Abstract
Looking to nature, animals frequently utilize tails to work alongside or in place of their legs to maneuver, stabilize, and/or propel to achieve highly agile motions. Although the single-link robotic tail shows its dynamical superiority and practical effectiveness in mobile platform maneuvering, most tails observed in nature have multi-link structures. Therefore, to investigate this novel tail structure, bio-inspired and biomimetic multi-link robotic tails were proposed and implemented. However, due to the lack of a whole-body dynamic model, previous research focused on investigating the tail subsystem independently without considering the mobile platform’s motions, which introduces deficiencies on both analysis and control. To bridge this theoretical gap, this paper presents a unified dynamics model that incorporates both the quadruped and the tail subsystems as a complete coupled dynamic system. Classical multibody dynamics formulation based on the principle of virtual work is utilized to derive the dynamic model. Based on the new whole-body dynamic model, three typical tail structures, including a single-link pendulum tail, a multi-link rigid tail, and a multi-link flexible tail are evaluated. The results indicate that by using a center of mass-based benchmark, the multi-link tail structure is dynamically equivalent to the single-link tail structure for bending motion. However, for rolling motions, the multi-link structure illustrates noticeable dynamical benefits compared to a single-link structure due to its higher inertia. In addition, a multi-link flexible structure shows significant oscillations and uncontrollable dynamic behaviors due to its under-actuation feature, which may limit its usage for highly dynamic applications.
Similar content being viewed by others
References
Briggs, R., Lee, J., Haberland, M., Kim, S.: Tails in biomimetic design: analysis, simulation, and experiment. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Portugal (2012)
Casarez, C.S., Fearing, R.S.: Steering of an underactuated legged robot through terrain contact with an active tail. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Madrid, Spain (2018)
Chang-Siu, E., Libby, T., Tomizuka, M., Full, R.J.: A lizard-inspired active tail enables rapid maneuvers and dynamic stabilization in a terrestrial robot. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, San Francisco, USA (2011)
Codourey, A.: Dynamic modeling of parallel robots for computed-torque control implementation. Int. J. Robot. Res. 17(12), 1325–1336 (1998)
Dawson, R.S., Warburton, N.M., Richards, H.L., Milne, N.: Walking on five legs: investigating tail use during slow gait in kangaroos and wallabies. Aust. J. Zool. 63(3), 192–200 (2015)
De, A., Koditschek, D.E.: Parallel composition of templates for tail-energized planar hopping. In: Proceedings of the IEEE International Conference on Robotics and Automation, Seattle, USA (2015)
Featherstone, R.: Rigid Body Dynamics Algorithms. Springer, Berlin (2014)
Freymiller, G.A., Whitford, M.D., Higham, T.E., Clark, R.W.: Escape dynamics of free-ranging desert kangaroo rats (Rodentia: heteromyidae) evading rattlesnake strikes. Biol. J. Linn. Soc. 127(1), 164–172 (2019)
Heim, S.W., Ajallooeian, M., Eckert, P., Vespignani, M., Ijspeert, A.J.: On designing an active tail for legged robots: simplifying control via decoupling of control objectives. Ind. Robot 43(3), 338–346 (2016)
Hickman, G.C.: The mammalian tail: a review of functions. Mamm. Rev. 9(4), 143–157 (1979)
Jusufi, A., Kawano, D.T., Libby, T., Full, R.J.: Righting and turning in mid-air using appendage inertia: reptile tails, analytical models and bio-inspired robots. Bioinspir. Biomim. 5(4), 045001 (2010)
Libby, T., Moore, T.Y., Chang-Siu, E., Li, D., Cohen, D.J., Jusufi, A., Full, R.J.: Tail-assisted pitch control in lizards, robots and dinosaurs. Nature 481(7380), 181–184 (2012)
Libby, T., Johnson, A.M., Chang-Siu, E., Full, R.J., Koditschek, D.E.: Comparative design, scaling, and control of appendages for inertial reorientation. IEEE Trans. Robot. 32(6), 1380–1398 (2016)
