# Camera Calibration in High-Speed Robotic Assembly Operations
## 2 State of the Art  
Industry 4.0 represents the ongoing stage of macro-industrial development. Historically, each industrial development stage was powered by a huge leap in a certain scientific field: Industry 1.0 was triggered by mechanical devices and steam power, Industry 2.0 was triggered by electricity, and Industry 3.0 was triggered by electronics [9]. Following the same trend, Industry 4.0 was triggered by software and networking development. The manufacturing systems and the robots themselves are evolving on the \"smart\" path, being more and more capable of solving certain issues and adapting to significant changes on their own. On the other hand, the trend is to facilitate human integration in the industrial environment, somewhat reversing the long-standing status of industrial robots as machines that replace human work. This aspect is illustrated by the growing segment of collaborative applications [10; 11; 12; 13; 14]. Industry 4.0 is based on sensors, M2M communication, networking, ML, and, more recently, AI. As an important element in the sensors ecosystem, robotic vision has been approached by a large number of research works. An interrogation on Google Scholar returned more than 17,000 results published since 2020. One of the most important issues in the field is linked to camera calibration, as shown by [15; 16; 17; 18; 19; 20]. Camera calibration is performed in order to establish a link between the captured image coordinates and an external reference, such as the coordinates of the application or the coordinates of the robot workspace. Defining this relationship is necessary in order to develop a framework that can be used to convert coordinates from one reference to another. This is essential for acquiring relevant geometric information from the work scene, including workobject characteristics. Furthermore, using such a framework ensures that the collected data are transposed into a format that can be used outside of camera (image) frame of reference [21]. A comprehensive study of the relevant scientific literature revealed several methods and approaches regarding camera calibration in robotic vision applications. [PERSON] et al. [15] identified three groups of parameters that should be calibrated: camera parameters, hand-eye parameters, and structured light plane parameters. The research used a planar checkerboard as the calibration plane. Considering the robot base and tool coordinate systems as well as the camera coordinate system, the algorithm uses homogenous transformation matrices to determine the intrinsic and extrinsic parameters of the camera. For camera parameters calibration, the workpiece pose is changed several times while the robot-held camera is stationary. Then, the camera is moved to several different poses while the workpiece remains stationary. Using the data collected through the experimental procedure, the hand-eye relation was determined as a homogenous transformation matrix. Furthermore, the plane equation for the measured points expressed in the robot base coordinate system was determined using the least square fitting. \[ \begin{array}{c}E\\ C\end{array} M= \begin{pmatrix}R&T\\ 0&1\end{pmatrix}  \tag{1}\]  
The ultimate goal of any camera calibration and detection algorithm is to correctly recognize patterns, features, shapes, and other data in a format that can be further used in a broader context. [PERSON] and [PERSON]. [22] proposed an iterative closest point algorithm approach to compare the object point cloud to a model point cloud and to perform the transformation using several iterations. The studied robotic task belonged to the bin-picking category. Matrix calculation based on homogenous transformation is used. The method assumes that the shape of the work object is known from the beginning and does not vary. Thus, a model of the part can be structured and used as a reference. The only variables remaining in the task environment are linked to the part position and orientation. For calibration purposes, a checkered board is used, as previously.