Uniform exponential stability result for the rigid-body attitude tracking control problem

This work proves that uniform exponential stability is achieved for the attitude control problem by adopting a PD+ control law that retains the classical proportional-derivative (PD) structure plus feedforward terms associated with tracking the desired attitude state. Previously, this controller was only known to offer the weaker result of uniform asymptotic stability. This thesis parameterizes the kinematics through the three-dimensional Modified Rodrigues Parameter (MRP), assumes perfect measurement of the full-state (i.e., both orientation and angular rate signals) and guarantees a stronger uniform exponential stability (UES) result. It should be emphasized that no additional restrictions on the reference trajectory or high-gain feedback assumptions are placed in achieving this new exponential stability result for the closed loop system. The design of a new Lyapunov function permits this stronger UES result which further allows facilitating 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 kinematicsAerospace Engineerin