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Modeling discrete and rhythmic movements through motor primitives: a review

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Abstract

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.

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References

  • Adamovich S, Levin M, Feldman A (1994) Merging different motor patterns: coordination between rhythmical and discrete single-joint movements. Exp Brain Res 99(2): 325–337

    Article  CAS  PubMed  Google Scholar 

  • Ashe J (2005) What is coded in the primary cortex?. In: Riehle A, Vaadia E (eds) Motor cortex in voluntary movements. CRC, Boca Raton, FL

    Google Scholar 

  • Barbeau H, Rossignol S (1994) Enhancement of locomotor recovery following spinal cord injury. Curr Opin Neurol 7(6): 517–524

    Article  CAS  PubMed  Google Scholar 

  • Bizzi E, Accornero N, Chapple W, Hogan N (1984) Posture control and trajectory formation during arm movement. J Neurosci 4(11): 2738–2744

    CAS  PubMed  Google Scholar 

  • Bizzi E, Mussa-Ivaldi FA, Giszter S (1991) Computations underlying the execution of movement: a biological perspective. Science 253(5017): 287–291

    Article  CAS  PubMed  Google Scholar 

  • Bizzi E, Cheung VCK, d’Avella A, Saltiel P, Tresch M (2008) Combining modules for movement. Brain Res Rev 57(1): 125– 133

    Article  CAS  PubMed  Google Scholar 

  • Bridgeman B (2007) Efference copy and its limitations. Comput Biol Med 37(7): 924–929

    Article  PubMed  Google Scholar 

  • Brown T (1912) The factors in rhythmic activity of the nervous system. Proc R Soc Lond Ser 85(579): 278–289

    Article  Google Scholar 

  • Bullock D, Grossberg S (1988) The VITE model: a neural command circuit for generating arm and articulator trajectories. In: Kelso J, Mandell A, Shlesinger M (eds) Dynamic patterns in complex systems. World Scientific, Singapore, pp 206–305

    Google Scholar 

  • Bullock D, Grossberg S (1989) VITE and FLETE: neural models for trajectory formation and postural control. In: Hershberger WA (eds) Volitional action. North-Holland, Amsterdam, pp 253– 297

    Chapter  Google Scholar 

  • Capaday C (2002) The special nature of human walking and its neural control. Trends Neurosci 25(7): 370–376

    Article  CAS  PubMed  Google Scholar 

  • Cheng J, Stein R, Jovanovic K, Yoshida K, Bennett D, Han Y (1998) Identification, localization, and modulation of neural networks for walking in the mudpuppy (necturus maculatus) spinal cord. J Neurosci 18(11): 4295–4304

    CAS  PubMed  Google Scholar 

  • Cohen A, Wallen P (1980) The neural correlate of locomotion in fish: “fictive swimming” induced in an in vitro preparation of the lamprey spinal cord. Exp Brain Res 41: 11–18

    Article  CAS  PubMed  Google Scholar 

  • d’Avella A, Portone A, Fernandez L, Lacquaniti F (2006) Control of fast-reaching movements by muscle synergy combinations. J Neurosci 26(30): 7791–7810

    Article  PubMed  Google Scholar 

  • De Rugy A, Sternad D (2003) Interaction between discrete and rhythmic movements: reaction time and phase of discrete movement initiation during oscillatory movements. Brain Res 994(2): 160–174

    Article  CAS  PubMed  Google Scholar 

  • Degallier S, Righetti L, Natale L, Nori F, Metta G, Ijspeert A (2008) A modular bio-inspired architecture for movement generation for the infant-like robot icub. In: Proceedings of the 2nd IEEE RAS / EMBS international conference on biomedical robotics and bio-mechatronics, BioRob

  • Delcomyn F (1980) Neural basis of rhythmic behavior in animals. Science 210: 492–498

    Article  CAS  PubMed  Google Scholar 

  • Delvolvé I, Branchereau P, Dubuc R, Cabelguen JM (1999) Fictive rhythmic motor patterns induced by NMDA in an in vitro brain stem-spinal cord preparation from an adult urodele. J Neurophysiol 82: 1074–1077

    PubMed  Google Scholar 

  • Dietz V, Harkema SJ (2004) Locomotor activity in spinal cord-injured persons. J Appl Physiol 96(5): 1954–1960

    Article  CAS  PubMed  Google Scholar 

  • Dietz V, Muller R, Colombo G (2002) Locomotor activity in spinal man: significance of afferent input from joint and load receptors. Brain 125(12): 2626–2634

