Optimal control of a Formula One car on a three-dimensional track-part 2: Optimal control - Limebeer, D; Perantoni, G (American Society of Mechanical Engineers, 2015)
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 modelling 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 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.