A study of Fitts' law on goal-directed aiming task with moving targets

Most research based on Fitts' law define a log-linear relationship between temporal and spatial accuracy in goal-directed aiming tasks using stationary targets. Whether this relationship holds or not when the targets have varying velocities, and how the behavioral strategies and physical activities may change accordingly are of interest. The aim of this study was to investigate the relationship between temporal and spatial accuracy in goal-directed aiming tasks with moving targets. Participants were asked to aim at two target widths using a joystick. Results demonstrated that in a goal-directed aiming task there was a negative effect on performance when target velocity was increased or target width was decreased. Participants moved faster and then made more systematic errors in a high-velocity target condition. Results may be applicable to the complex perceptual-motor behavior of people who perform tasks using computers.     

A note on the information-theoretic basis of Fitts' law

Fitts' law is an information-theoretic view of human motor behavior developed from Shannon's Theorem, 17, a fundamental theorem of communications systems. Using data from Fitts' original experiments, we demonstrate that Fitts' choice of an equation that deviates slightly from the underlying principal is perhaps unfounded, and that the relationship is improved by using an exact adaptation of Shannon's equation.     

Finger width corrections in Fitts' law: implications for speed-accuracy research

This note points out that using the finger as a test probe in a Fitts task may lead to misleading results, because of the increased target tolerance resulting from the width of the finger pad. An experiment demonstrates the need to use a corrected target width when calculating the index of difficulty; without this correction, information processing rates are overestimated. An example is given of a developmental study in which the finger pad size changes with age. The resulting changes in the calculated rates of information processing are shown to be markedly different for the different age groups.     

Deductive temporal reasoning with constraints

When modelling realistic systems, physical constraints on the resources available are often required. For example, we might say that at most N processes can access a particular resource at any moment, exactly M participants are needed for an agreement, or an agent can be in exactly one mode at any moment. Such situations are concisely modelled where literals are constrained such that at most N, or exactly M, can hold at any moment in time. In this paper we consider a logic which is a combination of standard propositional linear time temporal logic with cardinality constraints restricting the numbers of literals that can be satisfied at any moment in time. We present the logic and show how to represent a number of case studies using this logic. We propose a tableau-like algorithm for checking the satisfiability of formulae in this logic, provide details of a prototype implementation and present experimental results using the prover.     

Movement-produced feedback as a mechanism for the temporal anticipation of motor responses

That part of the input hypothesis of motor timing behavior which postulates that movement-produced feedback can serve as a mechanism for the temporal anticipation of motor responses was tested. 32 male college Ss temporally anticipated (no preview) the coincidence of a moving pointer with a stationary one and executed the timing response with his right hand while either a high (HFB) or low (LFB) level of movement-produced feedback was indirectly manipulated in the left arm. The HFB group temporally anticipated with greater accuracy than the LFB group which supported that part of the input hypothesis being tested. Apparently, Ss were relying on proprioceptive feedback about the position of their left arm movement to cue the timing response of their right hand.     

Fitts' law with an isometric controller: effects of order of control and control-display gain

Twenty-four male subjects performed a discrete positioning task using an isometric controller. Two levels of order of control (position and velocity) were factorially crossed with two levels of control-display gain. Fitts' law functions were found for each of the four conditions. The velocity control conditions had significantly steeper slopes than the corresponding position control conditions, but there was no main effect for gain. A predicted interaction between control-display gain and order of control was found, indicating that the relative benefit of high gain is greater for velocity control than for position control. The reaction time (RT) regression lines had steeper negative slopes than those attained by Jagacinski, Repperger, Moran, Ward, and Glass (1980), who used an isotonic controller. This is in agreement with the results of Falkenberg and Newell (1980), who found that as average velocity increases, RT decreases. The components of Fitts' law were investigated, and this showed that the RT finding was due to the amplitude of the target, which covaried with average velocity, but was not due to the width.     

Changes in motor synergies for tracking movement and responses to perturbations depend on task-irrelevant dimension constraints

We investigated the changes in the motor synergies of target-tracking movements of hands and the responses to perturbation when the dimensionalities of target positions were changed. We used uncontrolled manifold (UCM) analyses to quantify the motor synergies. The target was changed from one to two dimensions, and the direction orthogonal to the movement direction was switched from task-irrelevant directions to task-relevant directions. The movement direction was task-relevant in both task conditions. Hence, we evaluated the effects of constraints on the redundant dimensions on movement tracking. Moreover, we could compare the two types of responses to the same directional perturbations in one- and two-dimensional target tasks. In the one-dimensional target task, the perturbation along the movement direction and the orthogonal direction were task-relevant and -irrelevant perturbations, respectively. In the two-dimensional target task, the both perturbations were task-relevant perturbations. The results of the experiments showed that the variabilities of the hand positions in the two-dimensional target-tracking task decreased, but the variances of the joint angles did not significantly change. For the task-irrelevant perturbations, the variances of the joint angles within the UCM that did not affect hand position (UCM component) increased. For the task-relevant perturbations, the UCM component tended to increase when the available UCM was large. These results suggest that humans discriminate whether the perturbations were task-relevant or -irrelevant and then adjust the responses of the joints by utilizing the available UCM.     

