Uniform Exponential Stability Result for the Rigid-Body Attitude Tracking Control Problem

Abstract

Uniform exponential stability (UES) is proved for the rigid-body attitude control problem using a proportional-derivative (PD) controller with feedforward terms associated with the desired attitude state. Whereas this so-called “PD+” controller is classical and has been extensively analyzed in the literature for more than two decades, thus far it has only been shown to deliver uniform aysmptotic stability for the resulting closed-loop system. This paper parameterizes the kinematics through the three-dimensional modified Rodrigues parameter, assumes perfect measurement of the full-state, and guarantees a stronger UES result. It should be emphasized that no additional restrictions on the reference trajectory or high-gain feedback assumptions are placed in achieving this stronger stability result for the closed-loop system. The design of a new Lyapunov function is shown to permit UES, which further lends itself to robustness analysis in the possible presence of bounded unknown external disturbance torques. Saliently, this new Lyapunov function naturally extends to the classical Gibbs–Rodrigues parameterization of the attitude kinematics. The controller is also tested in simulation to compare the result with practical performance.