Fitts's Law Research Articles

Targeting the Fitts Law

Targeting the Fitts Law

Movement Duration, Fitts's Law, and an Infinite-Horizon Optimal Feedback Control Model for Biological Motor Systems

Optimization models explain many aspects of biological goal-directed movements. However, most such models use a finite-horizon formulation, which requires a prefixed movement duration to define a cost function and solve the optimization problem. To predict movement duration, these models have to be run multiple times with different prefixed durations until an appropriate duration is found by trial and error. The constrained minimum time model directly predicts movement duration; however, it does not consider sensory feedback and is thus applicable only to open-loop movements. To address these problems, we analyzed and simulated an infinite-horizon optimal feedback control model, with linear plants, that contains both control-dependent and control-independent noise and optimizes steady-state accuracy and energetic costs per unit time. The model applies the steady-state estimator and controller continuously to guide an effector to, and keep it at, target position. As such, it integrates movement control and posture maintenance without artificially dividing them with a precise, prefixed time boundary. Movement pace is determined by the model parameters, and the duration is an emergent property with trial-to-trial variability. By considering the mean duration, we derived both the log and power forms of Fitts's law as different approximations of the model. Moreover, the model reproduces typically observed velocity profiles and occasional transient overshoots. For unbiased sensory feedback, the effector reaches the target without bias, in contrast to finite-horizon models that systematically undershoot target when energetic cost is considered. Finally, the model does not involve backward and forward sweeps in time, its stability is easily checked, and the same solution applies to movements of different initial conditions and distances. We argue that biological systems could use steady-state solutions as default control mechanisms and might seek additional optimization of transient costs when justified or demanded by task or context.

Action graphs and user performance analysis

A user operating an interactive system performs actions such as “pressing a button” and these actions cause state transitions in the system. However to perform an action, a user has to do what amounts to a state transition themselves, from the state of having completed the previous action to the state of starting to perform the next action; this user transition is out of step with the system's transition. This paper introduces action graphs, an elegant way of making user transitions explicit in the arcs of a graph derived from the system specification. Essentially, a conventional transition system has arcs labeled in the form “user performs action A” whereas an action graph has arcs labelled in the form “having performed action P, the user performs Q.” Action graphs support many modelling techniques (such as GOMS, KLM or shortest paths) that could have been applied to the user's actions or to the system graph, but because it combines both, the modelling techniques can be used more powerfully.Action graphs can be used to directly apply user performance metrics and hence perform formal evaluations of interactive systems. The Fitts Law is one of the simplest and most robust of such user modelling techniques, and is used as an illustration of the value of action graphs in this paper. Action graphs can help analyze particular tasks, any sample of tasks, or all possible tasks a device supports—which would be impractical for empirical evaluations. This is an important result for analyzing safety critical interactive systems, where it is important to cover all possible tasks in testing even when doing so is not feasible using human participants because of the complexity of the system.An algorithm is presented for the construction of action graphs. Action graphs are then used to study devices (a consumer device, a digital multimeter, an infusion pump) and results suggest that: optimal time is correlated with keystroke count, and that keyboard layout has little impact on optimal times. Many other applications of action graphs are suggested.

Multilingual Touchscreen Keyboard Design and Optimization

A keyboard design, once adopted, tends to have a longlasting and worldwide impact on daily user experience. There is a substantial body of research on touch-screen stylus keyboard optimization. Most of it has focused on English only. Applying rigorous mathematical optimization methods and addressing diacritic character design issues, this article expands this body of work to French, Spanish, German, and Chinese. More important and counter to the intuition that optimization by nature is necessarily specific to each language, this article demonstrates that it is possible to find common layouts that are highly optimized across multiple languages for stylus (or single finger) typing. We first obtained a layout that is highly optimized for both English and French input. We then obtained a layout that is optimized for English, French, Spanish, German, and Chinese pinyin simultaneously, reducing its stylus travel distance to about half of QWERTY's for all of the five languages. In comparison to QWERTY's 3.31, 3.51, 3.7, 3.26, and 3.85 keys of movement for English, French, Spanish, German, and Chinese, respectively, the optimized multilingual layout has an average travel distance of 1.88, 1.86, 1.91, 1.77, and 1.68 keys, correspondingly. Applying Fitts's law with parameters validated by a word tapping experiment, we show that these multilingual keyboards also significantly reduce text input time for multiple languages over the standard QWERTY for experienced users. In comparison to layouts individually optimized for each language, which are also obtained in this article, simultaneously optimizing for multiple languages caused only a minor performance degradation for each language. This surprising result could help to reduce the burden of multilingual users having to switch and learn new layouts for different languages. In addition, we also present and analyze multiple ways of incorporating diacritic characters on multilingual keyboards. Taken together, the present work provides a quantitative foundation for the understanding and designing of multilingual touch-screen keyboards.

