Journal papers by Gawthrop in 2013

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.

Modular organisation in control architecture may underlie the versatility of human motor control; but the nature of the interface relating sensory input through task-selection in the space of performance variables to control actions in the space of the elemental variables is currently unknown. Our central question is whether the control architecture converges to a serial process along a single channel? In discrete reaction time experiments, psychologists have firmly associated a serial single channel hypothesis with refractoriness and response selection (psychological refractory period). Recently, we developed a methodology and evidence identifying refractoriness in sustained control of an external single degree-of-freedom system. We hypothesise that multi-segmental whole-body control also shows refractoriness. Eight participants controlled their whole body to ensure a head marker tracked a target as fast and accurately as possible. Analysis showed enhanced delays in response to stimuli with close temporal proximity to the preceding stimulus. Consistent with our preceding work, this evidence is incompatible with control as a linear time invariant process. This evidence is consistent with a single-channel serial ballistic process within the intermittent control paradigm with an intermittent interval of around 0.5 s. A control architecture reproducing intentional human movement control must reproduce refractoriness. Intermittent control is designed to provide computational time for an online optimisation process and is appropriate for flexible adaptive control. For human motor control we suggest that parallel sensory input converges to a serial, single channel process involving planning, selection and temporal inhibition of alternative responses prior to low dimensional motor output. Such design could aid robots to reproduce the flexibility of human control.

In biology, the control of physiological variables such as body position, blood pressure and body temperature is founded on negative feedback mechanisms governing homeostasic input-output relations. The conceptual models capturing the underlying control principles are often drawn from engineering control theory. The visuo-manual control of external systems (like balancing a stick on the palm of one's hand) has traditionally been interpreted using continuous paradigms such as the servo controller or the continuous optimal controller. These engineering controllers were designed for machine systems with precise sensors, consistent actuators, short time delays and fast computers. Quite the opposite is true for the human movement system that is characterized by long neuromuscular delays, variability, history dependence and fatigue. Serial ballistic control offers an alternative control paradigm in which smooth control proceeds as a sequence of sub-movements each planned using current sensory information but then intermittently executed “open loop”. In the current study we are the first to formally identify refractoriness, a behavioural characteristic that discriminates intermittent (serial ballistic) from continuous control, in the domain of sustained (non-discrete) control of first and second order systems providing definite evidence for the validity of intermittent open-loop control as a paradigm for sustained human control.