A feedback information-theoretic transmission scheme (FITTS) for modeling trajectory variability in aimed movements
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ORIGINAL ARTICLE
A feedback information-theoretic transmission scheme (FITTS) for modeling trajectory variability in aimed movements Julien Gori1
· Olivier Rioul2
Received: 25 June 2020 / Accepted: 20 November 2020 / Published online: 8 December 2020 © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2020
Abstract Trajectories in human aimed movements are inherently variable. Using the concept of positional variance profiles, such trajectories are shown to be decomposable into two phases: In a first phase, the variance of the limb position over many trajectories increases rapidly; in a second phase, it then decreases steadily. A new theoretical model, where the aiming task is seen as a Shannon-like communication problem, is developed to describe the second phase: Information is transmitted from a “source” (determined by the position at the end of the first phase) to a “destination” (the movement’s end-point) over a “channel” perturbed by Gaussian noise, with the presence of a noiseless feedback link. Information-theoretic considerations show that the positional variance decreases exponentially with a rate equal to the channel capacity C. Two existing datasets for simple pointing tasks are re-analyzed and observations on real data confirm our model. The first phase has constant duration, and C is found constant across instructions and task parameters, which thus characterizes the participant’s performance. Our model provides a clear understanding of the speed-accuracy tradeoff in aimed movements: Since the participant’s capacity is fixed, a higher prescribed accuracy necessarily requires a longer second phase resulting in an increased overall movement time. The well-known Fitts’ law is also recovered using this approach. Keywords Fitts’ law · Speed-accuracy tradeoff · Information theory · Feedback · Variance · Movement · Motor control
1 Introduction It has long been observed that people routinely adapt their speed to perform aimed movements in a reliable manner: The more accurate a movement, the slower its execution. This so-called speed-accuracy tradeoff has been studied for more than a century by many communities such as experimental psychology (Woodworth 1899; Fitts 1954; Welford 1960; Crossman and Goodeve 1983; Meyer et al. 1988; Crossman 1957), human–computer interaction (HCI) (Card et al. 1978; Soukoreff and MacKenzie 2004), cybernetics (Chan and Childress 1990; Gawthrop et al. 2011), robotics (SimCommunicated by Benjamin Lindner.
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Julien Gori [email protected] Olivier Rioul [email protected]
1
LRI, Université Paris-Saclay, CNRS, Inria, 91400 Orsay, France
2
LTCI, Télécom Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France
mons and Demiris 2005), and neuroscience (Flanagan and Rao 1995; Khan et al. 2006). Fitts (1954) provided a simple formula to describe the speed-accuracy tradeoff of simple aimed movements (Fitts’ law, see Sect. 2), focusing on the variability of the movement endpoints. Fitts’ law remains to this day heavily use
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