Abstract
Many organisms achieve locomotion through undulatory traveling-wave motions, both on land (e.g., snakes, caterpillars, and worms) and underwater (e.g., eels and flagellar single-celled organisms). Recently, caterpillar locomotion has been modeled using the theory of planar discrete elastic rods (PDER) and open-loop control. This work considers a planar discrete elastic rod model with closed-loop control over the intrinsic material parameters of length and curvature distributed along its length. We introduce local curvature feedback control laws to drive the shape of the robot to a desired traveling-wave reference trajectory, where the phase of the wave is determined via a central pattern generator or via distributed control with a circulant communication topology. Through numerical simulations utilizing simple models of fluid–body interaction forces we examine undulatory eel-like swimming gaits that give rise to net forward motion. These results show promise for the design of distributed feedback control laws in modular soft robotic systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, E. Grinspun, Discrete elastic rods. ACM Trans. Graph. 27(3), 63 (2008). https://doi.org/10.1145/1360612.1360662
F. Boyer, M. Porez, W. Khalil, Macro-continuous computed torque algorithm for a three-dimensional eel-like robot. IEEE Trans. Robot. 22(4), 763–775 (2006). https://doi.org/10.1109/TRO.2006.875492
C. Christianson, N.N. Goldberg, D.D. Deheyn, S. Cai, M.T. Tolley, Translucent soft robots driven by frameless fluid electrode dielectric elastomer actuators. Sci. Robot. 3(17), eaat1893 (2018). https://doi.org/10.1126/scirobotics.aat1893
H. Feng, Y. Sun, P.A. Todd, H.P. Lee, Body wave generation for anguilliform locomotion using a fiber-reinforced soft fluidic elastomer actuator array toward the development of the eel-inspired underwater soft robot. Soft Robot. 7(2), 233–250 (2020). https://doi.org/10.1089/soro.2019.0054
K.C. Galloway, K.P. Becker, B. Phillips, J. Kirby, S. Licht, D. Tchernov, R.J. Wood, D.F. Gruber, Soft robotic grippers for biological sampling on deep reefs. Soft Robot. 3(1), 23–33 (2016). https://doi.org/10.1089/soro.2015.0019
G.B. Gillis, Undulatory locomotion in elongate aquatic vertebrates: anguilliform swimming since Sir James Gray. Am. Zool. 36(6), 656–665 (1996). https://doi.org/10.1093/icb/36.6.656
N.N. Goldberg, X. Huang, C. Majidi, A. Novelia, O.M. O’Reilly, D.A. Paley, W.L. Scott, On planar discrete elastic rod models for the locomotion of soft robots. Soft Robot. 6(5), 595–610 (2019). https://doi.org/10.1089/soro.2018.0104
J. Gray, Studies in animal locomotion: I. the movement of fish with special reference to the eel. J. Exp. Biol. 10(1), 88–104 (1933). https://jeb.biologists.org/content/10/1/88
S. Hirose, Biologically-Inspired Robots: Snake-Like Locomotors and Manipulators (Oxford University Press, Oxford, 1993)
M.K. Jawed, A. Novelia, O.M. O’Reilly, A Primer on the Kinematics of Discrete Elastic Rods (Springer, Berlin, 2018)
E. Kelasidi, K.Y. Pettersen, J.T. Gravdahl, P. Liljebäck, Modeling of underwater snake robots, in IEEE International Conference on Robotics and Automation (ICRA) (2014), pp. 4540–4547. https://doi.org/10.1109/ICRA.2014.6907522
E. Kelasidi, P. Liljebäck, K.Y. Pettersen, J.T. Gravdahl, Experimental investigation of efficient locomotion of underwater snake robots for lateral undulation and eel-like motion patterns. Robot. Biomimetics 2(1), 8 (2015). https://doi.org/10.1186/s40638-015-0029-4
E. Kelasidi, P. Liljebäck, K.Y. Pettersen, J.T. Gravdahl, Integral line-of-sight guidance for path following control of underwater snake robots: theory and experiments. IEEE Trans. Robot. 33(3), 610–628 (2017). https://doi.org/10.1109/TRO.2017.2651119
C. McCaffrey, T. Umedachi, W. Jiang, T. Sasatani, Y. Narusue, R. Niiyama, Y. Kawahara, Continuum robotic caterpillar with wirelessly powered shape memory alloy actuators. Soft Robot. (2020, Available online ahead of print). https://doi.org/10.1089/soro.2019.0090
K.A. McIsaac, J.P. Ostrowski, Motion planning for anguilliform locomotion. IEEE Trans. Robot. Autom. 19(4), 637–652 (2003). https://doi.org/10.1109/TRA.2003.814495
J. Morison, J. Johnson, S. Schaaf, et al., The force exerted by surface waves on piles. J. Pet. Technol. 2(05), 149–154 (1950). https://doi.org/10.2118/950149-G
B. Mosadegh, P. Polygerinos, C. Keplinger, S. Wennstedt, R.F. Shepherd, U. Gupta, J. Shim, K. Bertoldi, C.J. Walsh, G.M. Whitesides, Pneumatic networks for soft robotics that actuate rapidly. Adv. Funct. Mater. 24(15), 2163–2170 (2014). https://doi.org/10.1002/adfm.201303288
M. Sato, M. Fukaya, T. Iwasaki, Serpentine locomotion with robotic snakes. IEEE Contr. Syst. Mag. 22(1), 64–81 (2002). https://doi.org/10.1109/37.980248
P.E. Schiebel, J.M. Rieser, A.M. Hubbard, L. Chen, D.Z. Rocklin, D.I. Goldman, Mechanical diffraction reveals the role of passive dynamics in a slithering snake. Proc. Natl. Acad. Sci. 116(11), 4798–4803 (2019). https://doi.org/10.1073/pnas.1808675116
Z. Wang, K. Li, Q. He, S. Cai, A light-powered ultralight tensegrity robot with high deformability and load capacity. Adv. Mater. 31(7), 1806849 (2019). https://doi.org/10.1002/adma.201806849
M. Wehner, R.L. Truby, D.J. Fitzgerald, B. Mosadegh, G.M. Whitesides, J.A. Lewis, R.J. Wood, An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature 536(7617), 451–455 (2016). https://doi.org/10.1038/nature19100
Acknowledgement
This work was supported in part by ONR Grant No. N000141712063.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Scott, W.L., Prakash, P.J., Paley, D.A. (2021). Distributed Control of a Planar Discrete Elastic Rod for Eel-Inspired Underwater Locomotion. In: Paley, D.A., Wereley, N.M. (eds) Bioinspired Sensing, Actuation, and Control in Underwater Soft Robotic Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-50476-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-50476-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-50475-5
Online ISBN: 978-3-030-50476-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)