Human stick balancing: an intermittent control explanation. Gawthrop, P., Lee, K., Halaki, M., & O'Dwyer, N. Biological Cybernetics, 107(6):637-652, Springer Berlin Heidelberg, 2013. Published online: 13th August 2013doi abstract bibtex There are two issues in balancing a stick pivoting on a finger tip (or mechanically on a moving cart): maintaining the stick angle near to vertical and maintaining the horizontal position within the bounds of reach or cart track. The (linearised) dynamics of the angle are second order (although driven by pivot acceleration), and so, as in human standing, control of the angle is not, by itself very difficult. However, once the angle is under control, the position dynamics are, in general, fourth order. This makes control quite difficult for humans (and even an engineering control system requires careful design). Recently, three of the authors have experimentally demonstrated that humans control the stick angle in a special way: the closed-loop inverted pendulum behaves as a non-inverted pendulum with a virtual pivot somewhere between the stick centre and tip and with increased gravity. Moreover, they suggest that the virtual pivot lies at the radius of gyration (about the mass centre) above the mass centre. This paper gives a continuous-time control-theoretical interpretation of the virtual-pendulum approach. In particular, by using a novel cascade control structure, it is shown that the horizontal control of the virtual pivot becomes a second-order problem which is much easier to solve than the generic fourth-order problem. Hence, the use of the virtual pivot approach allows the control problem to be perceived by the subject as two separate second-order problems rather than a single fourth-order problem, and the control problem is therefore simplified. The theoretical predictions are verified using the data previously presented by three of the authors and analysed using a standard parameter estimation method. The experimental data indicate that although all subjects adopt the virtual pivot approach, the less expert subjects exhibit larger amplitude angular motion and poorly controlled translational motion. It is known that human control systems are delayed and intermittent, and therefore, the continuous-time strategy cannot be correct. However, the model of intermittent control used in this paper is based on the virtual pivot continuous-time control scheme, handles time delays and moreover masquerades as the underlying continuous-time controller. In addition, the event-driven properties of intermittent control can explain experimentally observed variability.
@article{GawLeeHalODw13,
year = 2013,
issn = {0340-1200},
journal = {Biological Cybernetics},
volume = {107},
number = {6},
doi = {10.1007/s00422-013-0564-4},
title = {Human stick balancing: an intermittent control explanation},
publisher = {Springer Berlin Heidelberg},
author = {Gawthrop, Peter and Lee, Kwee-Yum and Halaki, Mark and O'Dwyer, Nicholas},
pages = {637-652},
language = {English},
note = {Published online: 13th August 2013},
abstract = { There are two issues in balancing a stick pivoting on a
finger tip (or mechanically on a moving cart):
maintaining the stick angle near to vertical and
maintaining the horizontal position within the
bounds of reach or cart track. The (linearised)
dynamics of the angle are second order (although
driven by pivot acceleration), and so, as in human
standing, control of the angle is not, by itself
very difficult. However, once the angle is under
control, the position dynamics are, in general,
fourth order. This makes control quite difficult for
humans (and even an engineering control system
requires careful design). Recently, three of the
authors have experimentally demonstrated that humans
control the stick angle in a special way: the
closed-loop inverted pendulum behaves as a
non-inverted pendulum with a virtual pivot somewhere
between the stick centre and tip and with increased
gravity. Moreover, they suggest that the virtual
pivot lies at the radius of gyration (about the mass
centre) above the mass centre. This paper gives a
continuous-time control-theoretical interpretation
of the virtual-pendulum approach. In particular, by
using a novel cascade control structure, it is shown
that the horizontal control of the virtual pivot
becomes a second-order problem which is much easier
to solve than the generic fourth-order
problem. Hence, the use of the virtual pivot
approach allows the control problem to be perceived
by the subject as two separate second-order problems
rather than a single fourth-order problem, and the
control problem is therefore simplified. The
theoretical predictions are verified using the data
previously presented by three of the authors and
analysed using a standard parameter estimation
method. The experimental data indicate that although
all subjects adopt the virtual pivot approach, the
less expert subjects exhibit larger amplitude
angular motion and poorly controlled translational
motion. It is known that human control systems are
delayed and intermittent, and therefore, the
continuous-time strategy cannot be correct. However,
the model of intermittent control used in this paper
is based on the virtual pivot continuous-time
control scheme, handles time delays and moreover
masquerades as the underlying continuous-time
controller. In addition, the event-driven properties
of intermittent control can explain experimentally
observed variability. }
}
