Path Tracking for Automated Driving: A Tutorial on Control System Formulations and Ongoing Research

In automated driving system architectures (see the classification according to [1]), three layers can be typically defined [2]: (i) The perception layer, aimed at detecting the conditions of the environment surrounding the vehicle, e.g., by identifying the appropriate lane and the presence of obstacles on the track; (ii) The reference generation layer, providing the reference signals, e.g., in the form of the reference trajectory to be followed by the vehicle, based on the inputs from the perception layer; (iii) The control layer, defining the commands required for ensuring the tracking performance of the reference trajectory. These commands are usually expressed in terms of reference steering angles (usually on the front axle only) and traction/braking torques. This chapter focuses on the control layer and, in particular, the steering control for autonomous driving, also defined as path tracking control. The foundations of path tracking control for autonomous driving date back to well-known theoretical and experimental studies on robotic systems and driver modeling, detailed in several papers and textbooks (e.g., see the driver model descriptions in [3–9]). Moreover, automated driving experiments with different controllers have been conducted since the 1950s and 1960s, by using inductive cables or magnetic markers embedded in roadways to indicate the reference path [10, 11]. This contribution presents a survey of the main control techniques and formulations adopted to ensure that the automatically driven vehicles follow the reference trajectory, including analysis of extreme maneuvering conditions. The discussion will be based on a selection of different control structures, at increasing levels of complexity and performance. The focus will be on whether complex steering controllers are actually beneficial to autonomous driving. This is an important point, considering that Stanley and Sandstorm, the vehicles that obtained the first two places at the DARPA Grand Challenge (2004–2005), used very simple steering control laws based on kinematic vehicle models. In contrast to this, Boss, the autonomous vehicle winning the DARPA Urban Challenge (2007), was characterized by a far more advanced model predictive control strategy [12–15]. The main formulas for the different steering control structures will be concisely provided as a tutorial on the control system implementations, so that the reader can actually appreciate the characteristics of each formulation, and ultimately refer to the original papers in the case of specific interest. Also, the main simulation and experimental results obtained through the implementation of each control structure will be reported and critically analyzed. The chapter is organized as follows: • Section 5.2 presents path tracking methods based on simple geometric relationships, and a chained controller relying on a vehicle kinematic model, i.e., developed under the approximation of zero slip angles on the front and rear tires. • The first part of Sect. 5.3 deals with conventional feedback controllers designed with a simplified dynamic model of the vehicle system, i.e., the well-known linear single-track vehiclemodel. The second half of Sect. 5.3 discusses relatively simple optimal control formulations, e.g., linear quadratic regulators, without and with feedforward contributions, and including the concept of preview in their most advanced declination. The layout of Sects. 5.2 and 5.3 mostly follows the guideline of a very relevant previous survey work [16], dating back to 2009, which critically assessed path tracking control methods through vehicle simulations with the software package CarSim. • Section 5.4 discusses a couple of sliding mode formulations, one of them based on the important concept of center of percussion, and briefly mentions other examples of path tracking controllers, e.g., based on H1 control and backstepping control. • Section 5.5 presents in detail the latest developments in the subject area, through a selection of examples of advanced controllers (i.e., path tracking controllers for autonomous racing and model predictive controllers) from recently published papers, including critical analysis of their specific benefits. • Section 5.6 provides concluding remarks and ideas for future research on the subject