Inertia-free spacecraft attitude trajectory tracking with internal-model-based disturbance rejection and almost global stabilization

We derive a continuous nonlinear control law for spacecraft attitude trajectory tracking of arbitrary C¹ attitude trajectories based on rotation matrices. This formulation provides almost global stabilizability, that is, Lyapunov stability of the desired equilibrium of the error system as well as convergence from all initial states except for a subset whose complement is open and dense. This controller thus overcomes the unwinding phenomenon associated with continuous controllers based on attitude representations, such as quaternions, that are not bijective. The controller requires no inertia information and no information on constant disturbance torques. For slew maneuvers, that is, maneuvers with a setpoint command, in the absence of disturbances, the controller specializes to the continuous, nonlinear PD-type almost globally stabilizing controller of Chaturvedi, in which case the torque inputs can be arbitrarily bounded a priori.