# Indoor Autonomous Vehicle Navigation--A Feasibility Study Based on Infrared Technology
## 3 Results and Discussion
### Trajectory Analysis of Path  
For a _semi-circular_ type invisible zone, the \"light and dark\" contrast of the _diameter_ margin is much stronger than that of the _circular arc_ margin. That is to say, the _semi-circular_ type invisible zone is suitable for straight type guidance. Ideally, the trajectory of the autonomous vehicle should be a straight line when the _semi-circular_ type invisible route is applied. Obviously, the key problem is: \"How wide is the line?\"  
Figure 14 shows the illustration of trajectory analysis of the path. \"W\" is the width of the car body, which equals the distance between two front wheels. \"S\" is the spacing between the two infrared receivers in front. However, \"D\" stands for the _longitudinal dynamic range_ of the trajectory. A detailed figure is shown in Figure 15.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline
**No.** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** \\ \hline Offset (mm) & +4 & +5 & \(-\)15 & \(-\)5 & \(-\)15 & \(-\)7 & \(-\)15 & \(-\)7 & \(-\)6 & \(-\)16 & \(-\)30 & +2 & \(-\)25 & \(-\)14 & \(-\)29 & \(-\)9 & \(-\)5 & \(-\)13 & 0 & +2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The data of the positioning experiment.  
Figure 13: The pictures captured around the positioning point.  
Apparently, \"D\" is highly positively correlated with \"S\". Precisely speaking, it can be expressed in the equation below:  
\[\mathrm{D-W<S} \tag{2}\]  
In this case, W = 165 mm and S = 30 mm. Table 2 shows the data of the experiment.  
Table 2 recorded 20 cruise trips of the test vehicle along the invisible route at a speed of 10 cm/s. For each trip, \"Left\" stands for the lowest level that the left wheel reached. Similarly, \"Right\" stands for the highest level that the right wheel reached. All of the data were measured in relative coordinate reference to a fixed point (origin). The final effort was to find out the _maximum of the highest levels_ (which was 268 mm in Table 2), and the _minimum of the lowest levels_ (which was 93 mm in Table 2). The \"D\"--i.e., the so-called _longitudinal dynamic range of the trajectory_--should be the difference between the two extreme values, which is:  
\[\mathrm{D=268-93=175\;(mm)} \tag{3}\]  
\[\mathrm{and,\;D-W=175-165=10\;(mm)<S\;(30\;mm)} \tag{4}\]  
In principle, the result is consistent with the above discussion. However, the obvious question is: is the smaller \"S\" better? Indeed, a larger \"S\" will lead to a relatively wider straight line of trajectory. But, a countereffect might arise when the \"S\" is smaller than a threshold. Figure 16 indicates the trajectories for different settings of \"S\".  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline
**No.** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** \\ \hline Left (mm) & 94 & 95 & 96 & 96 & 95 & 96 & 95 & 96 & 94 & 94 & 93 & 94 & 94 & 95 & 94 & 95 & 94 & 95 & 94 & 96 \\ Right (mm) & 265 & 267 & 268 & 267 & 266 & 266 & 265 & 264 & 265 & 263 & 263 & 263 & 264 & 265 & 265 & 265 & 266 & 264 & 265 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The data of the longitudinal dynamic range of the trajectory.  
Figure 14: An illustration of the trajectory analysis of the path.  
Figure 15: The illustration of the longitudinal dynamic range of the trajectory.  
Not only would the \"D\" stop decreasing, the average velocity of the test vehicle could also be significantly reduced when the \"S\" is smaller than a threshold. In this research, by trial and error, - 2-4 cm is the suitable \"S\" for navigation on the _invisible route_. In fact, the _cruising speed_ is another point of concern for setting \"S\". However, we have not devoted too much effort to this issue.