Inertia-Free Spacecraft Attitude Tracking with Disturbance 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 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.

Torque-saturated, Inertia-Free Spacecraft Attitude Control

“…The goal of the present paper is to extend the results of [1] by modifying the attitude-tracking control laws to satisfy a constraint on the torque magnitude. We consider two specific problems.…”

“…The assumption of zero on-board momentum storage is removed in [2], where the results of [1] are extended to the case of reaction wheel actuation. However, torque limits are not considered in [2].…”

“…The starting point for the present paper is [1], which provides attitude-tracking control laws for rigid spacecraft in the presence of unmeasured harmonic disturbances. The control law in [1] requires knowledge of the spectrum of the disturbance, but no knowledge of the spacecraft's mass distribution. This control law is thus inertia-free.…”

“…The actuation considered in [1] is based on continuously variable torques without momentum storage and without a bound on the torque magnitude. The assumption of zero on-board momentum storage is removed in [2], where the results of [1] are extended to the case of reaction wheel actuation.…”

“…For the M2R problem, the controller developed in [1] is a static feedback control law that acts directly on measurements of attitude and angular velocity. For the M2S problem, the controller is a dynamic a 6th-order feedback compensator that uses on-line estimates of the spacecraft inertia.…”