Two Methods for Interpolating Rigid Body Motions

This paper investigates methods for computing a smooth motion that interpolates a given set of positions and orientations of a rigid body. To make the interpolation independent of the representation of the motion, we use the coordinate-free framework of differential geometry. Inertial and body-fixed reference frames must be chosen to describe the position and orientation of the rigid body. We show that trajectories that are independent of the choice of these frames can be obtained by using the exponential map. Since these trajectories may exhibit rapid changes in velocity or its higher derivatives, a method for finding the maximally smooth interpolating curve is developed. Trajectories computed by both methods are compared on an example.