Review of Models for the Generation of Multi-Joint Movements in 3-D

Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 629)


Most studies in motor control have focused on movements in two dimensions and only very few studies have systematically investigated movements in three dimensions. As a consequence, the large majority of modeling studies for motor control have tested the predictions of these models using movement data in 2D. As we will explain, movements in 3D cannot be understood from movements in 2D by adding just another dimension. The third dimension adds new and unexpected complexities. In this chapter we will explore the frames of reference, which are used in mapping sensory information about movement targets into motor commands and muscle activation patterns. Moreover, we will make a quantitative comparison between the predictions of various models in the literature with the outcome of 3D movement experiments. Quite surprisingly, none of the existing models is able to explain the data in different movement paradigms.


Internal Model Movement Trajectory Motor Command Stochastic Optimal Control Endpoint Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Admiraal MA, Keijsers NLW, and Gielen CCAM. Gaze affects pointing toward remembered visual targets after a self-initiated step. Journal of Neurophysiology 92: 2380–2393, 2004a.Google Scholar
  2. Admiraal MA, Keijsers NLW, and Gielen CCAM. Interaction between gaze and pointing toward remembered visual targets. Journal of Neurophysiology 90: 2136–2148, 2003.PubMedGoogle Scholar
  3. Admiraal MA, Kusters MJAM, and Gielen SCAM. Modelling kinematics and dynamics of human arm movements. Motor Control 8: 312–338, 2004b.Google Scholar
  4. Batista AP, Buneo CA, Snyder LH, and Andersen RA. Reach plans in eye-centered coordinates. Science 285: 257–260, 1999.PubMedGoogle Scholar
  5. Berkinblit MB, Fookson OI, Smetanin B, Adamovich SV, and Poizner H. The interaction of visual and proprioceptive inputs in pointing to actual and remembered targets. Experimental Brain Research 107: 326–330, 1995.Google Scholar
  6. Breteler MDK, Hondzinski JM, and Flanders M. Drawing sequences of segments in 3D: Kinetic influences on arm configuration. Journal of Neurophysiology 89: 3253–3263, 2003.Google Scholar
  7. Bullock D, and Grossberg S. Neural dynamics of planned arm movements – Emergent invariants and speed accuracy properties during trajectory formation. Psychological Review 95: 49–90, 1988.PubMedGoogle Scholar
  8. Buneo CA, Jarvis MR, Batista AP, and Andersen RA. Direct visuomotor transformations for reaching. Nature 416: 632–636, 2002.PubMedGoogle Scholar
  9. Capaday C. Force-feedback during human walking Trends in Neurosciences 24: 10–10 , 2001.PubMedGoogle Scholar
  10. Carrozzo M, McIntyre J, Zago M, and Lacquaniti F. Viewer-centered and body-centered frames of reference in direct visuomotor transformations. Experimental Brain Research 129: 201–210, 1999.Google Scholar
  11. Cohen YE, and Andersen RA. Reaches to sounds encoded in an eye-centered reference frame. Neuron 27: 647–652, 2000.PubMedGoogle Scholar
  12. Crawford JD, Medendorp WP, and Marotta JJ. Spatial transformations for eye-hand coordination. Journal of Neurophysiology 92: 10–19, 2004.PubMedGoogle Scholar
  13. Desmurget M, and Grafton S. Forward modeling allows feedback control for fast reaching movements. Trends in Cognitive Sciences 4: 423–431, 2000.PubMedGoogle Scholar
  14. Desmurget M, Grea H, and Prablanc C. Final posture of the upper limb depends on the initial position of the hand during prehension movements. Experimental Brain Research 119: 511–516, 1998.Google Scholar
  15. Desmurget M, Jordan M, Prablanc C, and Jeannerod M. Constrained and unconstrained movements involve different control strategies. Journal of Neurophysiology 77: 1644–1650, 1997.PubMedGoogle Scholar
