Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-08T19:55:12.612Z Has data issue: false hasContentIssue false
  • English
  • Français

Planar Multi-Link Swimmers: Experiments and Theoretical Investigation using “Perfect Fluid” Model

Published online by Cambridge University Press:  18 February 2019

Evgenia Virozub ,
Oren Wiezel Open the ORCID record for Oren Wiezel [Opens in a new window] ,
Alon Wolf  and
Yizhar Or
Evgenia Virozub
Affiliation:
Faculty of Mechanical Engineering, Technion –Israel Institute of Technology, Haifa 32000, Israel. E-mails: [email protected], [email protected], [email protected]
Oren Wiezel
Affiliation:
Faculty of Mechanical Engineering, Technion –Israel Institute of Technology, Haifa 32000, Israel. E-mails: [email protected], [email protected], [email protected]
Alon Wolf
Affiliation:
Faculty of Mechanical Engineering, Technion –Israel Institute of Technology, Haifa 32000, Israel. E-mails: [email protected], [email protected], [email protected]
Yizhar Or*
Affiliation:
Faculty of Mechanical Engineering, Technion –Israel Institute of Technology, Haifa 32000, Israel. E-mails: [email protected], [email protected], [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Robotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer’s hydrodynamics in order to optimize its structure and control inputs. In this work, we study a planar snake-like multi-link swimmer by using the “perfect fluid” model that accounts for inertial hydrodynamic forces while neglecting viscous drag effects. The swimmer’s dynamic equations of motion are formulated and reduced into a first-order system due to symmetries and conservation of generalized momentum variables. Focusing on oscillatory inputs of joint angles, we study optimal gaits for 3-link and 5-link swimmers via numerical integration. For the 3-link swimmer, we also provide a small-amplitude asymptotic solution which enables obtaining closed-form approximations for optimal gaits. The theoretical results are then corroborated by experiments and motion measurement of untethered robotic prototypes with three and five links floating in a water pool, showing a reasonable agreement between the experiments and the theoretical model.

Keywords

Robot dynamicsMarine roboticsControl of robotic systemsRobotic locomotionGait optimization
Type
Articles
Information
Robotica , Volume 37 , Issue 8 , August 2019 , pp. 1289 - 1301
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This work has been supported by the Israeli Science Foundation under Grant 567/14 and Technion Autonomous Systems Program Grant No. 2021776.

