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Journal ArticleDOI

Signal-dependent noise determines motor planning

20 Aug 1998-Nature (Nature Publishing Group)-Vol. 394, Iss: 6695, pp 780-784
TL;DR: This theory provides a simple and powerful unifying perspective for both eye and arm movement control and accurately predicts the trajectories of both saccades and arm movements and the speed–accuracy trade-off described by Fitt's law.
Abstract: When we make saccadic eye movements or goal-directed arm movements, there is an infinite number of possible trajectories that the eye or arm could take to reach the target1,2. However, humans show highly stereotyped trajectories in which velocity profiles of both the eye and hand are smooth and symmetric for brief movements3,4. Here we present a unifying theory of eye and arm movements based on the single physiological assumption that the neural control signals are corrupted by noise whose variance increases with the size of the control signal. We propose that in the presence of such signal-dependent noise, the shape of a trajectory is selected to minimize the variance of the final eye or arm position. This minimum-variance theory accurately predicts the trajectories of both saccades and arm movements and the speed–accuracy trade-off described by Fitt's law5. These profiles are robust to changes in the dynamics of the eye or arm, as found empirically6,7. Moreover, the relation between path curvature and hand velocity during drawing movements reproduces the empirical ‘two-thirds power law’8,9. This theory provides a simple and powerful unifying perspective for both eye and arm movement control.
Citations
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Journal ArticleDOI
TL;DR: This work shows that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions, and proposes an alternative theory based on stochastic optimal feedback control, which emerges naturally from this framework.
Abstract: A central problem in motor control is understanding how the many biomechanical degrees of freedom are coordinated to achieve a common goal. An especially puzzling aspect of coordination is that behavioral goals are achieved reliably and repeatedly with movements rarely reproducible in their detail. Existing theoretical frameworks emphasize either goal achievement or the richness of motor variability, but fail to reconcile the two. Here we propose an alternative theory based on stochastic optimal feedback control. We show that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions. This strategy does not enforce a desired trajectory, but uses feedback more intelligently, correcting only those deviations that interfere with task goals. From this framework, task-constrained variability, goal-directed corrections, motor synergies, controlled parameters, simplifying rules and discrete coordination modes emerge naturally. We present experimental results from a range of motor tasks to support this theory.

2,776 citations

Journal ArticleDOI
TL;DR: The 'minimum variance model' is another major recent advance in the computational theory of motor control, strongly suggesting that both kinematic and dynamic internal models are utilized in movement planning and control.

2,469 citations

Journal ArticleDOI
TL;DR: How noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise are highlighted, and noise's potential benefits are discussed.
Abstract: Noise — random disturbances of signals — poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.

2,350 citations

Journal ArticleDOI
TL;DR: A major challenge for neuroscientists is to test ideas for how this might be achieved in populations of neurons experimentally, and so determine whether and how neurons code information about sensory uncertainty.

2,067 citations


Cites background from "Signal-dependent noise determines m..."

  • ...ments, given the signal-dependent of motor noise [ 8 ], and when costs and gains for different are independently subjects adjust their aim points...

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Journal ArticleDOI
TL;DR: This goal is to demonstrate how specific models emerging from the computational approach provide a theoretical framework for movement neuroscience.
Abstract: Unifying principles of movement have emerged from the computational study of motor control. We review several of these principles and show how they apply to processes such as motor planning, control, estimation, prediction and learning. Our goal is to demonstrate how specific models emerging from the computational approach provide a theoretical framework for movement neuroscience.

1,896 citations


Cites background from "Signal-dependent noise determines m..."

  • ...Recently, a model has been proposed which provides a unifying cost for goal-directed eye and arm movement...

