## Appendix B Vehicle Dynamics of the ROboMObil
In the first line of Equation (12), the modified velocity \(v_{\mathrm{mod}}^{\mathrm{C}}\)[12] is defined as:  
\[v_{\mathrm{mod}}^{\mathrm{C}}=\frac{\sqrt{v_{\mathrm{C}}^{\mathrm{C}}v_{ \mathrm{C}}^{\mathrm{C}}+4v_{\mathrm{min}}v_{\mathrm{min}}}+v_{\mathrm{C}}^{ \mathrm{C}}}{2}. \tag{13}\]  
This prevents division by zero if the velocity of the vehicle becomes zero. It should be noted that \(v_{\mathrm{mod}}^{\mathrm{C}}\approx v_{\mathrm{C}}^{\mathrm{C}}\) for \(v_{\mathrm{C}}^{\mathrm{C}}\gg v_{\mathrm{min}}\). By choosing a small \(v_{\mathrm{min}}\) the vehicle dynamics is only altered insignificantly by introducing \(v_{\mathrm{mod}}^{\mathrm{C}}\) as defined in Equation (13). The forces \(F_{x}^{\mathrm{C}}\) and \(F_{y}^{\mathrm{C}}\) in Equation (12) denote the forces on the vehicle's center of gravity (CoG) and are determined by  
\[ \begin{split} F_{x}^{\mathrm{C}}=-\sin(\delta_{\mathrm{f}})F_{ \mathrm{s}}^{\mathrm{W}_{\mathrm{f}}}-\sin(\delta_{\mathrm{f}})F_{\mathrm{s} }^{\mathrm{W}_{\mathrm{r}}}+\cos(\delta_{\mathrm{f}})F_{1}^{\mathrm{W}_{ \mathrm{f}}}+\cos(\delta_{\mathrm{r}})F_{1}^{\mathrm{W}_{\mathrm{r}}}-F_{ \mathrm{Air}_{x}}^{\mathrm{C}}\\ F_{y}^{\mathrm{C}}=\cos\left(\delta^{\mathrm{f}}\right)F_{\mathrm{s }}^{\mathrm{W}_{\mathrm{f}}}+\cos(\delta_{\mathrm{r}})F_{\mathrm{s}}^{ \mathrm{W}_{\mathrm{r}}}+\sin\left(\delta^{\mathrm{f}}\right)F_{1}^{\mathrm{W} _{\mathrm{f}}}+\sin(\delta_{\mathrm{r}})F_{1}^{\mathrm{W}_{\mathrm{r}}}-F_{ \mathrm{Air}_{y}}^{\mathrm{C}}\end{split}  \tag{14}\]  
with the longitudinal wheel forces \(F_{1}^{\mathrm{W}_{\mathrm{f}}}\) and \(F_{1}^{\mathrm{W}_{\mathrm{r}}}\) and the lateral wheel forces \(F_{\mathrm{s}}^{\mathrm{W}_{\mathrm{f}}}\) and \(F_{\mathrm{s}}^{\mathrm{W}_{\mathrm{r}}}\) of the front and rear wheel, respectively. Furthermore, \(F_{\mathrm{Air}_{x}}^{\mathrm{C}}\) and \(F_{\mathrm{Air}_{y}}^{\mathrm{C}}\) denote the external longitudinal and lateral air drag forces. The longitudinal wheel forces \(F_{1}^{\text{W}_{t}}\) and \(F_{1}^{\text{W}_{r}}\) are calculated by  
\[ \begin{split} F_{1}^{\text{W}_{t}}&=2\frac{\tau_{ \text{F}}}{R}-f_{r,\
u}\Big{(}\frac{mLg}{l_{\text{F}}+l_{\text{F}}}\Big{)}\\ F_{1}^{\text{W}_{r}}&=2\frac{\tau_{\text{F}}}{R}-f_{r, \
u}\Big{(}\frac{mlg}{l_{\text{F}}+l_{\text{F}}}\Big{)}\end{split}  \tag{10}\]  
where \(R\) denotes the wheel radius, \(g\) the gravity and \(f_{r,\
u}\) the speed dependent rolling resistance. The latter is given by  
\[f_{r,\
u}=f_{\text{R0}}+\frac{f_{\text{R1}}v_{\text{mod}}^{\text{C}}}{100}+f_{ \text{R4}}\Bigg{(}\frac{v_{\text{mod}}^{\text{C}}}{100}\Bigg{)}^{4}. \tag{11}\]  
with the rolling resistance parameters \(f_{\text{R0}}\), \(f_{\text{R1}}\) and \(f_{\text{R4}}\). The lateral wheel forces \(F_{\text{s}}^{\text{W}_{t}}\) and \(F_{\text{s}}^{\text{W}_{r}}\) are based on [PERSON]'s Magic Formula (MF) [19] and are calculated by  
\[ \begin{split} F_{\text{s}}^{\text{W}_{t}}&=\mu F_{ \text{z}}^{\text{f}}D\sin\big{(}\text{Catan}\big{(}B\alpha^{\text{W}_{t}}-E \big{(}B\alpha^{\text{W}_{t}}-\text{atan}\big{(}B\alpha^{\text{W}_{t}}\big{)} \big{)}\big{)}\big{)}\\ F_{\text{s}}^{\text{W}_{r}}&=\mu F_{\text{z}}^{ \text{r}}D\sin\big{(}\text{Catan}\big{(}B\alpha^{\text{W}_{r}}-E\big{(}B\alpha ^{\text{W}_{r}}-\text{atan}\big{(}B\alpha^{\text{W}_{r}}\big{)}\big{)}\big{)} \big{)},\end{split}  \tag{12}\]  
with \(B\), \(C\), \(D\) and \(E\) being the parameters of [PERSON]'s MF, \(\mu\) the friction coefficient between the tires and the street, and \(F_{\text{z}}^{\text{f}}\) and \(F_{\text{z}}^{\text{r}}\) the load on the front and rear axles, respectively. Note that the friction coefficient \(\mu\) is being randomized during training. The side slip angles in Equation (12) of the front and rear wheels are given by  
\[