In this paper, we show that even an extremely simple nonlinear vehicle and driver model can show complex behaviors, like multi-stability and sensible dependence on the initial condition. The mechanical model of the car has two degrees of freedom, and the related equations of motion contain the nonlinear characteristics of the tires. The driver model is described by a single (nonlinear) equation, characterized by three parameters that describe how the driver steers the vehicle. Namely such parameters are the gain (steering angle per lateral deviation from desired path), the preview distance, and the reaction time delay. Bifurcation analysis is adopted to characterize straight ahead motion at different speeds, considering separately the two cases of understeering or oversteering cars. In the first case, we show that at suitable speeds the model can have three different attracting oscillating trajectories on which the system can work and that are reached due to different disturbances. In the second case, we confirm that instability arises if the forward speed is too high. The final results of the paper, bifurcation diagrams, can be used for many considerations critical both from the theoretical and from the practical viewpoints.

### Analysis of the lateral dynamics of a vehicle and driver model running straight ahead

#### Abstract

In this paper, we show that even an extremely simple nonlinear vehicle and driver model can show complex behaviors, like multi-stability and sensible dependence on the initial condition. The mechanical model of the car has two degrees of freedom, and the related equations of motion contain the nonlinear characteristics of the tires. The driver model is described by a single (nonlinear) equation, characterized by three parameters that describe how the driver steers the vehicle. Namely such parameters are the gain (steering angle per lateral deviation from desired path), the preview distance, and the reaction time delay. Bifurcation analysis is adopted to characterize straight ahead motion at different speeds, considering separately the two cases of understeering or oversteering cars. In the first case, we show that at suitable speeds the model can have three different attracting oscillating trajectories on which the system can work and that are reached due to different disturbances. In the second case, we confirm that instability arises if the forward speed is too high. The final results of the paper, bifurcation diagrams, can be used for many considerations critical both from the theoretical and from the practical viewpoints.
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2017
Bifurcation analysis; Driver; Multi-stability; Nonlinear systems; Vehicle system dynamics; Control and Systems Engineering; Aerospace Engineering; Ocean Engineering; Mechanical Engineering; Applied Mathematics; Electrical and Electronic Engineering
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11311/1023992`