**5. Conclusions**

This paper presents four mathematical algorithms to find an initial estimation of a kinematic structure of a serial robotic manipulator. The input values are the number of joints, the position of the base of the manipulator, and the target pose of its TCP. The outputs are the standard DH parameters of a kinematic structure that can reach the given pose either by position or by position and orientation. The presented methods are applicable in the topic of synthesis of the kinematic structure of robotic manipulators, where they can serve as an initial guess of a structure.

The examples of three poses for all four algorithms are shown and compared using the manipulability measure and the arm length. However, it is not easy to determine which method out of these four is the best as it is always depending on the input, especially the TCP pose. The manipulability measure indicates that the D type algorithm, which can fully satisfy any given pose, provides the best manipulability in general, because it avoids placing joints on a single line and places them on a Bézier curve instead. In addition to that, the joints also tend to prevent collisions. On the other hand, if the given pose is representing a specific case, as a parallel axis or axes with a base frame axis or axes, one should be always watchful and comparison with the other presented algorithms is suggested. As expected, algorithm types A and B achieved the best results in the case of the arm length measure, when only a position is desired. However, in some cases, the C and D algorithms may fully achieve a pose with a manipulator with similarly long links.

Future steps are to implement this method in an optimisation algorithm and to observe if the convergence is faster or if the obtained result and the values of objective functions are better.

The algorithms were tested in MATLAB and the scripts are available as Supplementary Material for this paper or with eventual updates as an open source package on a public repository [35].

**Supplementary Materials:** The source code of algorithms presented in this paper is available as open source repository on the Github page of the Department of Robotics, VSB-Technical University of Ostrava, Czech Republic: github.com/robot-vsb-cz/initial-estimation accessed on 15 April 2021. **Author Contributions:** Conceptualisation, D.H. (Daniel Huczala) and T.K.; methodology, D.H. (Daniel Huczala); software, D.H. (Daniel Huczala) and P.O.; validation, D.H. (Daniel Huczala), M.P. and D.H. (Dominik Heczko); formal analysis, V.M.; investigation, D.H. (Dominik Heczko); resources, P.O.; data curation, T.K.; writing—original draft preparation, D.H. (Daniel Huczala); writing—review and editing, T.K. and M.P.; visualisation, D.H. (Dominik Heczko); supervision, M.P.; project administration, V.M.; funding acquisition, V.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This article has been elaborated under support of the project Research Centre of Advanced Mechatronic Systems, reg. no. *CZ*.02.1.01/0.0/0.0/16\_019/0000867 in the frame of the Operational Program Research, Development and Education. This article has been also supported by specific research project *SP*2021/47 and financed by the state budget of the Czech Republic.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Source code available on: github.com/robot-vsb-cz/initial-estimation accessed on 15 April 2021.

**Conflicts of Interest:** The authors declare no conflict of interest.
