Accurate physical modeling of vehicle dynamics requires extensive a priori knowledge of the studied vehicle. In contrast, data-driven modeling approaches require only a set of data that are a good account of the vehicle's driving envelope. In this brief, we compare, for the first time, the prediction capabilities of both approaches applied to a large-scale real-world driving data set. The data set contains several cornering maneuvers, acceleration, and deceleration stages and was collected over public roads. Linear and nonlinear physical models were identified through nonlinear optimization of their unknown parameters. Closed-form subspace identification methods were used to initialize the estimate of a linear state-space model, and the initialization was then refined through nonlinear optimization. The optimized models were validated against 59 km of independent driving data. The model fits, in the longitudinal velocity, were 68.9% versus 80.2% for the nonlinear physical model and linear data-driven (second-order) model, respectively, and, in the yaw rate, 43.0% versus 63.5%. These results show that, for this vehicle, a simple linear data-driven model outperformed both linear and nonlinear physical models under real-world driving conditions. This has important implications for control design approaches in autonomous vehicles.

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.

This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists in breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part.