Fast Tube Model Predictive Control for Driverless Cars Using Linear Data-Driven Models

Model predictive control (MPC) has been widely applied to different aspects of autonomous driving, typically using nonlinear physically derived models for prediction. However, feedback control systems inherently correct for model errors, and thus in many applications it is sufficient to use a linear time-invariant (LTI) model for control design, especially when using robust control methods. This philosophy of approach appears to have been neglected in current driverless car research and is the research gap that we aim to address here. Namely, instead of deriving meticulous nonlinear physical models of vehicle dynamics and solving a correspondingly complex optimal control problem (OCP), we identify a low-order data-driven LTI model and handle its uncertainty via robust linear MPC methods. We develop a two-step control scheme for driverless cars based on tube MPC (TMPC), which introduces structural robustness, ensuring constraint compliance despite modeling error in the data-driven prediction model. Furthermore, we use fast optimization methods designed to exploit the special structure of the linear MPC problem. We evaluate the proposed control scheme using a vehicle model identified from real-world data and simulations in IPGCarmaker, where the model of the vehicle under control is inherently nonlinear and uses detailed 3-D physics. Our results show that an LTI model can be effectively used for the task of lane-keeping, that TMPC can prevent lane departure and possible collisions due to model uncertainty, and that linear models allow for several algorithmic improvements that can decrease computation time by an order of magnitude compared with naive MPC implementations.