Abstract

We present two experiments that test the range of applicability of a movement planning model (MEGaMove) based on statistical decision theory. Subjects attempted to earn money by rapidly touching a green target region on a computer screen while avoiding nearby red penalty regions. In two experiments we varied the magnitudes of penalties, the degree of overlap of target and penalty regions, and the number of penalty regions. Overall, subjects acted so as to maximize gain in a wide variety of stimulus configurations, in good agreement with predictions of the model.

© 2003 Optical Society of America

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  1. J. Trommershäuser, L. T. Maloney, M. S. Landy, “Statistical decision theory and trade-offs in the control of motor response,” Spatial Vis. 16(3–4), 255–275 (2003).
    [CrossRef]
  2. J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd ed. (Springer, New York, 1985).
  3. D. Blackwell, M. A. Girschick, Theory of Games and Statistical Decisions (Wiley, New York, 1954).
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  7. J. F. Soechting, F. Lacquaniti, “Invariant characteristics of a pointing movement in man,” J. Neurosci. 1, 710–720 (1981).
    [PubMed]
  8. M. Dornay, Y. Uno, M. Kawato, R. Suzuki, “Minimum muscle-tension chance trajectories predicted by using a 17-muscle model of the monkey’s arm,” J. Motor Behav. 2, 83–100 (1996).
    [CrossRef]
  9. T. Flash, N. Hogan, “The coordination of arm movements: An experimentally confirmed mathematical model,” J. Neurosci. 5, 1688–1707 (1985).
    [PubMed]
  10. Y. Uno, M. Kawato, R. Suzuki, “Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model,” Biol. Cybern. 61, 89–101 (1989).
  11. J. F. Soechting, C. A. Bunea, U. Herrmann, M. Flanders, “Moving effortlessly in three dimensions: Does Donders’ law apply to arm movement?” J. Neurosci. 15, 6271–6280 (1995).
    [PubMed]
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    [CrossRef] [PubMed]
  13. U. Castiello, “The effects of abrupt onset of 2-D and 3-D distractors on prehension movements,” Percept. Psychophys. 63, 1014–1025 (2001).
    [CrossRef] [PubMed]
  14. J. Dean, M. Brüwer, “Control of human arm movements in two dimensions: paths and joint control in avoiding simple linear obstacles,” Exp. Brain Res. 97, 497–514 (1994).
    [CrossRef] [PubMed]
  15. L. A. Howard, S. P. Tipper, “Hand deviations away from visual cues: indirect evidence for inhibition,” Exp. Brain Res. 113, 144–152 (1997).
    [CrossRef] [PubMed]
  16. M. Mon-Williams, J. J. Tresilian, V. L. Coppard, R. G. Carson, “The effect of obstacle position on reach-to-grasp movements,” Exp. Brain Res. 137, 497–501 (2001).
    [CrossRef] [PubMed]
  17. S. P. Tipper, L. A. Howard, S. R. Jackson, “Selective reaching to grasp: evidence for distractor interference effects,” Vision Cogn. 4, 1–38 (1997).
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    [PubMed]
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    [CrossRef] [PubMed]
  23. E. Todorov, M. I. Jordan, “Optimal feedback control as a theory of motor coordination,” Nat. Neurosci. 5, 1226–1235 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. R. Plamondon, A. M. Alimi, “Speed/accuracy trade-offs in target-directed movements,” Behav. Brain Sci. 20, 279–349 (1997).
    [CrossRef] [PubMed]
  26. N. Smyrnis, I. Evdokimidis, T. S. Constantinidis, G. Kastrinakis, “Speed-accuracy trade-offs in the performance of pointing movements in different directions in two-dimensional space,” Exp. Brain Res. 134, 21–31 (2000).
    [CrossRef] [PubMed]
  27. J. D. Connolly, M. A. Goodale, “The role of visual feedback of hand position in the control of manual prehension,” Exp. Brain Res. 125, 281–286 (1999).
    [CrossRef] [PubMed]
  28. M. Desmurget, S. Grafton, “Forward modeling allows feedback control for fast reaching movements,” Trends Cogn. Sci. 4, 423–431 (2000).
    [PubMed]
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    [CrossRef]
  31. D. G. Pelli, “The videotoolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
    [CrossRef] [PubMed]
  32. It is instructive to consider the extent to which visual feedback plays a role in our results. The movement times were 300–400 ms, which is barely enough time to allow for an influence of visual feedback during the movement. We ran one subject in a version of experiment 1 in which the visual stimulus disappeared as soon as the space bar was re-leased. This manipulation eliminates feedback from the relative positions of the hand and the visible target during the movement but allows for feedback by using the view of the hand and apparatus. The results were unaffected, including the movement variability and the pattern of movement end points.
  33. D. Kahneman, P. Slovic, A. Tversky, eds., Judgment un-der Uncertainty: Heuristics and Biases (Cambridge U. Press, Cambridge, UK, 1982).
  34. In the 16 practice (warm-up) trials of this experiment, subjects pointed to each of the configurations twice in the penalty=0condition. Subjects were exposed to the eight novel configurations in the penalty=500condition for the first time during the experiment.

