Conditions for a linear speed-accuracy trade-off in aimed movements

A linear speed-accuracy trade-off has been found for rapid, precisely timed movements from a home position toward a target point. In this trade-off, W_e = K₁ + K₂(D/T), where D is the distance between the home position and the target, T is a pre-specified movement time, and W_e is the standard deviation of the distances actually moved. This result differs from Fitts' law, the commonly observed logarithmic trade-off in aimed movements. A new experiment with wrist rotations was performed to determine what conditions induce the linear trade-off rather than Fitts' law. Three types of condition are considered: movement brevity, feedback deprivation, and temporal precision. The experiment yielded a linear trade-off for precisely timed movements even when their durations significantly exceeded an amount of time (200 ms) sufficient to process visual feedback. This result suggests that the linearity does not depend on movement brevity and/or feedback deprivation per se. Instead it supports a temporal-precision hypothesis that the linear trade-off occurs when aimed movements must have precisely specified durations.

A linear speed-accuracy trade-off has been found for rapid, precisely timed movements from a home position toward a target point. In this trade-off, W_e = K₁ + K₂(D/T), where D is the distance between the home position and the target, T is a pre-specified movement time, and W_e is the standard deviation of the distances actually moved. This result differs from Fitts' law, the commonly observed logarithmic trade-off in aimed movements. A new experiment with wrist rotations was performed to determine what conditions induce the linear trade-off rather than Fitts' law. Three types of condition are considered: movement brevity, feedback deprivation, and temporal precision. The experiment yielded a linear trade-off for precisely timed movements even when their durations significantly exceeded an amount of time (200 ms) sufficient to process visual feedback. This result suggests that the linearity does not depend on movement brevity and/or feedback deprivation per se. Instead it supports a temporal-precision hypothesis that the linear trade-off occurs when aimed movements must have precisely specified durations.     

Extending Fitts' law to a three-dimensional pointing task

An attempt was made to extend Fitts' law to a three-dimensional movement (pointing) task to enhance its predictive performance in this domain. An experiment was conducted in which 10 subjects performed three-dimensional pointing movements under the manipulation of target size, distance to target and direction to target. As expected, the duration of these three-dimensional movements was rather variable and affected markedly by direction to target. As a result, the variance in the movement times produced was not satisfactorily explained by the conventional Fitts' model. The conventional model was extended by incorporating a directional parameter into the model. The extended model was shown to better fit the data than the conventional Fitts' model, both in terms of r(2) and the standard error of the residual between the measured movement time and the value predicted by model fit.     

Interactions among end-effectors and movement parameters influence reaction time in discrete, rapid aimed movements.

Two reliable findings in discrete, rapid aimed movements are that reaction time increases with decrease in target diameter (for the short-length movements), and reaction time is not affected by movement length [Journal of Experimental Psychology, Human Perception and Performance 104 (2) (1975) 147]. Participants normally use a short stylus (SS) to tap targets located on either side of a central (aligned with body midline) start-point with no restrictions imposed on the initial posture of the limb or segmental recruitment except as determined by movement conditions. Thus, the effects of movement parameters on reaction time in previous work are potentially confounded with the effect of initial posture of the limb at the start-point, along with order and amount of the contribution of segments recruited in response execution. Two experiments were performed to resolve the confounding between initial posture and recruitment of limb segments. In the first experiment a conventional stylus (pen-like) was employed and the starting position of the limb was aligned either with the body midline or with the participant's right shoulder. The effect of starting position on reaction time was not significant. In the second experiment the starting position was in line with the right shoulder. Two groups participated. One group used a conventional stylus. For the second group a modified (lengthened) stylus was used that permitted initial limb posture and number of limb segments recruited to be held constant across an extended range of movement lengths. When similar sets of limb segments were used, reaction time increased with decreasing movement length and diminishing target diameter. These findings suggest that uncontrolled initial limb posture, uncontrolled order of joint(s) recruitment, and the subsequent inclusion of reaction time values from incompatible sources may, in the final analysis, have confounded previous work investigating movement amplitude and target diameter effects on reaction time.     

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.     

Three-dimensional movement trajectories in Fitts' task: Implications for control

According to Fitts (1954), movement time (MT) is a function of the combined effects of movement amplitude and target width (index of difficulty). Aiming movements with the same index of difficulty and MT may have different planning and control processes depending on the specific combination of movement amplitude and target size. Trajectories were evaluated for a broad range of amplitudes and target sizes. A three-dimensional motion recording system (WATSMART) monitored the position of a stylus during aiming movements. MT results replicated Fitts' Law. Analysis of the resultant velocity profiles indicated the following significant effects: As amplitude of movement increased, so did the time to peak resultant velocity; peak resultant velocity increased slightly with target size, and to a greater extent with increases in the amplitude of movement; the time after peak resultant velocity was a function of both amplitude and target size. Resultant velocity profiles were normalized in the time domain to look for scalar relation in the trajectory shape. This revealed that: the resultant velocity profiles were not symmetrical; the proportion of time spent prior to and after peak speed was sensitive to target size only, i.e. as target size decreased, the profiles became more skewed to the right, indicating a longer decelerative phase; for a given target size, a family of curves might be defined and scaled on movement amplitude. These results suggest that a generalized program (base trajectory representation) exists for a given target width and is parameterized or scaled according to the amplitude of movement.     

