# Retro-Reflective-Marker-Aided Target Pose Estimation in a Safety-Critical Environment
## 2 Methods
### Automatic Offline Calibration Routine  
During operation inside the reactor, it is expected that cameras' calibration parameters will be affected by shocks, vibration, temperature changes, or other unforeseeable environment factors. Even though there are not yet experimental data on how volatile these parameters will be (since the reactor is under construction), there is a definite need to develop reliable methods for calibration of activated cameras (cameras that have been exposed to radiation and, therefore, cannot be in the same environment as the operators at the same time). The developed calibration procedure should happen offline in the hot-cell facility (dedicated area outside of the operating environment to process activated components) and without manual intervention. The method of choice for camera calibration throughout our work is Matlab's implementation [35] of [PERSON]'s widely known algorithm for photogrammetric camera calibration [36] using the distortion model of [37]. This method relies on a manual calibration image capture step, which means that the operator would have to move the manipulator and the attached cameras in the vicinity of a calibration pattern and capture a minimum of three calibration images at different camera orientations. This is an  
Figure 4: Illustration of our proposed marker, the off-the-shelf glass prism, retro-reflective tape, and a white diffuse element. Data on the left side of the figure are obtained by averaging the pixel values within the marker area in images taken at several incident angles. undesirable, time-consuming, and repetitive procedure with a low level of repeatability, since different manipulator positions provide slightly different calibration results. Some methods have been proposed in the literature for automatizing the image capturing step through the display of virtual targets on a screen [38]. These methods are, however, not applicable to our application due to the difficulty of introducing additional electronics in the hot-cell facility. Therefore, we developed a calibration routine to be performed autonomously by the robotic arm that produces fairly repeatable results. As a target, we used a checkerboard pattern that was placed in the hot-cell facility prior to the start of the calibration routine. Even though the same procedure could be used to re-calibrate the cameras in the reactor, based on the known relative position of the retro-reflective markers, we did not explore this option, mostly due to the tight space constraints in the environment. As a preliminary step, we summarize what is established as a good set of calibration images: Even though it is possible to obtain a calibration estimate from a smaller number of images [36], it is often recommended to acquire at least 10 images of the calibration pattern at different orientations relative to the camera. The images should be captured at a distance that corresponds roughly to the operating distance so that the pattern is in focus. The positions of the pattern shall be such that:  
(1) The checkerboard is at an angle lower than 45 degrees relative to the camera plane. According to the original work [36], when tested on synthetic data, the calibration method obtains most accurate estimates when the angle between the calibration target and image plane is higher. However, in real imaging conditions, where blur and distortion must be taken into account, angles close to 45 degrees might compromise the accuracy of corner detection, depending on the size of the checkerboard and the depth of field of the camera-lens system. (2) Feature points should be detectable on as much of the image frame as possible for adequate estimation of the lens distortion parameters. In our scenario, additional practical considerations need to be taken into account, such as the work-space limitations of the robotic arm and singularity regions of its joints.