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Slow Movements of Bio-Inspired Limbs

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Abstract

Slow and accurate finger and limb movements are essential to daily activities, but the underlying mechanics is relatively unexplored. Here, we develop a mathematical framework to examine slow movements of tendon-driven limbs that are produced by modulating the tendons’ stiffness parameters. Slow limb movements are driftless in the sense that movement stops when actuations stop. We demonstrate, in the context of a planar tendon-driven system representing a finger, that the control of stiffness suffices to produce stable and accurate limb postures and quasi-static (slow) transitions among them. We prove, however, that stable postures are achievable only when tendons are pretensioned, i.e., they cannot become slack. Our results further indicate that a non-smoothness in slow movements arises because the precision with which individual stiffnesses need to be altered changes substantially throughout the limb’s motion.

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References

  • An, K., Ueba, Y., Chao, E., Cooney, W., Linscheid, R.: Tendon excursion and moment arm of index finger muscles. J. Biomech. 16(6), 419–425 (1983)

    Article  Google Scholar 

  • Asatryan, D.G., Feldman, A.G.: Functional tuning of the nervous system with control of movement or maintenance of a steady posture: I. mechanographic analysis of the work of the joint or execution of a postural task. Biophysics 10(5), 925–934 (1965)

    Google Scholar 

  • Bizzini, M., Mannion, A.F.: Reliability of a new, hand-held device for assessing skeletal muscle stiffness. Clin. Biomech. 18(5), 459–461 (2003)

    Article  Google Scholar 

  • Boscain, U., Chitour, Y.: On the minimum time problem for driftless left-invariant control systems on so (3). Commun. Pure Appl. Anal. 1, 285–312 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Burdet, E., Osu, R., Franklin, D., Yoshioka, T., Milner, T., Kawato, M.: A method for measuring endpoint stiffness during multi-joint arm movements. J. Biomech. 33(12), 1705–1709 (2000)

    Article  Google Scholar 

  • Burdet, E., Osu, R., Franklin, D.W., Milner, T.E., Kawato, M.: The central nervous system stabilizes unstable dynamics by learning optimal impedance. Nature 414(6862), 446–449 (2001)

    Article  Google Scholar 

  • Chen, J., Tian, J., Iwasaki, T., Friesen, W.O.: Mechanisms underlying rhythmic locomotion: dynamics of muscle activation. J. Exp. Biol. 214(11), 1955–1964 (2011)

    Article  Google Scholar 

  • Chuang, L.-L., Wu, C.-Y., Lin, K.-C.: Reliability, validity, and responsiveness of myotonometric measurement of muscle tone, elasticity, and stiffness in patients with stroke. Arch. Phys. Med. Rehabil. 93(3), 532–540 (2012)

    Article  Google Scholar 

  • Cooke, J.: The organization of simple, movements. In: Stelmach, G.E., Requin, J. (eds.) Tutorials in Motor Behavior, pp. 199–212. North Holland Publishing Company, Amsterdam (1980)

    Chapter  Google Scholar 

  • Darling, W.G., Cole, K.J., Miller, G.F.: Coordination of index finger movements. J. Biomech. 27(4), 479–491 (1994)

    Article  Google Scholar 

  • De Luca, A., Oriolo, G., Samson, C.: Feedback Control of a Nonholonomic Car-like Robot, Book Section 4, pp. 171–253. Springer, New York (1998)

    Google Scholar 

  • Evans, C., Baker, S.N.: Task-dependent intermanual coupling of 8-hz discontinuities during slow finger movements. Eur. J. Neurosci. 18(2), 453–456 (2003)

    Article  Google Scholar 

  • Feldman, A.: Functional tuning of the nervous system with control of movement or maintenance of a steady posture. ii. controllable parameters of the muscle. Biophysics 11(3), 565–578 (1966)

    Google Scholar 

  • Feldman, A.G., Levin, M.F.: The Equilibrium-Point Hypothesis-Past, Present and Future, vol. 629. Springer, Berlin (2009)

