A free-trajectory quasi-steady-state optimal-control method for minimum lap-time of race vehicles

Minimum lap time problems are usually solved employing quasi-steady-state models on a pre- determined (fixed) trajectory or employing dynamic models on a free (i.e. not predetermined) trajectory. This work describes a third approach, where the minimum-lap-time problem is solved using quasi-steady-state models and free trajectory. The method builds upon g-g maps that can either be derived numerically or experimentally. Such g-g-speed surfaces can either represent the performance of a car or a motorcycle. Both a double-track car model and a motorcycle model are employed as examples of applications. The effect of the free-trajectory vs. fixed-trajectory assumption is also discussed

Minimum-lap-time optimisation and simulation

The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with trajectories that are either pre-assigned or free to be optimised. The fundamentals of nonlinear optimal control are summarised. These fundamentals are the basis of most of the vehicular optimal control methodologies and solution procedures reported in the literature. The key features of three-dimensional road modelling, vehicle positioning and vehicle modelling are also summarised with a focus on recent developments. Both cars and motorcycles are considered

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