Experimental Brain Research

, Volume 208, Issue 1, pp 73–87 | Cite as

Target switching in curved human arm movements is predicted by changing a single control parameter

Research Article

Abstract

Straight-line movements have been studied extensively in the human motor-control literature, but little is known about how to generate curved movements and how to adjust them in a dynamic environment. The present work studied, for the first time to my knowledge, how humans adjust curved hand movements to a target that switches location. Subjects (n = 8) sat in front of a drawing tablet and looked at a screen. They moved a cursor on a curved trajectory (spiral or oval shaped) toward a goal point. In half of the trials, this goal switched 200 ms after movement onset to either one of two alternative positions, and subjects smoothly adjusted their movements to the new goal. To explain this adjustment, we compared three computational models: a superposition of curved and minimum-jerk movements (Flash and Henis in J Cogn Neurosci 3(3):220–230, 1991), Vector Planning (Gordon et al. in Exp Brain Res 99(1):97–111, 1994) adapted to curved movements (Rescale), and a nonlinear dynamical system, which could generate arbitrarily curved smooth movements and had a point attractor at the goal. For each model, we predicted the trajectory adjustment to the target switch by changing only the goal position in the model. As result, the dynamical model could explain the observed switch behavior significantly better than the two alternative models (spiral: P = 0.0002 vs. Flash, P = 0.002 vs. Rescale; oval: P = 0.04 vs. Flash; P values obtained from Wilcoxon test on R2 values). We conclude that generalizing arbitrary hand trajectories to new targets may be explained by switching a single control command, without the need to re-plan or re-optimize the whole movement or superimpose movements.

Keywords

Behavioral experiment Target switch Curved movement Computational model Dynamical system Convergent force field 

