# Autonomous Manipulator of a Mobile Robot Based on a Vision System
## 5 Conclusions  
The proposed manipulator positioning system based on the vision system underwent rigorous testing. It is noteworthy that the system was successfully used to perform all the tasks involving autonomous panel operation required for the European Rover Challenge 2021 and 2022 competition, simulating some aspects of missions to Mars. Equipped with this autonomous positioning system, the manipulator is able to perform such tasks as pressing and releasing switches and buttons or turning knobs on the panel and picking up and placing objects. Because of the insufficient accuracy, the system is not suitable for high-precision operations, e.g., inserting a plug into a port or gripping very small objects. Incorporating this autonomous system into an unmanned ground vehicle requires that corrections to the position of the manipulator should be made in real time. The shock-absorbing suspension and other elements of the vehicle structure are responsible for changes in the tilt and thus changes in the position of the center of gravity of the moving robotic arm. Failure to introduce corrections in real time may result in failure to perform the required task. The tests that involved locking the suspension (tilt) showed that the manipulator performed the task correctly. There were also tests performed with non-stiffened suspension, which gave correct results. The resulting vision system error is very small if the manipulator is closer to the panel. In the case of a greater distance (above 340 mm), a larger error is not a problem, because after positioning the manipulator in front of the panel, corrections to the position are calculated in two places, in the base position and just in front of the switch. From the close proximity to the marker, the system calculates the position with high accuracy, which allows for accurate arrival and execution of the task, despite significant initial errors. In addition, the calculation of the correction is necessary due to the movable suspension of the entire robot. The results presented in the paper were obtained under laboratory conditions, with powerful artificial lighting (250 W lamp). However, the system also worked outdoors and indoors under daylight conditions and performed its function correctly. Further research on the system will focus on increasing the autonomy, which will involve recognizing and localizing markers on the panel by using artificial neural network models to handle unknown panels. Conceptualization, A.A.-M., P.A.L., J.Z. and D.S.P. ; methodology and software A.A.-M. and J.Z. ; validation, K.B. ([PERSON]), D.W., S.K., G.B. and K.B. ([PERSON]); formal analysis, investigation, and resources: A.A.-M., K.B. ([PERSON]), D.S.P., K.B. ([PERSON]), G.B. and S.K. ; writing--original draft preparation, P.A.L. ; writing--review and editing, A.A.-M., P.A.L. and D.S.P. ; visualization, A.A.-M., K.B. ([PERSON]), K.B. ([PERSON]), S.K. and D.W. All authors have read and agreed to the published version of the manuscript. Project co-financed Ministry of Education and Science No. SKN/SP/534769/2022. Not applicable. The authors declare no conflict of interest. This appendix provides details on the solution of the manipulator kinematic analysis. The transformation matrix takes the general form:  
\[\mathbf{M}= \begin{bmatrix}\mathbf{R}&\mathbf{t}\\ \mathbf{0}^{T}&1\end{bmatrix}  \tag{1}\]It can be decomposed into homogenous transformations of translation and rotation around the respective axes:  
\[Trans_{x,y,z}= \begin{bmatrix}1&0&0&x\\ 0&1&0&y\\ 0&0&1&z\\ 0&0&0&1\end{bmatrix} ;\;Rot_{x,\alpha}= \begin{bmatrix}1&0&0&0\\ 0&\cos\alpha&-\sin\alpha&0\\ 0&\sin\alpha&\cos\alpha&0\\ 0&0&0&1\end{bmatrix}  \tag{10}\]  
\[Rot_{y,\beta}= \begin{bmatrix}\cos\beta&0&\sin\beta&0\\ 0&1&0&0\\ -\sin\beta&0&\cos\beta&0\\ 0&0&0&1\end{bmatrix} ;\;Rot_{z,\gamma}= \begin{bmatrix}\cos\gamma&-\sin\gamma& 0&0\\ \sin\gamma&\cos\gamma&0&0\\ 0&0&1&0\\ 0&0&0&1\end{bmatrix}  \tag{11}\]  
The manipulator diagram is shown in Figure 11 with Denavit-Hartenberg parameters marked.