Interpolation and tracking of rigid body orientations

A method of interpolating and tracking rigid body motions in terms of its exponential coordinates is developed based on the differential of exponentials. The analytic closed-form expressions are provided for differential of exponential on SO(3) as well as its time-derivative. Complete methods for interpolating and tracking in terms of exponential coordinates of SO(3) are developed. In particular, interpolation is made with the boundary conditions including acceleration level. Reference acceleration is designed on SO(3) for linearized closed-loop dynamics in exponential coordinates.