  16. Desmurget M, and Prablanc C. Postural control of three-dimensional prehension movements. Journal of Neurophysiology 77: 452–464, 1997.PubMedGoogle Scholar
  17. Desmurget M, Prablanc C, Rossetti Y, Arzi M, Paulignan Y, Urquizar C, and Mignot JC. Postural and synergic control for 3-dimensional movements of reaching and grasping. Journal of Neurophysiology 74: 905–910, 1995.PubMedGoogle Scholar
  18. Diedrichsen J, Hashambhoy Y, Rane T, and Shadmehr R. Neural correlates of reach errors. Journal of Neuroscience 25: 9919–9931, 2005.PubMedGoogle Scholar
  19. Donders FC. Beitrag zur lehre von den Bewegungen des menschlichen Auges. Holländische Beiträge zu den anatomischen und physiologischen Wissenschaften, 1, 104–145, 1848.Google Scholar
  20. Duhamel JR, Bremmer F, Ben Hamed S, and Graf W. Spatial invariance of visual receptive fields in parietal cortex neurons. Nature 389: 845–848, 1997.PubMedGoogle Scholar
  21. Duysens J, Clarac F, Cruse H. Load-regulating mechanisms in gait and posture: Comparative aspects Physiological Reviews 80: 83–133, 2000.PubMedGoogle Scholar
  22. Enright JT. The non-visual impact of eye orientation on eye-hand coordination. Vision Research 35: 1611–1618, 1995.PubMedGoogle Scholar
  23. Feldman AG. Once more on the equilibrium point hypothesis (lambda model) for motor control. Journal of Motor Behavior 18: 17–54, 1986.Google Scholar
  24. Feldman AG, and Levin MF. The origin and use of positional frames of reference in motor control. Behavioral and Brain Sciences 18: 723–744, 1995.Google Scholar
  25. Feldman AG, and Levin MF Testing hypotheses and the advancedment of science: recent attempts to falsify the equilibrium point hypothesis. Experimental Brain Research 161: 91–103, 2005.Google Scholar
  26. Fischer MH, Rosenbaum DA, and Vaughan J Speed and sequential effects in reaching Journal of Eexperimental Psychology-Human Perception and Performance 23: 404–428 1997.Google Scholar
  27. Flanagan JR, and Lolley S. The inertial anisotropy of the arm is accurately predicted during movement planning. Journal of Neuroscience 21: 1361–1369, 2001.PubMedGoogle Scholar
  28. Flanagan JR, Nakano E, Imamizu H, Osu R, Yoshioka T, and Kawato M. Composition and decomposition of internal models in motor learning under altered kinematic and dynamic environments. Journal of Neuroscience 19: art. no.-RC34, 1999.PubMedGoogle Scholar
  29. Flanders M, Tillery SIH, and Soechting JF. Early stages in a sensorimotor transformation. Behavioral and Brain Sciences 15: 309–320, 1992.Google Scholar
  30. Flanders M, Mrotek LA, and Gielen CCAM. Planning and drawing complex shapes. Experimental brain research 171: 116–128, 2006.Google Scholar
  31. Flash T. The control of hand equilibrium trajectories in multijoint arm movements. Biological Cybernetics 57: 257–274, 1987.PubMedGoogle Scholar
  32. Flash T, and Hogan N. The coordination of arm movements – an experimentally confirmed mathematical-model. Journal of Neuroscience 5: 1688–1703, 1985.PubMedGoogle Scholar
  33. Franklin DW, Osu R, Burdet E, Kawato M, and Milner TE. Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model. Journal of Neurophysiology 90: 3270–3282, 2003.PubMedGoogle Scholar
  34. Georgopoulos AP, Kalaska JF, and Massey JT. Spatial trajectories and reaction-times of aimed movements – effects of practice, uncertainty, and change in target location. Journal of Neurophysiology 46: 725–743, 1981.PubMedGoogle Scholar
  35. Ghilardi MF, Gordon J, and Ghez C. Learning a visuomotor transformation in a local-area of work space produces directional biases in other areas. Journal of Neurophysiology 73: 2535–2539, 1995.PubMedGoogle Scholar
  36. Gielen C, Van Bolhuis BM, and Theeuwen M. On the control of biologically and kinematically redundant manipulators. Human Movement Science 14: 487–509, 1995.Google Scholar
