Optimal control for a Formula One car with variable parameters

• Published in: Vehicle system dynamics Vol. 52; no. 5; pp. 653 - 678
• Main Authors: Perantoni, Giacomo, Limebeer, David J.N.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 04-05-2014
• Subjects: Automotive engineering; Computing time; Derivatives; Formula One car modelling; lap-time simulation; Mathematical analysis; Mathematical models; Nonlinear programming; numerical optimal control; Optimal control; Optimization; parameter optimisation
• ISSN: 0042-3114; 1744-5159
• DOI: 10.1080/00423114.2014.889315

The minimum-lap-time optimal control problem for a Formula One race car is solved using direct transcription and nonlinear programming. Features of this work include significantly reduced full-lap solution times and the simultaneous optimisation of the driven line, the driver controls and multiple car set-up parameters. It is shown that significant reductions in the driven lap time can be obtained from track-specific set-up parameter optimisation. Reduced computing times are achieved using a combination of a track description based on curvilinear coordinates, analytical derivatives and model non-dimensionalisation. The curvature of the track centre line is found by solving an auxiliary optimal control problem that negates the difficulties associated with integration drift and trajectory closure.