Rotation-matrix-based attitude control without angular velocity measurements

Rigid-body attitude control without angular velocity measurements is considered. The error rotation matrix describing the attitude error is used directly within the control algorithm. A controller composed of a proportional control term and an angular velocity control term is first considered. The proportional control term is a function of the error rotation matrix, while the angular velocity control term is realized by a strictly positive real system. Asymptotic stability of a desired closed-loop equilibrium point is shown, and a derivative free implementation of the controller is identified for use when angular velocity measurements are not available. Numerical simulation results demonstrate successful set-point regulation and noise mitigation.