EEG correlates of Fitts’s law during preparation for action

Humans’ inability to move fast and accurately at the same time is expressed in Fitts’s law. It states that the movement time between targets depends on the index of difficulty, which is a function of the target width and the inter-target distance. The present study investigated the electrophysiological correlates of Fitts’s law during action planning using high-density electroencephalography. Movement times were scaled according to Fitts’s law, indicating that participants could not overcome the speed–accuracy trade-off during a 1-s preparation period. Importantly, the index of difficulty of the planned movement correlated linearly with the amplitudes of the cognitive N2 and P3b components, which developed during the planning period over parieto-occipital areas. These results suggest that the difficulty of a movement during action planning is represented at a level where perceptual information about the difficulty of the ensuing action is linked to motor programming of the required movement.

Comment on “Visual layout modulates Fitts’s law: The importance of first and last positions”

Pratt, Adam, and Fischer (2007) investigated the effect of surrounding targets on the time it took to move to an individual target and found that the movement time to a central target was above the Fitts's law line related to the first and last targets. They explained their results in terms of a "visuomotor hypothesis." Here, an alternative explanation is given in terms of a previously validated model of the "available target width" that is determined by the size of the target and the width of the finger pad that is being used to hit the target.

Tip of the Tongue Selectivity and Motor Learning in the Palatal Area

This study assessed the ability of the tongue tip to accurately select intraoral targets embedded in an upper palatal tongue-computer interface, using 18 able-bodied volunteers. Four performance measures, based on modifications to Fitts's Law, were determined for three different tongue-computer interface layouts. The layouts differed with respect to number and location of the targets in the palatal interface. Assessment of intraoral target selection speed and accuracy revealed that performance was indeed dependent on the location and distance between the targets. Performances were faster and more accurate for targets located farther away from the base of the tongue in comparison to posterior and medial targets. A regression model was built, which predicted intraoral target selection time based on target location and movement amplitude better than the predicted by using a standard Fitts's Law model. A 30% improvement in the speed and accuracy over three daily practice sessions of 30 min emphasizes the remarkable motor learning abilities of the tongue musculature and provides further evidence that the tongue is useful for operating computer-interface technologies.

Perception and the Fitts's Law Violation: Why is the last one the fastest one?

Perception and the Fitts's Law Violation: Why is the last one the fastest one?

The neural correlates of Fitts's law in action observation: An fMRI study

Previous neuroimaging studies support the assumption of a strong link between perception and action, demonstrating that the motor system is involved when others' actions are observed. One question that is still open to debate is which aspects of observed actions engage the motor system. The present study tested whether motor activation corresponds to the difficulty of the observed action, using Fitts's law. This law postulates that the difficulty of any movement (ID) is a function of the distance to the target (A) and the target width (W). In an observation task, the ID of the observed action was manipulated orthogonally to W (by using five different As). The results revealed activity in the primary motor cortex, the supplementary motor area, and the basal ganglia in response to increasing ID levels, but not in response to different levels of A or W. Thus, activation in the motor system during action observation is not driven by perceptual parameters but by the motor difficulty of the observed action.

Modulating Fitts's Law: Perceiving targets at the last placeholder

Fitts's Law predicts increasing movement times (MTs) with increasing movement amplitudes; however, when targets are placed in a structured perceptual array containing placeholders, MTs to targets in the last position are shorter than predicted. We conducted three experiments to determine if this modulation has a perceptual cause. Experiment 1, which used extremely diminished (three pixel) placeholders, showed that the modulation is not due to perceptual interference from neighboring placeholders. Experiment 2, which measured reaction times using a target detection task, showed that the modulation does not result from speeded perceptual processing at the last position of the array. Experiment 3, which measured accuracy using a masked letter-discrimination task, showed that the modulation does not result from the increased quality of perceptual representation at the last position of the array. Overall, these findings suggest that the changes in effectiveness of visual processing (less interference, speeded processing, and increased quality) at the last position in the perceptual array do not drive the modulation. Thus, while the locus of the Fitts's Law modulation appears to be in the movement planning stage, it is likely not due to perceptual mechanisms.

Human Motor Transfer Is Determined by the Scaling of Size and Accuracy of Movement

ABSTRACT A transfer of training design was used to examine the role of the Index of Difficulty (ID) on transfer of learning in a sequential Fitts's law task. Specifically, the role of the ratio between the accuracy and size of movement (ID) in transfer was examined. Transfer of skilled movement is better when both the size and accuracy of movement are changed by the same factor (ID is constant) than when only size or accuracy is changed. The authors infer that the size–accuracy ratio is capturing the control strategies employed during practice and thus promotes efficient transfer. Furthermore, efficient transfer is not dependent on maintaining relative timing invariance and thus the authors provide further evidence that relative timing is not an essential feature of movement control.

