Real-time control for at-limit handling driving on a predefined path

Autonomous driving at at-limit handling represents a big challenge due to the nonlinear behaviour of a vehicle. In this paper, a hierarchical control scheme composed of two Nonlinear Model Predictive Controls (NMPCs) for path following is proposed. This structure allows for real-time feasibility without having to simplify excessively the vehicle model. The higher level NMPC operates on a long prediction horizon with a point-mass model which constraints are given by a tyre dependant ‘g–g diagram’. The output of the higher level is a velocity profile which is used as terminal constraint by the lower level NMPC. This operates on a short horizon and is based on a seven degrees of freedom vehicle model with full Pacejka Magic Formula tyre formulation on all tyres, load transfers and Limited Slip Differential. Because of the terminal set computed by the higher level, it is possible to use a short horizon and exploit the vehicle performance in real-time. For both controllers, the full Nonlinear Optimisation Problem is solved at each step. The algorithm is tested in a Model-in-the-Loop environment where a validated Vi-Grade vehicle model is controlled in co-simulation. The results show the effectiveness and feasibility of real-time control with complex vehicle models.