*2.1. Three-Degrees-of-Freedom Bicycle Model*

The horizontal motion of the vehicle was computed using the bicycle model shown in Figure 3. Neglecting aerodynamic drag forces, the bicycle model is defined as follows:

. *<sup>β</sup>* <sup>=</sup> *Fy f* cos(*δ*)+*Fyr <sup>m</sup>* − *r*, . *<sup>r</sup>* <sup>=</sup> *Fy f* cos(*δ*)−*lrFyr Izz* , . *vx* <sup>=</sup> *Fxr*−*Fy f* sin(*δ*) *<sup>m</sup>* + *rvxβ*. (1)

**Figure 3.** Bicycle model for describing the horizontal motion of the vehicle.

Table 1 defines the notations used in this study. The state variables of the vehicle model in Equation (1) are the sideslip angle (*β*), yaw rate (*r*), and forward velocity (*vx*). The control inputs are the rear tire force (*Fxr*) and the steering angle (*δ*).

**Table 1.** Nomenclature of the present study.

