Fitts' Law in two dimensions with hand and head movements

Subjects performed two-dimensional discrete movements either with a helmet-mounted sight or with a joystick. Fitts' Law was found to be a good predictor of the speed-accuracy tradeoff for both systems. The joystick produced faster movement times than the helmet-mounted sight. For both systems, horizontal and vertical movements were slightly faster than diagonal movements. Two dimensional generalizations of Fitts' Law were discussed in terms of multidimensional scaling. The obtained pattern of movement times was found to be intermediate to the predictions of Euclidean and City-block models of the movement space. Muscle coordination strategies were considered, and a strictly serial coordination model was rejected. A strictly parallel model was also rejected for the helmet-mounted sight, but not for the joystick.     

Deficits in executed and imagined aiming performance in brain-injured children

Motor disorders are a frequent consequence of acquired brain injury (ABI) in children and much effort is currently invested in alleviating these deficits. The aim of the present study was to test motor imagery (MI) capabilities in children with ABI (n=25) and an age- and gender-matched control group (n=25). A computerized Virtual Radial Fitts Task (VRFT) was used to investigate the speed-accuracy trade-offs (or Fitts' law) that occur as target size is varied for both executed and imagined performance. In the control group, the speed for accuracy trade-off for both executed and imagined performance conformed to Fitts' law. In the ABI group, only executed movements conformed to Fitts' law. These findings suggest that children with ABI show an inferior ability to imagine the time needed to complete goal-directed movements with differential difficulty levels.     

Fine motor deficiencies in children with developmental coordination disorder and learning disabilities: an underlying open-loop control deficit

Thirty-two children with Developmental Coordination Disorder (DCD) and learning disabilities (LD) and their age-matched controls attending normal primary schools were investigated using kinematic movement analysis of fine-motor performance. Three hypotheses about the nature of the motor deficits observed in children with LD were tested: general slowness hypothesis, limited information capacity hypothesis, and the motor control mode hypothesis. Measures of drawing movements were analyzed under different task conditions using a Fitts' paradigm. In a reciprocal aiming task, the children drew straight-line segments between two targets 2.5 cm apart. Three Target Sizes were used (0.22, 0.44, and 0.88 cm). Children used an electronic pen that left no trace on the writing tablet. To manipulate the degree of open-loop movement control, the aiming task was performed under two different control regimes: discrete aiming and cyclic aiming. The kinematic analysis of the writing movements of the 32 children with DCD/LD that took part in the experimental study confirmed that besides learning disabilities they have a motor learning problem as well. Overall, the two groups did not differ in response time, nor did they respond differently according to Fitts' Law. Both groups displayed a conventional trade-off between Target Size and average Movement Time. However, while movement errors for children with DCD/LD were minimal on the discrete task, they made significantly more errors on the cyclic task. This, together with faster endpoint velocities, suggests a reduced ability to use a control strategy that emphasizes the terminal control of accuracy. Taken together, the results suggest that children with DCD/LD rely more on feedback during movement execution and have difficulty switching to a feedforward or open-loop strategy.     

Structure of the visual array and saccadic latency: implications for oculomotor control

Subjects were required to look saccadically at single targets selected from one- or two-dimensional arrays of different numbers of possible alternative targets. Saccadic latencies varied with the direction but not the distance of the target, with practice and with individual subject. The effect of number of alternatives was complex, and it is suggested that an important factor influencing saccadic latency is not the number of targets per se but the number of possible directions in which a saccade may have to go.     

Kinematics properties of rapid aimed hand movements

Generalized motor program theory and the models of Schmidt, Zelaznik, and Frank (1978), and Meyer, Smith, and Wright (1982) of speed-accuracy relationships in aimed hand movements require that the underlying acceleration-time patterns exhibit time rescalability, in which all acceleration-time functions in an aimed hand movement are generated from one rescalable pattern. We examined this property as a function of movement time in Experiment 1, and as a function of movement time and movement distance in Experiment 2. Both experiments failed to demonstrate strict time rescalability in acceleration-time patterns, with the time to peak positive acceleration being invariant across movement time. This suggests that time rescalability is not a necessary condition for the linear relation between speed and spatial variability. A second major finding was that the variability in distance traveled at the end of positive acceleration was independent of movement time, contrary to the symmetric-impulse-variability model of Meyer et al. (1982). The findings of both experiments suggest that the processes involved in decelerating the limb play an important, but yet to be understood, role in determining the linear speed-accuracy trade-off. Finally, these results suggest that generalized motor programs are not based on simple, time-rescalable acceleration patterns.     

Feedback versus motor programming in the control of aimed movements.

