Prediction with Approximated Gaussian Process Dynamical Models

TL;DR

This paper introduces approximated Gaussian process dynamical models (GPDMs) that are Markovian, enabling better control analysis and reducing computational costs, thus improving modeling of complex dynamical systems like soft robotics.

Contribution

The paper proposes a novel approximation of GPDMs that are Markovian, analyzes their control properties, and demonstrates reduced computational time with maintained accuracy.

Findings

Approximated GPDMs are Markovian, facilitating control analysis.

The approximation reduces computational time significantly.

Numerical examples validate the effectiveness of the approximated models.

Abstract

The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often challenging or even infeasible due to the complexity of the system dynamics. In contrast, data-driven approaches need only a minimum of prior knowledge and scale with the complexity of the system. In particular, Gaussian process dynamical models (GPDMs) provide very promising results for the modeling of complex dynamics. However, the control properties of these GP models are just sparsely researched, which leads to a "blackbox" treatment in modeling and control scenarios. In addition, the sampling of GPDMs for prediction purpose respecting their non-parametric nature results in non-Markovian dynamics making the theoretical analysis challenging. In this article, we present approximated GPDMs which are Markov and analyze their control theoretical properties. Among others, the approximated error is analyzed and conditions for boundedness of the trajectories are provided. The outcomes are illustrated with numerical examples that show the power of the approximated models while the the computational time is significantly reduced.