Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity

Abstract

Sensory uncertainties and imperfections in motor control play important roles in neural control and Bayesian approaches to neural encoding. However, it is difficult to estimate these uncertainties experimentally. Here, we show that magnitude of the uncertainties during the generation of motor control force can be measured for a virtual stick balancing task by varying the feedback delay, τ. It is shown that the shortest stick length that human subjects are able to balance is proportional to τ 2. The proportionality constant can be related to a combined effect of the sensory uncertainties and the error in the realization of the control force, based on a delayed proportional-derivative (PD) feedback model of the balancing task. The neural reaction delay of the human subjects was measured by standard reaction time tests and by visual blank-out tests. Experimental observations provide an estimate for the upper boundary of the average sensorimotor uncertainty associated either with angular position or with angular velocity. Comparison of balancing trials with 27 human subjects to the delayed PD model suggests that the average uncertainty in the control force associated purely with the angular position is at most 14% while that associated purely with the angular velocity is at most 40%. In the general case when both uncertainties are present, the calculations suggest that the allowed uncertainty in angular velocity will always be greater than that in angular position.

The effects of sensory quantization and control torque saturation on human balance control

“…The control gains which are most robust in the face of stochastic fluctuations, sensory quantization and control torque saturation are those located in the left corner of the D-shaped stability region in the plane of the control gains. Similar observations have been obtained for pole balancing at the fingertip [46], virtual pole balancing [28], and in studies of the effects of structured, real perturbations on postural sway [21]. Estimations of the control gains for standing balance obtained by modeling the responses to mechanical perturbation also place the control gains in this same regions of parameter space (A. Zelei, J. Milton, G. Stepan and T. Insperger, in preparation).…”

Virtual stick balancing: skill development in Newtonian and Aristotelian dynamics

“…Note that both types of reaction times involve the input-to-output lag of the screen as well. The 'pure' human reaction time is therefore smaller and, based on [30], is in the range 160 -210 ms as reported in the literature for real and virtual stick balancing [12,14,20]; this is slightly larger than the delay in visual tracking [22,24,25].…”

“…x of the input device. Both the velocity and the acceleration of the subject's hand movement were determined by a numerical derivation scheme based on the pixel position of the cursor on the screen [20,30]. Owing to the finite size of the pixels, the numerical derivation results in a noisy signal, which was compensated by a resampling filter.…”

“…Virtual environments provide a convenient framework for such investigations by making it possible to program arbitrary tasks with arbitrary parameters within the employed software. Virtual set-ups are widely applied in bio-mechanical practice, such as the benchmark problem of stick balancing with visual [12,[18][19][20] or combined visual-haptic feedback [21,22], visuomotor tracking [23][24][25] or the task of moving a cup filled with liquid [2].…”

“…In a previous work by the authors [20], virtual stick balancing trials were performed by 27 subjects with different stick lengths and by adding extra delays artificially in the visualization loop. The critical length was used as a measure of human balancing performance: the shorter the stick that a subject can balance for a given time duration, the more skilled the subject.…”