2003 (1)

J. Trommershäuser, L. T. Maloney, M. S. Landy, “Statistical decision theory and trade-offs in the control of motor response,” Spatial Vis. 16(3–4), 255–275 (2003).
[CrossRef]

2002 (2)

A. F. C. Hamilton, D. M. Wolpert, “Controlling the statistics of action: obstacle avoidance,” J. Neurophysiol. 87, 2434–2440 (2002).
[PubMed]

E. Todorov, M. I. Jordan, “Optimal feedback control as a theory of motor coordination,” Nat. Neurosci. 5, 1226–1235 (2002).
[CrossRef] [PubMed]

2001 (3)

M. Mon-Williams, J. J. Tresilian, V. L. Coppard, R. G. Carson, “The effect of obstacle position on reach-to-grasp movements,” Exp. Brain Res. 137, 497–501 (2001).
[CrossRef] [PubMed]

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Posture-based motion planning: applications to grasping,” Psychol. Rev. 108, 709–734 (2001).
[CrossRef] [PubMed]

U. Castiello, “The effects of abrupt onset of 2-D and 3-D distractors on prehension movements,” Percept. Psychophys. 63, 1014–1025 (2001).
[CrossRef] [PubMed]

2000 (2)

N. Smyrnis, I. Evdokimidis, T. S. Constantinidis, G. Kastrinakis, “Speed-accuracy trade-offs in the performance of pointing movements in different directions in two-dimensional space,” Exp. Brain Res. 134, 21–31 (2000).
[CrossRef] [PubMed]

M. Desmurget, S. Grafton, “Forward modeling allows feedback control for fast reaching movements,” Trends Cogn. Sci. 4, 423–431 (2000).
[PubMed]

1999 (2)

J. D. Connolly, M. A. Goodale, “The role of visual feedback of hand position in the control of manual prehension,” Exp. Brain Res. 125, 281–286 (1999).
[CrossRef] [PubMed]

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Coordination of reaching and grasping by capitalizing on obstacle avoidance and other constraints,” Exp. Brain Res. 128, 92–100 (1999).
[CrossRef] [PubMed]

1998 (2)

P. N. Sabes, M. I. Jordan, D. M. Wolpert, “The role of inertial sensitivity in motor planning,” J. Neurosci. 18, 5948–5957 (1998).
[PubMed]

C. M. Harris, D. M. Wolpert, “Signal-dependent noise determines motor planning,” Nature 394, 780–784 (1998).
[CrossRef] [PubMed]

1997 (6)

P. N. Sabes, M. I. Jordan, “Obstacle avoidance and a perturbation sensitivity model for motor planning,” J. Neurosci. 17, 7119–7128 (1997).
[PubMed]

L. A. Howard, S. P. Tipper, “Hand deviations away from visual cues: indirect evidence for inhibition,” Exp. Brain Res. 113, 144–152 (1997).
[CrossRef] [PubMed]

S. P. Tipper, L. A. Howard, S. R. Jackson, “Selective reaching to grasp: evidence for distractor interference effects,” Vision Cogn. 4, 1–38 (1997).

