• formula SAE
• autonomous racing
• FSAE
• vehicle
• model predictive control
• MPC
• spatial formulation
• online

An online Model Predictive Control (MPC) for the Formula SAE race car of the University of Pisa is developed, based on a single-track model in which the controlled variables are steer angle, acceleration and braking forces. The approach chosen to be adopted in the problem formulation wants to develop a Nonlinear optimisation Problem (NLP) as lightweight as possible to be computed. A spatial formulation embeds the vehicle in the track reference frame, simplifying its constraints. A linearisation of tyre adherence constraints makes great impact on the problem complexity and, consequently, on the solver convergence rate. Race track representation is based on NURBS curves, whose formulation is extended to include road widths; the proposed formulation can cope with any track length without being burdened by it. The MPC formulation is expanded to consider unmeasured disturbances and plant-model mismatches by augmenting the vehicle model with disturbance states that act linearly in it, leading to the so-called zero-offset MPC formulation; its response in presence of both persistent disturbances and unmodeled dynamics is investigated and proven to be suppressed in many circumstances. The produced code is then deployed on a target embedded device and tested on simulations, leading to computational times theoretically acceptable in the control of the real vehicle.