• Direct Method
• Mesh Refinement
• Minimum-Lap-Time
• Multibody Model
• Optimal Control Problem
• Parallel Optimization
• Vehicle Dynamics

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.