Enhancing motion trajectory segmentation of rigid bodies using a novel screw-based trajectory-shape representation

TL;DR

This paper introduces a screw-based trajectory-shape representation for 3D rigid-body motions that improves segmentation robustness by incorporating translation and rotation invariance, validated through simulations and real-world data.

Contribution

The paper proposes a novel trajectory representation using screw theory that is invariant to time and reference point changes, enhancing segmentation of rigid-body motions.

Findings

More robust detection of submotions

Improved segmentation consistency

Validated on real and simulated data

Abstract

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.