Structure-Preserving Learning Using Gaussian Processes and Variational Integrators
This work addresses the need for safe and accurate modeling of mechanical systems in robotics or control applications, though it is incremental as it builds on existing methods.
The authors tackled the problem of learning unknown dynamical systems by combining Gaussian process regression with variational integrators to preserve physical properties like energy conservation and constraint satisfaction, achieving exact constraint satisfaction and desirable energy conservation in simulations.
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some generic discretization technique, which might however disregard properties of the underlying physical system. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation and satisfaction of explicit kinematic constraints. In this work, we present a novel structure-preserving learning-based modelling approach that combines a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with general theoretical results and demonstrates exact constraint satisfaction for constrained dynamical systems.