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References
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Journal ArticleDOI
TL;DR: The motor system in the present case is defined as including the visual and proprioceptive feedback loops that permit S to monitor his own activity, and the information capacity of the motor system is specified by its ability to produce consistently one class of movement from among several alternative movement classes.
Abstract: Information theory has recently been employed to specify more precisely than has hitherto been possible man's capacity in certain sensory, perceptual, and perceptual-motor functions (5, 10, 13, 15, 17, 18). The experiments reported in the present paper extend the theory to the human motor system. The applicability of only the basic concepts, amount of information, noise, channel capacity, and rate of information transmission, will be examined at this time. General familiarity with these concepts as formulated by recent writers (4, 11,20, 22) is assumed. Strictly speaking, we cannot study man's motor system at the behavioral level in isolation from its associated sensory mechanisms. We can only analyze the behavior of the entire receptor-neural-effector system. However, by asking 51 to make rapid and uniform responses that have been highly overlearned, and by holding all relevant stimulus conditions constant with the exception of those resulting from 5"s own movements, we can create an experimental situation in which it is reasonable to assume that performance is limited primarily by the capacity of the motor system. The motor system in the present case is defined as including the visual and proprioceptive feedback loops that permit S to monitor his own activity. The information capacity of the motor system is specified by its ability to produce consistently one class of movement from among several alternative movement classes. The greater the number of alternative classes, the greater is the information capacity of a particular type of response. Since measurable aspects of motor responses, such as their force, direction, and amplitude, are continuous variables, their information capacity is limited only by the amount of statistical variability, or noise, that is characteristic of repeated efforts to produce the same response. The information capacity of the motor Editor's Note. This article is a reprint of an original work published in 1954 in the Journal of Experimental Psychology, 47, 381391.

7,599 citations


"Signal-dependent noise determines m..." refers methods in this paper

  • ...This minimum-variance theory accurately predicts the trajectories of both saccades and arm movements and the speed–accuracy trade-off described by Fitt's la...

    [...]

Book
01 Jan 1967

6,041 citations


"Signal-dependent noise determines m..." refers background in this paper

  • ...gif" NDATA ITEM> ]> When we make saccadic eye movements or goal-directed arm movements, there is an infinite number of possible trajectories that the eye or arm could take to reach the targe...

    [...]

Journal ArticleDOI
TL;DR: A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements, and is successful only when formulated in terms of the motion of the hand in extracorporal space.
Abstract: This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.

4,226 citations

Journal ArticleDOI
29 Sep 1995-Science
TL;DR: A sensorimotor integration task was investigated in which participants estimated the location of one of their hands at the end of movements made in the dark and under externally imposed forces, providing direct support for the existence of an internal model.
Abstract: On the basis of computational studies it has been proposed that the central nervous system internally simulates the dynamic behavior of the motor system in planning, control, and learning; the existence and use of such an internal model is still under debate. A sensorimotor integration task was investigated in which participants estimated the location of one of their hands at the end of movements made in the dark and under externally imposed forces. The temporal propagation of errors in this task was analyzed within the theoretical framework of optimal state estimation. These results provide direct support for the existence of an internal model.

3,137 citations

Journal ArticleDOI
TL;DR: The investigation of how the CNS learns to control movements in different dynamical conditions, and how this learned behavior is represented, suggests that the elements of the adaptive process represent dynamics of a motor task in terms of the intrinsic coordinate system of the sensors and actuators.
Abstract: We investigated how the CNS learns to control movements in different dynamical conditions, and how this learned behavior is represented. In particular, we considered the task of making reaching movements in the presence of externally imposed forces from a mechanical environment. This environment was a force field produced by a robot manipulandum, and the subjects made reaching movements while holding the end-effector of this manipulandum. Since the force field significantly changed the dynamics of the task, subjects' initial movements in the force field were grossly distorted compared to their movements in free space. However, with practice, hand trajectories in the force field converged to a path very similar to that observed in free space. This indicated that for reaching movements, there was a kinematic plan independent of dynamical conditions. The recovery of performance within the changed mechanical environment is motor adaptation. In order to investigate the mechanism underlying this adaptation, we considered the response to the sudden removal of the field after a training phase. The resulting trajectories, named aftereffects, were approximately mirror images of those that were observed when the subjects were initially exposed to the field. This suggested that the motor controller was gradually composing a model of the force field, a model that the nervous system used to predict and compensate for the forces imposed by the environment. In order to explore the structure of the model, we investigated whether adaptation to a force field, as presented in a small region, led to aftereffects in other regions of the workspace. We found that indeed there were aftereffects in workspace regions where no exposure to the field had taken place; that is, there was transfer beyond the boundary of the training data. This observation rules out the hypothesis that the subject's model of the force field was constructed as a narrow association between visited states and experienced forces; that is, adaptation was not via composition of a look-up table. In contrast, subjects modeled the force field by a combination of computational elements whose output was broadly tuned across the motor state space. These elements formed a model that extrapolated to outside the training region in a coordinate system similar to that of the joints and muscles rather than end-point forces. This geometric property suggests that the elements of the adaptive process represent dynamics of a motor task in terms of the intrinsic coordinate system of the sensors and actuators.

2,505 citations


"Signal-dependent noise determines m..." refers background in this paper

  • ...These profiles are robust to changes in the dynamics of the eye or arm, as found empiricall...

    [...]