Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.

Recent successes in the field of machine learning, as well as the availability of increased sensing and computational capabilities in modern control systems, have led to a growing interest in learning and data-driven control techniques. Model predictive control (MPC), as the prime methodology for constrained control, offers a significant opportunity to exploit the abundance of data in a reliable manner, particularly while taking safety constraints into account. This review aims at summarizing and categorizing previous research on learning-based MPC, i.e., the integration or combination of MPC with learning methods, for which we consider three main categories. Most of the research addresses learning for automatic improvement of the prediction model from recorded data. There is, however, also an increasing interest in techniques to infer the parameterization of the MPC controller, i.e., the cost and constraints, that lead to the best closed-loop performance. Finally, we discuss concepts that leverage MPC to augment learning-based controllers with constraint satisfaction properties.

In this paper, we present a learning-based control approach for autonomous racing with an application to the AMZ Driverless race car gotthard. One major issue in autonomous racing is that accurate vehicle models that cover the entire performance envelope of a race car are highly nonlinear, complex and complicated to identify, rendering them impractical for control. To address this issue, we employ a relatively simple nominal vehicle model, which is improved based on measurement data and tools from machine learning. The resulting formulation is an online learning data-driven Model Predictive Controller, which uses Gaussian Processes regression to take residual model uncertainty into account and achieve safe driving behavior. To improve the vehicle model online, we select from a constant inflow of data points according to a criterion reflecting the information gain, and maintain a small dictionary of 300 data points. The framework is tested on the full-size AMZ Driverless race car, where it is able to improve the vehicle model and reduce lap times by 10% while maintaining safety of the vehicle.

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning.

High-precision trajectory tracking is fundamental in robotic manipulation. While industrial robots address this through stiffness and high-performance hardware, compliant and cost-effective robots require advanced control to achieve accurate position tracking. In this paper, we present a model-based control approach, which makes use of data gathered during operation to improve the model of the robotic arm and thereby the tracking performance. The proposed scheme is based on an inverse dynamics feedback linearization and a data-driven error model, which are integrated into a model predictive control formulation. In particular, we show how offset-free tracking can be achieved by augmenting a nominal model with both a Gaussian Process, which makes use of offline data, and an additive disturbance model suitable for efficient online estimation of the residual disturbance via an extended Kalman filter. The performance of the proposed offset-free GPMPC scheme is demonstrated on a compliant 6 degrees of freedom (DoF) robotic arm, showing significant performance improvements compared to other robot control algorithms.