    Article  PubMed  Google Scholar 

  • Dimitrijevic MR, Gerasimenkp Y, Pinter MM (1998) Evidence for a spinal central pattern generator in humans. Ann New York Acad Sci 860: 360–376

    Article  CAS  Google Scholar 

  • Edgerton VR, Tillakaratne NJ, Bigbee AJ, de Leon RD, Roy RR (2004) Plasticity of the spinal neural circuitry after injury. Annu Rev Neurosci 27(1): 145–167

    Article  CAS  PubMed  Google Scholar 

  • Elble R, Higgins C, Hughes L (1994) Essential tremor entrains rapid voluntary movements. Exp Neurol 126: 138–143

    Article  CAS  PubMed  Google Scholar 

  • Feldman A (2009) New insights into actionperception coupling. Exp Brain Res 194(1): 39–58

    Article  PubMed  Google Scholar 

  • Forssberg H (1985) Ontogeny of human locomotor control. I: Infant stepping, supported locomotion and transition to independent locomotion. Exp Brain Res 57(3): 480–493

    Article  CAS  PubMed  Google Scholar 

  • Gandevia S, Burke D (1992) Does the nervous system depend on kinesthesic information to control natural limb movements?. Behav Brain Sci 15: 614–632

    Google Scholar 

  • Gaudiano P, Grossberg S (1992) Adaptive vector integration to endpoint: Self-organizing neural circuits for control of planned movement trajectories. Hum Mov Sci 11(1–2): 141–155

    Article  Google Scholar 

  • Georgopoulos AP (1996) On the translation of directional motor cortical commands to activation of muscles via spinal interneuronal systems. Brain Res Cogn Brain Res 3(2): 151–155

    Article  CAS  PubMed  Google Scholar 

  • Giszter SF, Mussa-Ivaldi FA, Bizzi E (1993) Convergent force fields organized in the frog’s spinal cord. J Neurosci 13(2): 467–491

    CAS  PubMed  Google Scholar 

  • Goodman D, Kelso J (1983) Exploring the functional signifiance of physiological tremor: a biospectroscopic approach. Exp Brain Res 49: 419–431

    Article  CAS  PubMed  Google Scholar 

  • Graziano MSA, Taylor CSR, Moore T, Cooke DF (2002) The cortical control of movement revisited. Neuron 36: 349–362

    Article  CAS  PubMed  Google Scholar 

  • Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228(4696): 143–149

    Article  CAS  PubMed  Google Scholar 

  • Grillner S (2006) Biological pattern generation: the cellular and computational logic of networks in motion. Neuron 52(5): 751–766

    Article  CAS  PubMed  Google Scholar 

  • Grillner S, Zangger P (1984) The effect of dorsal root transection on the efferent motor pattern in the cat’s hindlimb during locomotion. Acta Physiol Scand 120(3): 393–405

    Article  CAS  PubMed  Google Scholar 

  • Guiard Y (1993) On fittss and hookes laws: simple harmonic movement in upper-limb cyclical aiming. Acta Psychol Amst 82: 139–159

    Article  CAS  PubMed  Google Scholar 

  • Haiss F, Schwarz C (2005) Spatial segregation of different modes of movement control in the whisker representation of rat primary motor cortex. J Neurosci 25(6): 1579–1587

    Article  CAS  PubMed  Google Scholar 

  • Hanna JP, Frank JI (1995) Automatic stepping in the pontomedullary stage of central herniation. Neurology 45(5): 985–986

    CAS  PubMed  Google Scholar 

  • Hogan N, Sternad D (2007) On rhythmic and discrete movements: reflections, definitions and implications for motor control. Exp Brain Res 181(1): 13–30

    Article  PubMed  Google Scholar 

  • Ijspeert AJ (2008) Central pattern generators for locomotion control in animals and robots: a review. Neural Netw 21(4): 642–653

    Article  PubMed  Google Scholar 

  • Ivanenko YP, Dominici N, Cappellini G, Lacquaniti F (2005) Kinematics in newly walking toddlers does not depend upon postural stability. J Neurophysiol 94(1): 754–763

    Article  PubMed  Google Scholar 

  • Jeannerod M (1988) The neural and the behavioural organization of goal directed movements. Oxford Science, Oxford

    Google Scholar 

  • Kandel ER, Schwartz J, Jessell TM (2000) Principles of neural science. McGraw-Hill, New York

    Google Scholar 

  • Kargo W, Giszter S (2000) Rapid correction of aimed movements by summation of force-field primitives. J Neurosci 20(1): 409–426

