The stability analysis using Lyapunov exponents for high-DOF nonlinear vehicle plane motion

Abstract

The Lyapunov exponents method is an excellent approach for analyzing the vehicle plane motion stability, and the researchers demonstrated the effectiveness under 2-DOF vehicle model. However, whether the Lyapunov exponents approach can effectively reveal the characteristics of high-DOF nonlinear vehicle model is the key problem at present. In this paper, the Lyapunov exponents is applied to quantitatively analyze the stability of the nonlinear three and five degree of freedom vehicle plane motion system. The different characteristics between 2-DOF and high-DOF model are revealed and explained by using Lyapunov exponents. It illustrates the feasibility of using Lyapunov exponents to analyze the stability of high-DOF vehicle models, which supplements and perfects the existing quantitative analysis conclusion.

Keywords

Vehicle dynamics stability analysis Lyapunov exponents nonlinear vehicle model nonlinear tire model

Get full access to this article

View all access options for this article.

References

Abe

Vehicle handling dynamics: theory and application. Oxford: Butterworth-Heinemann, 2015.

Rajamani

Vehicle dynamics and control. Berlin: Springer, 2006.

Hernandez

Kuo

CY.

Lateral control of higher order nonlinear vehicle model in emergency maneuvers using absolute positioning GPS and magnetic markers. IEEE Trans Vehicular Technol 2004; 53: 372–384.

Inagaki

Kushiro

Yamamoto

Analysis on vehicle stability in critical cornering using phase-plane method. JSAE Rev 1995; 2: 216.

Ono

Hosoe

Doi

Bifurcation in vehicle dynamics and robust front wheel steering control. IEEE Trans Control Syst Technol 1998; 6: 412–420.

Johnson

Huston

JC.

Nonlinear lateral stability analysis of road vehicles using Liapunov’s second method. SAE Trans 1984; 93: 798–805.

Samsundar

Huston

JC.

Estimating lateral stability region of a nonlinear 2 degree-of-freedom vehicle. SAE Trans 1998; 107: 1791–1797.

Lee

JM.

Estimation of the stability region of a vehicle in plane motion using a topological approach. Int J Veh Des 2002; 30: 181–192.

Genesio

Tartaglia

Vicino

On the estimation of asymptotic stability regions: state of the art and new proposals. IEEE Trans Automat Contr 1985; 30: 747–755.

10.

Song

CK.

Vehicle modeling with nonlinear tires for vehicle stability analysis. Int J Autom Technol 2010; 11: 339–344.

11.

Horiuchi

Okada

Nohtomi

Analysis of accelerating and braking stability using constrained bifurcation and continuation methods. Veh Syst Dyn 2008; 46: 585–597.

12.

Shi

Wang

, et al. Analysis of the vehicle driving stability region based on the bifurcation of the driving torque and the steering angle. Proc IMechE, Part D: J Automobile Engineering 2017; 231: 984–998.

13.

Sadri

Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents. Veh Syst Dyn 2013; 51: 906–924.

14.

Shi

Modified tire-slip-angle model for chaotic vehicle steering motion. Automot Innov 2018; 1: 177–186.

15.

ISO 8855:1991-12. Road vehicles–vehicle dynamics and road-holding ability–vocabulary, 2013.

16.

Rajamani

Vehicle dynamics and control. Berlin: Springer Science Business Media, 2011.

17.

Pacejka

Tire and vehicle dynamics. Amsterdam: Elsevier, 2005.

18.

Wang

Shi

Vehicle coupled bifurcation analysis of steering angle and driving torque. Proc IMechE, Part D: J Automobile Engineering 2021; 235: 1864–1875.

19.

Nguyen

Vehicle handling, stability, and bifurcaiton analysis for nonlinear vehicle models. MSc Thesis, University of Maryland, College Park, MD, 2005.

20.

Wang

Shi

Liu

, et al. Analysis of driving mode effect on vehicle stability. Int J Autom Technol 2013; 14: 363–373.

21.

Ramasubramanian

Sriram

MS.

A comparative study of computation of Lyapunov spectra with different algorithms. Physica D 2000; 139: 72–86.

22.

Wolf

Swift

Swinney

, et al. Determining Lyapunov exponents from a time series. Physica D 1985; 16: 285–317.

23.

Benettin

Galgani

Giorgilli

, et al. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: theory. Meccanica 1980; 15: 9–20.

24.

Nusse

Yorke

JA.

Dynamics: numerical explorations: accompanying computer program dynamics. Berlin: Springer, 2012.