Biological Cybernetics

, Volume 103, Issue 4, pp 319–338 | Cite as

Modeling discrete and rhythmic movements through motor primitives: a review

  • Sarah DegallierEmail author
  • Auke Ijspeert


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.


Motor primitives Discrete movements Rhythmic movements Dynamical systems Central pattern generators Force fields Muscle synergies 


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  1. Adamovich S, Levin M, Feldman A (1994) Merging different motor patterns: coordination between rhythmical and discrete single-joint movements. Exp Brain Res 99(2): 325–337CrossRefPubMedGoogle Scholar
  2. Ashe J (2005) What is coded in the primary cortex?. In: Riehle A, Vaadia E (eds) Motor cortex in voluntary movements. CRC, Boca Raton, FLGoogle Scholar
  3. Barbeau H, Rossignol S (1994) Enhancement of locomotor recovery following spinal cord injury. Curr Opin Neurol 7(6): 517–524CrossRefPubMedGoogle Scholar
  4. Bizzi E, Accornero N, Chapple W, Hogan N (1984) Posture control and trajectory formation during arm movement. J Neurosci 4(11): 2738–2744PubMedGoogle Scholar
  5. Bizzi E, Mussa-Ivaldi FA, Giszter S (1991) Computations underlying the execution of movement: a biological perspective. Science 253(5017): 287–291CrossRefPubMedGoogle Scholar
  6. Bizzi E, Cheung VCK, d’Avella A, Saltiel P, Tresch M (2008) Combining modules for movement. Brain Res Rev 57(1): 125– 133CrossRefPubMedGoogle Scholar
  7. Bridgeman B (2007) Efference copy and its limitations. Comput Biol Med 37(7): 924–929CrossRefPubMedGoogle Scholar
  8. Brown T (1912) The factors in rhythmic activity of the nervous system. Proc R Soc Lond Ser 85(579): 278–289CrossRefGoogle Scholar
  9. 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 206–305Google Scholar
  10. 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– 297CrossRefGoogle Scholar
  11. Capaday C (2002) The special nature of human walking and its neural control. Trends Neurosci 25(7): 370–376CrossRefPubMedGoogle Scholar
  12. 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): 4295–4304PubMedGoogle Scholar
  13. 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: 11–18CrossRefPubMedGoogle Scholar
  14. d’Avella A, Portone A, Fernandez L, Lacquaniti F (2006) Control of fast-reaching movements by muscle synergy combinations. J Neurosci 26(30): 7791–7810CrossRefPubMedGoogle Scholar
  15. 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): 160–174CrossRefPubMedGoogle Scholar
  16. 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, BioRobGoogle Scholar
  17. Delcomyn F (1980) Neural basis of rhythmic behavior in animals. Science 210: 492–498CrossRefPubMedGoogle Scholar
  18. 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: 1074–1077PubMedGoogle Scholar
  19. Dietz V, Harkema SJ (2004) Locomotor activity in spinal cord-injured persons. J Appl Physiol 96(5): 1954–1960CrossRefPubMedGoogle Scholar
  20. Dietz V, Muller R, Colombo G (2002) Locomotor activity in spinal man: significance of afferent input from joint and load receptors. Brain 125(12): 2626–2634CrossRefPubMedGoogle Scholar
  21. Dimitrijevic MR, Gerasimenkp Y, Pinter MM (1998) Evidence for a spinal central pattern generator in humans. Ann New York Acad Sci 860: 360–376CrossRefGoogle Scholar
  22. 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): 145–167CrossRefPubMedGoogle Scholar
  23. Elble R, Higgins C, Hughes L (1994) Essential tremor entrains rapid voluntary movements. Exp Neurol 126: 138–143CrossRefPubMedGoogle Scholar
  24. Feldman A (2009) New insights into actionperception coupling. Exp Brain Res 194(1): 39–58CrossRefPubMedGoogle Scholar
  25. Forssberg H (1985) Ontogeny of human locomotor control. I: Infant stepping, supported locomotion and transition to independent locomotion. Exp Brain Res 57(3): 480–493CrossRefPubMedGoogle Scholar
  26. Gandevia S, Burke D (1992) Does the nervous system depend on kinesthesic information to control natural limb movements?. Behav Brain Sci 15: 614–632Google Scholar
  27. 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): 141–155CrossRefGoogle Scholar