    CAS  PubMed  Google Scholar 

  • Kawato M (1996) Learning internal models of the motor apparatus. In: Bloedel JR, Ebner TJ (eds) The acquistion of motor behavior in vertebrates. MIT Press, Cambridge, pp 409–430

    Google Scholar 

  • Krouchev N, Kalaska JF, Drew T (2006) Sequential activation of muscle synergies during locomotion in the intact cat as revealed by cluster analysis and direct decomposition. J Neurophysiol 96(4): 1991–2010

    Article  PubMed  Google Scholar 

  • Marder E, Bucher D (2001) Central pattern generators and the control of rhythmic movements. Curr Biol 11(23): R986–R996

    Article  CAS  PubMed  Google Scholar 

  • Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52: 367–376

    Article  CAS  PubMed  Google Scholar 

  • Miall RC, Ivry R (2004) Moving to a different beat. Nat Neurosci 7(10): 1025–1026

    Article  CAS  PubMed  Google Scholar 

  • Michaels C, Bongers R (1994) The dependence of discrete movements on rhythmic movements: simple RT during oscillatory tracking. Hum Mov Sci 13: 473–493

    Article  Google Scholar 

  • Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42(2): 223–227

    Article  CAS  PubMed  Google Scholar 

  • Morishita I, Yajima A (1972) Analysis and simulation of networks of mutually inhibiting neurons. Biol Cybern 11(3): 154–165

    CAS  Google Scholar 

  • Mussa-Ivaldi FA (1999) Modular features of motor control and learning. Curr Opin Neurobiol 9(6): 713–717

    Article  CAS  PubMed  Google Scholar 

  • Mussa-Ivaldi FA, Bizzi E (2000) Motor learning through the combination of primitives. Philos Trans R Soc Lond B Biol Sci 355(1404): 1755–1769

    Article  CAS  PubMed  Google Scholar 

  • Mussa-Ivaldi FA, Giszter SF, Bizzi E (1994) Linear combinations of primitives in vertebrate motor control. Proc Natl Acad Sci USA 91: 7534–7538

    Article  CAS  PubMed  Google Scholar 

  • Overduin SA, d’Avella A, Roh J, Bizzi E (2008) Modulation of muscle synergy recruitment in primate grasping. J Neurosci 28(4): 880–892

    Article  CAS  PubMed  Google Scholar 

  • Pearson KG (2000) Neural adaptation in the generation of rhythmic behavior. Annu Rev Physiol 62: 723–753

    Article  CAS  PubMed  Google Scholar 

  • Peiper A, Nagler B (1963) Cerebral function in infancy and childhood. Pitman Medical, London

    Google Scholar 

  • Reiss RF (1962) A theory and simulation of rhythmic behavior due to reciprocal inhibition in small nerve nets. In: Proceedings of the ACM spring joint computer conference, San Francisco, 1–3 May 1962, pp 171–194

  • Ronsse R, Sternad D, Lefévre P (2009) A computational model for rhythmic and discrete movements in uni- and bimanual coordination. Neural Comput 21(5): 1335–1370

    Article  PubMed  Google Scholar 

  • Rossignol S, Schwab M, Schwartz M, Fehlings MG (2007) Spinal cord injury: time to move?. J Neurosci 27(44): 11,782–11,792

    Article  CAS  Google Scholar 

  • Saltiel P, Tresch MC, Bizzi E (1998) Spinal cord modular organization and rhythm generation: an NMDA iontophoretic study in the frog. J Neurophysiol 80(5): 2323–2339

    CAS  PubMed  Google Scholar 

  • Saltiel P, Wyler-Duda K, d’Avella A, Ajemian RJ, Bizzi E (2005) Localization and connectivity in spinal interneuronal networks: the adduction-caudal extension-flexion rhythm in the frog. J Neurophysiol 94(3): 2120–2138

    Article  CAS  PubMed  Google Scholar 

  • Schaal S, Kotosaka S, Sternad D (2000) Nonlinear dynamical systems as movement primitives. In: International conference on humanoid robotics (Humanoids00), Springer, Berlin Heidelberg New York, pp 117–124

  • Schaal S, Sternad D, Osu R, Kawato M (2004) Rhythmic arm movement is not discrete. Nat Neurosci 7(10): 1136–1143

    Article  CAS  PubMed  Google Scholar 

  • Schöner G, Santos C (2001) Control of movement time and sequential action through attractor dynamics: a simulation study demonstrating object interception and coordination. In: Stein P, Stuart D, Selverston A (eds) Neurons, networks and motor behavior. MIT Press, Cambridge, MA

    Google Scholar 

  • Sherrington CS (1910) Flexion-reflex of the limb, crossed extension-reflex, and reflex stepping and standing. J Physiol Lond 40: 28–121

