Nonlinear modeling and analysis of vehicle planar motion 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. In this paper, a nonlinear vehicle model was developed 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 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. As illustrated in a numerical example, this strategy has been successfully used to analyze the nonlinear behavior of vehicle planar motion.