Skip to main content

Assisted passive snake-like robots: conception and dynamic modeling using Gibbs–Appell method

  • Gholamreza Vossoughi (a1), Hodjat Pendar (a1), Zoya Heidari (a1) and Saman Mohammadi (a1)

In this paper, we present a novel structure of a snake-like robot. This structure enables passive locomotion in snake-like robots. Dynamic equations are obtained for motion in a horizontal plane, using Gibbs–Appell method. Kinematic model of the robot include numerous nonholonomic constraints, which can be omitted at the beginning by choosing proper coordinates to describe the model in Gibbs–Appell framework. In such a case, dynamic equations will be significantly simplified, resulting in considerable reduction of simulation time. Simulation results show that, by proper selection of initial conditions, joint angles operate in a limit cycle and robot can locomote steadily on a passive trajectory. It can be seen that the passive trajectory is approximately a Serpenoid curve.

Corresponding author
*Corresponding author. E-mail:
Hide All
1.Gray J., Animal Locomotion (Norton, New York, 1993) pp. 166193.
2.Hirose S., Biomechanical Engineering (Kougyou Tyousa Kai, Tokyo, Japan, 1987).
3.Hirose S., Biologically Inspired Robots: Snake-like Locomotor and Manipulator (Oxford University Press, New York, 1993).
4.Takanashi O., Aoki K. and Yashima S., “A Gait Control for the Hyper-Redundant Robot O-RO-CHI,” Proceedings of the ROBOMECÕ96, (Ube, Japan, 1996) pp. 7880.
5.Worst R. and Linnemann R., “Construction and Operation of a Snake-Like robot,” Proceedings of the IEEE International Joint Symposia on Intelligence and Systems, (Los Alamitos, CA, IEEE Press, 1996) pp. 164169.
6.Mori M. and Hirose S., “Development of active cord mechanism ACM-R3 with agile 3D mobility,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (Outrigger Wailea Resort, Maui, Hawaii, USA, IEEE Industrial Electronics Society, 2001) pp. 1552–1557.
7.Prautsch P. and Mita , “Control and Analysis of the Gait of Snake Robots”, Proceedings of IEEE International Conference on Control Applications, (Hawaii, 1999) pp. 502–507.
8.Ute J. and Ono K., “Fast and Efficient Locomotion of a Snake Robot Based on Self-Excitation Principle,” IEEE Proceedings of AMC, (Maribor, Slovenia, 2002) pp. 532–539.
9.Chirikjian G. S.Hyper-Redundant Manipulators Dynamics—A Continuum Approximation,” Adv. Robot., 9 (3), 217243 (1995).
10.Jones B. A. and Walker I. D., “Kinematics for multi-section continuum robots,” IEEE Trans Robot. 22 (1), 4355 (2006).
11.Saito M., Fukaya M. and Iwasaki T., “Serpentine Locomotion with Robotic Snakes,” IEEE Contr. Syst. Mag. 22 (1), 6481 (2002).
12.McMahon T. A., “The role of compliance in mammalian running gaits,” J. Exp. Biology 115 (11), 263282 (1985).
13.Ahmadi M., Stable Control of a One-Legged Robot Exploiting Passive Dynamics Ph.D. Thesis Mechanical Engineering Department, McGill University, 1998).
14.Seifert H. S., “The lunar pogo stick,” J. Spacecraft, 4 (7), 914943 (1967).
15.McGeer T., “Passive dynamic walkingInt. J. Robot Res. 9 (2), 6282 (1990).
16.Raibert M. H. and Thompson C. M., “Passive Dynamic Running,” In:Experimental Robotics I (Hayward V. and Khatib O., eds.) (Springer-Verlag NY, 1989) pp. 7483.
17.Featherstone R., Robot Dynamics Algorithms (Kluwer Academic Publishers, Nor-Well, MA, 1987).
18.Ginsberg J. H., Advanced Engineering Dynamics, (New York, Cambridge University Press, 2nd ed. 1998).
19.Kane T. R. and Levinson D. A., Dynamics: Theory and Applications (New York, McGraw-Hill 1985).
20. D. E.Rosenthal, An Order n Formulation for Robotic Systems,” J. Astronaut. Sci. 38 (4)511529 (1990).
21.Vukobratovi'c M. K., Filaretov V. F. and Korzun A. I., “A Unified Approach to Mathematical Modeling of Robotic Manipulator Dynamics,” Robotica 12 (5), 411420 (1994).
22.Jerkovsky W., “The Structure of Multibody Dynamics Equations,” J. Guid. Cont., 1 (3)173182 (1978).
23.Baraff D., “Linear-time dynamics using Lagrange multipliers,” Proc. Annu. Conf. Comp. Graph. Interact. Techn. 30 137–146 (ACM Press, New York, 1996).
24.Anderson K. S. and Critchley J. H., “Improved ‘Order-N’ performance algorithm for the simulation of constrained multi-rigid-body dynamic systems,” Multibody Syst. Dyn. 9 (2), pp. 185212 (Springer 2003).
25.Desoyer K. and Lugner P., “Recursive formulation for the analytical or numerical application of the Gibbs–Appell method to the dynamics of robots,” Robotica 7 (4)343347 (1989).
26.Rudas I. and Toth A., “Efficient recursive algorithm for inverse dynamics,” Mechatronics 3(2), 205–214 (1993).
27.Mata V., Provenzano S., Cuadrado J. I. and Valero F., “An O(n) Algorithm for Solving the Inverse Dynamic Problem in Robots by Using the Gibbs–Appell Formulation,” Proceedings of 10th World Congress on Theory of Machines and Mechanisms, Oulu, Finland (XXX, 1999) pp. 1208–1215.
28.Tavakoli Nia H., Pishkenari H. Nejat and Meghdari A., “A Recursive Approach for Analysis of Snake Robots Using Kane's Equations,” Proceedings of IDETC/CIE (Long Beach, CA, 2005).
29.Naudet J., Lefeber D. and Terze Z., “General Formulation of an Efficient Recursive Algorithm Based On Canonical Momenta for Forward Dynamics of Open-loop Multibody Systems,” IDMEC/IST, Lisbon, Portugal (Jul. 1–4, 2003). Jal'on J. Garc'ıa and Bayo E., Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge (Springer-Verlag), 1994.
31.Brenan K. E., Campbell S. L. and Petzold L. R., “The Numerical Solution of Initial Value Problems in Differential-Algebraic Equations,” (Elsevier Science Publishing New York, 1989).
32.Ma S. and Tadokoro N., “Analysis of Creeping Locomotion of a Snake-like Robot on a Slope,” J. Autonom. Robots 20 (1), 1523 (2006).
33.Ma S., “Analysis of creeping locomotion of a snake-like robot,” Advan. Robot. 15 (2), 205224 (2001).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 27 *
Loading metrics...

Abstract views

Total abstract views: 220 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 16th January 2018. This data will be updated every 24 hours.