Dynamic Gaussian Process Models for Model Predictive Control of Vehicle Roll

Abstract

The machine learning method Gaussian process (GP) regression is used to learn the vehicle dynamics without any prior knowledge. The model formed with GP regression demonstrates characteristics that make it useful in model predictive control (MPC). Previous applications of model predictive control used linearized models to balance the need for fast computation and predictive accuracy. This work aims to make nonlinear predictions in a timely manner. A method of clustering the training data is also developed in order to further speed calculation of dynamic predictions necessary for MPC. An architecture to take advantage of the nature of GP regression calculations is then developed. The efficacy of the approach is examined through training and validation using data recorded from an instrumented all-terrain vehicle (ATV) and through a series of simulations.

The instrumented all-terrain vehicle allowed GPS, inertial, and encoder data to be used for training and validation of the GP-based dynamic model. A series of maneuvers approximating sinusoids of varying frequency and amplitude is used to excite the vehicle for the purpose of generating a training dataset. That training dataset allows GP regression to learn the functions describing a nonlinear state-space model of the vehicle dynamics. The data recorded during a separate set of maneuvers is used to validate the predictions generated from the GP-based model. The speed of computation is examined and methods of speeding the nonlinear portion of GP regression are presented. The result of this is a model that can provide accurate estimates in a timely fashion. The speed of computation is sufficient to allow for MPC to be implemented on a modest, contemporary desktop PC.

A method of further decreasing computation time is then presented. Clustering of training data has been mentioned in the literature though specifics regarding the choice of algorithm and parameter selection are conspicuously omitted. Clustering has been applied in the closely related method of support vector machine classification where similarity is easily defined. A definition of similarity is offered here for the purposes of regression. An algorithm is selected to leverage that definition of similarity. Parameter selection is addressed by basing the cluster size on the characteristic length scale of the function being regressed. Evaluation of the clustering algorithm and parameter is performed on two illustrative examples as well as the GP model formed from the recorded ATV data.