D. H. Brainard, “The psychophysical toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef]

D. G. Pelli, “The videotoolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

R. Plamondon, A. M. Alimi, “Speed/accuracy trade-offs in target-directed movements,” Behav. Brain Sci. 20, 279–349 (1997).
[CrossRef] [PubMed]

1996 (1)

M. Dornay, Y. Uno, M. Kawato, R. Suzuki, “Minimum muscle-tension chance trajectories predicted by using a 17-muscle model of the monkey’s arm,” J. Motor Behav. 2, 83–100 (1996).
[CrossRef]

1995 (1)

J. F. Soechting, C. A. Bunea, U. Herrmann, M. Flanders, “Moving effortlessly in three dimensions: Does Donders’ law apply to arm movement?” J. Neurosci. 15, 6271–6280 (1995).
[PubMed]

1994 (1)

J. Dean, M. Brüwer, “Control of human arm movements in two dimensions: paths and joint control in avoiding simple linear obstacles,” Exp. Brain Res. 97, 497–514 (1994).
[CrossRef] [PubMed]

1989 (1)

Y. Uno, M. Kawato, R. Suzuki, “Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model,” Biol. Cybern. 61, 89–101 (1989).

1988 (1)

D. E. Meyer, R. A. Abrams, S. Kornblum, C. E. Wright, J. E. Smith, “Optimality in human motor performance: ideal control of rapid aimed movements,” Psychol. Rev. 95, 340–370 (1988).
[CrossRef] [PubMed]

1986 (1)

T. Kaminsky, A. M. Gentile, “Joint control strategies and hand trajectories in multijoint pointing movements,” J. Motor Behav. 18, 261–278 (1986).
[CrossRef]

1985 (1)

T. Flash, N. Hogan, “The coordination of arm movements: An experimentally confirmed mathematical model,” J. Neurosci. 5, 1688–1707 (1985).
[PubMed]

1981 (1)

J. F. Soechting, F. Lacquaniti, “Invariant characteristics of a pointing movement in man,” J. Neurosci. 1, 710–720 (1981).
[PubMed]

Abrams, R. A.

D. E. Meyer, R. A. Abrams, S. Kornblum, C. E. Wright, J. E. Smith, “Optimality in human motor performance: ideal control of rapid aimed movements,” Psychol. Rev. 95, 340–370 (1988).
[CrossRef] [PubMed]

Alimi, A. M.

R. Plamondon, A. M. Alimi, “Speed/accuracy trade-offs in target-directed movements,” Behav. Brain Sci. 20, 279–349 (1997).
[CrossRef] [PubMed]

Berger, J. O.

J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd ed. (Springer, New York, 1985).

Blackwell, D.

D. Blackwell, M. A. Girschick, Theory of Games and Statistical Decisions (Wiley, New York, 1954).

Brainard, D. H.

D. H. Brainard, “The psychophysical toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef]

Brüwer, M.

J. Dean, M. Brüwer, “Control of human arm movements in two dimensions: paths and joint control in avoiding simple linear obstacles,” Exp. Brain Res. 97, 497–514 (1994).
[CrossRef] [PubMed]

Bunea, C. A.

J. F. Soechting, C. A. Bunea, U. Herrmann, M. Flanders, “Moving effortlessly in three dimensions: Does Donders’ law apply to arm movement?” J. Neurosci. 15, 6271–6280 (1995).
[PubMed]

Carson, R. G.

