On optimal recovery from terminal understeer
Journal article, 2014

This paper addresses the problem of terminal understeer and its mitigation via integrated brake control. The scenario considered is when a vehicle enters a curve at a speed that is too high for the tyre-road friction limits and an optimal combination of braking and cornering forces is required to slow the vehicle down and to negotiate the curve. Here, the driver commands a step steering input, from which a circular arc reference path is inferred. An optimal control problem is formulated with an objective to minimize the maximum off-tracking from the reference path, and two optimal control solutions are obtained. The first is an explicit analytical solution for a friction-limited particle; the second is a numerically derived open-loop brake control sequence for a nonlinear vehicle model. The particle solution is found to be a classical parabolic trajectory associated with a constant acceleration vector of the global mass center. The independent numerical optimization for the vehicle model is found to approximate closely the kinematics of the parabolic path reference strategy obtained for the particle. Using the parabolic path reference strategy, a closed-loop controller is formulated and verified against the solution from numerical optimization. The results are further compared with understeer mitigation by yaw control, and the parabolic path reference controller is found to give significant improvement over yaw control for this scenario.


Matthijs Klomp

E-AAM Driveline Systems

Mathias R Lidberg

Chalmers, Applied Mechanics, Vehicle Safety

Timothy James Gordon

University of Lincoln

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering

0954-4070 (ISSN)

Vol. 228 4 412-425

Areas of Advance


Subject Categories

Vehicle Engineering



More information

Latest update