# Non-Cooperative Spacecraft Pose Measurement with Binocular Camera and TOF Camera Collaboration
## 4 Experiment and Analysis
### Numerical Simulation
#### 4.2.2 Pose Measurement Experiment  
The target was a specific distance from the camera system. The camera system was kept still, and the target rotated 360\({}^{\circ}\) under the control of the robotic arm to simulate the tumbling state of the non-cooperative target in the space environment. Several frames of visual images and point cloud were captured. Figure 14 shows the left and right camera images and the point cloud data in a specific state.  
Rotation Experiment at Low Speed  
The target was set to a low-speed rotation rate (approximately 6 degrees per frame) in this experiment. Figure 15a,b present the X-, Y-, and Z-axis position and Euler angle curve  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Circular Board** & **Checkerboard** \\ \hline X-axis & 0.95 pixel & 1.78 pixels \\ Y-axis & 0.78 pixel & 1.71 pixels \\ \hline \hline \end{tabular}
\end{table}
Table 2: Reprojection errors of the two calibration boards.  
Figure 14: Left and right camera images and TOF camera data: (**a**) left image; (**b**) right image; (**c**) point cloud.  
results during the low-speed rotation process. Figure 15c,d show the X-, Y-, and Z-axis, position and Euler angle error results during the rotation process.  
Since the measurement coordinate system of the camera system was not parallel to the coordinate system of the robot arm, the X-axis and Y-axis rotated with it simultaneously when the target rolled around the Z-axis. The X-axis and Y-axis positions had a large amount of movement. Both the pitch and yaw angles had nutation of approximately 20 degrees. The maximum error and average error of the X, Y, and Z three-axis position of the proposed method was 7.6, 5.9, and 4.4 mm and 2.1, 1.4, and 0.76 mm, respectively. The maximum error and average error of the X, Y, and Z three-axis angle of the proposed method were 0.81\({}^{\circ}\), 0.61\({}^{\circ}\), and 0.81\({}^{\circ}\) and 0.22\({}^{\circ}\), 0.16\({}^{\circ}\), and 0.23\({}^{\circ}\), respectively.  
Figure 16 illustrates the X, Y, and Z three-axis position and Euler angle error results obtained by the proposed method, the stereo vision method, the traditional fast point feature histograms (FPFH) [31], and the ICP algorithm throughout the low-speed process.  
Figure 15: Pose estimation experimental results at low speed: (**a**) absolute position; (**b**) absolute angle; (**c**) error of position; (**d**) error of angle.  
Figure 16: Comparison of the error results of the different methods at low speed: (**a**) X-axis position error; (**b**) Y-axis position error; (**c**) Z-axis position error; (**d**) X-axis angle error; (**e**) Y-axis angle error; (**f**) Z-axis angle error.  
As shown in Figure 16, it can intuitively be seen that the pose result obtained from the stereo vision method had a larger error. The maximum error and average error of the X, Y, and Z three-axis position of the stereo vision method was 24.9, 20.4, and 8.3 mm and 6.2, 7.9, and 1.8 mm, respectively. The maximum error and average error of the X, Y, and Z three-axis angle of the stereo vision method was 2.85\({}^{\circ}\), 1.53\({}^{\circ}\), and 2.59\({}^{\circ}\) and 0.66\({}^{\circ}\), 0.47\({}^{\circ}\), and 0.67\({}^{\circ}\), respectively.  
The traditional FPFH algorithm can also obtain the initial value, mainly by applying the fast point feature histogram to extract the key features, employing the initial sampling consistency registration algorithm for rough registration. The ICP fine registration and pose correction were conducted in this comparison experiment. The maximum error and average error of the X, Y, and Z three-axis position of the FPFH method was 18.3, 14.2, and 5.7 mm and 4.8, 4.0, and 1.4 mm, respectively. The maximum error and average error of the X, Y, and Z three-axis angle of the FPFH method were 0.99\({}^{\circ}\), 0.88\({}^{\circ}\), and 2.57\({}^{\circ}\) and 0.28\({}^{\circ}\), 0.20\({}^{\circ}\), and 0.64\({}^{\circ}\), respectively.