Keywords: modular robotics, modular robotic systems, self-reconfigurable modular robots, autonomous robots, forward kinematics, inverse kinematics
Analysis of methods for solving inverse kinematics of modular reconfigurable systems
UDC 519.688; 519.715
DOI: 10.26102/2310-6018/2021.35.4.025
The relevance of this work is due to the actualization of methods for solving the inverse kinematics in relation to various kinematic structures (formations) of reconfigurable modular systems. The purpose of the work is to analyze methods for solving the inverse kinematics, which can be applied to various formations of self-configuring multilink robotic systems. A study of the forward kinematics of modular robotic systems various formations is conducted on the basis of the previously obtained research results of other scientists. The analysis of methods for solving the inverse kinematics of modular reconfigurable systems was carried out and an assessment of their possible application for various kinematic structures of modular systems was made. Analytical and numerical methods of solution were considered, and examples of practical application were also given. In addition, the paper analyzed various machine learning methods. With regard to the results of the study, the advantages and disadvantages of various methods for solving the inverse kinematics of modular robotic systems were highlighted. Potentially suitable methods for solving this problem from the point of view of computational complexity and application possibilities for systems with a redundant number of degrees of freedom are identified. Among the methods considered, particular solutions of the inverse kinematics of a certain modular reconfigurable system kinematic structure are often evaluated. As a result of the analysis, it is possible to isolate areas of research related to the development of machine learning methods that are potentially suitable for use in control problems for self-reconfiguring modular robotic systems. The development of such a method will enable to reduce the number of preliminary analytical calculations, to implement a control system that does not require significant changes in algorithms, and also to expand the possibilities of using modular systems by adapting this system to the movement surface.
1. Yim M., Duff D.G., Roufas K. Modular reconfigurable robots, an approach to urban search and rescue. 1st Intl. Workshop on Human-friendly Welfare Robotics Systems. 2000:69–76.
2. Støy K. Reconfigurable robots. Springer Handbook of Computational Intelligence. Springer, Berlin, Heidelberg. 2015:1407-1421. https://doi.org/10.1007/978-3-662-43505-2_73.
3. Brunete A., Ranganath A., Segovia S., de Frutos J.P., Hernando M., Gambao E. Current trends in reconfigurable modular robots design. International Journal of Advanced Robotic Systems. 2017;14(3):1729881417710457. https://doi.org/10.1177/1729881417710457.
4. Liu J., Zhang X., Hao G. Survey on research and development of reconfigurable modular robots. Advances in Mechanical Engineering. 2016;8(8):1687814016659597. https://doi.org/10.1177/1687814016659597.
5. Jones A.B., Cameron T., Eichholz B., Loegering D., Kray T., Straub J. Self-reconfiguring modular robot learning for lower-cost space applications. 2019 IEEE Aerospace Conference. IEEE. 2019:1-6. https://doi.org/10.1109/AERO.2019.8742133.
6. Pacheco M., Fogh R., Lund H.H., Christensen D.J. Fable II: Design of a modular robot for creative learning. 2015 IEEE International Conference on Robotics and Automation (ICRA). IEEE. 2015:6134-6139. https://doi.org/10.1109/ICRA.2015.7140060.
7. Li Y., Zhu S., Wang Z., Zhang L., Ma X., Cui Z. The kinematics analysis of a novel self-reconfigurable modular robot based on screw theory. DEStech Transactions on Engineering and Technology Research. 2016. DOI: 10.12783/dtetr/mime2016/10196.
8. Feczko J., Manka M., Krol P., Giergiel M., Uhl T., Pietrzyk A. Review of the modular self-reconfigurable robotic systems. 2015 10th International Workshop on Robot Motion and Control (RoMoCo). IEEE. 2015:182–187. https://doi.org/10.1109/RoMoCo.2015.7219733.
9. Yim M., Shen W.M., Salemi B. et al. Modular self-reconfigurable robot systems [grand challenges of robotics]. IEEE Robotics & Automation Magazine. 2007;14(1):43–52. https://doi.org/10.1109/MRA.2007.339623.
10. Blinov D., Vatamaniuk I., Saveliev A. Method for Reconfiguring Kinematic Structure of Modular Robots Using Deep Reinforcement Learning. Proceedings of the Computational Methods in Systems and Software. Springer, Cham. 2021:443–451. https://doi.org/10.1007/978-3-030-90321-3_36.
