Proceedings of The Physiological Society
University of Manchester (2010) Proc Physiol Soc 19, C14
Human control of an inverted pendulum: Is intermittent control effective?
I. Loram1, M. Lakie2, H. Gollee3, P. Gawthrop3
1. IRM, Manchester Metropolitan University, Manchester, Cheshire, United Kingdom. 2. School of Sport and Exercise Science, University of Birmingham, Birmingham, United Kingdom. 3. Dept of Mechanical Engineering, University of Glasgow, Glasgow, United Kingdom.
Figure 1. Histogram showing the incidence of adopted tapping frequencies between 0.2 and 6.5 Hz. Frequency is the inverse of the time interval between taps. The conditions shown are minimise position, minimise velocity and maximise non-intervention for control by intermittent contact. Solid and dashed lines represent mean
Previously, using ultrasound, we observed calf muscle behaviour during human standing (1, 2). Changes in calf muscle length related well to whole body centre of mass motion when interpreted as an inverted pendulum in which calf muscles act on the body via a compliant tendon linkage. Control of the centre of mass was associated with impulsive actions of the muscle at a modal rate two actions per second. Following the observations and intermittent, ballistic hypothesis of Craik (3-5), we hypothesised (i) that control of standing balance proceeded via intermittent, ballistic impulses at an optimal rate, minimising serial interference, of two actions per second, and (ii) this control by intermittent, ballistic actions was generic with human visual-manual tracking (2). Here we examine visual-manual tracking of a virtual, inverted pendulum load, with unstable time constant equivalent to a standing human. Subjects controlled the load using a sensitive joystick. We compared two methods of control: intermittent contact (gentle tapping) and continuous contact. Control by gentle tapping is explicitly intermittent - control is ballistic between taps. We ask two questions. First, is control by intermittent contact natural and effective? Second, do subjects show a preferred tapping frequency of two taps per second? Eleven, healthy adults participated. Load motion was observed using an oscilloscope dot. Trials lasted 200 s and an unpredictable "motor noise" disturbance was added to the load. Participants were instructed to achieve the following randomised goals (a) "minimise position" - keep the dot centred, (b) "minimise velocity" - keep the dot still, but anywhere on the screen (c) "maximise non intervention" - wait as long as possible before intervening, while keeping the dot on the screen. Contact was detected from joystick motion: the algorithm was subsequently validated using an electrical skin-contact signal. All participants managed control by intermittent contact (tapping) with ease. Control was superior using intermittent rather than continuous contact. When instructed to minimise “position” or minimise “velocity” the velocity of the load was significantly and more consistently lower when using intermittent (4.4±1 mms-1, mean±s.d.) rather than continuous (5.5±2 mms-1) contact (Kruskal Wallis, N=44, p=0.01). When instructed to minimise “position”, deviation from the centre was significantly lower using intermittent (2.4±1mm) rather than continuous contact (3.3±1 mm), (Wilcoxon, paired samples, signed rank, N=22, p=0.03). Intermittent contact was made at a modal frequency of 2 taps per second, which reduced to 0.6 taps per second when maximising "non-intervention" (Fig 1). We conclude: (i) human intermittent control of an inverted pendulum is natural and effective, (ii) consistent with Craik, two ballistic actions per second is preferred for maximum control.
Where applicable, experiments conform with Society ethical requirements