Skip to main content
SpringerLink
Log in

Estimation of maximum road friction coefficient based on Lyapunov method

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

With the real time and accurate information of motor torque and rotation speed of the four-in-wheel-motordrive electric vehicles, a slip based algorithm for estimating maximum road friction coefficient is designed using Lyapunov stability theory. Modified Burckhardt tire model is used to describe longitudinal slip property of the tire. By introducing a new state variable, a nonlinear estimator is proposed to estimate the longitudinal tire force and the maximum road friction coefficient simultaneously. With the appropriate selection of estimation gain, the convergence of the estimation error of the tire longitudinal force and maximum road friction coefficient is proved through Lyapunov stability analysis. In addition, the error is exponentially stable near the origin. Finally the method is validated with Carsim-Simulink co-simulation and real vehicle tests under multi working conditions in acceleration situation which demonstrate high computational efficiency and accuracy of this method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ahn, C., Peng, H. and Tseng, H. E. (2012). Robust estimation of road friction coefficient using lateral and longitudinal vehicle dynamics. Veh. Syst. Dyn. 50, 6, 961–985.

    Article  Google Scholar 

  • Ahn, C., Peng, H. and Tseng, H. E. (2013). Robust Estimation of Road Frictional Coefficient. IEEE Trans. Control Systems Technology 21, 1, 1–13.

    Article  Google Scholar 

  • Alvarez, L., Yi, J., Horowitz, R. and Olmos, L. (2004). Dynamic friction modelbased tire-road friction estimation and emergency braking control. J. Dyn. Syst., Meas., Control 127, 1, 22–32.

    Article  Google Scholar 

  • Burckhardt, M. (1993). Vehicle Chassis Technology-Wheel Sub System. Wurtzburg: Vogel-Verlag.

    Google Scholar 

  • Chen, L., Bian, M., Luo, Y. and Li, K. (2015). Real-time identification of the tyre–road friction coefficient using an unscented Kalman filter and mean-square-errorweighted fusion. Proc. IMechE Part D: J. Automobile Engineering, 1–15.

    Google Scholar 

  • Chen, Y. and Wang, J. (2011). Adaptive vehicle speed control with input injections for longitudinal motion independent road frictional condition estimation. IEEE Trans. Vehicular Technology 60, 3, 839–848.

    Article  Google Scholar 

  • Choi, M., Oh, J. and Choi, S. (2013). Linearized recursive least squares methods for real-time identification of tire–Road friction coefficient. IEEE Trans. Vehicular Technology 62, 7, 2906–2918.

    Article  Google Scholar 

  • Erdogan, G., Alexander, L. and Rajamani, R. (2011). Estimation of tire-road friction coefficient using a novel wireless piezoelectric tire sensor. IEEE Sensors J. 11, 2, 267–279.

    Article  Google Scholar 

  • Grip, H. F., Johansen, T. A., Imsland, L. and Kaasa, G. (2010). Parameter estimation and compensation in systems with nonlinearly parameterized perturbations. Automatica 46, 1, 19–28.

    Article  MathSciNet  MATH  Google Scholar 

  • Gustafsson, F. (1997). Slip-based tire-road friction estimation. Automatica 33, 6, 1087–1099.

    Article  MathSciNet  MATH  Google Scholar 

  • Haffner, L., Kozek, M., Shi, J. and Jorgl, H. P. (2008). Estimation of the maximum friction coefficient for a passenger vehicle using the instantaneous cornering stiffness. American Control Conf., Seattle, Washington, USA.

    Google Scholar 

  • Hori, Y. (2004). Future vehicle driven by electricity and control-research on four-wheel-motored “UOT electric march II”. IEEE Trans. Industrial Electronics 51, 5, 954–962.

    Article  MathSciNet  Google Scholar 

  • Imsland, L., Fossen, T. I., Johansen, T. A., Grip, F. G., Kalkkuhl, J. C. and Suissa, A. (2006). Vehicle velocity estimation using nonlinear observers. Automatica 42, 12, 2091–2103.

    Article  MathSciNet  MATH  Google Scholar 

  • Jin, C., Xiong, L., Yu, Z. and Feng, Y. (2014). Path following control for skid steering vehicles with vehicle speed adaption. SAE Paper No. 2014-01-0277.

    Book  Google Scholar 

  • Khalil, H. K. (2002). Nonlinear Systems. Prentice-Hall. Upper Saddle River, New Jersey, USA.

    Google Scholar 

  • Krstic, M., Kanellakopoulos, I. and Kokotovic, P. V. (1995). Nonlinear and Adaptive Control Design. Wiley. New York.

    MATH  Google Scholar 

  • Li, K., Misener, J. A. and Hedrick, K. (2007). On-board road condition monitoring system using slip-based tyreroad friction estimation and wheel speed signal analysis. Proc. Institution of Mechanical Engineers Part K: J. Multi-body Dynamics 221, 1, 129–146.

    Google Scholar 

  • Li, L., Jia, G., Song, J. and Ran, X. (2013). Progress on vehicle dynamics stability control system. Chinese J. Mechanical Engineering 49, 24, 95–107.

    Article  Google Scholar 

  • Li, L., Wang, F. Y. and Zhou, Q. (2006). Integrated longitudinal and lateral tire/road friction modeling and monitoring for vehicle motion control. IEEE Trans. Intelligent Transportation Systems 7, 1, 1–19.

