Optimal Control of a Formula One Car on a Three-Dimensional Track-Part 1: Track Modeling and Identification

Giacomo Perantoni, David J.N. Limebeer

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


The identification of three-dimensional (3D) race track models from noisy measured GPS data is treated as a problem in the differential geometry of curves and surfaces. Curvilinear coordinates are adopted to facilitate the use of the track model in the solution of vehicular optimal control problems. Our proposal is to model race tracks using a generalized Frenet-Serret apparatus, so that the track is specified in terms of three displacement-dependent curvatures and two edge variables. The optimal smoothing of the curvature and edge variables is achieved using numerical optimal control techniques. Track closure is enforced through the boundary conditions associated with the optimal control problem. The Barcelona formula one track is used as an illustrative example.

Original languageEnglish
Article number051018
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Issue number5
Publication statusPublished - 1 May 2015
Externally publishedYes


  • curvilinear coordinates
  • Darboux frame
  • differential geometry
  • Frenet-Serret apparatus
  • optimal control
  • ribbons
  • Road modeling

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications


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