A Robust Attitude Tracking Controller for Spacecraft Based on Singularity-Free Quaternion Nonlinear Dynamic Inversion Framework

This paper presents a robust attitude-tracking control architecture for rigid spacecraft subject to model mismatches and external disturbances. Quaternions are utilized for attitude representation to prevent the gimbal lock associated with Euler angles. While conventional nonlinear dynamic inversion (NDI) relies on Newtonian mechanics and input–output linearization—which inadvertently generates internal zero dynamics and encounters severe control derivative discontinuities at the q₀ = 0 singularity—this study proposes a novel NDI framework derived strictly from Udwadia’s Lagrangian formulation. This approach realizes an exact input-state linearization directly on the 6-degree-of-freedom active holonomic constraint manifold, completely eliminating internal zero dynamics and mathematical singularities. To ensure robustness against physical uncertainties, the singularity-free NDI is augmented with a nonlinear disturbance observer (DOBC) and an outer-loop linear quadratic (LQ) tracking controller. A rigorous composite Lyapunov stability analysis is conducted for the complete closed-loop architecture. The analysis formally guarantees that both the isolated disturbance estimation error and the fully interconnected dual-loop NDI-DOBC system are Uniformly Ultimately Bounded (UUB), even in the presence of realistic, time-varying disturbances with non-vanishing derivatives (\({ \boldsymbol {\dot{d}} \neq \textbf{0}}\)). Comprehensive numerical simulations, parameterized by a physical spherical air-bearing testbed subject to state-dependent gravitational imbalance torques, validate the architecture’s exceptional tracking precision, smooth transient response, and robust disturbance rejection.