Predictive feedback control and Fitts–law

Abstract

Fitts' law is a well established empirical formula, known for encapsulating the "speed-accuracy trade-off". For discrete, manual movements from a starting location to a target, Fitts' law relates movement duration to the distance moved and target size. The widespread empirical success of the formula is suggestive of underlying principles of human movement control. There have been previous attempts to relate Fitts' law to engineering-type control hypotheses and it has been shown that the law is exactly consistent with the closed-loop step-response of a time-delayed, first-order system. Assuming only the operation of closed-loop feedback, either continuous or intermittent, this paper asks whether such feedback should be predictive or not predictive to be consistent with Fitts law. Since Fitts' law is equivalent to a time delay separated from a first-order system, known control theory implies that the controller must be predictive. A predictive controller moves the time-delay outside the feedback loop such that the closed-loop response can be separated into a time delay and rational function whereas a nonpredictive controller retains a state delay within feedback loop which is not consistent with Fitts' law. Using sufficient parameters, a high-order non-predictive controller could approximately reproduce Fitts' law. However, such high-order, "non-parametric" controllers are essentially empirical in nature, without physical meaning, and therefore are conceptually inferior to the predictive controller. It is a new insight that using closed-loop feedback, prediction is required to physically explain Fitts' law. The implication is that prediction is an inherent part of the "speed-accuracy trade-off".

Fitts’ Law in early postural adjustments

“…Several recent studies have linked speed-accuracy trade-off to predictive processes within the central nervous system (Duarte and Latash, 2007; Gawthrop et al, 2008; Bertucco and Cesari, 2010; Radulescu et al, 2010). These conclusions fit well the hypothesis offered about 20 years ago that Fitts’ Law originates at the level of movement planning (Latash and Gutman, 1993).…”

Intermittent control models of human standing: similarities and differences

“…In engineering terms, it is well known that a predictor can be used to overcome time delay (Smith 1959; Kleinman 1969; Gawthrop 1982). As discussed by many authors (Kleinman et al 1970; Baron et al 1970; McRuer 1980; Miall et al 1993b; Wolpert et al 1998; Bhushan and Shadmehr 1999; Van Der Kooij et al 2001; Gawthrop et al 2008, 2009, 2011; Loram et al 2012), it is plausible that physiological control systems have built in model-based prediction. Gawthrop et al (2011) base their intermittent controller on an underlying predictive design; Bottaro et al (2008); Asai et al (2009) and Kowalczyk et al (2012) do not.…”

Control Theoretic Models of Pointing

“…For a given D and W , the sequence of sub-movements would always be the same, and it is not possible to explain why the target is missed at times. Gawthrop et al [25] demonstrate that a simple predictive controller can be consistent with Fitts' law, while non-predictive controllers cannot. The same paper also presents the link between intermittent control, predictive control and human motor control, and further develops this in [24].…”