M. Mon-Williams, J. J. Tresilian, V. L. Coppard, R. G. Carson, “The effect of obstacle position on reach-to-grasp movements,” Exp. Brain Res. 137, 497–501 (2001).
[CrossRef] [PubMed]

Castiello, U.

U. Castiello, “The effects of abrupt onset of 2-D and 3-D distractors on prehension movements,” Percept. Psychophys. 63, 1014–1025 (2001).
[CrossRef] [PubMed]

Connolly, J. D.

J. D. Connolly, M. A. Goodale, “The role of visual feedback of hand position in the control of manual prehension,” Exp. Brain Res. 125, 281–286 (1999).
[CrossRef] [PubMed]

Constantinidis, T. S.

N. Smyrnis, I. Evdokimidis, T. S. Constantinidis, G. Kastrinakis, “Speed-accuracy trade-offs in the performance of pointing movements in different directions in two-dimensional space,” Exp. Brain Res. 134, 21–31 (2000).
[CrossRef] [PubMed]

Coppard, V. L.

M. Mon-Williams, J. J. Tresilian, V. L. Coppard, R. G. Carson, “The effect of obstacle position on reach-to-grasp movements,” Exp. Brain Res. 137, 497–501 (2001).
[CrossRef] [PubMed]

Dean, J.

J. Dean, M. Brüwer, “Control of human arm movements in two dimensions: paths and joint control in avoiding simple linear obstacles,” Exp. Brain Res. 97, 497–514 (1994).
[CrossRef] [PubMed]

Desmurget, M.

M. Desmurget, S. Grafton, “Forward modeling allows feedback control for fast reaching movements,” Trends Cogn. Sci. 4, 423–431 (2000).
[PubMed]

Dornay, M.

M. Dornay, Y. Uno, M. Kawato, R. Suzuki, “Minimum muscle-tension chance trajectories predicted by using a 17-muscle model of the monkey’s arm,” J. Motor Behav. 2, 83–100 (1996).
[CrossRef]

Evdokimidis, I.

N. Smyrnis, I. Evdokimidis, T. S. Constantinidis, G. Kastrinakis, “Speed-accuracy trade-offs in the performance of pointing movements in different directions in two-dimensional space,” Exp. Brain Res. 134, 21–31 (2000).
[CrossRef] [PubMed]

Ferguson, T. S.

T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach (Academic, New York, 1997).

Flanders, M.

J. F. Soechting, C. A. Bunea, U. Herrmann, M. Flanders, “Moving effortlessly in three dimensions: Does Donders’ law apply to arm movement?” J. Neurosci. 15, 6271–6280 (1995).
[PubMed]

Flash, T.

T. Flash, N. Hogan, “The coordination of arm movements: An experimentally confirmed mathematical model,” J. Neurosci. 5, 1688–1707 (1985).
[PubMed]

Gentile, A. M.

T. Kaminsky, A. M. Gentile, “Joint control strategies and hand trajectories in multijoint pointing movements,” J. Motor Behav. 18, 261–278 (1986).
[CrossRef]

Girschick, M. A.

D. Blackwell, M. A. Girschick, Theory of Games and Statistical Decisions (Wiley, New York, 1954).

Goodale, M. A.

J. D. Connolly, M. A. Goodale, “The role of visual feedback of hand position in the control of manual prehension,” Exp. Brain Res. 125, 281–286 (1999).
[CrossRef] [PubMed]

Grafton, S.

M. Desmurget, S. Grafton, “Forward modeling allows feedback control for fast reaching movements,” Trends Cogn. Sci. 4, 423–431 (2000).
[PubMed]

Hamilton, A. F. C.

A. F. C. Hamilton, D. M. Wolpert, “Controlling the statistics of action: obstacle avoidance,” J. Neurophysiol. 87, 2434–2440 (2002).
[PubMed]

Harris, C. M.

