# Autonomous Manipulator of a Mobile Robot Based on a Vision System
## 4 Discussion  
Based on the research on the positioning of the manipulator, it was determined that in more than 90% of cases, the error is less than 1 mm. The standard deviation was 0.617 mm. Half of the errors obtained were below the value of 0.4 mm, and 75% were below the value of 0.6 mm. This means that the positioning of the manipulator works with good accuracy, sufficient for robot applications. The maximum error was 3 mm, and the minimum error was 0 mm. The vision system tests have shown that the distance measurement is relatively accurate, and the measurement error is, in most cases, less than 1 mm. The relative error is small, in most cases less than 0.5%, and it becomes noticeably bigger for longer distances above 340 mm and is in the range of 0.7-1.5%. Measurements of rotation around the axis of the coordinate system are burdened with greater error, and they can even exceed 3\({}^{\circ}\), which has a significant influence on the operation of the entire manipulator control system. The tests were performed at different distances from the marker and at different angles. For long distances above 340 mm, the error in measuring the distance could be much greater and could even be a few millimeters. The vision system settings allow the detection of a marker from a distance in the range of approximately 200-420 mm for a marker with a side of 50 mm. The error in measuring the distance grows as the angle of inclination relative to the marker increases. In Table 2, the first half of the measurements were made from a position opposite the panel; in this group, the maximum error was 0.97 mm and the minimum error was 0.13 mm. The second group consisted of measurements for an increasing angle. The unfavorable position resulted in a large error of 5.9 mm. For the performed measurements, the standard deviation was 1.69 mm. Half of the measurements had an error below 0.61 mm and 75% of the measurements were below 0.94 mm. In other work, authors obtained similar results of position measurement using the vision system. However, in each study, the research was carried out on a different scale. For example, in the case of navigation, longer distances (several meters) were measured against larger markers (15-20 cm). An example can be seen in a previous study [20], where the authors obtained a relative error usually below 1%, and for long distances, below 2%. In another study [6], tests were carried out for a distance of up to 150 cm and a marker with a size of 100 mm. In a range of up to 1 m, the authors obtained an error close to zero for small distances, which increased to several millimeters with the increasing distance. Another study [14] examined the problem on the micro scale, and the obtained relative error did not exceed 1%. The most similar study was performed in the paper [18], in which the estimation of the manipulator position was studied. The authors obtained an average absolute error for position measurements using a vision system of 1.8 mm, 0.2 mm, and 3.5 mm for the \(x\), \(y\), and \(z\) axes, and an average relative error of 1.6%, 0.2%, and 0.2%, respectively. Measurements were performed for a distance of 100-120 cm and a board with ArUco markers (A4 sheet of paper in size). Based on the research on the operation of the combined system, it was observed that the positioning error was greater than it would appear from separate studies of the systems, which had much lower errors. This error is, on average, a few millimeters. It was influenced by the error in the rotation measurement, which was up to several degrees. The system was tested by starting the measurement at various distances ranging from 300 to 400 mm and at different angles to the panel, from a straight view to approximately 45\({}^{\circ}\) sweating. For larger camera angles and longer distances, the positioning error was greater.