Dynamics exploration of a single-track rigid car model with load transfer

In this paper we explore the dynamics of a single-track car model. We develop a model of a rigid car inspired to the well known bicycle model. The bicycle model is a planar rigid model that approximates the vehicle as a rigid body with two wheels. However, the bicycle model does not allow to describe the effect of load transfer, since it does not model the suspensions. Using an explicit formulation of the holonomic constraints imposed on the rigid model, we are able to model the load transfer of the car. The resulting model can be seen as a limit condition of a model with suspensions whose stiffness goes to infinity. The load transfer allows to have a more accurate model for the tires. We use a standard model known as Pacejka model that provides empirical curves describing the forces generated by the tires. With this model in hand, we perform an analysis of the equilibrium manifold of the vehicle and, as main contribution of the paper, we explore the trajectories of the system by use of novel nonlinear optimal control techniques. These techniques allow us to compute aggressive trajectories of the car vehicle and study how the vehicle behaves depending on its parameters. We compute trajectories for the vehicle on a real car testing track.