Coordinate-invariant rigid-body interpolation on a parametric C1 dual quaternion curve

We present a method to generate first-order continuous rigid-body motion by interpolation. The input is a sequence of rigid-body poses at given timesteps, which the body is required to pass through (key poses). Different from frequently employed interpolation schemes, the generated rigid-body motion is unique no matter what reference coordinate systems are chosen. Our method is novel in that the user can optionally prescribe key velocity data, too. If key velocities are not prescribed, parametric velocities are computed and incorporated into the interpolating function. The parameters allow to subsequently adjust the rigid-body trajectory. Another purpose of this article is a comprehensive derivation of coordinate-invariant interpolation along with a concise collection of proofs. The derivation enables the reader to straight-forwardly implement this method. Numerical examples are given to highlight the benefits and motivate the implementation.