    Article  Google Scholar 

  • Li, L., Yang, K., Jia, G., Song, J. and Han, Z.-Q. (2015). Comprehensive tire-road friction coefficient estimation based on signal fusion method under complex maneuvering operations. Mechanical Systems and Signal Processing, 56-57, 259–276.

    Article  Google Scholar 

  • Li, L., Zhu, H., Chen, J., Song, J. and Ran, X. (2014). Road Friction identification algorithm for the vehicle stability control. Chinese J. Mechanical Engineering 50, 2, 132–138.

    Article  Google Scholar 

  • Lin, F. and Huang, C. (2013). Unscented Kalman filter for road friction coefficient estimation. J. Harbin Institute of Technology University 45, 7, 115–120.

    Google Scholar 

  • Matuško, J., Petrovic, I. and Peric, N. (2007). Neural network based tire/road friction force estimation. Engineering Applications of Artificial Intelligence 21, 3, 442–456.

    Article  Google Scholar 

  • Müller, S., Uchanski, M. and Hedrick, K. (2004). Estimation of the maximum tire-road friction coefficient. J. Dyn. Syst., Meas., Control 125, 4, 1–11.

    Google Scholar 

  • Patel, N., Edwards, C. and Spurgeon, S. K. (2008). Tyreroad friction estimation-A comparative study. Proc. IMechE Part D: J. Automobile Engineering 222, 12, 2337–2351.

    Article  Google Scholar 

  • Pohl, A., Steindl, R. and Reindl, L. (1999). The intelligent tire utilizing passive SAW sensors measurement of tire friction. IEEE Trans. Instrumentation and Measurement 48, 6, 1041–1046.

    Article  Google Scholar 

  • Qi, Z., Taheri, S., Wang, B. and Yu, H. (2015). Estimation of the tyre–Road maximum friction coefficient and slip slope based on a novel tyre model. Veh. Syst. Dyn. 53, 4, 506–525.

    Article  Google Scholar 

  • Rajamani, R. (2005). Vehicle Dynamics and Control. Springer-Verlag. New York.

    MATH  Google Scholar 

  • Rajamani, R., Piyabongkarn, D., Lew, J. Y., Yi, K. and Phanomchoeng, G. (2010). Tire-road friction-coefficient estimation. IEEE Control Systems 30, 4, 54–69.

    Article  MathSciNet  Google Scholar 

  • Rath, J. J., Veluvolu, K. C., Defoort, M. and Soh, Y. C. (2014). Higher-order sliding mode observer for estimation of tyre friction in ground vehicles. IET Control Theory and Applications 8, 6, 399–408.

    Article  MathSciNet  Google Scholar 

  • Ray, L. R. (1997). Nonlinear tire force estimation and road friction identification: Simulation and experiments. Automatica 33, 10, 1819–1833.

    Article  MathSciNet  MATH  Google Scholar 

  • Sato, Y., Kobay, A. D., Kageyama, I., Watanabe, K., Kuriyagawa, Y. and Kuriyagawa, Y. (2007). Study on recognition method for road friction condition. JSAE Trans., 38, 51–56.

    Google Scholar 

  • Singh, A. and Khalil, H. K. (2005). Regulation of nonlinear systems using conditional integrators. Int. J. Robust Nonlinear Control 15, 8, 339–362.

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, F., Huang, X., Rudolph, J. and Lolenko, K. (2015). Vehicle state estimation for anti-lock control with nonlinear observer. Control Eng. Practice, 43, 69–84.

    Article  Google Scholar 

  • Van, Z. (2000). Bosch ESP systems: 5 years of experience. SAE Paper No. 2000-01-1633.

    Google Scholar 

  • Wang, X., Xiong, L. and Jin, C. (2014). A control strategy for slip regulation coordinated with driver intention. Applied Mechanics & Materials, 556-562, 4045–4050.

    Article  Google Scholar 

  • Wit, C. C., Horowitz, R. and Tsiotras, P. (2007). Modelbased observers for tire/road contact friction prediction. Lecture Notes in Control and Information Sciences, 244, 23–42.

    MATH  Google Scholar 

  • Xu, S., Yu, Z. and Xiong, L. (2015). Control of novel integrated-electro-hydraulic brake system for automotive. SAE Paper No. 2015-01-2699.

    Book  Google Scholar 

  • Yu, Z., Feng, Y. and Xiong, L. (2013). Review on vehicle dynamics control of distributed drive electric vehicle. Chinese J. Mechanical Engineering 49, 8, 105–114.

    Article  Google Scholar 

  • Yu, Z., Zuo, J. and Zhang, L. (2006). A summary on the development status quo of tire-road friction coefficient estimation techniques. Automotive Engineering 28, 6, 546–549.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automotive Studies, Tongji University, Shanghai, 201804, China

    X. Xia, L. Xiong, K. Sun & Z. P. Yu

  2. National “2011” Collaborative Innovation Center, Tongji University, Shanghai, 201804, China

    X. Xia, L. Xiong, K. Sun & Z. P. Yu

Authors
  1. X. Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Z. P. Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Xiong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xia, X., Xiong, L., Sun, K. et al. Estimation of maximum road friction coefficient based on Lyapunov method. Int.J Automot. Technol. 17, 991–1002 (2016). https://doi.org/10.1007/s12239-016-0097-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-016-0097-7

Keywords

Search

Navigation