    Google Scholar 

  • Frecker, M., Snyder, A.J.: Surgical robotics: multifunctional end effectors for robotic surgery. Oper. Techn. Gen. Surg. 7(4), 165–169 (2005)

    Article  Google Scholar 

  • Giszter, S., Patil, V., Hart, C.: Primitives, premotor drives, and pattern generation: a combined computational and neuroethological perspective. Prog. Brain Res. 165, 323–346 (2007)

    Article  Google Scholar 

  • Giszter, S.F.: Motor primitives–new data and future questions. Curr. Opin. Neurobiol. 33, 156–165 (2015)

    Article  Google Scholar 

  • Gross, J., Timmermann, L., Kujala, J., Dirks, M., Schmitz, F., Salmelin, R., Schnitzler, A.: The neural basis of intermittent motor control in humans. Proc. Natl. Acad. Sci. 99(4), 2299–2302 (2002)

    Article  Google Scholar 

  • Hill, A.: The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B Biol. Sci. 126(843), 136–195 (1938)

    Article  Google Scholar 

  • Hogan, N.: Adaptive control of mechanical impedance by coactivation of antagonist muscles. Autom. Control IEEE Trans. 29(8), 681–690 (1984)

    Article  MATH  Google Scholar 

  • Hogan, N.: Impedance control: an approach to manipulation: Part II–implementation. J. Dyn. Syst. Meas. control 107(1), 8–16 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  • Inouye, J.M., Kutch, J.J., Valero-Cuevas, F.J.: A novel synthesis of computational approaches enables optimization of grasp quality of tendon-driven hands. Robot. IEEE Trans. 28(4), 958–966 (2012)

    Article  Google Scholar 

  • Inouye, J.M., Valero-Cuevas, F.J.: Muscle synergies heavily influence the neural control of arm endpoint stiffness and energy consumption. PLoS Comput. Biol. 12(2), e1004737 (2016)

    Article  Google Scholar 

  • Ivaldi, F.M., Morasso, P., Zaccaria, R.: Kinematic networks. Biol. Cybern. 60(1), 1–16 (1988)

    Article  Google Scholar 

  • Jing, F., Alben, S.: Optimization of two-and three-link snakelike locomotion. Phys. Rev. E 87(2), 022711 (2013)

    Article  Google Scholar 

  • Jung, S.-Y., Kang, S.-K., Lee, M.-J., Moon, I.: Design of robotic hand with tendon-driven three fingers. In: Control, Automation and Systems, 2007. ICCAS’07. International Conference on, IEEE, Year, pp. 83–86

  • Kanso, E.: Swimming due to transverse shape deformations. J. Fluid Mech. 631, 127–148 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Kanso, E., Marsden, J.E., Rowley, C.W., Melli-Huber, J.: Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15(4), 255–289 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Lee, Y.-T., Choi, H.-R., Chung, W.-K., Youm, Y.: Stiffness control of a coupled tendon-driven robot hand. Control Syst. IEEE 14(5), 10–19 (1994)

    Article  Google Scholar 

  • McMahon, T.A.: Muscles, Reflexes, and Locomotion. Princeton University Press, Princeton (1984)

    Google Scholar 

  • Mussa-Ivaldi, F.A., Hogan, N.: Integrable solutions of kinematic redundancy via impedance control. Int. J. Robot. Res. 10(5), 481–491 (1991)

    Article  Google Scholar 

  • Mustalampi, S., Häkkinen, A., Kautiainen, H., Weir, A., Ylinen, J.: Responsiveness of muscle tone characteristics to progressive force production. The. J. Strength Cond. Res. 27(1), 159–165 (2013)

    Article  Google Scholar 

  • Rätsep, T.O., Asser, T.: Changes in viscoelastic properties of skeletal muscles induced by subthalamic stimulation in patients with parkinson’s disease. Clin. Biomech. 26(2), 213–217 (2011)

