# Steering Assist Control for Bicycles with Variable Trail Effect
## 3 Results  
Based on the signal processing described in the previous section, we analyze the bicycle steering angle during slalom biking and show that the proposed steering assist control is effective in the case with a load in the front basket. A rider may only partially mishandle the handlebars of a bicycle. Therefore, we extract from the handlebar angle data only those areas where the rider is not operating the handlebars well. The extracted sections are defined as the sections where handlebar angle overshoot occurs. We extract three large amplitude points for each situation in the section selected for analysis. The data extracted in this experiment are shown in Table 2.  
Figures 12-14 show the steering angle profile during the slalom biking for each rider. Each figure contains three time series of the steering angle with blue, red, and yellow charts representing the first, second, and third trial biking, respectively. As explained in the previous section, based on the change in yaw angle, we focus on the steering angles when the bicycle returns to straight biking after turning a corner. The framed area in each graph corresponds to such a situation. The green frame indicates the first corner, followed by the blue and purple frames indicating the second and third corners. Correspondingly, the labels data1, data2, and data3 in Table 2 correspond to the blue, orange, and yellow charts in the graph, respectively. In the same manner, the labels 1, 2, and 3 in the \"corner\" column mean the first, second, and third corners, respectively. As the first investigation, we evaluate the steering angle profiles without and with a 12 kg load in the front basket. In other words, that is to check the influence of the load put in the front basket on the steering angles. For this purpose, the trend component of the steering angles' profile is removed from the steering angle of the area enclosed by the frame. And, its frequency characteristics are analyzed by FFT. The results of the frequency analysis based on FFT are shown in Figure 15a-d. As in Figure 12-14, blue, red, and yellow charts indicate the first, second, and third trial runs, respectively. For the first rider, it can be seen that the steering angles during biking with a load have increased the vibration components of 0.6-0.8 Hz by 7 deg compared to the steering angles in the case of no load. In the case of the second rider, similarly to that of the first rider, the steering angles during biking with load show increased vibration components of 0.6-0.8 Hz and 0.4 Hz by up to 4 deg compared to the steering angles in the case of no load. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Rider 1**} & \multicolumn{2}{c}{**Rider 2**} & \multicolumn{2}{c}{**Rider 3**} \\ \hline
**Situation** & **Data** & **Corner** & **Data** & **Corner** & **Data** & **Corner** \\ \hline \multirow{4}{*}{No load} & data1 & 2 & data1 & 1 & data1 & 1 \\ \cline{2-6}  & data1 & 3 & data1 & 3 & data1 & 2 \\ \cline{2-6}  & data2 & 2 & data2 & 1 & data2 & 3 \\ \hline \multirow{4}{*}{12 kg weight} & data2 & 1 & data1 & 2 & data1 & 1 \\ \cline{2-6}  & data2 & 2 & data1 & 3 & data2 & 3 \\ \cline{2-6}  & data3 & 2 & data3 & 3 & data3 & 2 \\ \hline \multirow{4}{*}{Variable trail control} & data1 & 1 & data1 & 2 & data2 & 2 \\ \cline{2-6}  & data2 & 2 & data2 & 1 & data3 & 1 \\ \cline{2-6}  & data3 & 2 & data3 & 1 & data3 & 2 \\ \hline \multirow{4}{*}{Proportional assist control} & data1 & 1 & data1 & 1 & data2 & 1 \\ \cline{2-6}  & data1 & 2 & data1 & 2 & data2 & 2 \\ \cline{1-1} \cline{2-6}  & data1 & 3 & data2 & 1 & data3 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measurement data and labels to distinguish each data. In the case of the third rider, the steering angles in the case with the load show a significant increase in the low frequency component of 0.4 Hz compared to the steering wheel steering in case of no load.