Visuomotor tracking on a computer screen—an experimental paradigm to study the dynamics of motor control
Introduction
Computational principles of human motor control like motor planning, estimation, prediction and learning have recently attracted much attention (e.g. [6]). A particular class of problems, the continuous feedback control, is especially suited to derive dynamical properties and mechanisms underlying the control of body movements. Examples for such feedback systems include the control of body posture [2] where noise-induced transitions between coexisting periodic orbits account for the dynamics of the body center-of-pressure [3]; and the problem of balancing a stick at the fingertip where the existence of parametric noise and on-off intermittency have been demonstrated [1]. These two systems, however, allow only for a limited manipulation of system parameters. In postural sway, body mass and height are basically fixed and in stick balancing, only the mass and the geometry of the stick can be altered deliberately. Here we introduce an experimental paradigm for the study of human motor control that allows for a more flexible variation of system parameters: The visually guided control of a target on a computer screen by moving a computer mouse. The reaction time of a human subject may be changed by an additional delay and even the whole dynamics of the system may be altered. This makes it possible to test models of the reaction against the change of those parameters.
Section snippets
Experimental setup
Subjects are presented two dots on a computer screen. The first dot m represents the position of the subject's hand and is controlled by the computer mouse. The second dot t is the target, which is to be balanced by the subject. The subject's task is to keep both dots as closely together as possible, while avoiding the escape of either point off the screen. The target moves according to , where and are the positions of the target t and the mouse pointer m
Results
Under this experimental paradigm subjects produce balancing trajectories as shown in Fig. 1. In Fig. 2 the distance between m and t is shown. There are regions where m closely tracks t. In other regions, where t is on the verge to escape, larger and faster movements of m are necessary and the distance r becomes larger.
This behavior is also reflected in the power spectrum of r (Fig. 3). Nine balancing sequences were accumulated to produce this power spectrum. The power spectrum
A model with parametric noise
As a simple model for balancing, i.e., the movements of the target and mouse, we propose the following:
The target moves according to the same equation as in the experiment. The target is modeled as an inverted pendulum with respect to the suspension point: . The reaction of the subject to a movement of the target away from the equilibrium is modeled by a restoring force . The reaction has a delay τr that is consistent with the reaction time of a human subject:
Conclusion
Here we have shown a flexible experimental paradigm which can add to the understanding of balancing and related problems. We have shown some important features of the experimental data, as the double power law in the power spectrum and the power law in the laminar phases distribution. A simple model accounts for the two scaling regions in the power spectrum. An improved model should increase both the balancing time and τ to more realistic values. The parameter τ exists in real balancing
Ronald Bormann, born in 1971, studied physics at the universities of Bremen and Maryland. In 1998 he finished his master's thesis in Bremen. After a brief stay at the University of Hamburg he joined Prof. Schwegler's neurophysics group at the University of Bremen in 2000 as a Ph.D. student.
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Ronald Bormann, born in 1971, studied physics at the universities of Bremen and Maryland. In 1998 he finished his master's thesis in Bremen. After a brief stay at the University of Hamburg he joined Prof. Schwegler's neurophysics group at the University of Bremen in 2000 as a Ph.D. student.
Juan Luis Cabrera, got his Ph.D. in Nonlinear Phenomena in Physics in 1997 from UNED (Madrid, Spain). During 1998–1999 he enjoyed a postdoc position in the Astrobiology Center at the Instituto Nacional de Técnica Aeroespacial at Madrid (Spain), during 1999–2002 he was Research Assistant at the Neurology Department in the University of Chicago. Since 2002 he enjoys a research position in the Physics Center of the Venezuelan Institute of Scientific Research.
John G. Milton, got his Ph.D. in Biophysical Chemistry in 1975 from McGill University (Montreal, Canada). He received his MDCM from McGill University in 1982. From 1987 until 1988 he was Assistant Professor at the Department of Physiology at McGill University. After various guest faculties he became Adjunct Professor at the Center of Nonlinear Dynamics in Physiology and Medicine at McGill University. Since 1996 he is also Associate Professor at the Department of Neurology at the University of Chicago.
Christian Eurich, born in 1965, got his Ph.D. in Theoretical Physics in 1995 from the University of Bremen (Germany). As a postdoc, he worked in the Departments of Mathematics and Neurology at the University of Chicago. In 2001, he held a professorship for Cognitive Neuroinformatics at the University of Osnabrück. Currently, Christian Eurich is Research Assistant at the Institute for Theoretical Neurophysics at the University of Bremen.