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The (linearised) dynamics of the angle are second order (although driven by pivot acceleration), and so, as in human standing, control of the angle is not, by itself very difficult. However, once the angle is under control, the position dynamics are, in general, fourth order. This makes control quite difficult for humans (and even an engineering control system requires careful design). Recently, three of the authors have experimentally demonstrated that humans control the stick angle in a special way: the closed-loop inverted pendulum behaves as a non-inverted pendulum with a virtual pivot somewhere between the stick centre and tip and with increased gravity. Moreover, they suggest that the virtual pivot lies at the radius of gyration (about the mass centre) above the mass centre. This paper gives a continuous-time control-theoretical interpretation of the virtual-pendulum approach. In particular, by using a novel cascade control structure, it is shown that the horizontal control of the virtual pivot becomes a second-order problem which is much easier to solve than the generic fourth-order problem. Hence, the use of the virtual pivot approach allows the control problem to be perceived by the subject as two separate second-order problems rather than a single fourth-order problem, and the control problem is therefore simplified. The theoretical predictions are verified using the data previously presented by three of the authors and analysed using a standard parameter estimation method. The experimental data indicate that although all subjects adopt the virtual pivot approach, the less expert subjects exhibit larger amplitude angular motion and poorly controlled translational motion. It is known that human control systems are delayed and intermittent, and therefore, the continuous-time strategy cannot be correct. However, the model of intermittent control used in this paper is based on the virtual pivot continuous-time control scheme, handles time delays and moreover masquerades as the underlying continuous-time controller. In addition, the event-driven properties of intermittent control can explain experimentally observed variability. ","bibtex":"@article{GawLeeHalODw13,\n year = 2013,\n issn = {0340-1200},\n journal = {Biological Cybernetics},\n volume = {107},\n number = {6},\n doi = {10.1007/s00422-013-0564-4},\n title = {Human stick balancing: an intermittent control explanation},\n publisher = {Springer Berlin Heidelberg},\n author = {Gawthrop, Peter and Lee, Kwee-Yum and Halaki, Mark and O'Dwyer, Nicholas},\n pages = {637-652},\n language = {English},\n note = {Published online: 13th August 2013},\n abstract = { There are two issues in balancing a stick pivoting on a\n finger tip (or mechanically on a moving cart):\n maintaining the stick angle near to vertical and\n maintaining the horizontal position within the\n bounds of reach or cart track. The (linearised)\n dynamics of the angle are second order (although\n driven by pivot acceleration), and so, as in human\n standing, control of the angle is not, by itself\n very difficult. However, once the angle is under\n control, the position dynamics are, in general,\n fourth order. This makes control quite difficult for\n humans (and even an engineering control system\n requires careful design). Recently, three of the\n authors have experimentally demonstrated that humans\n control the stick angle in a special way: the\n closed-loop inverted pendulum behaves as a\n non-inverted pendulum with a virtual pivot somewhere\n between the stick centre and tip and with increased\n gravity. Moreover, they suggest that the virtual\n pivot lies at the radius of gyration (about the mass\n centre) above the mass centre. This paper gives a\n continuous-time control-theoretical interpretation\n of the virtual-pendulum approach. In particular, by\n using a novel cascade control structure, it is shown\n that the horizontal control of the virtual pivot\n becomes a second-order problem which is much easier\n to solve than the generic fourth-order\n problem. Hence, the use of the virtual pivot\n approach allows the control problem to be perceived\n by the subject as two separate second-order problems\n rather than a single fourth-order problem, and the\n control problem is therefore simplified. The\n theoretical predictions are verified using the data\n previously presented by three of the authors and\n analysed using a standard parameter estimation\n method. The experimental data indicate that although\n all subjects adopt the virtual pivot approach, the\n less expert subjects exhibit larger amplitude\n angular motion and poorly controlled translational\n motion. It is known that human control systems are\n delayed and intermittent, and therefore, the\n continuous-time strategy cannot be correct. However,\n the model of intermittent control used in this paper\n is based on the virtual pivot continuous-time\n control scheme, handles time delays and moreover\n masquerades as the underlying continuous-time\n controller. In addition, the event-driven properties\n of intermittent control can explain experimentally\n observed variability. }\n}\n\n","author_short":["Gawthrop, P.","Lee, K.","Halaki, M.","O'Dwyer, N."],"key":"GawLeeHalODw13","id":"GawLeeHalODw13","bibbaseid":"gawthrop-lee-halaki-odwyer-humanstickbalancinganintermittentcontrolexplanation-2013","role":"author","urls":{},"metadata":{"authorlinks":{}},"html":""},"bibtype":"article","biburl":"https://bibbase.org/network/files/BoMEw3ZkhpWoBCsME","dataSources":["sFgyQRq3R79dSSigG","AoKgsmPkyovbPMuLx"],"keywords":[],"search_terms":["human","stick","balancing","intermittent","control","explanation","gawthrop","lee","halaki","o'dwyer"],"title":"Human stick balancing: an intermittent control explanation","year":2013}