Modelling orientation trajectories

We describe a modelling approach for orientation trajectories. The initial and final orientations of the object are taken as known and the problem of how the object will transition between the endpoints is considered. Orientations are represented as quaternions and mapped to a tangent space. The deviation from the geodesic connecting the endpoints is introduced and called the slerp residual. Modelling the slerp residuals substantially reduces the distortion caused by mapping to the tangent space. Bézier curves are used to compactly model the trajectories and provide a linkage to potential predictors. Data from an experiment to study human motion while reaching to perform a wide variety of grasps are considered. The orientation trajectories of the hand are modelled in several ways resulting in a simple yet interpretable model.