11. Singh T.P., Suresh P., Chandan S. Forward and inverse kinematic analysis of robotic manipulators. International Research Journal of Engineering and Technology (IRJET). 2017;4(2):1459–1468.
12. Craig J.J. Introduction to Robotics: mechanics and control. 2009:408 p.
13. Kelemen M., Virgala I., Lipták T., Miková Ľ., Filakovský F., Bulej V.A. novel approach for a inverse kinematics solution of a redundant manipulator. Applied Sciences. 2018;8(11):2229. https://doi.org/10.3390/app8112229.
14. Martín A., Barrientos A., Del Cerro J. The natural-CCD algorithm, a novel method to solve the inverse kinematics of hyper-redundant and soft robots. Soft robotics. 2018;5(3):242–257. https://doi.org/10.1089/soro.2017.0009.
15. Merlet J.P. A new generic approach for the inverse kinematics of cable-driven parallel robot with 6 deformable cables. Advances in Robot Kinematics 2016. Springer, Cham. 2018:209-216. https://doi.org/10.1007/978-3-319-56802-7_22.
16. Aristidou A., Lasenby J., Chrysanthou Y., Shamir A. Inverse kinematics techniques in computer graphics: A survey. Computer Graphics Forum. 2018;37(6):35–58. https://doi.org/10.1111/cgf.13310.
17. Wu W., Guan Y., Li H., Su M., Zhu H., Zhou X., Zhang H. Task-oriented inverse kinematics of modular reconfigurable robots. 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. IEEE. 2013:1187–1192. https://doi.org/10.1109/AIM.2013.6584255.
18. Chen I.M., Yang G., Kang I.G. Numerical inverse kinematics for modular reconfigurable robots. Journal of Robotic Systems. 1999;16(4):213-225. https://doi.org/10.1002/(SICI)1097-4563(199904)16:4%3C213::AID-ROB2%3E3.0.CO;2-Z.
19. Chen W., Chen I.M., Lim W.K., Yan, G. Cartesian coordinate control for redundant modular robots. Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics.'cybernetics evolving to systems, humans, organizations, and their complex interactions'. 2000;5:3253–3258. https://doi.org/10.1109/ICSMC.2000.886505.
20. Aristidou A., Lasenby J. Inverse kinematics: a review of existing techniques and introduction of a new fast iterative solver. 2009.
21. Saveliev A.I., Blinov D.V., Erashov A.A. Selection of kinematic structure of modular robotic system depending on type of surface for movement. Proceedings of the Southwest State Universityа. 2021;25(3). (In Russ.) (In Press).
22. Neubert J., Lipson H. Soldercubes: a self-soldering self-reconfiguring modular robot system. Autonomous Robots. 2016;40(1):139-158. https://doi.org/10.1007/s10514-015-9441-4.
23. Jing G., Tosun T., Yim M., Kress-Gazit H. Accomplishing high-level tasks with modular robots. Autonomous Robots. 2018;42(7):1337-1354. https://doi.org/10.1007/s10514-018-9738-1.
24. Pavliuk N.A., Krestovnikov K.D., Pykhov D.E. Mobile autonomous reconfigurable system. Problemele energeticii regionale. 2018;1:125-135. DOI: 10.5281/zenodo.1217296.
25. Rocha C.R., Tonetto C.P., Dias A. A comparison between the Denavit–Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators. Robotics and Computer-Integrated Manufacturing. 2011;27(4):723–728. https://doi.org/10.1016/j.rcim.2010.12.009.
26. Pfotzer L., Ruehl S., Heppner G., Roennau A., Dillmann R. KAIRO 3: A modular reconfigurable robot for search and rescue field missions. 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014). IEEE. 2014:205–210. https://doi.org/10.1109/ROBIO.2014.7090331.
27. Chen I.M., Yang G. Inverse kinematics for modular reconfigurable robots. Proceedings. 1998 IEEE International Conference on Robotics and Automation. IEEE. 1998;2:1647-1652. https://doi.org/10.1109/ROBOT.1998.677390.
28. Zhao J., Cui X., Zhu Y., Tang S. UBot: a new reconfigurable modular robotic system with multimode locomotion ability. Industrial Robot: An International Journal. 2012:178–190. https://doi.org/10.1108/01439911211201645.
