  Trajectory segmentation refers to dividing a trajectory 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 incorporates 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 submotions
with distinct features and a more consistent segmentation compared to
conventional representations. We believe that other existing segmentation
methods may benefit from using this trajectory representation to improve their
invariance.