Liu, Y., Ben-Tzvi, P.: Dynamic modeling of a quadruped with a robotic tail using virtual work principle. In: Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Quebec City, Canada (2018)
Liu, Y., Ben-Tzvi, P.: Design, analysis, and integration of a new two-degree-of-freedom articulated multi-link robotic tail mechanism. J. Mech. Robot. 12(2), 021101 (2020)
Liu, G.H., Lin, H.Y., Lin, H.Y., Chen, S.T., Lin, P.C.: A bio-inspired hopping kangaroo robot with an active tail. J. Bionics Eng. 11(4), 541–555 (2014)
Liu, Y., Wang, J., Ben-Tzvi, P.: A cable length invariant robotic tail using a circular shape universal joint mechanism. J. Mech. Robot. 11(5), 051005 (2019)
Machairas, K., Papadopoulos, E.: On quadruped attitude dynamics and control using reaction wheels and tails. In: Proceedings of the European Control Conference, Linz, Austria (2015)
Mistry, M., Buchli, J., Schaal, S.: Inverse dynamics control of floating base systems using orthogonal decomposition. In: Proceedings of the IEEE International Conference on Robotics and Automation, Anchorage AK, USA (2010)
Nabeshima, J., Saraiji, M.Y., Minamizawa, K.: Arque: artificial biomimicry-inspired tail for extending innate body functions. In: ACM SIGGRAPH 2019 Posters, Los Angeles, CA, USA (2019)
O’Connor, S.M., Dawson, T.J., Kram, R., Donelan, J.M.: The kangaroo’s tail propels and powers pentapedal locomotion. Biol. Lett. 10(7), 20140381 (2014)
Ouezdou, F.B., Bruneau, O., Guinot, J.C.: Dynamic analysis tool for legged robots. Multibody Syst. Dyn. 2(4), 369–391 (1998)
Patel, A., Boje, E.: On the conical motion of a two-degree-of-freedom tail inspired by the cheetah. IEEE Trans. Robot. 31(6), 1555–1560 (2015)
Rone, W., Ben-Tzvi, P.: Dynamic modeling and simulation of a yaw-angle quadruped maneuvering with a planar robotic tail. J. Dyn. Syst. Meas. Control 138(8), 084502 (2016)
Rone, W.S., Liu, Y., Ben-Tzvi, P.: Maneuvering and stabilization control of a bipedal robot with a universal-spatial robotic tail. Bioinspir. Biomim. 14(1), 016014 (2018)
Rone, W.S., Saab, W., Ben-Tzvi, P.: Design, modeling, and integration of a flexible universal spatial robotic tail. J. Mech. Robot. 10(4), 041001 (2018)
Saab, W., Rone, W.S., Ben-Tzvi, P.: Robotic tails: a state-of-the-art review. Robotica 36(9), 1263–1277 (2018)
Saab, W., Rone, W.S., Ben-Tzvi, P.: Discrete modular serpentine robotic tail: design, analysis and experimentation. Robotica 36(7), 994–1018 (2018)
Saab, W., Rone, W., Kumar, A., Ben-Tzvi, P.: Design and integration of a novel spatial articulated robotic tail. IEEE/ASME Trans. Mechatron. 24(2), 434–446 (2019)
Santiago, J.L.C., Godage, I.S., Gonthina, P., Walker, I.D.: Soft robots and kangaroo tails: modulating compliance in continuum structures through mechanical layer jamming. Soft Robot. 3(2), 54–63 (2016)
Shah, S.V., Saha, S.K., Dutt, J.K.: Modular framework for dynamic modeling and analyses of legged robots. Mech. Mach. Theory 49, 234–255 (2012)
Simon, B., Sato, R., Choley, J.Y., Ming, A.: Development of a bio-inspired flexible tail systemxs. In: Proceedings of the 12th France-Japan and 10th Europe-Asia Congress on Mechatronics, Tsu, Japan (2018)
Tsai, L.W.: Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work. J. Mech. Des. 122(1), 3–9 (2000)
Wang, J., Gosselin, C.M.: A new approach for the dynamic analysis of parallel manipulators. Multibody Syst. Dyn. 2(3), 317–334 (1998)
Young, J.W., Russo, G.A., Fellmann, C.D., Thatikunta, M.A., Chadwell, B.A.: Tail function during arboreal quadrupedalism in squirrel monkeys (Saimiri boliviensis) and tamarins (Saguinus oedipus). J. Exp. Zool. Part A: Ecol. Genet. Physiol. 323(8), 556–566 (2015)
Zeglin, G.J.: Uniroo – a one legged dynamic hopping robot. Bachelor thesis, Massachusetts Institute of Technology, Cambridge, MA, USA (1991)
Zhao, J., Zhao, T., Xi, N., Mutka, M.W., Xiao, L.: Msu tailbot: controlling aerial maneuver of a miniature-tailed jumping robot. IEEE/ASME Trans. Mechatron. 20(6), 2903–2914 (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, Y., Ben-Tzvi, P. Dynamic modeling, analysis, and comparative study of a quadruped with bio-inspired robotic tails. Multibody Syst Dyn 51, 195–219 (2021). https://doi.org/10.1007/s11044-020-09764-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11044-020-09764-8