In the Fitts paradigm the subject moves a stylus to the left or right of an initial rest position to reach targets that vary in size and in distance from the initial position. The classic finding for relatively long movements is that movement time, measured from leaving the initial position until contact with the target, depends on both distance and target size according to a relationship known as "Fitts' law." By contrast, reaction time, measured from the signal to move until the stylus leaves the initial position, is independent of these parameters. While replicating these results for long movements, the present data show a different pattern for very short movements, for which Fitts' law no longer holds and for which reaction time increases as the size of the target is decreased. These findings were interpreted as implying that long movements are under feedback control, whereas short movements are predominately programmed and ballistic. This conclusion was supported by the additional finding that elimination of visual feedback was more disruptive to the long than to the short movements.     

Abnormalities of motor and praxis imagery in children with DCD

In an earlier study using the visually guided pointing task (VGPT) the authors showed that the timing of imagined movement sequences in children with developmental coordination disorder (DCD) does not conform to the conventional speed-for-accuracy trade-off (or Fitts' law [P.M. Fitts, Journal of Experimental Psychology 47 (1954) 381-391]) that occurs when the distance and accuracy requirements of movements are varied [P. Maruff, P.H. Wilson, M. Trebilcock, J. Currie, Neuropsychologia 37 (1999b) 1317-1324]. The present study sought to replicate this earlier finding and to examine (using a weight manipulation) whether this deficit was also attributable to inaccurate programming of relative force. The chronometry of real and imagined movements was investigated in a group of 20 children with DCD aged between 8 and 12 years and a group of controls matched on age and verbal IQ (VIQ). Movement duration was tested for real and imagined movements using the preferred hand, with the VGPT performed under two load conditions: with and without the addition of a weight attached to a pen. Group means of each subjects' mean movement duration were calculated and plotted against target width for each of the four conditions [Movement type (2) x Load (2)] and a logarithmic curve was fitted to the data points. In the control group, the speed-for-accuracy trade-off for both real and imagined performance conformed to Fitts' law under each load condition. In the DCD group only real movements conformed to Fitts' law. Moreover, the effect of load differed between groups--for real movements, movement duration did not differ between load and no-load conditions for either group, while for imagined movements, movement duration increased under the load condition for the control group only. These results replicate and extend the results of our earlier study. This pattern of performance suggests that children with DCD have an impairment in the ability to generate internal representations of volitional movements which may reflect an impaired ability to process efference copy signals. The ability to programme both relative force and timing appears to underly this difficulty. Results have implications for the use of (guided) motor imagery training in order to facilitate the development of motor skill in children with DCD.     

Task specificity and the timing of discrete aiming movements

In discrete aiming movements the task criteria of time-minimization to a spatial target (e.g., Fitts, 1954) and time-matching to a spatial-temporal goal (e.g., Schmidt et al., 1979) tend to produce different functions of the speed-accuracy trade-off. Here we examined whether the task-related movement speed-accuracy characteristics were due to differential space-time trade-offs in time-matching, velocity-matching and time-minimizing task goals. Twenty participants performed 100 aiming trials for each of 15 combinations of task-type (3) and space-time condition (5). The prevalence of the primary types of sub-movement (none, pre-peak, post-peak, undershooting and overshooting) was determined from the kinematics of the movement trajectory. There were comparable distributions of trajectory sub-movement profiles and space-time movement outcomes across the three tasks at the short movement duration that became increasingly dissimilar over decreasing movement velocity and increasing movement time conditions. Movement time was the most influential variable in mediating sub-movement characteristics and the spatial/temporal outcome accuracy and variability of discrete aiming tasks – a role that was magnified in the explicit task demands of time-matching. The time-matching and time-minimization task goals in discrete aiming induce qualitatively different control processes that progressively contribute beyond the minimal time conditions to task-specific space-time accuracy and variability characteristics of the respective movement speed-accuracy functions.     

Light reinforcement in the rat: The effects of continuous and discontinuous periods of apparatus familiarization

The effects of continuous and discontinuous periods of apparatus familiarization on light reinforcement in rats were examined. A previous finding that the light reinforcement effect is greater with longer pretest periods in the dark box was confirmed by comparing 270 min and 30 min periods in the box prior to testing 24 h later. A discontinuous period of 9 daily 30 min sessions, however, produced a bigger effect than the 270 min continuous period. It was concluded that the degree of familiarization with the apparatus is a more important factor than length of time per se in the dark in determining the effectiveness of light as a reinforcer.     

Proprioceptive control of goal-directed movements in man, studied by means of vibratory muscle tendon stimulation

The purpose of this study was to investigate the role of propriomuscular feedback in the control of pluriarticular pointing movements, performed without visual feedback toward visual targets. The proprioceptive inputs were distorted during movements by applying vibration to the distal tendon of the biceps muscle. Various movement and vibration durations were imposed. The results show that vibration affects the spatial outcome of the movements. The effects of vibration were movement time-independent when the durations were shorter than 450 ms and became movement time-dependent with longer durations. Moreover, the effects of vibration became more marked when a short vibration was applied at the end rather than at the beginning of a slow movement. These studies suggest that at least two types of proprioceptive control loops may be involved in correcting this kind of movement, depending on the execution time. In slow movements, the final phase might be a privileged period for on-line, propriomuscular-based corrections. Lastly, it emerged that the regulation of a goal-directed movement on the basis of proprioceptive feedback processing can take place within at most 200 ms.     

