Inertia-Free Spacecraft Attitude Tracking withDisturbance Rejection and Almost Global Stabilization

Abstract

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 inertiainformation,noinformation onconstant-disturbance torques,andonlyfrequencyinformation forsinusoidal 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 casethe torque inputs can be arbitrarily bounded a priori. For arbitrary maneuvers, we present an approximate saturation technique for bounding the control torques.