Recognition of 6 DOF rigid body motion trajectories using a coordinate-free representation

This paper presents an approach to recognize 6 DOF rigid body motion trajectories (3D translation + rotation), such as the 6 DOF motion trajectory of an object manipulated by a human. As a first step in the recognition process, 3D measured position trajectories of arbitrary and uncalibrated points attached to the rigid body are transformed to an invariant, coordinate-free representation of the rigid body motion trajectory. This invariant representation is independent of the reference frame in which the motion is observed, the chosen marker positions, the linear scale (magnitude) of the motion, the time scale and the velocity profile along the trajectory. Two classification algorithms which use the invariant representation as input are developed and tested experimentally: one approach based on a Dynamic TimeWarping algorithm, and one based on Hidden Markov Models. Both approaches yield high recognition rates (up to 95 % and 91 %, respectively). The advantage of the invariant approach is that motion trajectories observed in different contexts (with different reference frames, marker positions, time scales, linear scales, velocity profiles) can be compared and averaged, which allows us to build models from multiple demonstrations observed in different contexts, and use these models to recognize similar motion trajectories in still different contexts.