References

Vaidyanathan, R., Chiel, H. J. and Quinn, R. D., “A hydrostatic robot for marine applications,” Rob. Auton. Syst. 30(1), 103–113 (2000).CrossRefGoogle Scholar
Kwak, B. and Bae, J., “Design of a robot with biologically-inspired swimming hairs for fast and efficient mobility in aquatic environment,” 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Daejeon, Korea, IEEE (2016) pp. 4970–4975.CrossRefGoogle Scholar
Li, G., Deng, Y., Osen, O. L., Bi, S. and Zhang, H., “A bio-inspired swimming robot for marine aquaculture applications: From concept-design to simulation,” OCEANS 2016-Shanghai, IEEE (2016) pp. 1–7.Google Scholar
Bayat, B., Crespi, A. and Ijspeert, A., “Envirobot: A bio-inspired environmental monitoring platform,” Autonomous Underwater Vehicles (AUV), 2016 IEEE/OES, Tokyo, Japan, IEEE (2016) pp. 381–386.CrossRefGoogle Scholar
Kelasidi, E., Liljeback, P., Pettersen, K. Y. and Gravdahl, J. T., “Innovation in underwater robots: Biologically inspired swimming snake robots,” IEEE Robot. Autom. Mag. 23(1), 44–62 (2016).CrossRefGoogle Scholar
McIsaac, K. A. and Ostrowski, J. P., “Experimental verification of open-loop control for an underwater eel-like robot,” Int. J. Rob. Res. 21(10–11), 849–859 (2002).CrossRefGoogle Scholar
Crespi, A., Karakasiliotis, K., Guignard, A. and Ijspeert, A. J., “Salamandra robotica ii: An amphibious robot to study salamander-like swimming and walking gaits,” IEEE Trans. Rob. 29(2), 308–320 (2013).CrossRefGoogle Scholar
Ijspeert, A. J., “Biorobotics: Using robots to emulate and investigate agile locomotion,” Science 346(6206), 196–203 (2014).CrossRefGoogle ScholarPubMed
Hirose, S., Biologically Inspired Robot (Oxford University Press, Oxford, UK, 1993).Google Scholar
Gong, C., Travers, M. J., Astley, H. C., Li, L., Mendelson, J. R., Goldman, D. I. and Choset, H., “Kinematic gait synthesis for snake robots,” Int. J. Rob. Res. 35(1–3), 100–113 (2016).CrossRefGoogle Scholar
Onal, C. D. and Rus, D., “Autonomous undulatory serpentine locomotion utilizing body dynamics of a fluidic soft robot,” Bioinspiration Biomim. 8(2), 026003 (2013).CrossRefGoogle ScholarPubMed
Morgansen, K A., Vela, P. A. and Burdick, J.W., “Trajectory stabilization for a planar carangiform robot fish,” Proceedings 2002, ICRA’02, IEEE International Conference on Robotics and Automation, Washington, DC, USA, vol. 1, IEEE (2002) pp. 756–762.Google Scholar
Crespi, A. and Ijspeert, A. J., “Online optimization of swimming and crawling in an amphibious snake robot,” IEEE Trans. Rob. 24(1), 75–87 (2008).CrossRefGoogle Scholar
Porez, M., Boyer, F. and Ijspeert, A. J., “Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons,” Int. J. Rob. Res. 33(10), 1322–1341 (2014).CrossRefGoogle Scholar
Kelasidi, E., Pettersen, K. Y. and Gravdahl, J. T., “Modeling of underwater snake robots moving in a vertical plane in 3d,” 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014), Chicago, IL, USA, IEEE (2014) pp. 266–273.CrossRefGoogle Scholar
Sfakiotakis, M. and Tsakiris, D. P., “Biomimetic centering for undulatory robots,” Int. J. Rob. Res. 26(11–12), 1267–1282 (2007).CrossRefGoogle Scholar
Tallapragada, P. and Kelly, S. D., “Self-propulsion of free solid bodies with internal rotors via localized singular vortex shedding in planar ideal fluids,” Eur. Phys. J. Spec. Top. 224(17–18), 3185–3197 (2015).CrossRefGoogle Scholar
Zhu, Q., Wolfgang, M. J., Yue, D. K. P. and Triantafyllou, M. S., “Three-dimensional flow structures and vorticity control in fish-like swimming,” J. Fluid Mech. 468, 1–28 (2002).CrossRefGoogle Scholar
Kanso, E., Marsden, J. E., Rowley, C. W. and Melli-Huber, J. B., “Locomotion of articulated bodies in a perfect fluid,” J. Nonlinear Sci. 15(4), 255–289 (2005).CrossRefGoogle Scholar
Melli, J. B., Rowley, C. W. and Rufat, D. S., “Motion planning for an articulated body in a perfect planar fluid,” SIAM J. Appl. Dyn. Syst. 5(4), 650–669 (2006).CrossRefGoogle Scholar
Lee, T., Leok, M. and McClamroch, N. H., “Dynamics of connected rigid bodies in a perfect fluid,” American Control Conference, 2009, ACC’09, St. Louis, MO, USA, IEEE (2009) pp. 408–413.CrossRefGoogle Scholar
Lamb, H., Hydrodynamics, vol. 43 (Dover, New York, 1945).Google Scholar
Ostrowski, J. and Burdick, J., “Gait kinematics for a serpentine robot,” Proceedings of 1996 IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA vol. 2, IEEE (1996) pp. 1294–1299.CrossRefGoogle Scholar
Shammas, E. A., Choset, H. and Rizzi, A. A., “Geometric motion planning analysis for two classes of underactuated mechanical systems,” Int. J. Rob. Res. 26(10), 1043–1073 (2007).CrossRefGoogle Scholar
Gutman, E. and Or, Y., “Symmetries and gaits for Purcell’s three-link microswimmer model,” IEEE Trans. Rob. 32(1), 53–69 (2016).CrossRefGoogle Scholar
Hatton, R. L. and Choset, H., “Geometric swimming at low and high Reynolds numbers,” IEEE Trans. Rob. 29(3), 615–624 (2013).CrossRefGoogle Scholar
Ostrowski, J. and Burdick, J., “The geometric mechanics of undulatory robotic locomotion,” Int. J. Rob. Res. 17(7), 683–701 (1998).CrossRefGoogle Scholar
Kelly, S. D. and Murray, R. M., “Geometric phases and robotic locomotion,” J. Robot. Syst., 12(6), 417–431 (1995).CrossRefGoogle Scholar
Hatton, R. L. and Choset, H., “Geometric motion planning: The local connection, Stokes’ theorem, and the importance of coordinate choice,” Int. J. Rob. Res. 30(8), 988–1014 (2011).CrossRefGoogle Scholar
Hatton, R. L. and Choset, H., “Nonconservativity and noncommutativity in locomotion,” Eur. Phys. J. Spec. Top. 224(17–18), 3141–3174 (2015).CrossRefGoogle Scholar
Cortés, J., Martínez, S., Ostrowski, J. P. and McIsaac, K. A., “Optimal gaits for dynamic robotic locomotion,” Int. J. Rob. Res. 20(9), 707–728 (2001).CrossRefGoogle Scholar
Ostrowski, J. P., Desai, J. P. and Kumar, V., “Optimal gait selection for nonholonomic locomotion systems,” Int. J. Rob. Res. 19(3), 225–237 (2000).CrossRefGoogle Scholar
Tam, D. and Hosoi, A. E., “Optimal stroke patterns for Purcell’s three-link swimmer,” Phys. Rev. Lett. 98(6), 068105 (2007).CrossRefGoogle ScholarPubMed
Ramasamy, S. and Hatton, R. L., “Geometric gait optimization beyond two dimensions,” American Control Conference (ACC), 2017, Seattle, WA, USA, IEEE (2017) pp. 642–648.Google Scholar
Kelasidi, E., Liljebäck, P., Pettersen, K. Y. and Gravdahl, J. T., “Experimental investigation of efficient locomotion of underwater snake robots for lateral undulation and eel-like motion patterns,” Robotics Biomim. 2(1), 1–27 (2015).CrossRefGoogle ScholarPubMed
Nayfeh, A. H., Perturbation methods (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2008).Google Scholar
Wiezel, O. and Or, Y., “Optimization and small-amplitude analysis of Purcell’s three-link microswimmer model,” Proc. R. Soc. A 472(2192), 20160425 (2016).CrossRefGoogle ScholarPubMed
Wiezel, O. and Or, Y., “Using optimal control to obtain maximum displacement gait for Purcell’s threelink swimmer,” 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, USA, IEEE (2016) pp. 4463–4468.CrossRefGoogle Scholar
Alouges, F., DeSimone, A., Giraldi, L., Or, Y. and Wiezel, O., “Energy-optimal strokes for multi-link microswimmers: Purcell’s loops and Taylor’s waves reconciled,” arXiv preprint. arXiv:1801.04687.Google Scholar

Virozub et al. supplementary material

Virozub et al. supplementary material 1

Download Virozub et al. supplementary material(Video)
Video 8.1 MB