The effects of objectives and constraints on motor control strategy in reciprocal aiming movements

The goal of this study was to examine how the kinematics of reciprocal aiming movements were affected by both the objective of the movement and the constraints operating on that movement. In Experiment 1, the objective of the movement was indirectly manipulated by capitalizing on the fact that subjects determine their own accuracy and speed limits, despite uniform task instructions to move as quickly and accurately as possible. A Fitts' type reciprocal aiming paradigm was employed, in which 69 subjects were asked to move a stylus repetitively between two spatially separated targets. Four target widths were orthogonally combined with four movement amplitudes, resulting in 16 conditions. Movements were made on an X-Y digitizing tablet. Based on the mean variable error produced on both targets, subjects were differentiated post hoc into three movement objective groups: speed, accuracy, and speed-plus-accuracy. Kinematic analyses revealed that the programming and execution of movements were systematically influenced by both the movement objective and the movement constraints. That is, movement time, peak velocity, dwell time, acceleration and deceleration time, normalized acceleration and normalized deceleration varied systematically as a function of both the speed-accuracy movement objective and the movement constraints of target size and movement distance. Moreover, the consequences of changing the constraints of the movement were affected by an interaction with the objective of the movement. In Experiment 2, the objective of the movement was directly manipulated by varying speed and/or accuracy instructions to subjects. The basic results of Experiment 1 were substantiated. Overall, the results were consistent with the view that motor control is dependent upon sensory consequences.     

Extended practice of reciprocal wrist and arm movements of varying difficulties

An experiment was designed to determine the degree to which reciprocal aiming movements of the wrist and arm with various accuracy requirements (Fitts' tasks) are enhanced by extended practice. The vast majority of research on motor learning shows performance improvement over practice. However, literature examining the effect of practice on Fitts' task performance is limited and inconclusive. Participants were asked to flex/extend their limb/lever in the horizontal plane at the wrist (arm stabilized) or elbow joint (wrist stabilized) in an attempt to move back and forth between two targets as quickly and accurately as possible. The targets and current position of the limb were projected on the screen in front of the participant. Target width was manipulated with amplitude constant (16°) in order to create indexes of difficulty (ID) of 1.5, 3, 4.5, and 6. Contrary to the earlier reports, after 20 days of practice, we found minimal changes in movement time or the movement time-ID relationships for the arm and wrist over practice. However, the variability in the movement endpoints decreased over practice and wrist movements at ID=6 were characterized by shorter movement times and longer dwell times relative to arm movements with dwell time for the wrist increasing over practice. These data are consistent with the notion that Fitts' tasks provide a stable measure of perceptual-motor capabilities.     

Visual Feedback of Target Position Affects Accuracy of Sequential Movements at Even Spaces

The role of visual feedback during movement is attributed to its accuracy, but findings regarding the utilization of this information are inconsistent. We developed a novel dot-placing task to investigate the role of vision in arm movements. Participants conducted pointing-like movements between two target stimuli at even spaces. In Experiment 1, visual feedback of targets and response positions was manipulated. Although visual loss of target stimuli hindered accuracy of movements, the absence of the position of previously placed dots had little effect. In Experiment 2, the effect of movement time on accuracy was assessed, as the relationship between these has been traditionally understood as a speed/accuracy trade-off. Results revealed that duration of movement did not impact movement accuracy.     

Goal-directed aiming under restricted viewing conditions with confirmatory sensory feedback

A substantial body of research has examined the speed-accuracy tradeoff captured by Fitts’ law, demonstrating increases in movement time that occur as aiming tasks are made more difficult by decreasing target width and/or increasing the distance between targets. Yet, serial aiming movements guided by internal spatial representations, rather than by visual views of targets have not been examined in this manner, and the value of confirmatory feedback via different sensory modalities within this paradigm is unknown. Here we examined goal-directed serial aiming movements (tapping back and forth between two targets), wherein targets were visually unavailable during the task. However, confirmatory feedback (auditory, haptic, visual, and bimodal combinations of each) was delivered upon each target acquisition, in a counterbalanced, within-subjects design. Each participant performed the aiming task with their pointer finger, represented within an immersive virtual environment as a 1 cm white sphere, while wearing a head-mounted display. Despite visual target occlusion, movement times increased in accordance with Fitts’ law. Though Fitts’ law captured performance for each of the sensory feedback conditions, the slopes differed. The effect of increasing difficulty on movement times was least influential in the haptic condition, suggesting more efficient processing of confirmatory haptic feedback during aiming movements guided by internal spatial representations.     