  28. 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): 151–155CrossRefPubMedGoogle Scholar
  29. Giszter SF, Mussa-Ivaldi FA, Bizzi E (1993) Convergent force fields organized in the frog’s spinal cord. J Neurosci 13(2): 467–491PubMedGoogle Scholar
  30. Goodman D, Kelso J (1983) Exploring the functional signifiance of physiological tremor: a biospectroscopic approach. Exp Brain Res 49: 419–431CrossRefPubMedGoogle Scholar
  31. Graziano MSA, Taylor CSR, Moore T, Cooke DF (2002) The cortical control of movement revisited. Neuron 36: 349–362CrossRefPubMedGoogle Scholar
  32. Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228(4696): 143–149CrossRefPubMedGoogle Scholar
  33. Grillner S (2006) Biological pattern generation: the cellular and computational logic of networks in motion. Neuron 52(5): 751–766CrossRefPubMedGoogle Scholar
  34. 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): 393–405CrossRefPubMedGoogle Scholar
  35. Guiard Y (1993) On fittss and hookes laws: simple harmonic movement in upper-limb cyclical aiming. Acta Psychol Amst 82: 139–159CrossRefPubMedGoogle Scholar
  36. 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): 1579–1587CrossRefPubMedGoogle Scholar
  37. Hanna JP, Frank JI (1995) Automatic stepping in the pontomedullary stage of central herniation. Neurology 45(5): 985–986PubMedGoogle Scholar
  38. Hogan N, Sternad D (2007) On rhythmic and discrete movements: reflections, definitions and implications for motor control. Exp Brain Res 181(1): 13–30CrossRefPubMedGoogle Scholar
  39. Ijspeert AJ (2008) Central pattern generators for locomotion control in animals and robots: a review. Neural Netw 21(4): 642–653CrossRefPubMedGoogle Scholar
  40. Ivanenko YP, Dominici N, Cappellini G, Lacquaniti F (2005) Kinematics in newly walking toddlers does not depend upon postural stability. J Neurophysiol 94(1): 754–763CrossRefPubMedGoogle Scholar
  41. Jeannerod M (1988) The neural and the behavioural organization of goal directed movements. Oxford Science, OxfordGoogle Scholar
  42. Kandel ER, Schwartz J, Jessell TM (2000) Principles of neural science. McGraw-Hill, New YorkGoogle Scholar
  43. Kargo W, Giszter S (2000) Rapid correction of aimed movements by summation of force-field primitives. J Neurosci 20(1): 409–426PubMedGoogle Scholar
  44. 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 409–430Google Scholar
  45. 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): 1991–2010CrossRefPubMedGoogle Scholar
  46. Marder E, Bucher D (2001) Central pattern generators and the control of rhythmic movements. Curr Biol 11(23): R986–R996CrossRefPubMedGoogle Scholar
  47. Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52: 367–376CrossRefPubMedGoogle Scholar
  48. Miall RC, Ivry R (2004) Moving to a different beat. Nat Neurosci 7(10): 1025–1026CrossRefPubMedGoogle Scholar
  49. Michaels C, Bongers R (1994) The dependence of discrete movements on rhythmic movements: simple RT during oscillatory tracking. Hum Mov Sci 13: 473–493CrossRefGoogle Scholar
  50. Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42(2): 223–227CrossRefPubMedGoogle Scholar
  51. Morishita I, Yajima A (1972) Analysis and simulation of networks of mutually inhibiting neurons. Biol Cybern 11(3): 154–165Google Scholar
  52. Mussa-Ivaldi FA (1999) Modular features of motor control and learning. Curr Opin Neurobiol 9(6): 713–717CrossRefPubMedGoogle Scholar
  53. Mussa-Ivaldi FA, Bizzi E (2000) Motor learning through the combination of primitives. Philos Trans R Soc Lond B Biol Sci 355(1404): 1755–1769CrossRefPubMedGoogle Scholar
  54. Mussa-Ivaldi FA, Giszter SF, Bizzi E (1994) Linear combinations of primitives in vertebrate motor control. Proc Natl Acad Sci USA 91: 7534–7538CrossRefPubMedGoogle Scholar
  55. Overduin SA, d’Avella A, Roh J, Bizzi E (2008) Modulation of muscle synergy recruitment in primate grasping. J Neurosci 28(4): 880–892CrossRefPubMedGoogle Scholar
  56. Pearson KG (2000) Neural adaptation in the generation of rhythmic behavior. Annu Rev Physiol 62: 723–753CrossRefPubMedGoogle Scholar
  57. Peiper A, Nagler B (1963) Cerebral function in infancy and childhood. Pitman Medical, LondonGoogle Scholar