C. M. Harris, D. M. Wolpert, “Signal-dependent noise determines motor planning,” Nature 394, 780–784 (1998).
[CrossRef] [PubMed]

Herrmann, U.

J. F. Soechting, C. A. Bunea, U. Herrmann, M. Flanders, “Moving effortlessly in three dimensions: Does Donders’ law apply to arm movement?” J. Neurosci. 15, 6271–6280 (1995).
[PubMed]

Hogan, N.

T. Flash, N. Hogan, “The coordination of arm movements: An experimentally confirmed mathematical model,” J. Neurosci. 5, 1688–1707 (1985).
[PubMed]

Howard, L. A.

L. A. Howard, S. P. Tipper, “Hand deviations away from visual cues: indirect evidence for inhibition,” Exp. Brain Res. 113, 144–152 (1997).
[CrossRef] [PubMed]

S. P. Tipper, L. A. Howard, S. R. Jackson, “Selective reaching to grasp: evidence for distractor interference effects,” Vision Cogn. 4, 1–38 (1997).

Jackson, S. R.

S. P. Tipper, L. A. Howard, S. R. Jackson, “Selective reaching to grasp: evidence for distractor interference effects,” Vision Cogn. 4, 1–38 (1997).

Jansen, C.

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Posture-based motion planning: applications to grasping,” Psychol. Rev. 108, 709–734 (2001).
[CrossRef] [PubMed]

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Coordination of reaching and grasping by capitalizing on obstacle avoidance and other constraints,” Exp. Brain Res. 128, 92–100 (1999).
[CrossRef] [PubMed]

Jordan, M. I.

E. Todorov, M. I. Jordan, “Optimal feedback control as a theory of motor coordination,” Nat. Neurosci. 5, 1226–1235 (2002).
[CrossRef] [PubMed]

P. N. Sabes, M. I. Jordan, D. M. Wolpert, “The role of inertial sensitivity in motor planning,” J. Neurosci. 18, 5948–5957 (1998).
[PubMed]

P. N. Sabes, M. I. Jordan, “Obstacle avoidance and a perturbation sensitivity model for motor planning,” J. Neurosci. 17, 7119–7128 (1997).
[PubMed]

Kaminsky, T.

T. Kaminsky, A. M. Gentile, “Joint control strategies and hand trajectories in multijoint pointing movements,” J. Motor Behav. 18, 261–278 (1986).
[CrossRef]

Kastrinakis, G.

N. Smyrnis, I. Evdokimidis, T. S. Constantinidis, G. Kastrinakis, “Speed-accuracy trade-offs in the performance of pointing movements in different directions in two-dimensional space,” Exp. Brain Res. 134, 21–31 (2000).
[CrossRef] [PubMed]

Kawato, M.

M. Dornay, Y. Uno, M. Kawato, R. Suzuki, “Minimum muscle-tension chance trajectories predicted by using a 17-muscle model of the monkey’s arm,” J. Motor Behav. 2, 83–100 (1996).
[CrossRef]

Y. Uno, M. Kawato, R. Suzuki, “Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model,” Biol. Cybern. 61, 89–101 (1989).

Kornblum, S.

D. E. Meyer, R. A. Abrams, S. Kornblum, C. E. Wright, J. E. Smith, “Optimality in human motor performance: ideal control of rapid aimed movements,” Psychol. Rev. 95, 340–370 (1988).
[CrossRef] [PubMed]

Lacquaniti, F.

J. F. Soechting, F. Lacquaniti, “Invariant characteristics of a pointing movement in man,” J. Neurosci. 1, 710–720 (1981).
[PubMed]

Landy, M. S.

J. Trommershäuser, L. T. Maloney, M. S. Landy, “Statistical decision theory and trade-offs in the control of motor response,” Spatial Vis. 16(3–4), 255–275 (2003).
[CrossRef]

Maloney, L. T.

