Optimal Control of a Formula One Car on a Three-Dimensional Track - Part 2: Optimal Control

D. J.N. Limebeer, G. Perantoni

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


The optimal control of a Formula One car on a three-dimensional (3D) track is studied. The track is described by its geodesic and normal curvatures, and its relative torsion. These curvature parameters are obtained from noisy measurement data using the optimal estimation technique described in Part 1. The optimal control calculations presented are based on the aforementioned track model and a vehicle model that is responsive to the geometric features of a 3D track. For vehicle modeling purposes, the track is treated as a plane tangent to a nearby point on the track's spine. This tangent plane moves under the car and is orthogonal to the principal normal vector m at the nearby spine point. Results are presented that compare two-dimensional (2D) and 3D minimum-lap-time results, with the two compared. The Barcelona Formula One track studied in Part 1 is used again as an illustrative example.

Original languageEnglish
Article number051019
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Issue number5
Publication statusPublished - 1 May 2015
Externally publishedYes


  • Formula One car modeling
  • lap-time simulation
  • numerical optimal control
  • parameter optimization
  • pseudospectral methods

ASJC Scopus subject areas

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


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