# Camera Calibration in High-Speed Robotic Assembly Operations
## 5 Conclusions  
The presented study was focused on robotic vision systems, with the main subject being camera calibration for robotic applications. The main goal of the research was to develop a method for calibrating the camera with respect to the measurement plane--the plane in which the detected objects are placed. The calibration method was developed using two approaches, the first based on the law of cosines and the second based on plane interpolation. The calculations regarding camera inclination were checked in both cases using the experimental setup. Based on the obtained results, the following conclusions were drawn:  
* By using two approaches for camera calibration, with different calculation methods, the results could be discussed through comparative analysis. This allowed to highlight the advantages and disadvantages of each method. While the law of cosines approach is simpler and easier to implement, without further refining, the high error levels make it unsuitable to be integrated in robotic vision applications. * The average error of around 1% for the plane interpolation approach is acceptable for most robotic applications. At a wider angle, a 70\({}^{\circ}\) angle, for example, the error is around 0.7\({}^{\circ}\). * The planar interpolation approach has the advantage of an increased level of precision for wider spacing between the measurement points. Also, while there is a decrease in precision for greater camera heights, the error levels still remain around 1%. * The described method does not require any calibration sheet or other dedicated materials, which makes it suitable for almost any workspace configuration. Using this procedure, the calibration can be performed in any position during operation, thus lowering the time required. * Even though this calibration method sometimes has a lower accuracy, it is more suitable for some unstructured applications like those in which the position of the robot changes over time (i.e., robots mounted on mobile platforms, unstructured pick and place assembly operations), where other calibration methods, like the one implying a calibration pattern, are difficult to implement. This method could be implemented in real-time during robot operation, while other calibration methods are usually performed before robot operation. * The Python code is easy to develop for the proposed calibration algorithm and it can be integrated with most acquisition software. * By integrating the Python code with the acquisition software, the input data can be fed to the system in real-time, which means that the calibration can be performed while the application is running. Thus, the data acquisition software can adapt immediately to any changes in the working environment, and periodical calibration cycles are no longer necessary. * The calibration method described in this study holds significant potential to enhance results in industrial robotic applications, such as pick and place and assembly, and in other fields employing vision systems. The presented research developed a framework for camera calibration that has certain advantages, as highlighted above. Besides these considerations, it is also worth noting that the proposed method can be used to improve productivity for applications that require camera calibration. Since no separate calibration procedure is required and the developed Python subroutine can be used at any moment, the calibration can be performed without interrupting the robot program, which reduces cycle times. Also, these aspects make the procedure more convenient when compared to other approaches, even more so when taking into account that no printed calibration sheet is required. This implies that the need for a dedicated calibration area and correct calibration planning within the robot task is eliminated, which also frees up the robot workspace. Based on this framework, future studies can refine and improve the described methods, considering the specifics of various applications.