Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes

TL;DR

This paper introduces a Gaussian process model that integrates analytical mechanics principles, specifically Gauss' principle, to efficiently learn constrained dynamics of mechanical systems while respecting constraints and enabling knowledge transfer.

Contribution

It combines Gaussian process regression with Gauss' principle to improve data efficiency and constraint adherence in modeling constrained mechanical systems.

Findings

Model predicts system acceleration respecting constraints.

Enables inference of unconstrained acceleration from constrained data.

Facilitates transfer of knowledge across different constraint setups.

Abstract

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model's data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere to Gauss' principle of least constraint. In return, predictions of the system's acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations.