Semiparametrical Gaussian Processes Learning of Forward Dynamical Models for Navigating in a Circular Maze

TL;DR

This paper introduces a semiparametric Gaussian Process model for learning complex ball dynamics in a circular maze, enabling accurate prediction and trajectory optimization for navigation tasks.

Contribution

It combines physics-based basis functions with Gaussian Process Regression to improve modeling of non-linear, contact-influenced dynamics in a navigation environment.

Findings

Semiparametric model outperforms standard algorithms in prediction accuracy.

Model effectively estimates complex non-linear dynamics including friction and contact effects.

Proposed system serves as a reproducible benchmark for reinforcement and robot learning.

Abstract

This paper presents a problem of model learning for the purpose of learning how to navigate a ball to a goal state in a circular maze environment with two degrees of freedom. The motion of the ball in the maze environment is influenced by several non-linear effects such as dry friction and contacts, which are difficult to model physically. We propose a semiparametric model to estimate the motion dynamics of the ball based on Gaussian Process Regression equipped with basis functions obtained from physics first principles. The accuracy of this semiparametric model is shown not only in estimation but also in prediction at n-steps ahead and its compared with standard algorithms for model learning. The learned model is then used in a trajectory optimization algorithm to compute ball trajectories. We propose the system presented in the paper as a benchmark problem for reinforcement and robot learning, for its interesting and challenging dynamics and its relative ease of reproducibility.