Accuracy constraints upon rapid elbow movements

Kinematic and myoelectric variables associated with rapid elbow-flexion movements of various distances to targets of various widths were studied. The movement time in these experiments conformed to Fitts' law: movement time increased with target distance and decreased with target width. Peak movement velocity, electromyograph (EMG) duration, and EMG quantity were poorly described by Fitts' law, for increases in target width were accompanied by increases in these variables. We show with regression equations, using separate weighting coefficients, that kinematic and myoelectric variables can be related to distance and target width. The use of distance and target width as independent variables allows us to suggest that the literature does not agree on the relation between EMG and distance moved partly because of the influences of the target on this relationship. We propose that human voluntary movement involves a subject "strategy," or set of internal constraints, that affect movement outcome. Significant elements of this strategy, such as how accurately to perform the task, may not be recognized or controlled in many movement paradigms, in spite of uniform instruction to subjects and similar apparatus.     

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.     

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.     

Organization of drinking: postural characteristics of arm-head coordination

Postural characteristics of components of a natural movement-taking a sip from a mug filled with water-were studied. The authors hypothesized that important postural characteristics of each of the components involved in natural drinking can be described with a single or a few significant parameters. Seated participants (N = 7) took a small sip from a mug (selected from a set of 4) placed in front of them on the table. Movement components selected for analysis were transporting the mug, tilting the mug, moving and tilting the head, and opening the mouth. The ratio of mug diameter to the distance from the level of water to the rim of the mug was introduced as an index of difficulty (ID). ID showed significant logarithmic relationships to a number of parameters that described different components of the movement, including movement time (MT). Significant logarithmic relationships between ID and MT were observed during movements performed under visual control and with eyes closed. The authors tentatively suggest that those relationships are consequences of Fitts' law and that Fitts' law be expanded to tasks that are characterized by permissible error margin, not necessarily related to the size of a spatial target, and that are not constrained by the typical instruction "as fast and accurate as possible". A possible interpretation of the present observations is that the task constraints imposed on a number of movement parameters during the task of drinking can be described with a single parameter.     

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.     

Visual information: The control of aiming movements

The study examined the contribution of various sources of visual information utilised in the control of discrete aiming movements. Subjects produced movements, 15.24 cm in amplitude, to a 1.27 cm target in a movement time of 330 ms. Responses were carried out at five vision-manipulation conditions which allowed the subject complete vision, no vision, vision of only the target or stylus, and a combination of stylus and target. Response accuracy scores indicated that a decrement in performance occurred when movements were completed in the absence of visual information or when only the target was visible during the response. The stylus and the target plus stylus visual conditions led to response accuracy which was comparable to movements produced with complete vision. These results suggest that the critical visual information for aiming accuracy is that of the stylus. These findings are consistent with a control model based on a visual representation of the discrepancy between the position of the hand and the location of the target.     

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.     

Visual control of discrete aiming movements

An experiment is reported which investigated the visual control of discrete rapid arm movements. Subjects were required to move as rapidly as possible to several target width-movement distance combinations under both visual and non-visual conditions. The movement time (MT) data were supportive of Fitts' Law in that MT was linearly related and highly correlated to the Index of Difficulty (ID). MT was also similar for different target width-distance combinations sharing the same ID value. The error rate analysis, which compared visual to non-visual perfromance, indicated that vision was only used, and to varying degrees, when MT exceeded 200 ms (3.58 ID level). There was some evidence that vision was differentially used within target width-distance combinations sharing the same ID. Estimates of endpoint variability generally reflected the results of the error rate analysis. These results do not support the discrete correction model of Fitts' Law proposed by Keele (1968).     

