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 2013
doi  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.  }
}

Downloads: 0