    CAS  PubMed  Google Scholar 

  • Slotine JJ, Lohmiller W (2001) Modularity, evolution, and the binding problem: a view from stability theory. Neural Netw 14(2): 137–145

    Article  CAS  PubMed  Google Scholar 

  • Soffe S, Roberts A (1982) Tonic and phasic synaptic input to spinal cord motoneurons during fictive locomotion in frog embryos. J Neurophysiol 48(6): 1279–1288

    CAS  PubMed  Google Scholar 

  • St-Onge N, Qi H, Feldman A (1993) The patterns of control signals underlying elbow joint movements in humans. Neurosci Lett 164: 171–174

    Article  CAS  PubMed  Google Scholar 

  • Staude G, Dengler R, Wolf W (2002) The discontinuous nature of motor execution. II: merging discrete and rhythmic movements in a single-joint system—the phase entertainment effect. Biol Cybern 86(6): 427–443

    Article  CAS  PubMed  Google Scholar 

  • Stein P, Smith J (2001) Neural and biomechanical control strategies for different forms of verterbrates hindlimb motor tasks. In: Stein P, Stuart D, Selverston A (eds) Neurons, networks and motor behavior. MIT Press, Cambridge, MA

    Google Scholar 

  • Stein P, Grillner S, Selverston A, Stuart DE (1997) Neurons, networks and motor behavior. MIT Press, Cambridge, MA

    Google Scholar 

  • Stein RB (2008) The plasticity of the adult spinal cord continues to surprise. J Physiol 586(12): 2823–2823

    Article  CAS  PubMed  Google Scholar 

  • Sternad D (2007) Rhythmic and discrete movements—behavioral, modeling and imaging results. In: Fuchs A, Jirsa V (eds) Coordination dynamics. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Sternad D, Dean W, Schaal S (2000) Interaction of rhythmic and discrete pattern generators in single joint movements. Hum Mov Sci 19: 627–665

    Article  Google Scholar 

  • Strick P (2002) Stimulating research on motor cortex. Nat Neurosci 5(8): 714–715

    Article  CAS  PubMed  Google Scholar 

  • Strogatz SH (2001) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Perseus, New York

    Google Scholar 

  • Suzuki R, Katsuno I, Matano K (1971) Dynamics of neuron ring. Biol Cybern 8(1): 39–45

    CAS  Google Scholar 

  • Tang W, Zhang W, Huang C, Young M, Hwang I (2008) Postural tremor and control of the upper limb in air pistol shooters. J Sports Sci 26(14): 1579–1587 PMID: 18979336

    Article  PubMed  Google Scholar 

  • Thelen E, Cooke DW (1987) Relationship between newborn stepping and later walking: a new interpretation. Develop Med Child Neurol 29(3): 380–393

    Article  CAS  PubMed  Google Scholar 

  • Ting LH, Macpherson JM (2005) A limited set of muscle synergies for force control during a postural task. J Neurophysiol 93(1): 609–613

    Article  PubMed  Google Scholar 

  • Tresch M, Saltiel P, Bizzi E (1999) The construction of movement by the spinal cord. Nat Neurosci 2: 162–167

    Article  CAS  PubMed  Google Scholar 

  • van Mourik AM, Beek PJ (2004) Discrete and cyclical movements: unified dynamics or separate control. Acta Psychol Amst 117(2): 121–138

    Article  PubMed  Google Scholar 

  • Wierzbicka M, Staude G, Wolf W, Dengler R (1993) Relationship between tremor and the onset of rapid voluntary contraction in parkinsons disease. J Neurol Neurosurg Psychiatry 56: 782–787

    Article  CAS  PubMed  Google Scholar 

  • Wolpaw JR, Tennissen AM (2001) Activity-dependent spinal cord plasticity in health and disease. Annu Rev Neurosci 24(1): 807–843

    Article  CAS  PubMed  Google Scholar 

  • Won J, Hogan N (1995) Stability properties of human reaching movements. Exp Brain Res 107(1): 125–136

    Article  CAS  PubMed  Google Scholar 

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  1. Biorobotics Laboratory (BIOROB), School of Engineering, EPFL—Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Sarah Degallier & Auke Ijspeert

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  1. Sarah Degallier
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  2. Auke Ijspeert
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Correspondence to Sarah Degallier.

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Degallier, S., Ijspeert, A. Modeling discrete and rhythmic movements through motor primitives: a review. Biol Cybern 103, 319–338 (2010). https://doi.org/10.1007/s00422-010-0403-9

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