Abstract
Tire-road friction coefficient is of great significance for vehicle active safety systems, advanced driving assistance systems, and even future autonomous vehicles. Most of the dynamics-based methods for estimating the tire-road friction coefficient neglect the characteristic that the tire stiffness changes with the driving conditions, resulting in a limited number of driving conditions for which the friction coefficient can be effectively estimated. In order to improve the accuracy of the tire-road friction coefficient estimation results, an estimation method is proposed in which the tire stiffness can change adaptively according to the vertical load and the vehicle dynamics response. By analyzing the change in length of the tire-road contact patch, the relationship between vertical load and tire stiffness is established. By adding tire stiffness to the system state, the relationship between tire stiffness and vehicle dynamics response is established. A square-root cubature Kalman filter algorithm with rapid convergence by automatically adjusting the measurement noise covariance matrix is developed to enhance the real-time performance of the estimation method. Finally, the superiority of the method is verified under different test scenarios based on CarSim and MATLAB/Simulink co-simulation platform. The results also show that this method is able to make an accurate identification when tire damage happens.
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The datasets generated during and analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request.
References
Sun, W., Zhang, J., Liu, Z.: Two-time-scale redesign for antilock braking systems of ground vehicles. IEEE Trans. Ind. Electron. 66(6), 4577–4586 (2019)
Rajamani, R., Piyabongkarn, N., Lew, J., Yi, K., Phanomchoeng, G.: Tire-road friction-coefficient estimation. IEEE Control Syst. Mag. 30(4), 54–69 (2010)
Aligia, D.A., Magallan, G.A., De Angelo, C.H.: EV traction control based on nonlinear observers considering longitudinal and lateral tire forces. IEEE Trans. Intell. Transp. Syst. 19(8), 2558–2571 (2018)
Cui, Q., Ding, R., Zhou, B., Wu, X.: Path-tracking of an autonomous vehicle via model predictive control and nonlinear filtering. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 232(9), 1237–1252 (2017)
Khaleghian, S., Emami, A., Taheri, S.: A technical survey on tire-road friction estimation. Friction 5(2), 123–146 (2017)
Tuononen, A.J.: Optical position detection to measure tyre carcass deflections. Veh. Syst. Dyn. 46(6), 471–481 (2008)
Alonso, J., López, J.M., Pavón, I., Recuero, M., Asensio, C., Arcas, G., Bravo, A.: On-board wet road surface identification using tyre/road noise and support vector machines. Appl. Acoust. 76, 407–415 (2014)
Erdogan, G., Alexander, L., Rajamani, R.: Estimation of tire-road friction coefficient using a novel wireless piezoelectric tire sensor. IEEE Sens. J. 11(2), 267–279 (2011)
Paul, D., Velenis, E., Cao, D., Dobo, T.: Optimal \(\mu \)-estimation based regenerative braking strategy for an AWD HEV. IEEE Trans. Transp. Electrification 3(1), 249–258 (2017)
Guo, H., Yin, Z., Cao, D., Chen, H., Lv, C.: A review of estimation for vehicle tire-road interactions toward automated driving. IEEE Trans. Syst. Man Cybern. Syst. 49(1), 14–30 (2019)
Wang, Y., Hu, J., Wang, F., Dong, H., Yan, Y., Ren, Y., Zhou, C., Yin, G.: Tire road friction coefficient estimation: review and research perspectives. Chin. J. Mech. Eng. 35(1), 1–11 (2022)
Lee, C., Hedrick, K., Yi, K.: Real-time slip-based estimation of maximum tire-road friction coefficient. IEEE/ASME Trans. Mechatron. 9(2), 454–458 (2004)
Cui, G., Dou, J., Li, S., Zhao, X., Lu, X., Yu, Z.: Slip control of electric vehicle based on tire-road friction coefficient estimation. Math. Probl. Eng. 2017, 1–8 (2017)
Bakker, E., Pacejka, H.B., Lidner, L.: A new tire model with an application in vehicle dynamics studies. SAE Trans. 98, 101–113 (1989)
Pacejka, H.B., Bakker, E.: The magic formula tyre model. Veh. Syst. Dyn. 21(S1), 1–18 (1992)
Pacejka, H.B., Besselink, I.J.M.: Magic formula tyre model with transient properties. Veh. Syst. Dyn. 27(S1), 234–249 (1997)
Pacejka, H.B., Sharp, R.S.: Shear force development by pneumatic tyres in steady state conditions: a review of modelling aspects. Veh. Syst. Dyn. 20(3–4), 121–175 (1991)
Dugoff, H., Fancher, P.S., Segel, L.: An analysis of tire traction properties and their influence on vehicle dynamic performance. SAE Trans. 79, 1219–1243 (1970)
Dugoff, H., Fancher, P.S., Segel, L.: Tire performance characteristics affecting vehicle response to steering and braking control inputs. Tech. Rep., Highway Safety Research Institute (HSRI), University of Michigan, Ann Arbor, MI, USA (1969)
Zhao, Y.-Q., Li, H.-Q., Lin, F., Wang, J., Ji, X.-W.: Estimation of road friction coefficient in different road conditions based on vehicle braking dynamics. Chin. J. Mech. Eng. 30(4), 982–990 (2017)
Mooryong, C., Oh, J.J., Choi, S.B.: Linearized recursive least squares methods for real-time identification of tire-road friction coefficient. IEEE Trans. Veh. Technol. 62(7), 2906–2918 (2013)