Characteristics of Unintentional Movements by a Multijoint Effector

The authors explored the phenomenon of unintentional changes in the equilibrium state of a multijoint effector produced by transient changes in the external force. The subjects performed a position-holding task against a constant force produced by a robot and were instructed not to intervene voluntarily with movements produced by changes in the robot force. The robot produced a smooth force increase leading to a hand movement, followed by a dwell time. Then, the force dropped to its initial value leading to hand movement toward the initial position, but the hand stopped short of the initial position. The undershoot magnitude increased linearly with the peak hand displacement and exponentially with dwell time (time constant of about 1 s). For long dwell times, the hand stopped at about half the total distance to the initial position. The authors interpret the results as consequences of a drift of the referent hand coordinate. Our results provide support for back-coupling between the referent and actual body configurations during multijoint actions and produce the first quantitative analysis of this phenomenon. This mechanism can also explain the phenomena of slacking and force drop after turning visual feedback off during accurate force production task.     

Performance on a reciprocal tapping task with variations in intertapping interval

Fitts' law was investigated in a study of the effect of the index of difficulty (ID) and intertapping interval upon reaction time (RT) and movement time (MT) for a reciprocal tapping task. ID showed its well-established relationship with MT as described by Fitts' law: MT = aID + b. Improvement in the linearity of this relationship was, however, demonstrated by expressing MT in logarithmic units. While ID had an unsubstantial (though significant) effect on RT, increases in intertapping interval from zero to any level of discrete tapping led to significant increases in RT of about 135 msec. The results are interpreted as lending support to Fitts' thesis that RT and MT reflect independent phases of information processing.     

The coordination of bimanual aiming movements: Evidence for progressive desynchronization

It is known that when simultaneous bimanual aiming movements are made to targets with different IDs (Index of Difficulty), Fitts' Law is violated. There is massive slowing of the easy target hand, but a debate has arisen over the degree of synchronization between the hands and whether this effect represents a coordinative structure or interference due to neural cross-talk. This issue was investigated in an experiment with 12 subjects who moved styli forward in the sagittal plane to pairs of targets that differed in difficulty (0.77/3.73 ID and 0.77/5.17 ID). Reaction time, movement time, and kinematic measures of resultant velocity and acceleration were analysed. The results showed clear-cut timing differences between the hands that depended on both the ID difference between target pairs and elapsed time of the movement. The violation of Fitts' Law was confined to the easy target hand. Pronounced individual differences in both timing differences and left-right asymmetry were also noted. Neither the coordinative structure nor the neural cross-talk models can fully account for these data, and it is possible that the initial constraints on movement are moderated by visually driven corrective movements.     

Concurrent visual feedback and spatial accuracy in continuous aiming movements

The effect of concurrent visual feedback (CVF) on continuous aiming movements was investigated in the preferred hand of participants of college age (ns = 12 men, 8 women). Participants made continuous rapid reversal movements with a lightweight lever in the sagittal plane. Participants attempted to reach a short target (20 degrees) and a long target (60 degrees) in separate constant practice conditions, but alternated between the two targets in a variable practice condition. Four blocks of practice trials were provided in each condition, with 40 movements made in each. CVF of the position-time trace was provided for the first 20 movements of each block, but was removed for the remaining 20 movements in each block. Movements were more accurate and consistent during constant practice compared to variable practice where the short target was overshot and the long target was undershot. CVF reduced errors in all conditions, compared to movements without CVF, particularly for the short target during variable practice. The results suggest that the interference generated by alternating targets can be modulated by providing visual feedback, but once the visual feedback was removed, errors increased markedly.     

The Three-Dimensional Curvature of Straight-Ahead Movements

Three-dimensional curvature of point-to-point hand movements in the forward direction was examined. Subjects (N = 4) moved their hand from a position above the start point to a forward position above targets of different size and distance. Paths were curved as a result of an initial lateral and downward movement that was compensated for in the second half of the movement. The downward component of motion had a bell-shaped velocity profile and was temporally coupled to the forward motion. Curvature was greater for movements to near targets. Examination of the relation between kinematics and geometry revealed that velocity was related to radius of curvature by a power law with an exponent of 0.59. Simulations of the component of motion in the vertical plane reproduced the qualitative behavior of curvature and fit a power law relationship between velocity and radius of curvature     

The effect of the first glimpse at a scene on eye movements during search

Previewing scenes briefly makes finding target objects more efficient when viewing is through a gaze-contingent window (windowed viewing). In contrast, showing a preview of a randomly arranged search display does not benefit search efficiency when viewing during search is of the full display. Here, we tested whether a scene preview is beneficial when the scene is fully visible during search. Scene previews, when presented, were 250 ms in duration. During search, the scene was either fully visible or windowed. A preview always provided an advantage, in terms of decreasing the time to initially fixate and respond to targets and in terms of the total number of fixations. In windowed visibility, a preview reduced the distance of fixations from the target position until at least the fourth fixation. In full visibility, previewing reduced the distance of the second fixation but not of later fixations. The gist information derived from the initial glimpse of a scene allowed for placement of the first one or two fixations at information-rich locations, but when nonfoveal information was available, subsequent eye movements were only guided by online information.     

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.