References

  1. Alexander RM (1995) Simple models of human motion. Appl Mech Rev 48:461–469CrossRefGoogle Scholar
  2. Bizzi E, Mussa-Ivaldi FA, Giszter SF (1991) Computations underlying the execution of movement: a biological perspective. Science 253(5017):287–291PubMedCrossRefGoogle Scholar
  3. Bizzi E, Cheung V, d’Avella A, Saltiel P, Tresch M (2008) Combining modules for movement. Brain Res Rev 57(1):125–133PubMedCrossRefGoogle Scholar
  4. Brainard DH (1997) The psychophysics toolbox. Spat Vis 10:433–436PubMedCrossRefGoogle Scholar
  5. Bullock D, Grossberg S (1988) Neural dynamics of planned arm movements: emergent invariants and speed-accuracy properties during trajectory formation. Psychol Rev 95(1):49–90PubMedCrossRefGoogle Scholar
  6. d’Avella A, Saltiel P, Bizzi E (2003) Combinations of muscle synergies in the construction of a natural motor behavior. Nat Neurosci 6(3):300–308PubMedCrossRefGoogle Scholar
  7. Feldman AG (1986) Once more on the equilibrium-point hypothesis (lambda model) for motor control. J Mot Behav 18(1):17–54PubMedGoogle Scholar
  8. Flash T, Henis E (1991) Arm trajectory modifications during reaching towards visual targets. J Cogn Neurosci 3(3):220–230CrossRefGoogle Scholar
  9. Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5(7):1688–1703PubMedGoogle Scholar
  10. Ghez C, Scheidt R, Heijink H (2007) Different learned coordinate frames for planning trajectories and final positions in reaching. J Neurophysiol 98(6):3614–3626PubMedCrossRefGoogle Scholar
  11. 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
  12. Gomi H, Kawato M (1996) Equilibrium-point control hypothesis examined by measured arm stiffness during multijoint movement. Science 272(5258):117–120PubMedCrossRefGoogle Scholar
  13. Gordon J, Ghilardi MF, Ghez C (1994) Accuracy of planar reaching movements. Exp Brain Res 99(1):97–111PubMedCrossRefGoogle Scholar
  14. Gribble PL, Ostry DJ, Sanguineti V, Laboissiere R (1998) Are complex control signals required for human arm movement. J Neurophysiol 79(3):1409–1424PubMedGoogle Scholar
  15. Harris CM, Wolpert DM (1998) Signal-dependent noise determines motor planning. Nature 394(6695):780–784PubMedCrossRefGoogle Scholar
  16. Hart CB, Giszter SF (2004) Modular premotor drives and unit bursts as primitives for frog motor behaviors. J Neurosci 24(22):5269–5282PubMedCrossRefGoogle Scholar
  17. Hastie T, Tibshirani R, Friedman JH (2003) The elements of statistical learning. Springer, BerlinGoogle Scholar
  18. Hatsopoulos N, Xu Q, Amit Y (2007) Encoding of movement fragments in the motor cortex. J Neurosci 27:5105–5114PubMedCrossRefGoogle Scholar
  19. Hinder MR, Milner TE (2003) The case for an internal dynamics model versus equilibrium point control in human movement. J Physiol 549:953–963PubMedCrossRefGoogle Scholar
  20. Hoff B, Arbib MA (1993) Models of trajectory formation and temporal interaction of reach and grasp. J Mot Behav 25(3):175–192PubMedCrossRefGoogle Scholar
  21. Hoffmann H, Schaal S (2007a) A computational model of human trajectory planning based on convergent flow fields. In: Society for neuroscience, Abstracts, San Diego, CAGoogle Scholar
  22. Hoffmann H, Schaal S (2007b) Human movement generation based on convergent flow fields: a computational model and a behavioral experiment. In: Shadmehr R, Todorov E (eds) Advances in computational motor control, vol VI. San Diego, CAGoogle Scholar
  23. Hoffmann H, Pastor P, Park DH, Schaal S (2009) Biologically-inspired dynamical systems for movement generation: automatic real-time goal adaptation and obstacle avoidance. In: IEEE international conference on robotics and automation, Kobe, JapanGoogle Scholar
  24. Ijspeert AJ, Nakanishi J, Schaal S (2002) Movement imitation with nonlinear dynamical systems in humanoid robots. In: International conference on robotics and automation. IEEE, Washington, pp 1398–1403Google Scholar
  25. Ijspeert AJ, Nakanishi J, Schaal S (2003) Learning attractor landscapes for learning motor primitives. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems. vol 15, MIT Press, Cambridge, pp 1523–1530Google Scholar
  26. Katayama M, Kawato M (1993) Virtual trajectory and stiffness ellipse during multijoint arm movement predicted by neural inverse models. Biol Cybern 69:353–362PubMedGoogle Scholar
  27. Kawato M (1996) Bi-directional theory approach to integration. In: Konczak J, Thelen E (eds) Attention and performance. vol XVI, MIT Press, Cambridge, pp 335–367Google Scholar
