Minimum stopping distance on split friction roads via joint control of steering and individual wheel braking

Journal article, 2026

This paper examines the problem of minimising stopping distance on split friction roads by joint control of individual wheel brakes and automated steering. A static optimisation problem is introduced that maximises braking on split friction roads without veering out-of-lane. The analysis of the optimal brake forces and counter-steering shows different properties of the optimal solution depending on the degree of split friction assymmetry between the left and right vehicle sides. The solutions are categorised into two regions: small and large split friction asymmetries. At a small split friction asymmetry, all the tyres are at their force peak in their force-slip curves and the slips are small. Therefore, the traditional ABS and a path-following controller give optimal braking and path deviation performance. Whereas at a large split friction asymmetry, it is shown that having all tyres at their force-slip peak is impossible. Instead, allowing larger slips at the low-friction tyres gives maximum braking. Surprisingly, constraining slip constraint on one low-friction tyre limits the available tyre force on the high-friction ones, ultimately leading to longer stopping distances. For braking at large splits, we propose using optimal static solutions to set a feedforward steering angle based on the split friction condition, together with a high-friction brake control to the yaw torque. This control framework is tested in vehicle simulation in the CarMaker environment. Closed-loop simulations of the proposed control framework are compared to an emulated driver response derived from measurements of a professional driver. Stopping distance gains of 6–13% are observed by automating the steering compensation. Further simulations demonstrate that the proposed control framework provides maximum braking even when one side has zero friction