Integrated Estimation Structure for the Tire Friction Forces in Ground Vehicles E. Hashemi, M. Pirani, A. Khajepour, B. Fidan, A. Kasaiezadeh, S-K. Chen, and B. Litkouhi Abstract—This paper presents a novel corner-based force estimation method to monitor tire capacities required for the traction and stability control systems. This is entailed for more advanced vehicle stability systems in harsh maneuvers. A novel estimation structure is proposed in this paper for the longitu- dinal, lateral, and vertical tire forces robust to the road friction condition. A nonlinear and a Kalman observer is utilized for estimation of the longitudinal and lateral friction forces. The stability and performance of the time-varying estimators are explored and it is shown that the developed integrated structure is robust to model uncertainties and does not require knowledge of the road friction. The proposed method is experimentally tested in several maneuvers on different road surface conditions and the results illustrate the accuracy and robustness of the state estimators. I. I NTRODUCTION Advanced vehicle stability control and active safety sys- tems require dependable vehicle states, which may not be readily accessible by measurements, thus needing to be estimated. One major practical issue that has dominated the vehicle state estimation field is a robust tire friction force estimation. Several studies first have focused on road friction estimation and identification of tire parameters, in order to estimate longitudinal and lateral tire forces. Alvarez et al. [1] used a parameter adaptation law, a Lyapunov- based state estimator, and the dynamic LuGre model [2] to estimate the road friction and longitudinal forces during an emergency brake condition. Employing the equivalent output error injection approach, Patel et al. proposed a second-order and third-order sliding mode observers in [3] to estimate the friction coefficient and consequently tire forces during brake conditions on the pseudostatic LuGre [4], dynamic LuGre, and parameter-based friction [5] models. Ghandour et al. [6] developed a force and road friction estimation structure based on an iterative quadratic minimization of the error between the developed lateral force estimator and the tire/road interaction Dugoff model. Rajamani et al. [7] suggest a recursive least square for road identification and a nonlinear observer for longitudinal force estimation having wheel torques and accurate slip-ratio data from GPS. These methods rely on simultaneous road condition identification, which may impose undesirable estimation error produced by the time-varying model parameters. A. Khajepour, B. Fidan, E. Hashemi, and M. Pirani are with the Department of Mechanical and Mechatronics Eng., University of Water- loo, Waterloo, ON, Canada (e-mail: a.khajepour, fidan, ehashemi, mpi- rani@uwaterloo.ca). B. Litkouhi, A. Kasaiezadeh, S-K. Chen, and are with the General Motors RD, Warren, MI, USA (e-mail: bakhtiar.litkouhi, alireza.kasaiezadeh, shih-ken.chen@gm.com). Estimation of longitudinal and lateral forces independent from the road condition may be classified on the basis of wheel dynamics and planar kinetics into the nonlinear, sliding mode, Kalman-based, and unknown input observers. A force estimation method based on the steering torque measurement is introduced in [8], which requires additional measurements. Hsu et al. provide a nonlinear observer to estimate tire slip angles as well as the road friction condition in [9] with steering torque measurement. Baffet et al. [10] proposed a cascaded structure for estimation of the tire forces and vehicle side-slip angle with a sliding mode observer and extended Kalman Filter (EKF). Doumiati et al. [11] estimate tire forces with EKF and UKF. In their approach, longitudinal and lateral force evolution is modelled with a random walk model. They assume that longitudinal and lateral tire forces and force sums on each track are associated according to the dispersion of vertical forces. Cho et al. [12] estimate lateral tire forces using the planar kinetics and a random- walk Kalman filter. A Kalman-based unknown input observer (UIO) is developed by Wang et al. [13], [14] for longitudinal and lateral force estimation with the wheel dynamics, planar kinetics, measured wheel speeds, wheel torques, and the yaw rate. Using UKF and the wheel dynamics, Hashemi et al. [15] developed a longitudinal force estimator robust to the road friction changes and uncertainties in the model such as i.e. effective rolling radius, measured wheel speed and torques. Similarly, employing UKF for an antilock braking control system, Sun et al. [16] propose a nonlinear observer robust to the road friction for the longitudinal force and slip ratio estimation during brake. Their approach is tested during brake maneuvers on different road conditions. In the following, a corner-based methodology for estima- tion of the longitudinal forces based on a nonlinear observer is first discussed, then an adaptive Kalman-based lateral force estimation is proposed in Section III. Vertical force estimation is also provided in Section III. Section IV presents experimental and simulation results used to corroborate the approach on different road conditions and in various ma- neuvers with high and low longitudinal/lateral excitations. Finally, conclusions are provided in Section V. II. PROBLEM STATEMENT Tire forces exhibit the vehicles capacity to perform re- quested maneuvers and provide information about the stabil- ity of the vehicle. Since tire force calculation requires road friction information, even accurate slip ratio/angle informa- tion from high precision GPS and high fidelity tire model will not lead to tire forces at each wheel. Therefore, estimation © IEEE 2017 Hashemi, E., Pirani, M., Khajepour, A., Fidan, B., Kasaiezadeh, A., Chen, S.-K., & Litkouhi, B. (2016). Integrated estimation structure for the tire friction forces in ground vehicles (pp. 1657–1662). IEEE. https://doi.org/10.1109/AIM.2016.7577008