Discrete (Two-State) Modular Hyper-Redundant Planar Manipulator

  • Ela Zawidzka Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland
  • Machi Zawidzki Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland


This paper presents a concept of an extremely simple planar manipulator composed of 24 congruent modules. Each module has only two possible discrete positions in relation to the previous module: left (-π/6) or right (π/6).  However, despite its conceptual simplicity, this manipulator can perform relatively demanding tasks, for  example as an inspection device. The manipulator is placed in an experimental environment, and the goal is to place its tip in close proximity to five given points without collisions. Despite the constraints of its motion, the manipulator effectively “crawls” inside the working space and visits assigned points. The control of the manipulator is executed by manual placing to desired configurations and interpolating the intermediate transitions. The preliminary results are promising and show that for certain practical types of tasks, the functionality and precision of this extremely simple manipulator could be sufficient, e.g., visual inspection, provision of survival supplies, placing of explosives, etc.


discrete manipulator, hyperredundant, snake robot, modular,


1. J. Gray, The mechanism of locomotion in snakes, Journal of Experimental Biology, 23(2): 101–120, 1946, doi: 10.1242/jeb.23.2.101.
2. S. Hirose, Biologically Inspired Robots: Snake-Like Locomotors and Manipulators, Oxford University Press, 1993.
3. A.J. Ijspeert, A. Crespi, Online trajectory generation in an amphibious snake robot using a lamprey-like central pattern generator model, [in:] Proceedings of the 2007 IEEE International Conference on Robotics and Automation (ICRA 2007), pp. 262–268, IEEE, 2007, doi: 10.1109/ROBOT.2007.363797.
4. G.S. Chirikjian, J.W. Burdick, Design and experiments with a 30 DOF robot, [in:] Proceedings IEEE International Conference on Robotics and Automation, Vol. 3, pp. 113—119, 1993, doi: 10.1109/ROBOT.1993.291862.
5. B. Klaassen, K.L. Paap, GMD-SNAKE2: a snake-like robot driven by wheels and a method for motion control, [in:] Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No. 99CH36288C), Vol. 4, pp. 3014–3019, IEEE, 1999, doi: 10.1109/ROBOT.1999.774055.
6. G. Miller, Snake robots for search and rescue, [in:] Neurotechnology for Biomimetic Robots, J. Ayers, J.L. Davis, A. Rudolph [Eds], MIT Press, pp. 16–21, 2002.
7. H.R. Choi, S.M. Ryew, Robotic system with active steering capability for internal inspection of urban gas pipelines, Mechatronics, 12(5): 713–736, 2002, doi: 10.1016/S0957-4158(01)00022-8.
8. D.P. Tsakiris, M. Sfakiotakis, A. Menciassi, G. la Spina, P. Dario, Polychaete-like undulatory robotic locomotion, [in:] Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp. 3018–3023, IEEE, 2005, doi: 10.1109/ROBOT.2005.1570573.
9. K.A. Melsaac, J.P. Ostrowski, A geometric approach to anguilliform locomotion: modelling of an underwater eel robot, [in:] Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No. 99CH36288C), Vol. 4, pp. 2843–2848, IEEE, 1999, doi: 10.1109/ROBOT.1999.774028.
10. C. Wilbur, W. Vorus, Y. Cao, S.N. Currie, A lamprey-based undulatory vehicle, Neurotechnology for Biomimetic Robots, MIT Press: Cambridge, MA, USA, pp. 285–296, 2002.
11. H. Yamada, S. Chigisaki, M. Mori, K. Takita, K. Ogami, S. Hirose, Development of amphibious snake-like robot ACM-R5, [in:] The 36th International Symposium on Robotics (ISR 2005), Tokyo, 2005.
12. A. Crespi, A. Badertscher, A. Guignard, A.J. Ijspeert, AmphiBot I: an amphibious snake-like robot, Robotics and Autonomous Systems, 50(4): 163–175, 2005, doi: 10.1016/j.robot.2004.09.015.
