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

TL;DR

A novel trajectory representation for rigid-body motions that incorporates both translation and rotation, and additionally exhibits several invariant properties is proposed, consisting of a geometric progress rate and a third-order trajectory-shape descriptor.

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.

Figures (8)

• Figure 1: Interpretation of the proposed progress rate $\dot{s}$ as the linear velocity of a point on the moving body at a distance $L$ from the ISA.
• Figure 2: Illustration of a pure couple of rotations $\boldsymbol{\omega}$ generating a pure translation $\boldsymbol{\nu}$ out of the plane. The two rotation axes, distanced by two times $a$, are depicted with dotted lines.
• Figure 3: Point $\boldsymbol{\tilde{p}}$ is defined as a characteristic reference point on the body. When $\boldsymbol{p}_\perp$ is within the spherical region with radius $b$, then $\boldsymbol{\tilde{p}} = \boldsymbol{p}_\perp$. Outside the sphere, $\boldsymbol{\tilde{p}}$ is the projection of $\boldsymbol{p}_\perp$ on the sphere's surface.
• Figure 4: Visualization of three rigid-body trajectories (red, green, and blue) representing simulated pouring motions performed with a kettle. Different body reference points ( P1, P2 and P3) were considered.
• Figure 5: (a) Human demonstration of a pouring motion using a teakettle to which an HTC VIVE tracker is attached. (b) Visualization of the first trial within a batch of six trials in the same simulation environment as Fig. \ref{['fig:simulated_pouring_motion']}.