J. Trommershäuser, L. T. Maloney, M. S. Landy, “Statistical decision theory and trade-offs in the control of motor response,” Spatial Vis. 16(3–4), 255–275 (2003).
[CrossRef]

L. T. Maloney, “Statistical decision theory and biological vision,” in Perception and the Physical World, D. Heyer, R. Mausfeld, eds. (Wiley, New York, 2002), pp. 145–189.

Meulenbrock, R. J.

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Posture-based motion planning: applications to grasping,” Psychol. Rev. 108, 709–734 (2001).
[CrossRef] [PubMed]

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Coordination of reaching and grasping by capitalizing on obstacle avoidance and other constraints,” Exp. Brain Res. 128, 92–100 (1999).
[CrossRef] [PubMed]

Meyer, D. E.

D. E. Meyer, R. A. Abrams, S. Kornblum, C. E. Wright, J. E. Smith, “Optimality in human motor performance: ideal control of rapid aimed movements,” Psychol. Rev. 95, 340–370 (1988).
[CrossRef] [PubMed]

Mon-Williams, M.

M. Mon-Williams, J. J. Tresilian, V. L. Coppard, R. G. Carson, “The effect of obstacle position on reach-to-grasp movements,” Exp. Brain Res. 137, 497–501 (2001).
[CrossRef] [PubMed]

Pelli, D. G.

D. G. Pelli, “The videotoolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

Plamondon, R.

R. Plamondon, A. M. Alimi, “Speed/accuracy trade-offs in target-directed movements,” Behav. Brain Sci. 20, 279–349 (1997).
[CrossRef] [PubMed]

Rosenbaum, D. A.

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Posture-based motion planning: applications to grasping,” Psychol. Rev. 108, 709–734 (2001).
[CrossRef] [PubMed]

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Coordination of reaching and grasping by capitalizing on obstacle avoidance and other constraints,” Exp. Brain Res. 128, 92–100 (1999).
[CrossRef] [PubMed]

Sabes, P. N.

P. N. Sabes, M. I. Jordan, D. M. Wolpert, “The role of inertial sensitivity in motor planning,” J. Neurosci. 18, 5948–5957 (1998).
[PubMed]

P. N. Sabes, M. I. Jordan, “Obstacle avoidance and a perturbation sensitivity model for motor planning,” J. Neurosci. 17, 7119–7128 (1997).
[PubMed]

Smith, J. E.

D. E. Meyer, R. A. Abrams, S. Kornblum, C. E. Wright, J. E. Smith, “Optimality in human motor performance: ideal control of rapid aimed movements,” Psychol. Rev. 95, 340–370 (1988).
[CrossRef] [PubMed]

Smyrnis, N.

N. Smyrnis, I. Evdokimidis, T. S. Constantinidis, G. Kastrinakis, “Speed-accuracy trade-offs in the performance of pointing movements in different directions in two-dimensional space,” Exp. Brain Res. 134, 21–31 (2000).
[CrossRef] [PubMed]

Soechting, J. F.

J. F. Soechting, C. A. Bunea, U. Herrmann, M. Flanders, “Moving effortlessly in three dimensions: Does Donders’ law apply to arm movement?” J. Neurosci. 15, 6271–6280 (1995).
[PubMed]

J. F. Soechting, F. Lacquaniti, “Invariant characteristics of a pointing movement in man,” J. Neurosci. 1, 710–720 (1981).
[PubMed]

Suzuki, R.

M. Dornay, Y. Uno, M. Kawato, R. Suzuki, “Minimum muscle-tension chance trajectories predicted by using a 17-muscle model of the monkey’s arm,” J. Motor Behav. 2, 83–100 (1996).
[CrossRef]

Y. Uno, M. Kawato, R. Suzuki, “Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model,” Biol. Cybern. 61, 89–101 (1989).

Tipper, S. P.