29. Zhu Y., Bie D., Iqbal S., Wang X., Gao Y., Zhao J. A simplified approach to realize cellular automata for ubot modular self-reconfigurable robots. Journal of Intelligent & Robotic Systems. 2015;79(1):37-54. https://doi.org/10.1007/s10846-014-0084-z.
30. Park H., Kwak B., Bae J. Inverse kinematics analysis and COG trajectory planning algorithms for stable walking of a quadruped robot with redundant DOFs. Journal of Bionic Engineering. 2018;15(4):610-622. https://doi.org/10.1007/s42235-018-0050-8.
31. Biswal P., Mohanty P.K. Development of quadruped walking robots: A review. Ain Shams Engineering Journal. 2021;12(2):2017-2031. https://doi.org/10.1016/j.asej.2020.11.005.
32. Espinal A., Rostro-Gonzalez H., Carpio M. et al. Quadrupedal robot locomotion: a biologically inspired approach and its hardware implementation. Computational intelligence and neuroscience. 2016;2016. https://doi.org/10.1155/2016/5615618.
33. Atique M.M.U., Sarker M.R.I., Ahad M.A.R. Development of an 8DOF quadruped robot and implementation of Inverse Kinematics using Denavit-Hartenberg convention. Heliyon. 2018;4(12). https://doi.org/10.1016/j.heliyon.2018.e01053.
34. Sastra J., Chitta S., Yim M. Dynamic rolling for a modular loop robot. The International Journal of Robotics Research. 2009;28(6):758–773. https://doi.org/10.1016/j.mechmachtheory.2018.11.004.
35. Wang X., Jin H., Zhu Y., Chen B., Bie D., Zhang Y., Zhao J. Serpenoid polygonal rolling for chain-type modular robots: A study of modeling, pattern switching and application. Robotics and Computer-Integrated Manufacturing. 2016;39:56–67. https://doi.org/10.1016/j.rcim.2015.12.003.
36. Peiper D.L. The kinematics of manipulators under computer control (No. CS-116). Stanford Univ Ca Dept Of Computer Science. 1968.
37. Kotlygin D.S., Sedelnikov I.A., Petukhov N.V. Analytical and numerical nethods of inverse kinematics problem solution for DELTA robot. Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta = Proceedings of Irkutsk State Technical University. 2017;21(5):87–96. (In Russ.)
38. Gupta A., Bhargava P., Agrawal S., Deshmukh A., Kadam B. Comparative Study of Different Approaches to Inverse Kinematics. International Conference on Advances in Computing and Data Sciences. Springer, Singapore. 2018:556–563. https://doi.org/10.1007/978-981-13-1813-9_55.
39. Kucuk S., Bingul Z. Inverse kinematics solutions for industrial robot manipulators with offset wrists. Applied Mathematical Modelling. 2014;38(7-8):1983–1999. https://doi.org/10.1016/j.apm.2013.10.014.
40. Aristidou A., Lasenby J. FABRIK: A fast, iterative solver for the Inverse Kinematics problem. Graphical Models. 2011;73(5):243–260. https://doi.org/10.1016/j.gmod.2011.05.003.
41. Iakovlev R., Denisov A., Prakapovich R. Iterative method for solving the inverse kinematics problem of multi-link robotic systems with rotational joints. Proceedings of 14th International Conference on Electromechanics and Robotics “Zavalishin's Readings”. Springer, Singapore. 2020:237-251. https://doi.org/10.1007/978-981-13-9267-2_20.
42. Kumar V., Sen S., Roy S.S., Das S.K., Shome S.N. Inverse kinematics of redundant manipulator using interval newton method. Int. J. Eng. Manuf. (IJEM). 2015;5(2):19–29. DOI: 10.5815/ijem.2015.02.03.
43. Angeles J. On the numerical solution of the inverse kinematic problem. The International Journal of Robotics Research. 1985;4(2):21–37. https://doi.org/10.1177%2F027836498500400203.
44. Uicker Jr J.J., Denavit J., Hartenberg R.S. An iterative method for the displacement analysis of spatial mechanisms. 1964;31(2):309-314. https://doi.org/10.1115/1.3629602.
