Abstract. The problems of semi-automatic control of a robot manipulator with position and orientation of the working tool set by a human operator are considered. Theoretical methods of setting robot tool orientation are discussed. Inverse kinematic problems solved in position control systems for a 6-link robot are formulated. Ways of solving such problems using iterative numerical methods with and without calculating the Jacobi matrix corresponding to the robot’s mechanism are studied. Examples of joint trajectories calculation for a 6-link robot moving the tool along a helical trajectory using different techniques of setting the tool orientation are presented. Convergence of iterative algorithms for solving inverse kinematic problems are analyzed.

Keywords: robot manipulator, semi-automatic robot control system, positional control, human operator, tool position and orientation, inverse kinematic problem, iterative numerical methods, algorithm testing, algorithm convergence

References:

1. Golovin V.F., Arkhipov M.V., Zhuravlev V.V. Mehatronika, Avtomatizacia, Upravlenie (Mechatronics, Automation, Control), 2011, no. 5, pp. 54–56. (in Russ.)
2. Kulakov F.M. Journal of Computer and Systems Sciences Intern., 2016, no. 4(55), pp. 635–682. (in Russ.)
3. Yurevich E.I. Osnovy robototekhniki (Fundamentals of Robotics), St. Petersburg, 2010. (in Russ.)
4. Cepolina F. and Michelini R.C. Intern. J. Med. Robot., 2004, no. 1(1), pp. 43–63.
5. Filaretov V.F., Katsurin A.A. Proc. on 11th Intern. Conf. on Control, Automation and Systems, KINTEX, Gyeonggi-do, Korea, 2011, pp. 649–654.
6. Filaretov V.F., Katsurin A.A. Advanced Materials Research, 2013, no. 717, pp. 573–578.
7. Soares B.F. ABCM Symposium Series in Mechatronics of the 21th International Congress of Mechanical Engineering, Natal, RN, Brazil, 2008, vol. 3, pp. 246–255.
8. Schilling Robotics/Technologies, www.fmctechnologies.com.
9. Wall J., Chandra V., Krummel T. Medical Robotics, I-Tech Education and Publishing, Vienna, Austria, 2008, рр. 491–506.
10. Rostova E., Rostov N., Sokolov B. Proc. of Interactive Collaborative Robotics, 3rd Intern. Conf., ICR 2018, Leipzig, Germany, 2018, рр. 222–232. https://doi.org/10.1007/978-3-319-99582-3_23.
11. Rostova E., Rostov N., Sobolevsky V., Zakharov V. Proc. of Interactive Collaborative Robotics, Third International Conference, ECMS 2019, Caserta, Italy, 2019, рр. 222–232. DOI: 10.7148/2019-0145.
12. Rostova E.N. Journal of Instrument Engineering, 2019, no. 11(62), pp. 989–996. https://doi.org/10.17586/0021-3454-2019-62-11-989-996. (in Russ.)
13. Zenkevich S.L., Yushchenko A.S. Osnovy upravleniya manipulyatsionnymi robotami (Fundamentals of Manipulation Robot Control), Moscow, 2004. (in Russ.)
14. Ignatova E.I., Lopota A.V., Rostov N.V. Sistemy upravleniya dvizheniyem robotov. Komp'yuternoye proyektirovaniye (Robot Motion Control Systems. Computer Design), St. Petersburg, 2014, 302 р. (in Russ.)
15. Park F., Lynch K. Modern Robotics: Mechanics, Planning and Control, Cambridge University Press, 2016, 544 p.
16. Rostov N.V. St. Petersburg State Polytechnical University Journal. Computer Science. Telecommunications and Control Systems, 2014, no. 5(205), pp. 93–99. (in Russ.)
17. Dennis J.E., Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Society for Industrial and Applied Mathematics, 1996.
18. Corke P.I. Robotics Toolbox 10.3.1 for MATLAB. Release 10. 2018.
19. Corke P.I. Robotics, Vision and Control. Fundamental Algorithms in MATLAB, Second edition, Springer International Publishing AG, 2017. ISBN 978-3-319-54413-7.