Tracking on lie group for robot manipulators

A method for tracking rigid body motion in terms of exponential coordinates is developed based on the differential of exponentials. The analytic closed-form expressions are provided for differential of exponential on SE(3) as well as its time-derivative. Respecting the property that SE(3), the group of rigid displacements, is the semi-product group of two groups, displacements and rotations, complete methods for tracking in terms of exponential coordinates of SE(3) are developed. In particular, Reference acceleration is designed on SE(3) for exponentially stable linearized closed-loop dynamics in exponential coordinates.