Learning-Based Model Predictive Control for Autonomous Racing

Abstract

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.

Learning-Based Model Predictive Control: Toward Safe Learning in Control

“…Due to its nonparametric nature, GP regression is particularly well suited to identifying discrepancies with a nominal system model, which are challenging to parameterize. Many techniques use the residual model uncertainty estimate to provide a heuristic constraint tightening and practical safety margins, as shown in Figure 2 for an autonomous racing application (86,90).…”

“…Techniques to address this issue include data selection and maintenance of a dictionary of data points of limited size, computational approximations of the GP [e.g., via inducing points (93) or selected basis functions (94)], and neglecting or simplifying the variance dynamics (i.e., the evolution of the uncertainty). Building on these ideas, successful applications of GP-based MPC to robotic systems have been presented, e.g., for trajectory tracking with robotic manipulators (95), path following of off-road mobile robots (87,96), autonomous racing (86,90,97), process control (98), and telescope systems in the context of periodic additive disturbances (99). Using autoregressive models, Jain et al (100) presented a simulation study for building control and demand response, which additionally addresses the problem of suitable exploration by maximizing the information gain.…”

“…Figure 2Gaussian process-based model predictive control for autonomous racing. (a) Application to a full-sized race car(90), showing the position constraint set (red); the predicted trajectory including uncertainty (gray), which is used for constraint tightening; and selected data points from previous rounds (green spheres). (b,c) The resulting trajectories of a similar approach applied to miniature radio-controlled cars(86), with the initial nominal controller shown in panel b and the improved trajectories after learning shown in panel c. For videos of these experiments, see References 91 and 92.…”

Adaptive Safe Distance Prediction Using MPC for Bridge Cranes Considering Anti-Swing in Dynamic Environment

“…where u 1 and u 2 are Lagrange multipliers of constraints (17), u 3 and u 4 are Lagrange multipliers of constraints (18)…”

Using First Principles for Deep Learning and Model-Based Control of Soft Robots

“…Among these, data-driven modeling specifically addresses many difficulties of physics-based modeling for control. Generally, data-driven control algorithms are based on various forms of machine learning, such as neural networks as in Thuruthel et al ( 2017 ) and Mohajerin et al ( 2018 ), Gaussian processes (GP) in Ostafew et al ( 2016 ), Kabzan et al ( 2019 ), Soloperto et al ( 2018 ), and Hewing et al ( 2020 ), reinforcement learning (RL) as in Thuruthel et al ( 2019 ), or sparse optimization (also known as SINDY) as in Kaiser et al ( 2018 ). Notably, deep learning has proven to be a valuable tool for robot modeling and control and is explored thoroughly in Pierson and Gashler ( 2017 ) and Sünderhauf et al ( 2018 ).…”