L. A. Howard, S. P. Tipper, “Hand deviations away from visual cues: indirect evidence for inhibition,” Exp. Brain Res. 113, 144–152 (1997).
[CrossRef] [PubMed]

S. P. Tipper, L. A. Howard, S. R. Jackson, “Selective reaching to grasp: evidence for distractor interference effects,” Vision Cogn. 4, 1–38 (1997).

Todorov, E.

E. Todorov, M. I. Jordan, “Optimal feedback control as a theory of motor coordination,” Nat. Neurosci. 5, 1226–1235 (2002).
[CrossRef] [PubMed]

Tresilian, J. J.

M. Mon-Williams, J. J. Tresilian, V. L. Coppard, R. G. Carson, “The effect of obstacle position on reach-to-grasp movements,” Exp. Brain Res. 137, 497–501 (2001).
[CrossRef] [PubMed]

Trommershäuser, J.

J. Trommershäuser, L. T. Maloney, M. S. Landy, “Statistical decision theory and trade-offs in the control of motor response,” Spatial Vis. 16(3–4), 255–275 (2003).
[CrossRef]

Uno, Y.

M. Dornay, Y. Uno, M. Kawato, R. Suzuki, “Minimum muscle-tension chance trajectories predicted by using a 17-muscle model of the monkey’s arm,” J. Motor Behav. 2, 83–100 (1996).
[CrossRef]

Y. Uno, M. Kawato, R. Suzuki, “Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model,” Biol. Cybern. 61, 89–101 (1989).

Vaughan, R. J.

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Posture-based motion planning: applications to grasping,” Psychol. Rev. 108, 709–734 (2001).
[CrossRef] [PubMed]

D. A. Rosenbaum, R. J. Meulenbrock, R. J. Vaughan, C. Jansen, “Coordination of reaching and grasping by capitalizing on obstacle avoidance and other constraints,” Exp. Brain Res. 128, 92–100 (1999).
[CrossRef] [PubMed]

Wolpert, D. M.

A. F. C. Hamilton, D. M. Wolpert, “Controlling the statistics of action: obstacle avoidance,” J. Neurophysiol. 87, 2434–2440 (2002).
[PubMed]

P. N. Sabes, M. I. Jordan, D. M. Wolpert, “The role of inertial sensitivity in motor planning,” J. Neurosci. 18, 5948–5957 (1998).
[PubMed]

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It is instructive to consider the extent to which visual feedback plays a role in our results. The movement times were 300–400 ms, which is barely enough time to allow for an influence of visual feedback during the movement. We ran one subject in a version of experiment 1 in which the visual stimulus disappeared as soon as the space bar was re-leased. This manipulation eliminates feedback from the relative positions of the hand and the visible target during the movement but allows for feedback by using the view of the hand and apparatus. The results were unaffected, including the movement variability and the pattern of movement end points.

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In the 16 practice (warm-up) trials of this experiment, subjects pointed to each of the configurations twice in the penalty=0condition. Subjects were exposed to the eight novel configurations in the penalty=500condition for the first time during the experiment.

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Figures (11)

Fig. 1
Fig. 1

Michael Ballack’s goal during the 2002 World Cup. (a) Ballack, must rapidly decide where to shoot. (b) A schematic of factors affecting the decision.

Fig. 2
Fig. 2

“Landscape” of expected gain for an optimal observer with a variance of σ2=4.83 (matching that of subject S2 in experiment 1). (a) Expected gain (in points per trial) as a function of the mean movement end point (x, y). The distribution is truncated for scores <-60 points. (b) The same landscape replotted as a contour plot with the mean movement end point of subject S2 (open squares) compared with optimal performance as predicted by the model [the contour regions are coded with the same gray-level scale as in (a)].

Fig. 3
Fig. 3

Layout of the stimuli in experiment 1. The six dashed regions indicate the six different positions at which the target could appear.

Fig. 4
Fig. 4

Sequence of events during a single trial. The trial would not start until the subject depressed and held the space bar. In screen 5 (feedback) the subject would be shown each of the regions that she or he hit (the region would “explode” graphically) and the associated gain (penalty or reward) incurred.

