## 4 Capability on Obstacle Avoidance
### Comparison with Passenger Cars and Motorcycles
#### 4.2.4 Mechanism of Superiority of PMV  
As shown in Figure 24, for the dynamics of passenger cars, centrifugal force acting on gravity center height (G.C.H.) and supporting force acting on ground height cause roll moment, and lateral transfer of vertical load causes opposite the direction roll moment. These two moments are balanced with each other and the balance angle is expressed by Equation (7). \[\tan\varphi_{e}\ =\ \tan\varphi_{t}\ =\ \frac{d_{t}}{\text{G.C.H.}} \tag{7}\]  
\[\tan\varphi_{e}\ =\ \tan\varphi_{a}\ =\ \frac{d_{a}}{\text{G.C.H.}} \tag{8}\] \begin{table}
\begin{tabular}{|l|c|c||c|c|} \hline \multicolumn{2}{|c||}{**Driver**} & \multicolumn{3}{c|}{**Maneuver**} \\ \hline
**Item** & **Unit** & **Value** & **Item** & **Model** \\ \hline \hline \multicolumn{2}{|c|}{comering cutting coefficient (cc)} & \multicolumn{1}{c|}{0.1} & Longitudinal dynamics & IFDDriver \\ \hline Max. longitudinal acceleration & m/s\({}^{2}\) & 3.0 & Lateral dynamics \textless{} 841.5 m & Follow course \\ \hline Max. longitudinal deceleration & m/s\({}^{2}\) & -4.0 & (\(D_{t}\) = 1.5 m) \textgreater{} 841.5 m & IFDDriver \\ \hline Max. lateral acceleration & m/s\({}^{2}\) & 20 & Lateral dynamics \textless{} 843.0 m & Follow course \\ \hline \multicolumn{2}{|c|}{PylonShiftFdcof} & \multicolumn{1}{c|}{0.15} & (\(D_{t}\) = 2.0 m) \textgreater{} 843.0 m & IFDDriver \\ \hline \multicolumn{2}{|c|}{} & \multicolumn{1}{c|}{} & Lateral dynamics \textless{} 844.0m & Follow course \\ \hline \multicolumn{2}{|c|}{} & \multicolumn{1}{c|}{} & (\(D_{t}\) = 2.5 m) \textgreater{} 844.0 m & IFDDriver \\ \hline \end{tabular}
\end{table} 
Table 4: Driver maneuvers were set to avoid feint motions. Figure 23: Comparison of capabilities on obstacle avoidance. \(\varphi_{\rm e}\): equivariant roll angle  
\(d_{\rm t}\): moment arm length on lateral transfer of load  
G.C.H. : gravity center height  
\(\varphi_{\rm a}\): actual roll angle  
\(d_{\rm a}\): moment arm length on actual roll  
In motorcycles, there is no lateral transfer of the vertical load. The roll moment due to the centrifugal force acting on the G.C.H. is balanced by the roll moment due to the combining of the vertical forces. The moment arm length moving in a lateral direction is caused by the actual vehicle roll angle. This is the balance angle of single-track vehicles such as bicycles and motorcycles and is expressed by Equation (8). In PMVs with active tilting mechanisms, the strokes on both wheels are given to get the roll angle. This is equivalent to positively generating the lateral transfer of the vertical load. After the roll angle is obtained as equivariantly the same as motorcycles, the vertical loads of both wheels settle equally as a result. However, while the response of the roll angle is delayed, lateral transfer of the vertical load occurs between both wheels as in passenger cars. As shown in Figure 25, the roll moment due to lateral transfer of the vertical load is the same as that of passenger cars, and the roll moment due to the actual roll angle of the vehicle body is the same as that of motorcycles. This is expressed by Equation (9). In the dynamics of passenger cars, lateral force and lateral acceleration on the front body occur without any delay due to the front tires slip angle by steering angle input. However, since the roll moment of inertia balances dynamically with the roll moment due to lateral acceleration, there is a slight delay in the lateral transfer of the vertical loads. In motorcycles, lateral acceleration can only be obtained when inward roll occurs in the vehicle body. This is a factor that causes a large delay in the lateral acceleration of motorcycles (slow avoidance motion), while delay in the lateral acceleration of a passenger car is not seen in avoiding obstacles. \[\tan\varphi_{e}\ =\ \tan\varphi_{a}+\tan\varphi_{t}\ =\ \frac{d_{a}+d_{t}}{ \text{G.C.H.}} \tag{9}\]  
Figure 24: Roll moment balance on car and motorcycle.