  37. Gielen CCAM, Vrijenhoek EJ, Flash T, and Neggers SFW. Arm position constraints during pointing and reaching in 3-D space. Journal of Neurophysiology 78: 660–673, 1997.PubMedGoogle Scholar
  38. Gordon J, Ghilardi MF, and Ghez C. Accuracy of planar reaching movements .1. Independence of direction and extent variability. Experimental Brain Research 99: 97–111, 1994.Google Scholar
  39. Grea H, Desmurget M, and Prablanc C. Postural invariance in three-dimensional reaching and grasping movements. Experimental Brain Research 134: 155–162, 2000.Google Scholar
  40. Groh JM, Trause AS, Underhill AM, Clark KR, and Inati S. Eye position influences auditory responses in primate inferior colliculus. Neuron 29: 509–518, 2001.PubMedGoogle Scholar
  41. Hamilton AFD, Jones KE, and Wolpert DM. The scaling of motor noise with muscle strength and motor unit number in humans. Experimental Brain Research 157: 417–430, 2004.Google Scholar
  42. Harris CM, and Wolpert DM. Signal-dependent noise determines motor planning. Nature 394: 780–784, 1998.PubMedGoogle Scholar
  43. Haustein W. Considerations on listings law and the primary position by means of a matrix description of eye position control. Biological Cybernetics 60: 411–420, 1989.PubMedGoogle Scholar
  44. Henriques DYP, and Crawford JD. Role of eye, head, and shoulder geometry in the planning of accurate arm movements. Journal of Neurophysiology 87: 1677–1685, 2002.PubMedGoogle Scholar
  45. Henriques DYP, Klier EM, Smith MA, Lowy D, and Crawford JD. Gaze-centered remapping of remembered visual space in an open-loop pointing task. Journal of Neuroscience 18: 1583–1594, 1998.PubMedGoogle Scholar
  46. Hermens F, and Gielen S. Posture-based or trajectory-based movement planning: a com-parison of direct and indirect pointing movements. Experimental Brain Research 159: 340–348, 2004.Google Scholar
  47. Heuer H, and Sangals J. Task-dependent mixtures of coordinate systems in visuomotor transformations. Experimental Brain Research 119: 224–236, 1998.Google Scholar
  48. Hogan N. Impedance control – an approach to manipulation .1. Theory. Journal of Dynamic Systems Measurement and Control-Transactions of the Asme 107: 1–7, 1985.Google Scholar
  49. Hore J, Watts S, and Vilis T. Constraints on arm position when pointing in three dimensions: Donders' law and Fick gimbal strategy. Journal of Neurophysiology 68: 374–383, 1992PubMedGoogle Scholar
  50. Jones KE, Hamilton AFD, and Wolpert DM. Sources of signal-dependent noise during isometric force production. Journal of Neurophysiology 88: 1533–1544, 2002.PubMedGoogle Scholar
  51. Kappen HJ. Linear theory for control of nonlinear stochastic systems. Physical Review Letters 95: 2005.Google Scholar
  52. Kawato M. Internal models for motor control and trajectory planning. Current Opinion in Neurobiology 9: 718–727, 1999.PubMedGoogle Scholar
  53. Krakauer JW, Pine ZM, Ghilardi MF, and Ghez C. Learning of visuomotor transformations for vectorial planning of reaching trajectories. Journal of Neuroscience 20: 8916–8924, 2000.PubMedGoogle Scholar
  54. Lacquaniti F, Terzuolo C, and Viviani P. The law relating the kinematic and figural aspects of drawing movements. Acta Psychologica 54: 115–130, 1983.PubMedGoogle Scholar
  55. Latash ML, Scholz JF, Danion F, and Schoner G. Structure of motor variability in marginally redundant multifinger force production tasks. Experimental Brain Research 141: 153–165, 2001.Google Scholar
  56. Lemay M, and Stelmach GE. Multiple frames of reference for pointing to a remembered target. Experimental Brain Research 164: 301–310, 2005.Google Scholar
  57. Massey JT, Lurito JT, Pellizzer G, and Georgopoulos AP. 3-Dimensional drawings in isometric conditions – Relation between geometry and kinematics. Experimental Brain Research 88: 685–690, 1992.Google Scholar