45. Goldenberg A.A., Apkarian J.A., Smith H.W. A new approach to kinematic control of robot manipulators. 1987;109(2):97–103. https://doi.org/10.1115/1.3143843.
46. Hall Jr A.S., Root R.R., Sandgren E. A dependable method for solving matrix loop equations for the general three-dimensional mechanism. 1977;99(3):547–550. https://doi.org/10.1115/1.3439277.
47. Almusawi A.R.J., Dülger L.C., Kapucu S. A new artificial neural network approach in solving inverse kinematics of robotic arm (denso vp6242). Computational intelligence and neuroscience. 2016;2016. https://doi.org/10.1155/2016/5720163.
48. Duka A.V. Neural network based inverse kinematics solution for trajectory tracking of a robotic arm. Procedia Technology. 2014;12:20–27. https://doi.org/10.1016/j.protcy.2013.12.451.
49. Smirnov P.A., Yakovlev R.N. Approach to Positioning Links of the Manipulator Using Neural Networks. Mekhatronika, Avtomatizatsiya, Upravlenie. 2019;20(12):732-739. (In Russ.) https://doi.org/10.17587/mau.20.732-739.
50. Momani S., Abo-Hammour Z.S., Alsmadi O.M.K. Solution of inverse kinematics problem using genetic algorithms. Applied Mathematics & Information Sciences. 2016;10(1):225. http://dx.doi.org/10.12785/amis/Solution*of*inverse*kinematics*problem.
51. Starke S. A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics. Diss. Universität Hamburg, Fachbereich Informatik. 2016.
52. El-Sherbiny A., Elhosseini M.A., Haikal A.Y. A comparative study of soft computing methods to solve inverse kinematics problem. Ain Shams Engineering Journal. 2018;9(4):2535-2548. https://doi.org/10.1016/j.asej.2017.08.001.
53. Galemov R.T., Masalsky G.B. Hybrid Search Method for Solving the Inverse Kinematics of a Multilink Manipulator. Mekhatronika, Avtomatizatsiya, Upravlenie. 2018;19(7):464–473. (In Russ.) https://doi.org/10.17587/mau.19.464-473.
54. Dobrynin D.A. Principles of learning management system for exoskeleton control task. Jekstremal'naja robototehnika = Extreme robotics. 2017;1(1):297–301. (In Russ.).
55. Dobrynin D. Simulation of Trainable Control System for Quadruped Robot. Electromechanics and Robotics. Springer, Singapore. 2022:155–164. https://doi.org/10.1007/978-981-16-2814-6_14.
56. Phaniteja S., Dewangan P., Guhan P., Sarkar A., Krishna K.M. A deep reinforcement learning approach for dynamically stable inverse kinematics of humanoid robots. 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE. 2017:1818-1823. https://doi.org/10.1109/ROBIO.2017.8324682.
57. Ansari Y., Falotico E., Mollard Y., Busch B., Cianchetti M., Laschi C. A multiagent reinforcement learning approach for inverse kinematics of high dimensional manipulators with precision positioning. 2016 6th IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob). IEEE. 2016:457–463. https://doi.org/10.1109/BIOROB.2016.7523669.
58. Ren H., Ben-Tzvi P. Learning inverse kinematics and dynamics of a robotic manipulator using generative adversarial networks. Robotics and Autonomous Systems. 2020;124: 103386. https://doi.org/10.1016/j.robot.2019.103386.
59. Blinov D., Saveliev A., Shabanova A. Deep Q-Learning Algorithm for Solving Inverse Kinematics of Four-Link Manipulator. Proceedings of 15th International Conference on Electromechanics and Robotics" Zavalishin's Readings". Springer, Singapore. 2021:279-291. https://doi.org/10.1007/978-981-15-5580-0_23.
Keywords: modular robotics, modular robotic systems, self-reconfigurable modular robots, autonomous robots, forward kinematics, inverse kinematics
For citation: Erashov A.A., Blinov D.V., Saveliev A.I. Analysis of methods for solving inverse kinematics of modular reconfigurable systems. Modeling, Optimization and Information Technology. 2021;9(4). URL: https://moitvivt.ru/ru/journal/pdf?id=1101 DOI: 10.26102/2310-6018/2021.35.4.025 .
Received 29.11.2021
Revised 22.12.2021
Accepted 28.12.2021
Published 31.12.2021