Exponential stability of trajectory tracking control in the orientation space utilizing unit quaternions

Trajectory tracking in the orientation space utilizing unit quaternions yields non linear error dynamics as opposed to Cartesian position. In this work, we study trajectory tracking in the orientation space utilizing the most popular quaternion error representations and angular velocity errors. By selecting error functions carefully we show exponential convergence in a region of attraction containing large initial errors. We further show that under certain conditions frequently en-countered in practice, the formulation respecting the geometric characteristics of the quaternion manifold and its tangent space yields linear tracking dynamics allowing us to guarantee a desired tracking performance by gain selection without tuning. Simulation and experimental results are provided.