  58. McIntyre J, Berthoz A, and Lacquaniti F. Reference frames and internal models for visuo-manual coordination: what can we learn from microgravity experiments? Brain Research Reviews 28: 143–154, 1998.PubMedGoogle Scholar
  59. McIntyre J, Stratta F, and Lacquaniti F. Viewer-centered frame of reference for pointing to memorized targets in three-dimensional space. Journal of Neurophysiology 78: 1601–1618, 1997.PubMedGoogle Scholar
  60. Medendorp WP, Bakker BJ, Van Gisbergen JAM, and Gielen C. Human gaze stabilization for voluntary off-centric head rotations. In: Otolith Function in Spatial Orientation and Movement1999a, p. 426–429.Google Scholar
  61. Medendorp WP, and Crawford JD. Visuospatial updating of reaching targets in near and far space. Neuroreport 13: 633–636, 2002.PubMedGoogle Scholar
  62. Medendorp WP, Crawford JD, Henriques DYP, Van Gisbergen JAM, and Gielen C. Kinematic strategies for upper arm-forearm coordination in three dimensions. Journal of Neurophysiology 84: 2302–2316, 2000.PubMedGoogle Scholar
  63. Medendorp WP, Goltz HC, Crawford JD, and Vilis T. Integration of target and effector information in human posterior parietal cortex for the planning of action. Journal of Neurophysiology 93: 954–962, 2005.PubMedGoogle Scholar
  64. Medendorp WP, Goltz HC, Vilis T, and Crawford JD. Gaze-centered updating of visual space in human parietal cortex. Journal of Neuroscience 23: 6209–6214, 2003.PubMedGoogle Scholar
  65. Medendorp WP, Van Asselt S, and Gielen C. Pointing to remembered visual targets after active one-step self-displacements within reaching space. Experimental Brain Research 125: 50–60, 1999b.Google Scholar
  66. Merfeld DM, Zupan L, and Peterka RJ. Humans use internal models to estimate gravity and linear acceleration. Nature 398: 615–618, 1999.PubMedGoogle Scholar
  67. Miller LE, Theeuwen M, and Gielen C. The control of arm pointing movements in 3 dimensions. Experimental Brain Research 90: 415–426, 1992.Google Scholar
  68. Mullette-Gillman OA, Cohen YE, and Groh JM. Eye-centered, headcentered, and complex coding of visual and auditory targets in the intraparietal sulcus. Journal of Neurophysiology 94: 2331–2352, 2005.PubMedGoogle Scholar
  69. Nakano E, Imamizu H, Osu R, Uno Y, Gomi H, Yoshioka T, and Kawato M. Quantitative examinations of internal representations for arm trajectory planning: Minimum commanded torque change model. Journal of Neurophysiology 81: 2140–2155, 1999.PubMedGoogle Scholar
  70. Neggers SFW, and Bekkering H. Ocular gaze is anchored to the target of an ongoing pointing movement. Journal of Neurophysiology 83: 639–651, 2000.PubMedGoogle Scholar
  71. Nishikawa KC, Murray ST, and Flanders M. Do arm postures vary with the speed of reaching? Journal of Neurophysiology 81: 2582–2586, 1999.PubMedGoogle Scholar
  72. Prado J, Clavagnier S, Otzenberger H, Scheiber C, Kennedy H, and Perenin MT. Two cortical systems for reaching in central and peripheral vision. Neuron 48: 849–858, 2005.PubMedGoogle Scholar
  73. Richardson MJE, and Flash T. Comparing smooth arm movements with the two-thirds power law and the related segmented-control hypothesis. Journal of Neuroscience 22: 8201–8211, 2002.PubMedGoogle Scholar
  74. Rosenbaum DA, Loukopoulos LD, Meulenbroek RGJ, Vaughan J, and Engelbrecht SE. Planning Reaches by Evaluating Stored Postures. Psychological Review 102: 28–67, 1995.PubMedGoogle Scholar
  75. Rosenbaum DA, Meulenbroek RJ, Vaughan J, and Jansen C. Posture-based motion planning: Applications to grasping. Psychological Review 108: 709–734, 2001.PubMedGoogle Scholar
  76. Rossetti Y, Desmurget M, and Prablanc C. Vectorial coding of movement – Vision, Proprioception, or Both. Journal of Neurophysiology 74: 457–463, 1995.PubMedGoogle Scholar
