Explicit Globally Asymptotically Stable Attitude Control with Reaction Wheel Angular Momentum and Torque Constraints

Overview & Synopsis

We present an explicit Lyapunov attitude controller for rigid spacecraft actuated by three orthogonally mounted reaction wheels, parameterized using Modified Rodrigues Parameters (MRPs), which enforces hard bounds on wheel angular momentum and applied torque at every instant without solving any online optimization. A barrier-inspired momentum feedback prevents wheel saturation; a continuous positive scalar uniformly scales the feedback whenever a torque limit would otherwise be breached, preserving Lyapunov convergence. For the regulation problem, global asymptotic stability (GAS) is established via LaSalle's invariance principle, and constraint satisfaction is proved analytically for arbitrary symmetric positive-definite inertia matrices. Replacing the barrier by an error-state counterpart extends the design to tracking, with asymptotic (though no longer global) stability and the same safety guarantees under explicit feasibility conditions on the reference. Simulations confirm convergence and constraint satisfaction, and compare performance against other controllers.