Nonlinear modeling and analysis of vehicle dynamics

Most of the vehicle directional dynamics analysis has been carried out based on a linearized model and the assumption of constant forward speed. However, the nonlinearities found in the vehicle dynamical system can give rise to a variety of phenomena such as instabilities and bifurcation that escape detection during standard linear analysis. These phenomena significantly affect the system performance. The nonlinear phenomena can only be predicted by analyzing the nonlinear system dynamics. In this proposal, we will develop a nonlinear vehicle model based on the concept of Lagrange equations of motion. The assumption of constant forward speed is considered as a constraint to define the driving force, which in turn is used to reduce the differential equations. Thus, the analysis of constant speed behavior is reduced to a study of nonlinear zero dynamics. The equilibrium surface (manifold) is constructed and used to identify bifurcation points of the nonlinear vehicle model in terms of two parameters: speed and steering angle. The bifurcations involve interesting subtleties because of the in the system. As illustrated in a numerical example, this strategy has been symmetry successfully used to analyze the nonlinear behavior of vehicle planar motion. These two tools, nonlinear modeling and equilibrium surface analysis, comprise a powerful and effective method to identify and classify the critical conditions of the nonlinear dynamic behavior.