# Environment Perception with Chameleon-Inspired Active Vision Based on Shifty Behavior for WMRs
## 4 Modelling of FOV in Chameleon-Inspired Active Vision Based on Shifty-Behavior Mode for WMRs
### FOV Model with Binocular Synchronous Motion  
The FOV model is shown in Figure 4 when the cameras are in synchronous motion, and the PTZ beam carrying the two cameras is rotated \(\alpha\) to the left around its central axis, resulting in the two cameras rotating \(\alpha\) to the left simultaneously. The direction of the beam rotating to the right around its central axis is defined as positive. In this paper, the FOV of the binocular vision system was analyzed by taking the horizontal FOV as an example. The parameters of the binocular visual system of WMRs are shown in Table 2.  
To reflect the size change relationship of the FOV, the inner tangent circle of the FOV defined to represent the size of the FOV [40], as shown in Figure 4a. In this binocular synchronous motion mode, the radii of the inner tangent circles of the monocular horizontal FOV, the binocular horizontal overlapping FOV, and the binocular horizontal merging FOV are calculated by the following equations:  
\[\left\{\begin{array}{l}r_{1}=r_{2}=\leavevmode\
obreak\ ad/\left(2\sqrt{a^{2 }/4+f^{2}}+a\right)\\ r_{12}=\leavevmode\
obreak\ (ad-lf)/\left(2\sqrt{a^{2}/4+f^{2}}+a\right)\\ r_{0}=\leavevmode\
obreak\ (ad+lf)/\left(2\sqrt{a^{2}/4+f^{2}}+a\right)\end{array}\right. \tag{7}\]  
To analyze the measurement accuracy of the binocular vision system, the resolution is analyzed. Figure 4b shows the imaging model of the binocular vision system, with \(OXZ\) representing the vision system's coordinate system and \(O_{1}X_{1}Z_{1},O_{2}X_{2}Z_{2}\) representing the left and right camera coordinate systems, respectively. Assuming that the image element size of CMOS is \(\Delta w\), then the resolution \(\Delta X,\Delta Z\) of the vision system in the \(X,Z\) direction in the binocular synchronous motion mode is given by the following equations:  
\[\left\{\begin{array}{l}\Delta X=\min\left(\left|\frac{\tilde{z}}{f}\right| \Delta w,\left|\frac{\tilde{z}}{f}\right|\Delta w\right)\\ \Delta Z=\min\left(\left|\frac{2z^{2}}{f(l+2x)}\right|\Delta w,\left|\frac{2z^ {2}}{f(l-2x)}\right|\Delta w\right)\end{array}\right. \tag{8}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Descriptions** & **Range (mm)** & **Parameters** & **Descriptions** & **Range (mm)** \\ \hline \(a\) & Length of CMOS target surface & \([3,6,12.7]\) & \(\theta_{1},\theta_{2}\) & Monocular horizontal FOV & \([9.3^{\circ},50.9^{\circ}]\) \\ \(f\) & Focal length & \([6,36]\) & \(\theta_{12}\) & Binocular overlapping horizontal FOV & N/A \\ \(l\) & Distance between two eyes & \([90,360]\) & \(\theta_{0}\) & Binocular merging horizontal FOV & N/A \\ \(d\) & Object distance & N/A & \(r_{1},r_{2}\) & Radius of the inner tangent circle of & N/A \\  & Distance from the object to the & & & & \\  & & & & & \\ \(d_{12}\) & vertex of the binocular horizontal & N/A & \(r_{12}\) & the binocular horizontal & N/A \\  & overlapping FOV & & & overlapping FOV & \\  & Distance from the object to the & & & & \\ \(d_{0}\) & vertex of the binocular horizontal & N/A & \(r_{0}\) & Radius of the inner tangent circle of & N/A \\  & merging FOV & & & & \\ \(A\) & Length of target object & N/A & \(\Delta w\) & Size of CMOS image element & \([0.002,0.01]\) \\ \(P(x,z)\) & Position of the target object in the & & N/A & & \\  & effective horizontal FOV & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the binocular visual system of WMRs.  
Figure 4: FOV model and imaging model in binocular synchronous motion mode: (**a**) horizontal field-of-view model of binocular vision system; (**b**) imaging model of binocular vision system.