13. G.S. Chirikjian, J.W. Burdick, An obstacle avoidance algorithm for hyper-redundant manipulators, [in:] Proceedings of the IEEE International Conference on Robotics and Automation, pp. 625–631. IEEE, 1990, doi: 10.1109/ROBOT.1990.126052.
14. K. Ning, F. Wörgötter, A novel concept for building a hyper-redundant chain robot, IEEE Transactions on Robotics, 25(6): 1237–1248, 2009, doi: 10.1109/TRO.2009.2032968.
15. B. Siciliano, O. Khatib, T. Kröger, Springer Handbook of Robotics, Vol. 200, Springer, 2008.
16. R.M. Murray, Z. Li, S.S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press, 1994.
17. M. Rolf, J.J. Steil, Efficient exploratory learning of inverse kinematics on a bionic elephant trunk, IEEE Transactions on Neural Networks and Learning Systems, 25(6): 1147–1160, 2014, doi: 10.1109/TNNLS.2013.2287890.
18. A. Melingui, C. Escande, N. Benoudjit, R. Merzouki, J.B. Mbede, Qualitative approach for forward kinematic modeling of a compact bionic handling assistant trunk, IFAC Proceedings Volumes, 47(3): 9353–9358, 2014, doi: 10.3182/20140824-6-ZA-1003.01758.
19. V. Falkenhahn, A. Hildebrandt, R. Neumann, O. Sawodny, Dynamic control of the bionic handling assistant, IEEE/ASME Transactions on Mechatronics, 22(1): 6–17, 2017, doi: 10.1109/TMECH.2016.2605820.
20. M. Galicki, A closed solution to the inverse kinematics of redundant manipulators, Mechanism and Machine Theory, 26(2): 221–226, 1991, doi: 10.1016/0094-114X(91)90085-I.
21. W. Jacak, A discrete kinematic model of robots in the Cartesian space, IEEE Transactions on Robotics and Automation, 5(4): 435–443, 1989, doi: 10.1109/70.88058.
22. W. Jacak, Strategies of searching for collision-free manipulator motions: automata theory approach, Robotica, 7(2):129–138, 1989, doi: 10.1017/S0263574700005439.
23. M. Galicki, A. Morecki, Finding collision-free trajectory for redundant manipulator by local information available, [in:] RoManSy 9, Lecture Notes in Control and Information Sciences, Vol. 187, pp. 61–71, Springer, Berlin, Heidelberg, 1993, doi: 10.1007/BFb0031432.
24. G.S. Chirikjian, J.W. Burdick, Hyper-redundant robot mechanisms and their applications, [in:] Proceedings IROS ’91: IEEE/RSJ International Workshop on Intelligent Robots and Systems ’91, pp. 185-190, Vol. 1, 1991, doi: 10.1109/IROS.1991.174447.
25. G.S. Chirikjian, J.W. Burdick, A hyper-redundant manipulator, IEEE Robotics & Automation Magazine, 1(4): 22–29, 1994, doi: 10.1109/100.388263.
26. M. Zawidzki, Animation of the Snake 2D, 2022, https://www.youtube.com/watch?v=P_70iVP5DCQ.
27. M. Zawidzki, J. Szklarski, Transformations of Arm-Z modular manipulator with particle swarm optimization, Advances in Engineering Software, 126(C): 147–160, 2018, doi: 10.1016/j.advengsoft.2018.05.003.
28. M. Zawidzki, Retrofitting of pedestrian overpass by Truss-Z modular systems using graph-theory approach, Advances in Engineering Software, 81: 41–49, 2015, doi: 10.1016/j.advengsoft.2014.11.004.
29. M. Zawidzki, L. Jankowski, Optimization of modular Truss-Z by minimum-mass design under equivalent stress constraint, Smart Structures and Systems, 21(6): 715–725, 2018, doi: 10.12989/sss.2018.21.6.715.
30. M. Zawidzki, Ł. Jankowski, Multiobjective optimization of modular structures: Weight versus geometric versatility in a Truss-Z system, Computer-Aided Civil and Infrastructure Engineering, 34(11): 1026–1040, 2019, doi: 10.1111/mice.12478.
Dec 7, 2022
How to Cite
ZAWIDZKA, Ela; ZAWIDZKI, Machi. Discrete (Two-State) Modular Hyper-Redundant Planar Manipulator. Computer Assisted Methods in Engineering and Science, [S.l.], v. 29, n. 4, p. 397–407, dec. 2022. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/550>. Date accessed: 27 jan. 2023. doi: http://dx.doi.org/10.24423/cames.550.