Enhancing Motion Trajectory Segmentation of Rigid Bodies Using a Novel Screw-Based Trajectory-Shape Representation

Trajectory segmentation refers to dividing a tra- jectory into meaningful consecutive sub-trajectories. This paper focuses on trajectory segmentation for 3D rigid-body motions. Most segmentation approaches in the literature represent the body’s trajectory as a point trajectory, considering only its translation and neglecting its rotation. We propose a novel trajectory representation for rigid-body motions that incorpo- rates both translation and rotation, and additionally exhibits several invariant properties. This representation consists of a geometric progress rate and a third-order trajectory-shape descriptor. Concepts from screw theory were used to make this representation time-invariant and also invariant to the choice of body reference point. This new representation is validated for a self-supervised segmentation approach, both in simulation and using real recordings of human-demonstrated pouring motions. The results show a more robust detection of consecutive sub- motions with distinct features and a more consistent segmenta- tion compared to conventional representations. We believe that other existing segmentation methods may benefit from using this trajectory representation to improve their invariance.