Elucidating Vehicle Lateral Dynamics Using a Bifurcation Analysis

Abstract

Issues of stability and bifurcation phenomena in vehicle lateral dynamics are presented. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamics model is obtained. Local stability and existence conditions for saddle-node bifurcation appearing in vehicle dynamics with respect to the variations in front wheel steering angle are then derived via system linearization and local bifurcation analysis. Bifurcation phenomena occurring in vehicle lateral dynamics might result in spin and/or system instability. A perturbation method is employed to solve for an approximation of system equilibrium near the zero value of the front wheel steering angle, which reveals the relationship between sideslip angle and the applied front wheel angle. Numerical simulations from an example model demonstrate the theoretical results.

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

“…Time-Invariant Case 1) Pure-slip model: The stability of the linear part of the system (16) with the pure-slip time-invariant assumption, i.e, constant longitudinal velocity u, can be addressed with the Hurwitz criterion on the state matrix A in (17). Having negative eigenvalues yields mχ 2 u 2 > mχ…”

“…In other words, the system (46) may be stable while A s (ω) is unstable. To find a physical condition (interpretation) for the current time-varying linear lateral models (17) and (36) similar to the condition (4) in the 2DOF bicycle model, the stability of the symmetric A s (ω) =…”

“…A theoretical analysis followed by a numerical study was performed in [16] and [17] to develop a new methodology for the local stability assessment of vehicle dynamics. The effects of the bifurcation phenomena on vehicle spin and system instability were examined using the Perturbation method.…”

A feedback linearization design for the control of vehicle’s lateral dynamics

“…Such a bifurcation phenomenon might result in the spin of a vehicle as steering angle changes. The application of bifurcation theory to engineering problems have been well exploited in the recent years (e.g., [10][11][12]). A theoretical analysis of vehicle dynamics has been obtained by applying the bifurcation theory [10], which revealed that the uncontrolled version of vehicle's lateral dynamics might undergo a stationary saddle-node bifurcation.…”

“…The application of bifurcation theory to engineering problems have been well exploited in the recent years (e.g., [10][11][12]). A theoretical analysis of vehicle dynamics has been obtained by applying the bifurcation theory [10], which revealed that the uncontrolled version of vehicle's lateral dynamics might undergo a stationary saddle-node bifurcation. In addition, the controllability and direct state feedback control laws were also proposed in [13] to stabilize the bifurcation points.…”