# Risk-Sensitive Rear-Wheel Steering Control Method Based on the Risk Potential Field
## 1 Introduction  
Autonomous driving systems have been practically used for normal driving as well as emergency avoidance driving to realize a safe and comfortable traffic system. Several autonomous driving systems, such as the lane keep assist system and automatic emergency steering, already exist in practical use. However, the control laws of these driving assistance systems differ in each situation. To achieve more versatile autonomous driving, it is necessary to develop a driving assistance system that can be designed with a uniform control law for both normal driving and emergency avoidance driving. Therefore, the risk potential field is used as a uniform control law in this study. There are many classic risks in vehicle dynamics control, such as sideslip, rollover, and collision. In a previous study, a rollover prevention system using a steer-by-wire system was proposed [1]. In this study, a risk potential field is used to reduce the collision risk among possible risks in vehicle control. Several studies have investigated this control method and applied it to various situations, such as highway merging scenes, emergency avoidance scenes, and shared control [2; 3; 4; 5; 6]. As a previous study in our research group, [PERSON] et al. applied a dynamic risk potential to a highway merging scene, wherein the risk potential changed based on the risk of road deviations. The system controls the steering angle, acceleration, and deceleration to drive safely without colliding with other vehicles or road boundaries. The simulation results showed that the dynamic risk potential could reproduce merging behavior identical to that of an expert driver [3]. As an another example of previous work, [PERSON] et al. applied the risk potential field to a shared control: a driver assistance system with both the human and machine controlling the vehicle. Herein, the driver and machine cooperate to ensure safe driving. They developed motionplanning for obstacle avoidance based on the risk potential field and proposed a control method that combined steering torque control with the direct yaw moment control. The results confirmed an improvement in the steering cooperativity between the driver and machine [4]. This series of papers describes how active chassis control technologies can potentially improve the safety of a vehicle in lane keeping and obstacle avoidance driving scenarios while keeping good cooperative driving between the driver and the machine. However, the control inputs are torque to the steering wheel or the braking and driving force to the tires in these control laws, and they do not control the rear steering angle. Nevertheless, several studies have explored four-wheel steering (4 WS) that steers the rear wheels [7]. A study compared the performance of zero-sideslip angle 4 WS and no phase lag in lateral acceleration 4 WS [8]. Recently, 4 WS equipped with actuators has been practically implemented. [PERSON] et al. developed a 4 WS system that improves turning performance at low velocity and vehicle stability at high velocity without affecting the comfort of the driver [9]. However, in these studies, the rear wheels only improved the vehicle dynamics and did not contribute to autonomous driving. [PERSON] proposed the vehicle control in obstacle avoidance situation and compared the performance of various active chassis control systems [10]. [PERSON] et al. studied obstacle avoidance performance using evasive steering maneuvers, including rear steering control [11]. [PERSON] et al. proposed the control of a four-wheel independent steer-by-wire system for robust steering command tracking [12; 13]. Recently, [PERSON] et al. presented the control of rear axle steering in a long-wheelbase production vehicle which can be used for improving handling dynamics and automated parking [14]. In this research, full automation using four-wheel steering control is discussed, while the cooperative driving and characteristics between the human and the system are still research issues.