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

Artikel i vetenskaplig tidskrift, 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