Applications and Methodologies for Minimum-Lap-Time Problems

The aim of this thesis is to formulate and create tools that address the Minimum- Lap-Time Problem (MLTP) from small to large scale dimension, across a spectrum of vehicle model complexities. As part of this thesis, a software designed to tackle MLTP is developed by using the MATLAB programming language. Minimum–Lap–Time Problem (or Planning) is a well-established problem in the race car industry to provide guidelines for drivers and optimize the vehicle’s setup. Initially, the study concentrates on elucidating the benefits that solving such problems can provide to the race car sector. Subsequently, the research shifts towards the development of tools that can effectively solve the MLTP for varying vehicle model complexities. This progression encompasses models ranging from the double-track to more intricate ones involving multibody vehicle model. In pursuit of these objectives, the proposed methodologies involve the optimal control approach to formulate MLTP as an Optimal Control Problem (OCP) which is then discretized using the direct collocation technique. The resulting Nonlinear Programming (NLP) is solved using the interior-point solver IPOPT interfaced with the CasADi optimization suite. Starting from a serial solution approach whereby the resulting NLP is solved all at once, a distributed optimization algorithm is developed to tackle MLTPs characterized by a large number of variables. Finally, complementary to the central research one interconnected subject is explored. In particular, a novel mesh refinement algorithm designed to enhance the required precision when solving a numerical optimal control problem is investigated.