## 4 Results  
A series of experiments were carried out to verify the validity of the proposed pose-estimation system. As shown in Figure 9, the automatic battery-replacement system was composed of the pose-estimation module, battery-extract module, and the robot manipulator. The electric automobile pulls over in the restricted parking spot, in front of the KUKA robot manipulator, then the image of the battery is captured by the camera. Meanwhile the laser rangefinder provides the real-time distance away from the car. The suction cups of the battery-extract module will take out the battery when the robot arm receives the pose information of the battery. Figure 8: The flow chart of model registration and pose estimation. Model registration is the first step before pose estimation. The image of the battery was recorded by the CCD camera (BM-500 GE, GigE Vision, JAI), with the resolution being 2456 \(\times\) 2058 and the unit cell size of the CCD sensor being 3.45 um \(\times\) 3.45 um. The camera was calibrated with a black and white chessboard by 96 corner points in eight rows and twelve columns. On the chessboard, 30 images were captured with different positions and orientations. The calibrated intrinsic parameters matrix of the camera is:  
\[A=\left[ \begin{array}{ccc}d_{u}f&s&u_{0}\\ 0&d_{y}f&v_{0}\\ 0&0&1\end{array} \right]=\left[ \begin{array}{ccc}2401.1&0&1251.8\\ 0&2410.6&1041.1\\ 0&0&1\end{array} \right] \tag{16}\]  
The lens distortion coefficient is [\(K_{1}\), \(K_{2}\), \(P_{1}\), \(P_{2}\)] = [\(-0.009549\), \(0.12061\), \(0.00015\), \(-0.00017\)], the higher order of distortion was too small to be considered. The feature matching result between reference image and scene image is shown in Figure 10. Compared to the ordinary method, the method based on spatial consistency rejected more than 40% of the outliers most of time. The KUKA robot manipulator with repeat positioning accuracy 0.2 mm was utilized to verify the validity of the system. The unique Euclidean 3D transformation between the camera coordinate system and the robot manipulator coordinate system was defined as a rotation matrix \(R^{\prime}\) and a 3D translation vector \(T^{\prime}\). The chessboard was used to calibrate the transformation model. To verify the accuracy of pose-estimation algorithm, the robot manipulator moved along the \(X\)-axis, \(Y\)-axis, and  
Figure 10: Feature matching result between reference image and image in scene; (a) Keypoints matching result based on ordinary method; (b) Keypoints matching result based on spatial consistency. Figure 9: (a) The pose-estimation module and battery-extract module are mounted onto the KUKA robot manipulator, the suction cup is used to pull the battery out of the electric automobile; (b) The scene of automatic battery-replacement process. \(Z\)-axis. Each time the robot manipulator moved forward for a certain distance, the camera captured the image of the battery. For every moving step along the axis, the pose-estimation module obtained the pose of the object relative to the robot manipulator. Then the relative computed distance between the consecutive two movements along each axis was easily obtained. Since the movement of the robot manipulator was easy to control, it was reasonable to compare it to the calculated distance along each axis and use the difference to indicate the accuracy of the pose estimation. As shown in Figure 11a, no matter which axis the robot manipulator moved along, the positioning error was lower than 1 mm. The estimation errors of the rotation matrix \(R\) are shown in Figure 11b, the rotation matrix \(R\) can be defined by the three angles: \(\theta\) (roll), \(\phi\) (pitch), \(\psi\) (yaw), which are the rotation angles around the \(Z\), \(X\), and \(Y\) axis, respectively. The errors of yaw angle were larger than that of roll angle and pitch angle, however that is acceptable for the estimation task in most cases. Even though the errors of yaw angle were acceptable for most cases in Figure 11, it was not reliable enough with errors of \(\pm 1^{\circ}\).