Fig. 5
Fig. 5

Experiment 1, results for five subjects under penalty conditions 0, 100, and 500. Left column, mean movement end points X¯ij (x coordinate) as a function of the optimal mean movement end point XijMEG predicted by the model for five subjects. Model predictions based on each subject’s variability were computed. Solid lines, perfect correspondence of model and experiment; dotted lines, center of the green target region. Data are uncorrected for bias; pointing bias is visible as a shift of the data above the prediction line. Right, shift of mean movement end points from the center of the green target region, corrected for pointing bias (x¯ij) as a function of the optimal shift of mean movement end point (xijMEG). Data for green target regions to the left of the penalty region (open symbols) were reflected; solid symbols indicate mean movement end points toward green target regions on the right of the penalty region. Data were corrected for constant pointing bias by subtracting the constant pointing bias given in Table 1. Average standard error of the mean is indicated in the key. Right, solid symbols indicate data for targets on the right side of the configuration.

Fig. 6
Fig. 6

Experiment 1, results for five subjects, listed in order of motor variability, for penalty conditions 0, 100, and 500. The values plotted on the vertical axis are average scores per target position displayed as a percentage of optimal performance predicted by the model for penalty=0. Normalizing in this way makes it easier to compare performance of subjects with different motor variabilities. The horizontal axis is the target position Xtarget relative to the penalty region. Model predictions based on each subject’s variability were computed. The curves (one per subject) represent the model predictions.

Fig. 7
Fig. 7

Experiment 1, trial-by-trial data of subject S1. Deviations of individual movement end points (x coordinate) from the mean movement end point x¯ (per condition) as a function of trial number are shown. Data are displayed for each location of the green target region and for two penalty conditions.

Fig. 8
Fig. 8

Layout of the stimuli in experiment 2.

Fig. 9
Fig. 9

Experiment 2, results: average movement end points (X¯, Y¯) for each of the eight stimulus configurations and the two penalty conditions, for each of the five subjects. Model predictions based on each subject’s variability were computed. Left column, results for conditions 1–4 (one red penalty region). Right column, results for conditions 5 to 8 (two red penalty regions); see Fig. 8 for details. Error bars represent ± one standard error in the x and y directions, computed from 24 data points per condition (less than 24 in the rare cases where data were dropped owing to a timeout). Model predictions were corrected for each subject by adding the constant pointing bias given in Table 3.

Fig. 10
Fig. 10

Average gain per trial and model predictions in the penalty=500 condition as function of the configuration (Fig. 8). Data displayed for each of the five subjects are based on 24 data points per configuration (less than 24 in the rare cases where data were dropped owing to a timeout). Model predictions based on each subject’s variability were computed.

Fig. 11
Fig. 11

Experiment 2, trial by trial data. Two-dimensional distance of individual movement end points (x, y) from the mean movement end point (x¯, y¯) as a function of trial number, displayed for configurations 2 and 7 (Fig. 8), for all five subjects individually and for penalty conditions 0 and 500.

Tables (4)

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Table 1 Experiment 1, Results a

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Table 2 Experiment 1, Comparison of Results with Model Predictions a

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Table 3 Experiment 2, Results a

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Table 4 Experiment 2, Comparison of Results with Model Predictions a

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Γ(S)=i=0NGiP(Ri|S)+GtimeoutP(timeout|S)+λB(S).
P(Ri|S)=Ri,timeoutP(τ|S)dτ,
Γ(x, y)=G0P(R0|x, y)+G1P(R1|x, y)+GtimeoutP(timeout|x, y)+λB(x, y),
Γ(x, y)=G0P(R0|x, y)+G1P(R1|x, y).
p(x, y|x, y)
=12πσ2exp{-[(x-x)2+(y-y)2]/2σ2},
P(Ri|x, y)=Rip(x, y|x, y)dxdy.

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