Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control

TL;DR

This paper introduces a method for controlling unstable robotic systems efficiently using Gaussian Process differentiation to create accurate, state-dependent linearized models from minimal data, enabling robust predictive control.

Contribution

It leverages Gaussian Process differentiability to produce accurate, data-efficient models for unstable systems, enhancing control robustness with minimal training data.

Findings

Successfully learned dynamics of a segway with only one minute of data.

The controller demonstrated robustness to unmodelled dynamics and disturbances.

Outperformed nominal model-based control methods under perturbations.

Abstract

We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized approximation of the true continuous dynamics that can be integrated with model predictive control. Our approach is compatible with most Gaussian process approaches for system identification, and can learn an accurate model using modest amounts of training data. We validate our approach by learning the dynamics of an unstable system such as a segway with a 7-D state space and 2-D input space (using only one minute of data), and we show that the resulting controller is robust to unmodelled dynamics and disturbances, while state-of-the-art control methods based on nominal models can fail under small perturbations. Code is open sourced at https://github.com/learning-and-control/core .