SAE 2017-01-1589 : 2017

The paper deals with the bifurcation analysis of a simple mathematical model describing an automobile running on an even surface. Bifurcation analysis is adopted as the proper procedure for an in-depth understanding of the stability of steady-state motion of cars (either cornering or running straight ahead). The aim of the paper is providing the fundamental information for inspiring further studies on vehicle dynamics with or without a human driver. The considered mechanical model of the car has two degrees of freedom, nonlinear tire characteristics are included. A simple driver model is introduced. Experimental validations of the model are produced. As a first step, bifurcation analysis is performed without driver (fixed control). Ten different combinations of front and rear tire characteristics (featuring understeer or oversteer automobiles) are considered. Steering angle and speed are varied. Many different dynamical behaviors of the model are found. Homoclinic bifurcations, stable and unstable limit cycles are found, giving a sound base of knowledge to control engineers who are asked to implement robust algorithms to reach stability. As a second step, bifurcation analysis is performed including the driver control action. Straight ahead motion is studied. Limit cycles exist that may suggest how complicated may be controlling the stability of such relatively simple running condition. The knowledge of the derived set of bifurcations seems important to fully understand the actual vehicle yaw motions occurring while running on an even surface and for conceiving robust control schemes for autonomous vehicles.

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