Vehicle sideslip estimation

2009 IEEE Control Systems  
Control systems that help the driver avoid accidents, or limit the damage in case of an accident, have become ubiquitous in modern passenger cars. For example, new cars typically have an anti-lock braking system (ABS), which prevents the wheels from locking during hard braking, and they often have an electronic stability control system (ESC), which stabilizes the lateral motion of the vehicle to prevent skidding. Collision warning and avoidance, rollover prevention, crosswind stabilization, and
more » ... preparation for an impending accident by adjusting seat positions and seat belts are additional examples of control systems for automotive safety. These systems rely on information about the state of the vehicle and its surroundings. To obtain this information, modern cars are equipped with various sensors. For a typical car with an ESC system, necessary measurements include the steering wheel angle, wheel angular velocities, lateral acceleration, and the rate of rotation around the vertical body-fixed axis, known as the yaw rate. These measurements alone contain a great deal of information about the state of the vehicle. The speed of the car can be estimated using the wheel angular velocities, and a linear reference model taking the speed, steering wheel angle, and additional measurements as inputs can be used to predict the behavior of the car under normal driving conditions. The predicted 1 behavior can be compared to the actual behavior of the car; ESC systems, for example, use the brakes to correct the deviation from a yaw reference model when the vehicle starts to skid [1]. Although some quantities are easily measured, others are difficult to measure because of high cost or impracticality. When some quantity cannot be measured directly, it is often necessary to estimate it using the measurements that are available. Observers combine the available measurements with dynamic models to estimate unknown dynamic states. Often, dynamic models of sufficient accuracy are not available, and must be carefully constructed as part of the observer design. The observer estimates can be used to implement control algorithms, as Figure 1 illustrates. Vehicle Sideslip Angle When a car is driven straight on a flat surface, the direction of travel at the center of gravity (CG) remains the same as the orientation of the vehicle (that is, the direction of the longitudinal axis). When the car turns, however, it exhibits a yaw rate, causing the orientation to change, and a lateral acceleration directed toward the center of the turn. The car also exhibits a velocity component perpendicular to the orientation, known as the lateral velocity. Nonzero lateral velocity means that the orientation of the vehicle and the direction of travel are no longer the same. The lateral velocity differs from one point on the vehicle body to another; as a point of reference, we use the vehicle's CG. The angle between the orientation of the vehicle and the direction of travel at the CG is called the vehicle sideslip angle. In production cars, the vehicle sideslip angle is not measured, because this measurement requires expensive equipment such as optical correlation sensors. 2 Under normal circumstances, when the car is driven safely without danger of losing road grip, the vehicle sideslip angle is small, not exceeding˙2 ı for the average driver [1] . Moreover, for a given speed in normal driving situations, the steering characteristics specify a tight connection between the steering wheel angle, yaw rate, lateral acceleration, and vehicle sideslip angle. The vehicle sideslip angle can therefore be estimated using a static model or a simple linear, dynamic model. In extreme situations, however, when the vehicle is pushed to the physical limits of adhesion between the tires and the road surface, the behavior of the car is highly nonlinear, and the tight coupling of the vehicle sideslip angle to various measured quantities is lost. This behavior is due to the nonlinearity of the friction forces between the tires and the road surface. In these situations, the vehicle sideslip angle can become large, and knowledge about it is essential for a proper description of vehicle behavior. Accurate online estimation of the vehicle sideslip angle has the potential to enable development of new automotive safety systems, and to improve existing algorithms that use information about the vehicle sideslip angle, such as ESC. Previous Research Many designs for estimating velocity and sideslip angle are found in the literature. These designs are typically based on linear or quasi-linear techniques [2]-[5]. A nonlinear observer linearizing the observer error dynamics is presented in [6], [7]. An observer based on forcing the dynamics of the nonlinear estimation error to follow the dynamics of a linear reference system is investigated in [8], [9]. In [8], [9] availability of the longitudinal road-tire friction forces is assumed, whereas in [10] the longitudinal forces used in the estimation algorithm are calculated from the brake pressure, clutch position, and throttle angle. An extended Kalman filter (EKF) based on a road-tire friction model, which includes estimation of a road-tire friction coefficient,
doi:10.1109/mcs.2009.934083 fatcat:fliyuw7ab5fc5dja47unus4omm