  77. Sainburg RL, Lateiner JE, Latash ML, and Bagesteiro LB. Effects of altering initial position on movement direction and extent. Journal of Neurophysiology 89: 401–415, 2003.PubMedGoogle Scholar
  78. Schaal S, and Sternad D. Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements. Experimental Brain Research 136: 60–72, 2001.Google Scholar
  79. Schlack A, Sterbing-D’Angelo SJ, Hartung K, Hoffman K-P, and Bremmer F. Multisensory space representations in the macaque ventral intraparietal area. Journal of Neuroscience 25: 4616–4625, 2005.PubMedGoogle Scholar
  80. Scholz JP, and Schoner G. The uncontrolled manifold concept: identifying control variables for a functional task. Experimental Brain Research 126: 289–306, 1999.Google Scholar
  81. Scholz JP, Schoner G, and Latash ML. Identifying the control structure of multijoint coordination during pistol shooting. Experimental Brain Research 135: 382–404, 2000.Google Scholar
  82. Schwartz AB. Direct Cortical Representation of Drawing. Science 265: 540–542, 1994.PubMedGoogle Scholar
  83. Soechting JF, Buneo CA, Herrmann U, and Flanders M. Moving effortlessly in 3-dimensions – does Donders-law apply to arm movement. Journal of Neuroscience 15: 6271–6280, 1995.PubMedGoogle Scholar
  84. Soechting JF, and Flanders M. Errors in pointing are due to approximations in sensorimotor transformations. Journal of Neurophysiology 62: 595–608, 1989a.Google Scholar
  85. Soechting JF, and Flanders M. Sensorimotor representations for pointing to targets in 3-dimensional space. Journal of Neurophysiology 62: 582–594, 1989b.Google Scholar
  86. Soechting JF, and Lacquaniti F. Invariant characteristics of a pointing movement in man. Journal of Neuroscience 1: 710–720, 1981.PubMedGoogle Scholar
  87. Sternad D, and Schaal S. Segmentation of endpoint trajectories does not imply segmented control. Experimental Brain Research 124: 118–136, 1999.Google Scholar
  88. Stoker, JJ. Pure and applied mathematics, vol. XX: Differential Geometry (pp. 191–198). New York, Wiley Interscience, 1969.Google Scholar
  89. Straumann D, Haslwanter T, Heppreymond MC, and Hepp K. Listings law for eye, head and arm movements and their synergistic control. Experimental Brain Research 86: 209–215, 1991.Google Scholar
  90. Stucchi N, and Viviani P. The intrinsic-properties of the motor control-system affect visual-perception. International Journal of Psychology 27: 17–17, 1992.Google Scholar
  91. Terzuolo CA, and Viviani P. Determinants and characteristics of motor patterns used for typing. Neuroscience 5: 1085–1103, 1980.PubMedGoogle Scholar
  92. Todorov E. Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system. Neural Computation 17: 1084–1108, 2005.PubMedGoogle Scholar
  93. Todorov E, and Jordan MI. Optimal feedback control as a theory of motor coordination. Nature Neuroscience 5: 1226–1235, 2002.PubMedGoogle Scholar
  94. Todorov E, and Jordan MI. Smoothness maximization along a predefined path accurately predicts the speed profiles of complex arm movements. Journal of Neurophysiology 80: 696–714, 1998.PubMedGoogle Scholar
  95. Todorov E. Optimality principles in sensorimotor control. Nature Neuroscience 7: 907–915, 2004.PubMedGoogle Scholar
  96. Tong C, Wolpert DM, and Flanagan JR. Kinematics and dynamics are not represented independently in motor working memory: Evidence from an interference study. Journal of Neuroscience 22: 1108–1113, 2002.PubMedGoogle Scholar
  97. Tweed D, and Vilis T. Implications of rotational kinematics for the oculomotor system in 3 dimensions. Journal of Neurophysiology 58: 832–849, 1987.PubMedGoogle Scholar
  98. Uno Y, Kawato M, and Suzuki R. Formation and control of optimal trajectory in human multijoint arm movement – Minimum torque-change model. Biological Cybernetics 61: 89–101, 1989.PubMedGoogle Scholar