Temporal generalization under time pressure in humans

In two experiments, participants performed a temporal generalization task in which they were asked to decide whether or not the durations of comparison stimuli were different from those of standard stimuli (750 ms, 1,000 ms, or 1,250 ms). One half of the participants was instructed to respond as quickly as possible, while the other half received no instruction concerning the speed of response. The relationship between stimulus duration and the time of response and the effect of time pressure on duration discrimination were examined. Response time increased as a linear function of the duration of the to-be-judged stimuli until a certain instant, which was defined as T₂ = s/(1 - b), where s refers to the internal representation of the standard duration and b to the decision threshold. Moreover, the participants systematically overestimated the presented intervals if they were asked to respond as fast as possible when the standard duration was either 1,000 ms or 1,250 ms, but not when the standard duration was 750 ms.     

Co-regulation of movement speed and accuracy by children with heavy prenatal alcohol exposure

The study investigated how children with heavy prenatal alcohol exposure regulate movement speed and accuracy during goal-directed movements. 16 children ages 7 to 17 years with confirmed histories of heavy in utero alcohol exposure, and 21 nonalcohol-exposed control children completed a series of reciprocal tapping movements between two spatial targets. 5 different targets sets were presented, representing a range of task difficulty between 2 and 6 bits of information. Estimates of percent error rate, movement time, slope, and linear fit of the resulting curve confirmed that for goal-directed, reciprocal tapping responses, performance of the group with prenatal alcohol exposure was described by a linear function, as predicted by Fitts' law, by sacrificing movement accuracy. The index of performance was the same for the two groups: it initially increased, then leveled off for more difficult movements.     

Visual perception of writing and pointing movements

Studies of movement production have shown that the relationship between the amplitude of a movement and its duration varies according to the type of gesture. In the case of pointing movements the duration increases as a function of distance and width of the target (Fitts' law), whereas for writing movements the duration tends to remain constant across changes in trajectory length (isochrony principle). We compared the visual perception of these two categories of movement. The participants judged the speed of a light spot that portrayed the motion of the end-point of a hand-held pen (pointing or writing). For the two types of gesture we used 8 stimulus sizes (from 2.5 cm to 20 cm) and 32 durations (from 0.2 s to 1.75 s). Viewing each combination of size and duration, participants had to indicate whether the movement speed seemed "fast", "slow", or "correct". Results showed that the participants' perceptual preferences were in agreement with the rules of movement production. The stimulus size was more influential in the pointing condition than in the writing condition. We consider that this finding reflects the influence of common representational resources for perceptual judgment and movement production.     

Proprioceptive feedback as a mediator in interlimb timing

Prior findings regarded as evidence for proprioceptive feedback as a mediator in interlimb timing can also be interpreted as evidence for motor outflow because they came from research that had subjects make voluntary movements, and such movements allow for both feedback and outflow to operate. The present study was designed to resolve this controversy by determining if these findings could be replicated with passive movements which allow for feedback, but not outflow, to operate. The interlimb timing task studied was one where subjects made the timing response with their right hand while moving their left arm during the 1.5-sec interval to be timed. Three groups of 16 male college students performed 50 trials of the right-hand response with knowledge of results, under one of three left-arm conditions: (a) passive movement, (b) voluntary movement, and (c) no movement. The results indicated that the findings were replicated with passive movements and this was interpreted as support for the involvement of proprioceptive feedback in interlimb timing.     

Programming precision in repetitive tapping

The present paper reports an experiment using the Fitts' tapping paradigm. It is concerned with a comparison of movement times and accuracy during blind and visual repetitive tapping. A blind condition was used to investigate rapid aiming movements under motor program control, whilst visual aiming was used to assess the role of visual feedback for control purposes. Subjects in the blind conditions were able to replicate the amplitude specifications of the task, whereas effective target width was constant for a set amplitude and did not reflect specified target width. Subjects, furthermore, responded more rapidly when tapping blind. These results are discussed in terms of the magnitude of forces being attempted as a result of performing a set amplitude, and the role of visual feedback.     

Simultaneous vs. sequential requests in resource dilemmas with incomplete information

We consider a class of resource dilemmas of the following form: members of groups of size n are asked to share a common resource pool whose exact size, x, is not known. Rather, x is sampled randomly from a probability distribution which is common knowledge. Each group member j (j = 1,…,n) requests r_j from the resource pool. Requests are made either simultaneously or sequentially. If (r₁+r₂+…+r_n) x all members are granted their requests; otherwise, group members get nothing.

For each protocol of play we present two alternative models - a game theoretical equilibrium solution and a psychological model incorporating the notion of focal points. We then report the results of two experiments designed to compare the two models under the two protocols of play.