An Adaptive Backstepping Geometric Control for Spacecraft Attitude Dynamics with Unknown Inertia Parameters

This paper presents an adaptive backstepping controller formulated on the special orthogonal group SO(3), designed to address uncertainties in the spacecraft’s inertia tensor without relying on gain scheduling. Taking advantage of the intrinsic Lie group-based attitude representation, the proposed controller provides adaptability to poorly modeled phenomena such as refueling, structural deployment, or damages. The effectiveness of the proposed controller is demonstrated both theoretically, through Lyapunov-based stability analysis, and numerically, via a simulation involving time-varying and unknown inertia, showing successful tracking of the desired reference attitude despite these difficulties. A comparison with a geometric PD tracking controller that includes feedforward and dynamic inversion demonstrates that the proposed adaptive approach is more accurate when the effort is comparable.