Longitudinal force distribution using quadratically constrained linear programming

Abstract

In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle–driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.

Keywords:

• vehicle dynamics control
• optimisation
• optimal force distribution
• non-linear programming

Acknowledgements

The author wishes to thank the Swedish National Research Program Intelligent Vehicle Safety Systems (IVSS) for financial support. Thanks are also due to Anders Boström, Bo Egardt and Mathias Lidberg from Chalmers University of Technology and Gunnar Olsson from Saab Automobile for supervision of this work. The author is grateful to Tim Gordon from the University of Michigan Transportation Research Institute for providing valuable feedback on this work. All figures are exported from Matlab^™ using print_pdf by Oliver Woodford.