  58. 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 171–194Google Scholar
  59. Ronsse R, Sternad D, Lefévre P (2009) A computational model for rhythmic and discrete movements in uni- and bimanual coordination. Neural Comput 21(5): 1335–1370CrossRefPubMedGoogle Scholar
  60. Rossignol S, Schwab M, Schwartz M, Fehlings MG (2007) Spinal cord injury: time to move?. J Neurosci 27(44): 11,782–11,792CrossRefGoogle Scholar
  61. 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): 2323–2339PubMedGoogle Scholar
  62. 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): 2120–2138CrossRefPubMedGoogle Scholar
  63. 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 117–124Google Scholar
  64. Schaal S, Sternad D, Osu R, Kawato M (2004) Rhythmic arm movement is not discrete. Nat Neurosci 7(10): 1136–1143CrossRefPubMedGoogle Scholar
  65. 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, MAGoogle Scholar
  66. Sherrington CS (1910) Flexion-reflex of the limb, crossed extension-reflex, and reflex stepping and standing. J Physiol Lond 40: 28–121PubMedGoogle Scholar
  67. Slotine JJ, Lohmiller W (2001) Modularity, evolution, and the binding problem: a view from stability theory. Neural Netw 14(2): 137–145CrossRefPubMedGoogle Scholar
  68. Soffe S, Roberts A (1982) Tonic and phasic synaptic input to spinal cord motoneurons during fictive locomotion in frog embryos. J Neurophysiol 48(6): 1279–1288PubMedGoogle Scholar
  69. St-Onge N, Qi H, Feldman A (1993) The patterns of control signals underlying elbow joint movements in humans. Neurosci Lett 164: 171–174CrossRefPubMedGoogle Scholar
  70. 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): 427–443CrossRefPubMedGoogle Scholar
  71. 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, MAGoogle Scholar
  72. Stein P, Grillner S, Selverston A, Stuart DE (1997) Neurons, networks and motor behavior. MIT Press, Cambridge, MAGoogle Scholar
  73. Stein RB (2008) The plasticity of the adult spinal cord continues to surprise. J Physiol 586(12): 2823–2823CrossRefPubMedGoogle Scholar
  74. Sternad D (2007) Rhythmic and discrete movements—behavioral, modeling and imaging results. In: Fuchs A, Jirsa V (eds) Coordination dynamics. Springer, Berlin Heidelberg New YorkGoogle Scholar
  75. Sternad D, Dean W, Schaal S (2000) Interaction of rhythmic and discrete pattern generators in single joint movements. Hum Mov Sci 19: 627–665CrossRefGoogle Scholar
  76. Strick P (2002) Stimulating research on motor cortex. Nat Neurosci 5(8): 714–715CrossRefPubMedGoogle Scholar
  77. Strogatz SH (2001) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Perseus, New YorkGoogle Scholar
  78. Suzuki R, Katsuno I, Matano K (1971) Dynamics of neuron ring. Biol Cybern 8(1): 39–45Google Scholar
  79. 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: 18979336CrossRefPubMedGoogle Scholar
  80. Thelen E, Cooke DW (1987) Relationship between newborn stepping and later walking: a new interpretation. Develop Med Child Neurol 29(3): 380–393CrossRefPubMedGoogle Scholar
  81. Ting LH, Macpherson JM (2005) A limited set of muscle synergies for force control during a postural task. J Neurophysiol 93(1): 609–613CrossRefPubMedGoogle Scholar
  82. Tresch M, Saltiel P, Bizzi E (1999) The construction of movement by the spinal cord. Nat Neurosci 2: 162–167CrossRefPubMedGoogle Scholar
  83. van Mourik AM, Beek PJ (2004) Discrete and cyclical movements: unified dynamics or separate control. Acta Psychol Amst 117(2): 121–138CrossRefPubMedGoogle Scholar
  84. 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: 782–787CrossRefPubMedGoogle Scholar
  85. Wolpaw JR, Tennissen AM (2001) Activity-dependent spinal cord plasticity in health and disease. Annu Rev Neurosci 24(1): 807–843CrossRefPubMedGoogle Scholar
  86. Won J, Hogan N (1995) Stability properties of human reaching movements. Exp Brain Res 107(1): 125–136CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Biorobotics Laboratory (BIOROB), School of EngineeringEPFL—Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland

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