Accuracy and speed trade‐off in robot‐assisted surgery

Controlling surgical task speed and maintaining accuracy are vital components of robotic surgical skills. This study was designed to investigate the relationship between accuracy and speed for robot-assisted surgical skills. Ten participants were asked to alternately touch two circular targets with various dimensions and distances between two targets, using the da Vinci Surgical System. The design of this study was based on Fitt's law. Statistical correlations between the index of difficulty (ID) and the movement time (MT), as well as the ID and the smoothness of the movement, were analysed. A significant linear correlation between MT and ID was shown. Speed was reduced to maintain accuracy as the level of task difficulty increased. There was no significant correlation between the smoothness of the movement and ID. The trade-off between speed and accuracy plays an important role in robot-assisted surgical proficiency.

Sequence effects during manual aiming: A departure from Fitts's Law?

Sequence effects during manual aiming: A departure from Fitts's Law?

Using Fitts's law for evaluating Tongue Drive System as a pointing device for computer access.

In this paper, the results of a 2-D center-out task in a Fitts's law experiment have been presented for measuring the performance of the Tongue Drive System (TDS). Although the end-user population for TDS is individuals with tetraplegia, in this study, we recruited 6 able-bodied subjects in 3 sessions, conducted in 3 consecutive days. They performed the same task with their right hand using a standard mouse for achieving a baseline as well as a standard keypad with their right index finger. The resulting average throughput for TDS, keypad, and mouse were 1.67, 2.17, and 3.99 bit/s, respectively.

Fitts's Law and the optimal planning of sequences of saccades

Fitts's Law and the optimal planning of sequences of saccades

Structured perceptual displays produce exceptions to Fitts's law

Structured perceptual displays produce exceptions to Fitts's law

Fitts's law for saliency

Fitts's law for saliency

Fitts’s Law violation and motor imagery: are imagined movements truthful or lawful?

Fitts's Law for the timing of targeted movements states that, when target width is held constant, movement time (MT) will increase as the travelled distance increases. Even imagined movements, mentally simulated actions without actual actions, obey Fitts's Law. Recently, a violation of Fitts's Law has been reported; when targets occur in a structured array, MT to the farthest target is shorter than that predicted by Fitts's Law. We conducted two experiments to determine if the violation also occurs for imagined movements. Results showed a close correspondence between real and imaginary MTs across target locations, including the Fitts's violation for the farthest target. We conclude that the violation of Fitts's Law occurs in motor imagery and that the locus of the violation is in the planning stage of action.

Evaluation of a modified Fitts law brain–computer interface target acquisition task in able and motor disabled individuals

A brain–computer interface (BCI) is a communication system that takes recorded brain signals and translates them into real-time actions, in this case movement of a cursor on a computer screen. This work applied Fitts' law to the evaluation of performance on a target acquisition task during sensorimotor rhythm-based BCI training. Fitts' law, which has been used as a predictor of movement time in studies of human movement, was used here to determine the information transfer rate, which was based on target acquisition time and target difficulty. The information transfer rate was used to make comparisons between control modalities and subject groups on the same task. Data were analyzed from eight able-bodied and five motor disabled participants who wore an electrode cap that recorded and translated their electroencephalogram (EEG) signals into computer cursor movements. Direct comparisons were made between able-bodied and disabled subjects, and between EEG and joystick cursor control in able-bodied subjects. Fitts' law aptly described the relationship between movement time and index of difficulty for each task movement direction when evaluated separately and averaged together. This study showed that Fitts' law can be successfully applied to computer cursor movement controlled by neural signals.

Fitts's law interpretation as ergonomic metrics for motor impaired users

This paper proposes a micromechanics algorithm utilising the finite element method (FEM) for the analysis of heterogeneous matter. The characterisation procedure takes the material properties of the constituents, axons and extracellular matrix (ECM) as input data. The material properties of both the axons and the matrix are assumed to have linear viscoelastic behaviour with a perfect bonding between them. The results of the modelling have been validated with experimental data with material white input from brainstem by considering the morphology of brainstem in which most axons are oriented in longitudinal direction in the form of a uniaxial fibrous composite material. The method is then employed to examine the undulations of axons within different subregions of white matter and to study the impact due to axon/matrix volume fractions. For such purposes, different unit cells composed of wavy geometries and with various volume factions have been exposed to the six possible loading scenarios. The results will clearly demonstrate the undulation and axon volume fraction impacts. In this respect, undulation affects the material stiffness heavily in the axon longitudinal direction, whereas the axons' volume fraction has a much greater impact on the mechanical properties of the white matter in general. Also the results show that the created stresses and strains in the axons and matrix under loading will be impacted by undulation change. With increase in undulation the matrix suffers higher stresses when subjected to tension, whereas axons suffer higher stresses in shear. The axons always exhibit higher stresses whereas the matrix exhibits higher strains. The evaluated time-dependent local stress and strain concentrations within a repeating unit cell of the material model are indicative of the mechanical behaviour of the white tissue under different loading scenarios.