Clustering of Motion Trajectories by a Distance Measure Based on Semantic Features

TL;DR

This paper tackles clustering of motion trajectories by compressing raw trajectories into sequences of semantic features (extrema, active constraints, roots) and measuring similarity with an SVRspell-based string-kernel distance that includes soft-matching and gap penalties. Distances across per-dimension feature sequences are combined into $d_{\text{final}} = (\sum_{i=1}^{n+m} d_i)^{-\frac{1}{2}}$ and fed to agglomerative hierarchical clustering with a single-linkage strategy. Across Furuta pendulum, Manutec r3 arm, and a real-world human-motion dataset, the approach yields competitive or superior clustering performance compared to DTW while delivering substantial runtime advantages, particularly for long trajectories. The method is flexible, interpretable, and memory-efficient, making it suitable for building scalable hierarchical motion databases and task-specific clustering in human–robot interaction settings.

Abstract

Clustering of motion trajectories is highly relevant for human-robot interactions as it allows the anticipation of human motions, fast reaction to those, as well as the recognition of explicit gestures. Further, it allows automated analysis of recorded motion data. Many clustering algorithms for trajectories build upon distance metrics that are based on pointwise Euclidean distances. However, our work indicates that focusing on salient characteristics is often sufficient. We present a novel distance measure for motion plans consisting of state and control trajectories that is based on a compressed representation built from their main features. This approach allows a flexible choice of feature classes relevant to the respective task. The distance measure is used in agglomerative hierarchical clustering. We compare our method with the widely used dynamic time warping algorithm on test sets of motion plans for the Furuta pendulum and the Manutec robot arm and on real-world data from a human motion dataset. The proposed method demonstrates slight advantages in clustering and strong advantages in runtime, especially for long trajectories.

Figures (8)

• Figure 1: The two events start of constrained arc ($\lbrace$) and end of constrained arc ($\rbrace$) and are merged into a single event constrained arc ($\varhexstar$) in the center of the constraint.
• Figure 2: Example of two simple trajectories, both have two features each, in different temporal distance.
• Figure 3: Example showing the representation of a trajectory graph with a feature sequence.
• Figure 4: The hierarchical structure of the clustering of test set Furuta 1 using different distance measures. The ground truth is given as colored bar on the x-axis.
• Figure 5: The hierarchical structure of the clustering of test sets Furuta 2 and Furuta 3 using different distance measures.