## 1 Introduction  
Over the past decade, research groups and the automobile industry have intensively explored autonomous driving because it is predicted to have impacts on several aspects of driving such as traffic flow, ride comfort, and road safety [1; 2; 3]. With respect to safety, autonomous driving has been expected to reduce social costs and damages incurred from drivers by preventing traffic accidents. As a result, a huge amount of papers on autonomous driving have been published in the meantime. According to the survey, it has been widely known that autonomous driving operations include perception, localization, planning, control and navigation, and system management [3]. Among them, planning or path planning generates a reference or target path based on information obtained from environments, and path tracking controls a vehicle, following the reference states with several actuators. This paper focuses on path tracking control (PTC). For the last decade, PTC has been intensively explored [4; 5; 6]. Consequently, a huge deal of papers have been published to date in the field of PTC [4; 5; 6; 7; 8; 9; 10]. To date, most path tracking controllers for autonomous driving have been designed on a high-friction road surface where the tire-road friction coefficient, \(\mu\), was set between 0.8 and 1.0. Since 2019, some papers concentrating on PTC under low-friction road conditions have been published [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. These papers are classified according to controller design methodologies, input configurations, actuator combinations and tire-road friction coefficient, as given in Table 1. As shown in Table 1, the lower limits of \(\mu\) were set between 0.25 and 0.4. In this paper, a low friction road condition means that \(\mu\) is 0.4 or less. In Table 1, \(\delta_{f}\), \(\delta_{r}\), \(\Delta F_{x}\) and \(\Delta M_{z}\) are the control inputs, which represent the front and rear steering angles, the control longitudinal force, and the control yaw moment, respectively. An input configuration is composed of those control inputs. In Table 1, seven input configurations were given. With those input configurations, a linear quadratic regulator (LQR), model predictive control (MPC), and sliding mode control (SMC) were adopted as a controller design methodology. From the point of view of an actuator for PTC, front wheel steering (FWS), rear wheel steering (RWS) and 4-wheel steering (4 WS) have been selected as an actuator for PTC to date. For the last decade, by virtue of development of in-wheel motor or e-corner module systems, 4-wheel independent steering/braking/driving (4 WIS/4 WIB/4 WID) has been available for vehicle stability control (VSC) and PTC. Several actuator combinations can be composed of those actuators, as shown in Table 1. If \(\Delta M_{z}\) or \(\Delta F_{x}\) is selected as a control input, a control allocation is needed to distribute it the control tire forces generated by RWS, 4 WID and 4 WIB. Naturally, on a low-friction road surface, the magnitudes of longitudinal and lateral tire forces, \(F_{x}\) and \(F_{y}\), become small because \(\mu\) is low [33; 34]. Among them, \(F_{y}\)'s generated at front wheels have significant effects on path tracking performance in cornering. Figure 1 shows \(F_{y}\) with respect to the tire slip angle, \(\alpha\), and \(\mu\). In Figure 1, the values of the tire slip angles, \(\alpha_{m}\) and \(\alpha_{\infty}\), are \(5^{\circ}\) and \(20^{\circ}\), which give the maximum and saturated lateral tire forces, \(F_{y,max}\) and \(F_{y,\infty}\), respectively. As shown in Figure 1, \(F_{y}\) is saturated and decreased to \(F_{y,\infty}\) as \(\alpha\) increases to \(\alpha_{\infty}\) over \(\alpha_{m}\) where \(F_{y,max}\) is generated. In other words, \(F_{y}\) becomes \(F_{y,\infty}\), which is smaller than \(F_{y,max}\) due to larger slip angle \(\alpha_{\infty}\) over \(\alpha_{m}\). For example in Figure 1, 16% of \(F_{y,max}\) is reduced at \(\alpha_{\infty}\) when \(\mu\) is 0.6.