Analysis of bifurcation and stability for a tractor semi-trailer in planar motion

Abstract

This paper is intended for bifurcation analysis of a nonlinear tractor semi-trailer vehicle model in planar motion and for investigating its stability under constant running conditions. Bifurcation analysis shows that bifurcation diagrams of a tractor semi-trailer are quite different from those of a single-unit vehicle. Some instability phenomena of the vehicle system such as jackknifing, sideslip, and spinning are explained by correlating them with the behaviour in the neighbourhood of unstable fixed points based on analysis of eigenvectors, phase trajectories, and status of lateral tyre force saturation. It is also found that yaw planar instability of a tractor semi-trailer is caused by lateral tyre force saturation of the tractor's rear axles and/or the trailer's axles. Moreover, the stability region in the state space is demarcated, and a stability index for evaluating size of the stability region in a feasible domain is proposed. Yaw stability under constant driving conditions is analysed by using the proposed stability index.

Assessing the influence of the road-tire friction coefficient on the yaw and roll stability of articulated vehicles

“…These results corroborate the findings in the literature indicating that for low friction coefficient, the risk of jackknife prevails. 23…”

“…Ding et al 23 trace the stability region of a nonlinear model of a tractor–semitrailer combination using the phase trajectory method. The variation of this region is also presented as a function of the vehicle speed and road-tire friction coefficient.…”

“…23 However, the associated stability region and the transition from one instability phenomenon to another, according to the friction coefficient value, are still not well understood. The present study addresses this issue by investigating the contribution of the friction coefficient to the occurrence of the instability events such as jackknife and rollover using the phase trajectory method, extending the works of Sun and He, 22 Ding et al 23 and Mendes. 24 In order to achieve this goal, the convergence region for different values of the friction coefficient is obtained and its boundaries are associated to the two investigated instability phenomena.…”

Investigation of road train divergent stability loss when moving along a program trajectory

“…In connection with the proposed further experiments with this installa tion and its improvement, attention is drawn to specialized studies on unstable driving conditions at high velocities [13]. And also on the features of the synthesis of safe control for AHV (Articulated Heavy Vehicle) systems [14]. Of particular interest are studies of the stability of the yaw of a tractorsemitrailer system in constant driving conditions, analyzed using the theory of bifurcations [15].…”

Bifurcation of Lane Change and Control on Highway for Tractor-Semitrailer under Rainy Weather

“…To protect the vehicle from spinning and realize improved cornering performance, van de Molengraft-Luijten et al employed the Routh-Hurwitz stability criterion and bifurcation theory method to get a system equilibrium approximation near the zero value for the forward speed and front wheel steering angle, which revealed the vehicle's instability under high speeds and substantial steering [6,7]. Similarly, Ding et al explained some instability phenomena of the vehicle system such as jackknifing, sideslip, and spinning by correlating them with the behavior in the neighborhood of unstable fixed points based on analysis of eigenvectors, phase trajectories, and status of lateral tire force saturation [8]. Sadri …”