附 录A 外文文献Calculating Longitudinal Wheel Slip and Tire Parameters Using GPS VelocityABSTRACTWhile tire parameters are quite important to both current vehicle control systems and proposed future systems, these parameters are subject to considerable variability and are difficult to estimate while driving due to the unavailability of absolute vehicle velocity. This paper details a method of generating longitudinal tire force-slip curves using absolute velocity information from the Global Positioning System (GPS). By combining GPS measurements with measured wheel speeds, the effective tire radius and longitudinal stiffness of the tires can be identified using a simple least-squares regression technique. Preliminary results demonstrate the feasibility of the technique, show that the effective radius can be identified with considerable precision and suggest that the identified longitudinal stiffness exhibits noticeable sensitivity to changes in inflation pressure.INTRODUCTIONThe longitudinal forces that produce acceleration and braking on ground vehicles with pneumatic tires arise due to deformation and sliding in the tire contact patch. While the actual motions that take place in the contact patch are somewhat complex, the force generation can generally be described with sufficient accuracy in terms of wheel slip a measure of the difference between the rotational speed of the wheel. and the translational velocity of the wheel center. The standard SAE definition of wheel slip is where V is the longitudinal speed of the wheel center, w is the angular speed of the tire and R, is the effective tire radius. The effective radius is defined to be the radius of the tire when rolling with no external torque applied about the spin axis. Since the tire flattens in the contact patch, this value lies somewhere between the tires undeformed radius and static loadearadius.A number of different tire models for predicting tire longitudinal force in terms of wheel slip have been derived from empirical data. Such models generally relate thelongitudinal force on a tire to the wheel slip for given values of normal force, road surface conditions, tire characteristics, and other factors (such as camber angle). Figure 1 demonstrates the general shape of such a curve generated from the commonly-used “Magic Formula” tire model . While models vary, several of the traits shown in Figure 1 are common to various mathematical models and empirical test data. First, the relation between force and slip is roughly linear at low values of slip below the point at which significant sliding occurs in the contact patch. In this region, force can be approximated as proportional to slip using an effective longitudinal stiffness of the tire. The stiffness depends on the foundation stiffness of the tire and the length of the contact patch between the tire and the road . As a result, this value depends strongly upon tire construction and inflation pressure. Beyond this linear region, the additional force generated per unit slip begins to decrease and ultimately reaches a peak, after which tire. force decreases and braking behavior becomes unstable. The peak force at which this occurs depends strongly upon the road surface and is often approximated by scaling by a peak friction value,p , as shown in Figure 1. Some experimental research has suggested that the longitudinal stiffness may also depend on road surface condition and this peak friction value . While consistent with many mathematical representations of force versus slip curves, such dependence violates the traditional brush models physical description of tire force generation .Since tire force generation can be described in terms of wheel slip, slip is a critical parameter in control algorithms for vehicle control systems such as anti-lock brake systems (ABS) and electronic stability control (ESP) . While many ABS algorithms rely primarily on the deceleration of the wheel , some estimate of slip is necessary to avoid lock-up on low friction surfaces. Although the definition of wheel slip in Equation 1 is quite simple, calculating slip on a vehicle is complicated by the lack of accurate measurements of either the radius or the absolute vehicle velocity. While an average radius value can usually be assumed without producing much error, some form of observer must be employed to estimate the vehicle speed . Other systems determine the vehicles absolute velocity by comparing the front and rear wheel speeds (assuming the car is two-wheel drive) . Recent work has demonstrated that velocity measurements derived from the Global Positioning System (GPS) can be used to provide an absolute velocity for calculating wheel slip . This avoids the drift problems inherent in observers based upon wheel speed measurement.The use of GPS velocity information has an even greater benefit beyond the