Vehicle velocity, side slip angles and yaw rate estimation

This paper presents a nonlinear body side slip angle and yaw rate observer based on an estimation of the vehicle velocity. The design of this observer uses a linearisa- tion which is modelled on the Luenberger observer and the output used for this observer is the lateral acceleration. The rotational equivalent wheel speeds are used to estimate the vehicle velocity. The observation error dynamic is stabilized using a Lyapunov function. It is shown that the required specifications are met by the designed observer. Simulation results are given. I. Introduction The lateral dynamic motion is a major component of a vehicle's dynamics. For this reason a number of works have been devoted to the control of the lateral velocity and the yaw rate: the increase of the two variables is a major cause of vehicle instability. Most of the algorithms which have been proposed in the literature assume the avail- ability of the lateral velocity or the body side slip angle. In practice this variable is never measured, the yaw rate is measured but the sensor is expensive, and the vehicle velocity is in general estimated. In the literature one may find works related to this lateral velocity estimation issue, see for instance (1), (2), (3), (4). Some problems resulting from lateral forces modelling errors such as the cornering stiffness coefficients Cf and Cr have been addressed in some works, see for instance (5), (3). In the latter works enough arguments have been brought for the relevance of the estimation of the latter coefficients. In the present work we propose a nonlinear observer of the two components of the lateral motion, namely the body side slip angle and the yaw rate, and an estimation of the vehicle velocity. When the wheel ground contact point velocities are approximated by the rotational equivalent wheel speeds, we can write a simple expression of the vehicle velocity. But the presence of the body side slip and the yaw rate in this expression prevent us to use it as an estimation. To solve this problem we take an observer derived from a linear bicycle model, and immediately another problem appears which is the vehicle velocity- dependence of the matrices of the linear model. The proposed solution in this paper is to replace the velocity in the linear model by its approximation, the resulting model are non-linear. In practice the available measure- ments in the lateral motion are the lateral acceleration and the yaw rate. In this work The used output is the lateral acceleration, and the yaw rate is observed even if we can get it with a sensor (to reduce the cost (6)), another advantage of the lateral acceleration is that we have an information about the body side slip angle and the yaw rate at each instant, which implies that the components of the Jacobian vector are different to zero and the determination of the gain vector is possible in the proposed observer. After a suitable choice of this gain vector which ensure the convergence we can estimate the vehicle velocity. The paper is organized as follows. In the first section, a simplified linear model (bicycle model) is presented to provide the basic understanding of the vehicle dynamics. In the next section we show how to compute the expression of the vehicle velocity and the equations of the nonlinear observer. In this section we propose a method to compute the gain vector of the nonlinear observer which ensure the convergence of the error observation to zero using a Lyapunov function. Finally, numerical simulations with a complete non-linear vehicle model are proposed and discussed to show the effectiveness of the proposed observer.