitude control, for identical design parameters in these two control systems, the MRPs-based control law requires smaller control magnitude and accomplishes smoother convergence of trajectories to the attractive manifold, but requires larger settling time for the attitude trajectories, compared with the quaternions-based adaptive control law.