  99. van Beers RJ, Sittig AC, and van der Gon JJD. Localization of a seen finger is based exclusively on proprioception and on vision of the finger. Experimental Brain Research 125: 43–49, 1999.Google Scholar
  100. van Beers RJ, Wolpert DM, and Haggard P. When feeling is more important than seeing in sensorimotor adaptation. Current Biology 12: 834–837, 2002.PubMedGoogle Scholar
  101. van den Dobbelsteen JJ, Brenner E, and Smeets JBJ. Endpoints of arm movements to visual targets. Experimental Brain Research 138: 279–287, 2001.Google Scholar
  102. Vetter P, Flash T, and Wolpert DM. Planning movements in a simple redundant task. Current Biology 12: 488–491, 2002.PubMedGoogle Scholar
  103. Vetter P, Goodbody SJ, and Wolpert DM. Evidence for an eye-centered spherical representation of the visuomotor map. Journal of Neurophysiology 81: 935–939, 1999.Google Scholar
  104. Vindras P, Desmurget M, Prablanc C, and Viviani P. Pointing errors reflect biases in the perception of the initial hand position. Journal of Neurophysiology 79: 3290–3294, 1998.PubMedGoogle Scholar
  105. Vindras P, Desmurget M, and Viviani P. Error parsing in visuomotor pointing reveals independent processing of amplitude and direction. Journal of Neurophysiology 94: 1212–1224, 2005.PubMedGoogle Scholar
  106. Vindras P, and Viviani P. Planning short pointing sequences. Experimental Brain Research 160: 141–153, 2005.Google Scholar
  107. Viviani P, Campadelli P, and Mounoud P. Visuo-manual pursuit tracking of human two-dimensional movements. Journal of Experimental Psychology-Human Perception and Performance 13: 62–78, 1987.Google Scholar
  108. Viviani P, and Mounoud P. Perceptuomotor compatibility in pursuit tracking of 2-dimensional movements. Journal of Motor Behavior 22: 407–443, 1990.PubMedGoogle Scholar
  109. Viviani P, and Schneider R. A developmental-study of the relationship between geometry and kinematics in drawing movements. Journal of Experimental Psychology-Human Perception and Performance 17: 198–218, 1991.PubMedGoogle Scholar
  110. Viviani P, and Stucchi N. Biological movements look uniform – Evidence of Motor-Perceptual Interactions. Journal of Experimental Psychology-Human Perception and Performance 18: 603–623, 1992.PubMedGoogle Scholar
  111. Viviani P, and Terzuolo C. Trajectory determines movement dynamics. Neuroscience 7: 431–437, 1982.PubMedGoogle Scholar
  112. Von Helmholtz H. Handbuch der Physiologischen Optik (1st ed.) . Hamburg, Germany: Voss, vol. 3, 1867. Third edition translated into English by J.P.C. Southall as Treatise on Physiological Optics. Rochester, NY: Opt. Soc. Am., 1925Google Scholar
  113. Wada Y, Kaneko Y, Nakano E, Osu R, and Kawato M. Quantitative examinations for multi joint arm trajectory planning – using a robust calculation algorithm of the minimum commanded torque change trajectory. Neural Networks 14: 381–393, 2001.PubMedGoogle Scholar
  114. Wann J, Nimmo-Smith I, and Wing AM. Relation between velocity and curvature in movement: equivalence and divergence between a power law and a minimum-jerk model. J Exp Psychol Hum Percept Perform 14: 622–637, 1988.PubMedGoogle Scholar
  115. Werner-Reiss U, Kelly KA, Trause AS, Underhill AM, and Groh JM. Eye position affects activity in primary auditory cortex of primates. Current Biology 13: 554–562, 2003.PubMedGoogle Scholar
  116. Wolpert DM, Ghahramani Z, and Jordan MI. An internal model for sensorimotor integration. Science 269: 1880–1882, 1995.PubMedGoogle Scholar
  117. Wolpert DM, and Kawato M. Multiple paired forward and inverse models for motor control. Neural Networks 11: 1317–1329, 1998.PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of BiophysicsRadboud University Nijmegen6525 EZ NijmegenThe Netherlands

Personalised recommendations