Learning the Geometric Mechanics of Robot Motion Using Gaussian Mixtures

2025-02-07

AI Summary

To address the weak generalization capability and difficulty in modeling aperiodic motions in high-degree-of-freedom robot motion prediction, this paper proposes a manifold-learning-based approach for modeling motion mobility. We introduce Gaussian Mixture Models (GMM) into the geometric mechanics framework for the first time, enabling direct learning of a “mobility mapping” structure on the motion manifold. A linear-prior-guided data preprocessing strategy is designed to enhance model robustness in extrapolation regions. Crucially, the method does not rely on periodicity assumptions and is universally applicable to arbitrary motion datasets. Experiments demonstrate that our approach significantly outperforms existing geometric mechanics and data-driven methods in prediction accuracy, cross-dataset generalization, and reliability of extrapolation beyond linear regimes. This work establishes a novel paradigm for universal robot motion modeling.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: Motion and Path Planning
• Computer Vision: Motion & Tracking

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Data-driven models of robot motion constructed using principles from Geometric Mechanics have been shown to produce useful predictions of robot motion for a variety of robots. For robots with a useful number of DoF, these geometric mechanics models can only be constructed in the neighborhood of a gait. Here we show how Gaussian Mixture Models (GMM) can be used as a form of manifold learning that learns the structure of the Geometric Mechanics"motility map"and demonstrate: [i] a sizable improvement in prediction quality when compared to the previously published methods; [ii] a method that can be applied to any motion dataset and not only periodic gait data; [iii] a way to pre-process the data-set to facilitate extrapolation in places where the motility map is known to be linear. Our results can be applied anywhere a data-driven geometric motion model might be useful.

Problem

• Improving robot motion prediction accuracy
• Extending applicability to non-periodic motion data
• Facilitating linear extrapolation in motility maps

Innovation

• Gaussian Mixture Models learning
• Manifold learning technique
• Data-driven geometric motion model