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Knowledge of the tyre-road interface traction limit during braking of a road vehicle can drastically improve safety and ensure stable braking on varied road conditions. This study proposes an optimal reference slip algorithm that determines the road surface while the vehicle is braking, by implicitly tracking the traction limit. It presents wheel slip variance regulation as a potential approach towards reference wheel slip estimation for wheel slip regulation (WSR). The variance regulation approach computes reference wheel slip using past wheel slip estimates and regulates wheel slip variation at a set point. This variance regulation problem was solved using least-squares estimation, yielding reference slip dynamics. A 3-staged nested control architecture was developed with reference slip dynamics to yield an anti-lock braking system (ABS) algorithm consisting of a brake controller, WSR algorithm and reference slip estimation. The algorithm was experimentally corroborated in a Hardware-in-Loop setup consisting of the pneumatic brake system of a heavy commercial road vehicle, and IPG TruckMaker®, a vehicle dynamics simulation software. The proposed ABS algorithm was tested on straight roads with homogeneous surfaces, split friction surfaces, and transition friction surfaces. It ensured stable braking in all road cases, with a 7%–18% reduction in braking distance on homogeneous road surfaces compared to the same vehicle without ABS. The vehicle directional stability was retained on a split-friction surface, and the ABS algorithm was observed to adapt to sudden transitions in the road surface.

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