    Article  Google Scholar 

  • Shadmehr, R.: The Equilibrium Point Hypothesis for Control of Movement. Department of Biomedical Engineering, Johns Hopkins University, Baltimore (1998)

    Google Scholar 

  • Shapere, A., Wilczek, F.: Geometry of self-propulsion at low reynolds number. J. Fluid Mech. 198, 557–585 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • Simaan, N., Xu, K., Wei, W., Kapoor, A., Kazanzides, P., Taylor, R., Flint, P.: Design and integration of a telerobotic system for minimally invasive surgery of the throat. Int. J. Robot. Res. 28(9), 1134–1153 (2009)

    Article  Google Scholar 

  • Srinivasan, M., Ruina, A.: Computer optimization of a minimal biped model discovers walking and running. Nature 439(7072), 72–75 (2006)

    Article  Google Scholar 

  • Teel, A.R., Murray, R.M., Walsh, G.C.: Non-holonomic control systems: from steering to stabilization with sinusoids. Int. J. Control 62(4), 849–870 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Valero-Cuevas, F.J.: A mathematical approach to the mechanical capabilities of limbs and fingers. In: Sternad, D. (ed.) Progress in Motor Control. Advances in Experimental Medicine and Biology, vol. 629, pp. 619–633. Springer (2009)

  • Valero-Cuevas, F.J.: Fundamentals of Neuromechanics, vol. 8 of Biosystems and Biorobotics. Springer, London (2015)

    Google Scholar 

  • Valero-Cuevas, F.J., Yi, J.-W., Brown, D., McNamara, R.V., Paul, C., Lipson, H.: The tendon network of the fingers performs anatomical computation at a macroscopic scale. Biomed. Eng. IEEE Trans. 54(6), 1161–1166 (2007)

    Article  Google Scholar 

  • Valero-Cuevas, F.J., Zajac, F.E., Burgar, C.G.: Large index-fingertip forces are produced by subject-independent patterns of muscle excitation. J. Biomech. 31(8), 693–703 (1998)

    Article  Google Scholar 

  • Vallbo, A., Wessberg, J.: Organization of motor output in slow finger movements in man. J. Phys. 469(1), 673–691 (1993)

    Google Scholar 

  • Whitney, D.E.: Resolved motion rate control of manipulators and human prostheses. IEEE Trans. Man Machine. MMS-10(2), 47–53 (1969). doi:10.1109/TMMS.1969.299896

  • Williams, E.R., Soteropoulos, D.S., Baker, S.N.: Coherence between motor cortical activity and peripheral discontinuities during slow finger movements. J. Neurophysiol. 102(2), 1296–1309 (2009)

    Article  Google Scholar 

  • Williams, T.L.: A new model for force generation by skeletal muscle, incorporating work-dependent deactivation. J. Exp. Biol. 213(4), 643–650 (2010)

    Article  Google Scholar 

Download references

Acknowledgments

S. B. and F. V. C. were partially supported by the grants NIH R01AR050520, NIH R01AR052345, NIDRR H133E080024 and NSF EFRI-COPN 0836042, and S. B. and E. K. by the Grants NSF CMMI-0644925 and NSF CCF-0811480. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Biomedical Engineering, University of Southern California, Los Angeles, CA, USA

    Sarine Babikian & Francisco J. Valero-Cuevas

  2. Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, CA, USA

    Francisco J. Valero-Cuevas

  3. Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, USA

    Sarine Babikian & Eva Kanso

Authors
  1. Sarine Babikian
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  2. Francisco J. Valero-Cuevas
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  3. Eva Kanso
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Correspondence to Eva Kanso.

Additional information

Communicated by Paul K. Newton.

Valero-Cuevas and Kanso have equal leadership of this paper.

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Babikian, S., Valero-Cuevas, F.J. & Kanso, E. Slow Movements of Bio-Inspired Limbs. J Nonlinear Sci 26, 1293–1309 (2016). https://doi.org/10.1007/s00332-016-9305-x

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