# Path Planning Based on Obstacle-Dependent Gaussian Model Predictive Control for Autonomous Driving
## 4 Experiment
### Evaluation Metrics  
We assessed three evaluation metrics and confirmed the experimental results:  
1. computation time evaluation metric,
2. safety metric, and
3. comfort level quantification metric  
The computational time evaluation metric is the evaluation of whether or not the operation is performed quickly.  
Safety (\(ST\)) [39] evaluates the path for a narrow road and is expressed by (36)-(38):  
\[FR=\frac{\sum\limits_{i=1}^{N-1}|\theta_{i}-\theta_{V}|}{(N-1)180^{\circ}}, \tag{36}\]  
\[DR=\sum\limits_{i=1}^{N}\frac{D_{i}}{N\times D_{V}}, \tag{37}\]  
\[ST=(1-FR)\times DR, \tag{38}\]  
where \(N\) indicates the number of points in the created path, and \(FR\) is the angular difference between the generated and road centerlines (i.e., the fluctuation ratio). In addition, \(DR\) is the ratio of the distance from the nearest obstacle path to the road centerline (i.e., the deviation rate). Further, \(\theta_{i}\) is the \(i\)th angle change of the path, and \(\theta_{V}\) is the angular road change (\(\theta_{V}=0\) for a straight road). Moreover, \(D_{i}\) is the closest distance from the obstacle to the \(i\)th line vertex, and \(D_{V}\) is the nearest distance from the obstacle to the midpoint of the path corresponding to the \(i\)th line's vertex. Figure 14 lists the physical meaning for each variable. The closer \(ST\approx 1\), implies a more stable path. Therefore, through Scenario 1,we verified the driving stability of how close the test mobile robot drives to the centerline during each algorithm's driving evaluation.  
According to ISO 2631-1, the comfort level has measured a method of quantifying whole-body vibration related to human comfort. Based on this, we measured the comfort level using ISO 2631-1, which uses the weighted root mean square (\(RMS\)) acceleration (\(a_{k}\)) of the \(k\)-axis:  
\[a_{wk}^{2}=\frac{1}{T}\int\limits_{0}^{T}a_{k}^{2}(t)dt, \tag{39}\]  
where \(T\) is the measurement time.  
\[a_{w}=\sqrt{W_{d}^{2}a_{wx}^{2}+W_{d}^{2}a_{wy}^{2}+W_{k}^{2}a_{wz}^{2}}, \tag{40}\]  
where \(a_{w}\) is the frequency weighted acceleration time; \(a_{wx}\), \(a_{wy}\), and \(a_{wz}\) are the weighted \(RMS\) acceleration frequency weightings; \(W_{d}\) (\(x\)- and \(y\)-directions) and \(W_{k}\) (\(z\)-direction) relate to comfort; and \(W_{d}\) is a constant. We use the weighted \(RMS\) acceleration used in [40,41], as in the following (41):  
\[\begin{array}{l}x\ axis:W_{d}=1.4,\\ y\ axis:W_{d}=1.4,\\ z\ axis:W_{k}=1.\end{array} \tag{41}\]  
Table 1 lists the comfort levels corresponding to various \(a_{w}\) to indicate the possibility of the driver's response to the vibration during driving according to ISO 2631-1 [42].  
[PERSON] et al. [41] scored ISO 2631 for the comfort level. We scored it as displayed in Table 2 to indicate the comfort level. Through Scenarios 2 and 3, we compared the comfort level of the experimental results using each algorithm.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Overall Acceleration (m/s2)** & **Perception** \\ \hline \(a_{w}<0.315\) & Comfortable \\ \hline \(0.315<a_{w}<0.63\) & A little uncomfortable \\ \hline \(0.8<a_{w}<1\) & Fairly uncomfortable \\ \hline \(0.8<a_{w}<1.6\) & Uncomfortable \\ \hline \(1.25<a_{w}<2.5\) & Very uncomfortable \\ \hline \(2.5<a_{w}\) & Extremely uncomfortable \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comfort level based on ISO 2631-1.  
Figure 14: Safety (ST) metric.