Robust observation of tractor-trailer vertical forces using inverse model and exact differentiator

In this paper, we are interested in developing a robust tire-force estimator for heavy duty vehicles. We use a combined model of the articulated vehicle: a yaw plane model for the chassis motion and a vertical plane model for the axles. In the proposed method, we make use of the on-board available sensors to which are added lowcost sensors. In order to optimize the sensors configuration, a robust differentiator is used in order to obtain accelerations from the measured velocities. Once the differentiation obtained, the model is inverted to determine the unknown input forces. The approach is validated by comparing the estimation results to those given by the software simulator prosper. INTRODUCTION The problem of the estimation of the contact forces for heavy duty vehicles is primordial for obtaining the necessary information on the interaction between the vehicle and the pavement. This information is particularly useful in order to avoid road and vehicle damage (tire, suspension, fragile payload) and to enhance security by preventing rollover of trucks. The issue of estimating vehicle contact forces is considered in many previous works. In [9] an Extended Kalman Filter (EKF) is applied to estimate the longitudinal and lateral forces in a vehicle bicycle model, the forces are considered as additional states and their dynamics are modeled by the use of a shaping filter driven by white noise. The authors in [11] have applied a similar estimation algorithm to an off-highway mining truck. The main limitation of this approach is that some assumptions are made on the behavior of the forces (slow variation) when tuning the shaping filter, this requires the exact knowledge of the nature of the forces and the way they vary. We can also cite [2], [8] who use sliding mode observers to estimate contact forces in heavy duty vehicles. First, the height of the wheel hub is estimated, then by measuring the road profile, the tire deflection is calculated by assuming the linear stiffness of the tire. An estimation of the vertical force is obtained by multiplying the tire deflection with its stiffness. The longitudinal and lateral forces are also derived using the Pacejka tire model. This method involves knowing accurately the vehicle and the pneumatic parameters and also to measure the road profile.