  28. Khatib O (1987) A unified approach for motion and force control of robot manipulators: the operational space formulation. IEEE J Robot Autom RA-3(1):43–53CrossRefGoogle Scholar
  29. Krakauer JW, Pine ZM, Ghilardi MF, Ghez C (2000) Learning of visuomotor transformations for vectorial planning of reaching trajectories. J Neurosci 20(23):8916–8924PubMedGoogle Scholar
  30. Kutch JJ, Kuo AD, Bloch AM, Rymer WZ (2008) Endpoint force fluctuations reveal flexible rather than synergistic patterns of muscle cooperation. J Neurophysiol 100(5):2455–71PubMedCrossRefGoogle Scholar
  31. Liu D, Todorov E (2007) Evidence for the flexible sensorimotor strategies predicted by optimal feedback control. J Neurosci 27(35):9354–9368PubMedCrossRefGoogle Scholar
  32. Loeb GE, Brown IE, Cheng EJ (1999) A hierarchical foundation for models of sensorimotor control. Exp Brain Res 126(1):1–18PubMedCrossRefGoogle Scholar
  33. Maybeck P (1979) Stochastic models estimation and controls. Prentice Hall, Englewood CliffsGoogle Scholar
  34. Mussa-Ivaldi FA, Bizzi E (2000) Motor learning through the combination of primitives. Philos Trans R Soc Lond B 355:1755–1769CrossRefGoogle Scholar
  35. Pastor P, Hoffmann H, Asfour T, Schaal S (2009) Learning and generalization of motor skills by learning from demonstration. In: IEEE international conference on robotics and automation, Kobe, JapanGoogle Scholar
  36. Pelli DG (1997) The videotoolbox software for visual psychophysics: transforming numbers into movies. Spat Vis 10:437–442PubMedCrossRefGoogle Scholar
  37. Popescu FC, Rymer WZ (2000) End points of planar reaching movements are disrupted by small force pulses: an evaluation of the hypothesis of equifinality. J Neurophysiol 84(5):2670–2679PubMedGoogle Scholar
  38. Pruszynski JA, Lillicrap TP, Scott SH (2010) Complex spatiotemporal tuning in human upper-limb muscles. J Neurophysiol 103:564–572PubMedCrossRefGoogle Scholar
  39. Raphael G, Tsianos GA, Loeb GE (2010) Spinal-like regulator facilitates control of a two-degree-of-freedom wrist. J Neurosci 30(28):9431–9444PubMedGoogle Scholar
  40. Scheidt RA, Ghez C (2007) Separate adaptive mechanisms for controlling trajectory and final position in reaching. J Neurophysiol 98(6):3600–3613PubMedCrossRefGoogle Scholar
  41. Shadmehr R, Mussa-Ivaldi F (1994) Adaptive representation of dynamics during learning of a motor task. J Neurosci 14(5):3208–3224PubMedGoogle Scholar
  42. Shadmehr R, Wise SP (2005) The computational neurobiology of reaching and pointing. MIT Press, CambridgeGoogle Scholar
  43. Siegel S (1956) Non-parametric statistics for the behavioral sciences. McGraw-Hill, New YorkGoogle Scholar
  44. Slotine J, Li W (1991) Applied nonlinear control. Prentice Hall, Englewood CliffsGoogle Scholar
  45. Snyder LH (2000) Coordinate transformations for eye and arm movements in the brain. Curr Opin Neurobiol 10:747–754PubMedCrossRefGoogle Scholar
  46. Spong MW, Vidyasagar M (1989) Robot dynamics and control. Wiley, New YorkGoogle Scholar
  47. Stein RB, Ogusztreli MN, Capaday C (1986) What is optimized in muscular movements?. In: Jones NL, McCartney N, McComas AJ (eds) Human muscle power. Human Kinetics Publisher, Champaign, pp 131–150Google Scholar
  48. Ting LH, Macpherson JM (2005) A limited set of muscle synergies for force control during a postural task. J Neurophysiol 93(1):609–613PubMedCrossRefGoogle Scholar
  49. Todorov E, Jordan MI (1998) Smoothness maximization along a predefined path accurately predicts the speed profiles of complex arm movements. J Neurophysiol 80(2):696–714PubMedGoogle Scholar
  50. Todorov E, Jordan MI (2002) Optimal feedback control as a theory of motor coordination. Nat Neurosci 5(11):1226–1235PubMedCrossRefGoogle Scholar
  51. Tsuji T, Morasso PG, Goto K, Ito K (1995) Human hand impedance characteristics during maintained posture. Biol Cybern 72(6):475–485PubMedCrossRefGoogle Scholar
  52. Viviani P, Flash T (1995) Minimum-jerk, two-thirds power law, and isochrony: converging approaches to movement planning. J Exp Psychol Hum Percept Perform 21(1):32–53PubMedCrossRefGoogle Scholar
  53. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80–83CrossRefGoogle Scholar
  54. Zajac FE, Biosci J, Physiol JC, Biol JE, Physiol ZV, Lond JZ, Physiol ZJ, Soc JGE, Acta BB, Biochem A (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng 17:359–411PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.HRL Laboratories, LLCMalibuUSA

Personalised recommendations