Inertia-free spacecraft attitude tracking with disturbance rejection and almost global stabilization

We derive a continuous nonlinear control law for spacecraft attitude tracking of arbitrary continuously differentiable 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 for which the 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 and without resorting to discontinuous switching. The controller requires no inertia information, no information on constant-disturbance torques, and only frequency information for sinusoidal disturbance torques. For slew maneuvers (that is, maneuvers with a setpoint command in the absence of disturbances), the controller specializes to a continuous, nonlinear, proportional-derivative-type, almost globally stabilizing controller, in which case the torque inputs can be arbitrarily bounded a priori. For arbitrary maneuvers, we present an approximate saturation technique for bounding the control torques.