Optimal control of road vehicles: theory and applications

In this thesis Optimal Control (OC) of road vehicles is studied especially focusing on minimum lap time simulations. The theory underlying the most used optimal control solving techniques is described, including both the Pontryagin Maximum Principle and the reduction to Nonlinear Programming. Direct and indirect methods for optimal control problems are presented and compared against minimum lap time simulations (LTS). Modelling of vehicles for OC-LTSs is studied in order to understand how different design choices can affect simulation outcomes. Novel multibody models of four wheeled vehicles - a GP2 car and a go-kart - for OC-LTSs are developed and validated thorough comparison with experimental data. Particular attention is dedicated to the simulation of tyre load dynamics, that is achieved by a proper modelling of the chassis and suspension motions and of the aerodynamic forces. OC-LTSs are applied to electric vehicles too, specifically to optimise the design of an electric motorbike taking part at the Tourist Trophy Zero competition. A concise yet effective model is proposed in order to perform reliable simulations on a 60km long road in a reasonable amount of time. Experimental data is used to validate the model. A direct full collocation transcription method for OCPs dealing with implicit differential equations and control derivatives is presented, moreover the structure of the resulting NLP problem is accurately described. The relationship between the first order necessary conditions and the Lagrange multipliers of the NLP and OC problems are derived under the adopted discretisation scheme. The presented transcription method is implemented into a software which is currently in use at the University of Padova to solve OC-LTSs.