Cognitive constraints on motor imagery

Executed bimanual movements are prepared slower when moving to symbolically different than when moving to symbolically same targets and when targets are mapped to target locations in a left/right fashion than when they are mapped in an inner/outer fashion [Weigelt et al. (Psychol Res 71:238–447, 2007)]. We investigated whether these cognitive bimanual coordination constraints are observable in motor imagery. Participants performed fast bimanual reaching movements from start to target buttons. Symbolic target similarity and mapping were manipulated. Participants performed four action conditions: one execution and three imagination conditions. In the latter they indicated starting, ending, or starting and ending of the movement. We measured movement preparation (RT), movement execution (MT) and the combined duration of movement preparation and execution (RTMT). In all action conditions RTs and MTs were longer in movements towards different targets than in movements towards same targets. Further, RTMTs were longer when targets were mapped to target locations in a left/right fashion than when they were mapped in an inner/outer fashion, again in all action conditions. RTMTs in imagination and execution were similar, apart from the imagination condition in which participants indicated the start and the end of the movement. Here MTs, but not RTs, were longer than in the execution condition. In conclusion, cognitive coordination constraints are present in the motor imagery of fast (<1600 ms) bimanual movements. Further, alternations between inhibition and execution may prolong the duration of motor imagery.     

Bi-phasic hitting with constraints on impact velocity and temporal precision

The aim of the experiment was to investigate how bi-phasic hitting movements are organized to comply with both impact and temporal precision constraints. 'Bi-phasic' refers to a sequential movement with a preparatory movement away from the interception location followed by a strike phase. The interception location was fixed, as the motion of the hitting device was constrained to follow a straight path orthogonal to that of the approaching balls. We manipulated the required temporal precision by projecting balls with different constant approach speeds (1, 1.5, and 2m/s). Different impact constraints were imposed by instructing participants first to simply hit the ball and subsequently to hit the ball to a designated target area located either 55 or 105 cm away from the interception location. We determined several kinematic variables and used Principal Component Factor Analysis to classify these variables. The analysis revealed two independent factors: a 'velocity' factor (formed by impact velocity, peak velocity of the preparatory phase, peak velocity of the strike phase, and amplitude of the strike) and a 'timing' factor (formed by onset of the preparatory phase, moment of peak velocity of the preparatory phase, and onset of the strike phase). The 'velocity' factor scaled significantly with the required impact constraint and the 'timing' factor scaled significantly with ball speed.     

Increasing the efficiency of instruction for a person with severe disabilities: The applicability of Fitts' law in predicting response time

The purpose of this study was to demonstrate the applicability of Fitts' law in predicting the response duration of instruction-specific head movements for a person with severe multiple disabilities. Fitts' law is a motoric algorithm that calculates an index of difficulty (ID) for responses in relation to the variables of stimulus width and stimulus amplitude. Four functional tasks from the learner's current continuing education plans were targeted: photocopying, using a paint well, model painting, and communication symbol sequencing. For each of the four tasks, two sets of indices were calculated by (1) holding constant stimulus width while varying amplitude, and (2) holding constant stimulus amplitude while varying width. Results showed that response duration varied as a function of ID variation.     

The temporal pattern of unconstrained drinking: Rats' responses to inversion and identity constraints

Rats obtained all of their water by licking a metal tube during a series of daily 1-hour sessions. When the tube was freely available throughout, each rat showed the classic temporal pattern of unconstrained drinking: As the session progressed, drinking bouts generally grew shorter and pauses grew longer. In subsequent sessions the tube was opened and closed independently of the rat's behavior, on a schedule that gave the rat a chance to duplicate the exact inverse of its unconstrained baseline pattern. Thus, as the inversion session progressed, the opportunities to drink generally grew longer and the enforced pauses grew shorter. When the rats were forced away from their unconstrained patterns of drinking and pausing, their total time spent drinking consistently fell short of previous values, but total licks and volumetric intake remained at previous levels. The same results occurred under an identity schedule, a series of openings and closings that duplicated the unconstrained pattern of drinking and pausing. The results have implications for theories that assume that instrumental performance under schedule constraint derives from the animal's defense of a measured set-point.     

