## 1 Introduction  
The rapidly growing demand for passenger and commercial vehicles increases the number of road accidents around the world. In addition to their negative influence on road safety, accidents also have an indirect harmful impact on the environment and cause threats to human health and life. In cases when the human factor plays an important role, modern electronics and control systems may support the driver's reaction and skills to improve the stability and performance of the vehicle and avoid accidents. Two of the most important on-board safety systems are ABS and ESP. Both systems have become mandatory for all passenger vehicles and most commercial vehicles. The ABS and ESP safety features in vehicle dynamics control have been known for a long time. However, the existing control algorithms are rarely investigated from the viewpoint of robust operation in different road conditions. Many of the results discussed in the published studies are describing simple maneuvers, such as straight-line braking with a uniform road surface. Few investigations are known for emergency braking on complex road profiles, such as a curved road with split-\(\upmu\) or a curved road with varying tire-road friction coefficients. Within the framework of the presented study, fuzzy theory has been selected for the controller implementation. The fuzzy logic controllers (FLC) are known as efficient tools in solving complex tasks such as ABS and ESP control. A combination of ABS and ESP can solve the robustness problem of the braking performance. To confirm it, the FLC-based braking will be discussed for the different complex maneuvers such as a combination of road profiles and split-\(\upmu\) road surfaces. The first ABS applications arose several decades ago [1] and still use rule-based methods as the dominant control approach. In the modern ABS systems installed in commercial vehicles, the braking pressure is increased or reduced based on the wheel speed and the slip switching threshold comparison [1]. The slip is set to a constant value, for instance 20% as it is optimal for the most common surface--dry asphalt. The braking surface is not recognized and the threshold value is equal for every road condition. This approach leads to energy losses because each road adhesive characteristic requires its optimal wheel slip value. This is why many researchers have focused on intelligent control algorithms for braking processes, trying to estimate an optimal one for every road condition slip threshold. However, the analysis of the bibliography presented in [2] shows that nowadays the FLC is also being intensively used in ABS and ESP design. One of the first ABS control mechanisms based on the fuzzy algorithm was patented in 1989 by the Nissan Motor Co., Ltd., (Yokohama, Japan) [3]. Furthermore, many other solutions based on the FLC were proposed. Thanks to its simplicity and robustness, FLC proved to be equally applicable to on-road [4] and off-road vehicles [5]. In [6], a model reference adaptive control (MRAC) was introduced to tune the FLC in order to be able to control all kinds of nonlinear systems. Furthermore, the MRAC was used in a braking system in [7] as an ABS intelligent control. The simulation results were shown for a variety of road conditions (from icy to wet). The proposed solution requires a reference slip value, which is set to 20% for any kind of road surface. A similar assumption for the constant value of the optimal wheel slip is also proposed for ABS, as described in [8]. Another example is the model-based Takagi-Sugeno (T-S) FLC designed for a single-car model [9]. The controller copes well in optimal braking wheel slip maintenance, which the model considers a reference constant. Many different fuzzy proportional-integral-derivative (PID) approaches were also investigated [10; 11; 12]. Yet the results are limited because the situation considered in most cases is braking on a straight road with an optimal slip of 20%.