Maxim Vochten

Arno Verduyn, Erwin Aertbeliën, Maxim Vochten et al.

Identifying the trajectories of rigid bodies and of interaction forces is essential for a wide range of tasks in robotics, biomechanics, and related domains. These tasks include trajectory segmentation, recognition, and prediction. For these tasks, a key challenge lies in achieving consistent results when the trajectory is expressed in different coordinate systems. A way to address this challenge is to utilize trajectory models that can generalize across coordinate systems. The focus of this paper is on such trajectory models obtained by transforming the trajectory into a coordinate-invariant representation. However, coordinate-invariant representations often suffer from sensitivity to measurement noise and the manifestation of singularities in the representation, where the representation is not uniquely defined. This paper aims to address this limitation by introducing the novel Dual-Upper-Triangular Invariant Representation (DUTIR), with improved robustness to singularities, along with its computational algorithm. The proposed representation is formulated at a level of abstraction that makes it applicable to both rigid-body trajectories and interaction-force trajectories, hence making it a versatile tool for robotics, biomechanics, and related domains.

Arno Verduyn, Maxim Vochten, Joris De Schutter

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.

Arno Verduyn, Erwin Aertbeliën, Glenn Maes et al.

When similar object motions are performed in diverse contexts but are meant to be recognized under a single classification, these contextual variations act as disturbances that negatively affect accurate motion recognition. In this paper, we focus on contextual variations caused by reference frame variations. To robustly deal with these variations, similarity measures have been introduced that compare object motion trajectories in a context-invariant manner. However, most are highly sensitive to noise near singularities, where the measure is not uniquely defined, and lack bi-invariance (invariance to both world and body frame variations). To address these issues, we propose the novel \textit{Bi-Invariant Local Trajectory-Shape Similarity} (BILTS) measure. Compared to other measures, the BILTS measure uniquely offers bi-invariance, boundedness, and third-order shape identity. Aimed at practical implementations, we devised a discretized and regularized version of the BILTS measure which shows exceptional robustness to singularities. This is demonstrated through rigorous recognition experiments using multiple datasets. On average, BILTS attained the highest recognition ratio and least sensitivity to contextual variations compared to other invariant object motion similarity measures. We believe that the BILTS measure is a valuable tool for recognizing motions performed in diverse contexts and has potential in other applications, including the recognition, segmentation, and adaptation of both motion and force trajectories.

Arno Verduyn, Maxim Vochten, Joris De Schutter

The ability of robots to recognize human gestures facilitates a natural and accessible human-robot collaboration. However, most work in gesture recognition remains rooted in reference frame-dependent representations. This poses a challenge when reference frames vary due to different work cell layouts, imprecise frame calibrations, or other environmental changes. This paper investigated the use of invariant trajectory descriptors for robust hand palm motion gesture recognition under reference frame changes. First, a novel dataset of recorded Hand Palm Motion (HPM) gestures is introduced. The motion gestures in this dataset were specifically designed to be distinguishable without dependence on specific reference frames or directional cues. Afterwards, multiple invariant trajectory descriptor approaches were benchmarked to assess how their performances generalize to this novel HPM dataset. After this offline benchmarking, the best scoring approach is validated for online recognition by developing a real-time Proof of Concept (PoC). In this PoC, hand palm motion gestures were used to control the real-time movement of a manipulator arm. The PoC demonstrated a high recognition reliability in real-time operation, achieving an $F_1$-score of 92.3%. This work demonstrates the effectiveness of the invariant descriptor approach as a standalone solution. Moreover, we believe that the invariant descriptor approach can also be utilized within other state-of-the-art pattern recognition and learning systems to improve their robustness against reference frame variations.