Stability and Bautin bifurcation of four-wheel-steering vehicle system with driver steering control

Pengcheng Miao; Denghui Li; Yuan Yue; Celso Grebogi

doi:10.1063/5.0158869

Stability and Bautin bifurcation of four-wheel-steering vehicle system with driver steering control

Chaos. 2023 Aug 1;33(8):083122. doi: 10.1063/5.0158869.

Authors

Pengcheng Miao¹, Denghui Li², Yuan Yue³, Celso Grebogi⁴

Affiliations

¹ School of Mechanical Engineering, Yangtze University, Jingzhou 434023, China.
² School of Mathematics and Statistics, Hexi University, Zhangye 734000, China.
³ School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China.
⁴ Institute for Complex Systems and Mathematical Biology King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.

PMID: 37549125
DOI: 10.1063/5.0158869

Abstract

In this paper, the stability and Bautin bifurcation of a four-wheel-steering (4WS) vehicle system, by considering driver steering control, are investigated. By using the central manifold theory and projection method, the first and second Lyapunov coefficients are calculated to predict the type of Hopf bifurcation of the vehicle system. The topological structure of Bautin bifurcation, a degenerate Hopf bifurcation of the 4WS vehicle system, is presented in parameter space, and it reveals the dynamics of the vehicle system of different choices of control parameters. The influences of system parameters on critical values of the bifurcation parameter are also analyzed. It is shown that with the increase in the frontal visibility distance of the driver control strategy coefficient and the cornering stiffness coefficients of rear wheels, the critical speed increases. Nevertheless, the critical speed decreases with the increase in the distance from the center of gravity of the vehicle to the front axles, Driver's perceptual time delay, and cornering stiffness coefficients of the front wheels.