Chen, L., Bian, M., Luo, Y., Li, K.: Maximum tire road friction estimation based on modified Dugoff tire model. In: International Conference on Mechanical and Automation Engineering, vol. 2013, pp. 56–61 (2013)
Singh, K.B., Taheri, S.: Estimation of tire-road friction coefficient and its application in chassis control systems. Syst. Sci. Control Eng. 3(1), 39–61 (2015)
Hsu, Y.-H.: Estimation and control of lateral tire forces using steering torque. Ph.D. dissertation, Stanford University (2009)
Singh, K.B., Sivaramakrishnan, S.: An adaptive tire model for enhanced vehicle control systems. SAE Int. J. Passeng. Cars Mech. Syst. 8(1), 128–145 (2015)
Kalman, R.E.: A new approach to linear filtering and prediction problems. J. Basic Eng. 82(1), 35–45 (1960)
Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic Press, New York (1970)
Julier, S.J., Uhlmann, J.K., Durrant-Whyte, H.F.: A new approach for filtering nonlinear systems. In: Proceedings of 1995 American Control Conference—ACC’95, vol. 3, Conference Proceedings, pp. 1628–1632
Julier, S.J.: The scaled unscented transformation. In: Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), vol. 6, Conference Proceedings, pp. 4555–4559
Arasaratnam, I., Haykin, S.: Cubature Kalman filters. IEEE Trans. Autom. Control 54(6), 1254–1269 (2009)
Hu, J., Rakheja, S., Zhang, Y.: Real-time estimation of tire-road friction coefficient based on lateral vehicle dynamics. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 234(10–11), 2444–2457 (2020)
Zhang, X., Xu, Y., Pan, M., Ren, F.: A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations. Veh. Syst. Dyn. 52(4), 475–503 (2014)
Qi, Z., Taheri, S., Wang, B., Yu, H.: Estimation of the tyre-road maximum friction coefficient and slip slope based on a novel tyre model. Veh. Syst. Dyn. 53(4), 506–525 (2015)
Fang, H., Tian, N., Wang, Y., Zhou, M., Haile, M.A.: Nonlinear Bayesian estimation: from Kalman filtering to a broader horizon. IEEE/CAA J. Autom. Sin. 5(2), 401–417 (2018)
Haykin, S.S.: Kalman Filtering and Neural Networks. John Wiley & Sons Inc, New York (2001)
Jia, B., Xin, M., Cheng, Y.: High-degree cubature Kalman filter. Automatica 49(2), 510–518 (2013)
Zarei, J., Shokri, E.: Nonlinear and constrained state estimation based on the cubature Kalman filter. Ind. Eng. Chem. Res. 53(10), 3938–3949 (2014)
Meng, Q., Li, X., Guo, Y.: An efficient Gauss–Seidel cubature Kalman filter. IEEE Trans. Circuits Syst. II Express Br. 69(3), 1932–1936 (2022)
Xu, G., Huang, Y., Gao, Z., Zhang, Y.: A computationally efficient variational adaptive Kalman filter for transfer alignment. IEEE Sens. J. 20(22), 13682–13693 (2020)
Nanda, S.K., Kumar, G., Bhatia, V., Singh, A.K.: Kalman filtering with delayed measurements in non-Gaussian environments. IEEE Access 9, 123231–123244 (2021)
Singh, A.K.: Fractionally delayed Kalman filter. IEEE/CAA J. Autom. Sin. 7(1), 169–177 (2020)
Chen, B., Liu, X., Zhao, H., Principe, J.C.: Maximum correntropy Kalman filter. Automatica 76, 70–77 (2017)
Liu, W., Pokharel, P.P., Principe, J.C.: Correntropy: properties and applications in non-Gaussian signal processing. IEEE Trans. Signal Process. 55(11), 5286–5298 (2007)
Erdogmus, D., Principe, J.C.: An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems. IEEE Trans. Signal Process. 50(7), 1780–1786 (2002)
Chen, B., Dang, L., Gu, Y., Zheng, N., Principe, J.C.: Minimum error entropy Kalman filter. IEEE Trans. Syst. Man Cybern. Syst. 51(9), 5819–5829 (2021)
Principe, J.C.: Information Theoretic Learning: Renyi’s Entropy and Kernel Perspectives. Springer, New York (2010)
Wu, Z., Peng, S., Chen, B., Zhao, H., Principe, J.: Proportionate minimum error entropy algorithm for sparse system identification. Entropy 17(12), 5995–6006 (2015)
Chen, B., Xing, L., Xu, B., Zhao, H., Príncipe, J.C.: Insights into the robustness of minimum error entropy estimation. IEEE Trans Neural Netw. Learn. Syst. 29(3), 731–737 (2018)
Chang, L., Hu, B., Chang, G., Li, A.: Huber-based novel robust unscented Kalman filter. IET Sci. Meas. Technol. 6(6), 502–509 (2012)
Tanelli, M., Savaresi, S.M., Piroddi, L.: Real-time identification of tire-road friction conditions. IET Control Theory Appl. 3(7), 891–906 (2009)
Oh, J.J., Choi, S.B.: Vehicle velocity observer design using 6-D IMU and multiple-observer approach. IEEE Trans. Intell. Transp. Syst. 13(4), 1865–1879 (2012)
Singh, K.B., Arat, M.A., Taheri, S.: Literature review and fundamental approaches for vehicle and tire state estimation. Veh. Syst. Dyn. 57(11), 1643–1665 (2018)
Pacejka, H.B.: Tire and Vehicle Dynamics. Springer, New York (2012)
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Ye, J., Zhang, Z., Jin, J. et al. Estimation of tire-road friction coefficient with adaptive tire stiffness based on RC-SCKF. Nonlinear Dyn 112, 945–960 (2024). https://doi.org/10.1007/s11071-023-09088-0
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DOI: https://doi.org/10.1007/s11071-023-09088-0