Children's comprehension of semantic constraints on temporal prepositions

Children's comprehension of the semantic rules for temporal prepositions was investigated. The temporal prepositions werein, on, andat. Lech's (1969) semantic analysis was used as the framework for the study. The contextual property [(x)]→TIM[PERI] with its related constraints indicates the ill-formedness of phrases like^* in noon,^* on January and^* at Saturday. Correct usage of these prepositions is based on the implicit distinction between time with or without duration (period versus moment). Comprehension differences among the prepositions, based on semantic differences were hypothesized, as well as developmental differences across age levels. Thirty-five children at each of three levels (kindergarten, grades 2, and 4) in Experiment 1, and 24 grade 4 children in Experiment 2, judged the appropriateness of sentences containing temporal prepositions and attempted to revise the ill-formed sentences. Significant developmental differences were observed. Kindergarten children could not discriminate between well- and ill-formed sentences; second grade children could discriminate but could not identify the reason for their discrimination, nor could they revise the ill-formed sentences. Fourth grade children could discriminate and identify or revise the ill-formedness. Ability to revise the prepositions was found to be related to cognitive developmental level. None of the children in either experiment were able to articulate the periodicity-moment temporal distinction which provides the basis for the semantic constraints. The awareness of semantic rules for temporal prepositions may be relatively late in developing, perhaps between the ages of 8 and 10 years. An advanced awareness of these rules may develop considerably later.     

Weber's law for the reproduction of temporal information

The main purpose of this research was to determine the numeric values of Weber's fraction when subjects were required to estimate temporal durations of 1, 3, 5, 7, and 9 sec. under the method of reproduction. The results provided evidence in support of a constant coefficient of proximity for time estimation of approximately 14.5%.     

Systematic variation in performance of an interceptive action with changes in the temporal constraints.

People are highly skilled at intercepting moving objects and are capable of remarkably accurate timing. The timing accuracy required depends upon the period of time for which contact with a moving target is possible--the "time window" for successful interception. Studies of performance in an experimental interception task that allows this time window to be manipulated suggest that people change aspects of their performance (movement time, MT, and movement speed) in response to changes in the time window. However, this research did not establish whether the observed changes in performance were the results of a response to the time window per se or of independent responses to the quantities defining the time window (the size and speed of a moving target). Experiment 1 was designed to resolve this issue. The speed and size of the target were both varied, resulting in variations in the time window; MT was the primary dependent measure. Predictions of the hypothesis that people respond directly to changes in the time window were verified. Predictions of the alternative hypothesis that responses to changes in target speed and size are independent of one another were not supported. Experiment 2 examined how the type of performance change observed in Experiment 1 was affected by changing the time available for executing the interception. The time available and the target speed were varied, and MT was again the primary dependent measure. MT was smaller when there was less time available, and the effect of target speed (and hence the time window) on MT was also smaller, becoming undetectable at the shortest available time (0.4 s). The results of the two experiments are interpreted as providing information about the "rule" used to preprogramme movement parameters in anticipatory interceptive actions.     

Trunk-assisted prehension: specification of body segments with imposed temporal constraints

The authors used a trunk-assisted prehension task to examine intersegment coordination. Participants (N = 7) reached to grasp an object placed beyond full arm extension, thus requiring trunk flexion to achieve the target object, under 4 varying temporal constraints. Kinematic analyses were performed in which the motions of the arm, the trunk, and the endpoint were characterized. The spatial trajectories and the segments' peak velocity data revealed that under high temporal constraints the arm was more responsible for endpoint motion than the trunk, whereas in the unconstrained condition the trunk was more involved. In addition, the arm exhibited a decline in spatial variability toward the end of the movement in all conditions, whereas the trunk did not. The present study is the first to show that when temporal demand is increased for a trunk-assisted prehensile task, the arm plays a larger role than the trunk in the transport of the hand to the object. The data also suggest that the arm participates in the fine accuracy control of the reach, whereas the trunk does not.     

Effect of temporal constraints on hemispheric asymmetries during spatial frequency processing

Studies on functional hemispheric asymmetries have suggested that the right vs. left hemisphere should be predominantly involved in low vs. high spatial frequency (SF) analysis, respectively. By manipulating exposure duration of filtered natural scene images, we examined whether the temporal characteristics of SF analysis (i.e., the temporal precedence of low on high spatial frequencies) may interfere with hemispheric specialization. Results showed the classical hemispheric specialization pattern for brief exposure duration and a trend to a right hemisphere advantage irrespective of the SF content for longer exposure duration. The present study suggests that the hemispheric specialization pattern for visual information processing should be considered as a dynamic system, wherein the superiority of one hemisphere over the other could change according to the level of temporal constraints: the higher the temporal constraints of the task, the more the hemispheres are specialized in SF processing.