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.     

Movement Speed and Accuracy in Space and Time: The Complementarity of Error Distributions

Movement speed-accuracy trade-off is a function of the space-time constraints of the task. We investigated the space-time account of Hancock and Newell (1985) and the hypothesis of complementarity between the four moments of the error distribution in space and time. Twelve participants performed 15 conditions in a line drawing task composed of different spatial (10, 20, and 30 cm) and temporal (250 to 2,500 ms) criteria. The results showed that all moments of distributions changed systematically between conditions but there were some departures from the Hancock and Newell predictions. In contrast, individual analysis revealed the complementarity of the spatial and temporal error including a trade-off between the four moments of error. These findings support a complementary space-time account of movement speed and accuracy.     

Aiming error under transformed spatial mappings suggests a structure for visual-motor maps

Transformed spatial mappings were used to perturb normal visual-motor processes and reveal the structure of internal spatial representations used by the motor control system. In a 2-D discrete aiming task performed under rotated visual-motor mappings, the pattern of spatial movement error was the same for all Ss: peak error between 90 degrees and 135 degrees of rotation and low error for 180 degrees rotation. A two-component spatial representation, based on oriented bidirectional movement axes plus direction of travel along such axes, is hypothesized. Observed reversals of movement direction under rotations greater than 90 degrees are consistent with the hypothesized structure. Aiming error under reflections, unlike rotations, depended on direction of movement relative to the axis of reflection (see Cunningham & Pavel, in press). Reaction time and movement time effects were observed, but a speed-accuracy tradeoff was found only for rotations for which the direction-reversal strategy could be used. Finally, adaptation to rotation operates at all target locations equally but does not alter the relative difficulty of different rotations. Structural properties of the representation are invariant under learning.     

Information entropy and the variability of space-time movement error

The authors investigated the effects of movement time and movement distance on the information entropy and variability of spatial and temporal error in a discrete aiming movement. In Experiment 1, the authors held movement distance (100 mm) constant and manipulated 11 movement times (300-800 ms) of 8 participants. In Experiment 2, the authors tested 6 movement distances at 2 given movement times (15-60 mm at 300 ms; 40-240 mm at 800 ms) in 8 participants. The variability and entropy for spatial error increased with average movement velocity, whereas the variability and entropy for temporal error decreased as a function of average movement velocity. The common variance between variable error and entropy averaged about 84% and 72% for spatial and temporal errors, respectively, suggesting that the probabilistic approach of entropy reveals features that are not present in the standard deviation index of variability. The findings provide further evidence that information entropy may be a useful single-index representation of variability in the movement speed-accuracy relation.     

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.     

Speed-accuracy characteristics of saccadic eye movements

Speed-accuracy trade-off characteristic of horizontal saccadic eye movements were examined in this study. Unlike limb movements, saccadic eye movements are preprogrammed, unidimensional, and do not involve target impact. Hence, they provide an optimal test of the impulse variability account of the speed-accuracy trade-off in rapid movements. Subjects were required to alternately look at two target lights as fast and as accurately as possible for a period of 10 s. Target lights subtended angles of 5, 10, 15, and 20 degrees. By restricting target distances to less than 20 degrees of arc, the speed-accuracy relation was examined for single horizontal saccadic movements of the eye. movement of the dominant eye was tracked with an infra-red eye monitoring device. Fifty saccadic movements of the eye were recorded for each target distance and used to compute the average amplitude, duration, and velocity of eye movements, as well as, movement endpoint variability. An increase in both average velocity and movement endpoint variability with increasing movement amplitude was found. This, together with the unique features of the eye movement system, support the impulse variability account of the speed-accuracy trade-off in rapid movements.     

Speed-accuracy tradeoff functions in choice reaction time: Experimental designs and computational procedures

The existence of tradeoffs between speed and accuracy is an important interpretative problem in choice reaction time (RT) experiments. A recently suggested solution to this problem is the use of complete speed-accuracy tradeoff functions as the primary dependent variable in choice RT ,experiments instead of a single mean RT and error rate. This paper reviews and compares existing procedures for generating empirical speed-accuracy tradeoff, functions for use as dependent variables in choice RT experiments. Two major types of tradeoff function are identified, and their experimental designs and computational procedures are discussed and evaluated. Systematic disparities are demonstrated between the two tradeoff functions in both empirical and computer-simulated data. Although all existing procedures for generating speed-accuracy tradeoff functions involve empirically untested assumptions, one procedure requires less stringent assumptions and is less sensitive to sources of experimental and statistical error. This procedure involves plotting accuracy against RT over a set of experimental conditions in which subjects’ criteria for speed vs. accuracy are systematically varied.     

Search Strategies in Practice: Movement Variability Affords Perception of Task Dynamics

Practice has been conceptualized in terms of a search process through an evolving perceptual-motor workspace. The experiment was set up to examine whether the inherent variability of the system would influence perception of the relevant properties of the task space. We reanalyzed the data from Hsieh, Liu, Mayer-Kress, and Newell (2013) in which participants performed a speed-accuracy aiming task and feedback emphasized either temporal or spatial accuracy in different conditions. The maximum variability in spatial error during practice differentiated individual's best performance in the fast speed-accuracy conditions. Additionally, we found that a threshold of variability predicted discontinuities during practice within individuals. The findings support the proposition that inherent variability affords perception of the relevant dimension of the task. The search motion through the perceptual-motor workspace was continuous or discontinuous depending on the constraints of the movement speed-accuracy condition.     

Speed-accuracy tradeoffs in rapid bimanual aiming movements

Two experiments reported the effect of movement time and knowledge of results on overall spatial errors in rapid simultaneous bimanual aiming movements. In Exps. 1 (n=32) and 2 (n=32), participants used light, aluminum levers oriented vertically in the sagittal plane to make reversal movements over the same distance (20 degrees - 20 degrees or 60 degrees - 60 degrees) or different distances (20 degrees - 60 degrees) in each arm in 250, 350, or 450 msec. to the reversal point. The participants in Exp. 1 were given knowledge of results on the spatial and temporal accuracy for both arms, while in Exp. 2 knowledge of results was provided for one arm only. Strong speed-accuracy tradeoffs were shown for all groups in both experiments, but errors were larger in the different distance movements compared to the same distance groups. Spatial errors were also elevated in Exp. 2 when knowledge of results was not available compared to those conditions where knowledge of results was available. Overall, bimanual speed-accuracy tradeoffs are similar to single arm movements when one moves the same distance in each arm and when knowledge of results is available.     

Impulse and Movement Space-Time Variability

In 3 experiments, the authors examined movement space-time variability as a function of the force-time properties of the initial impulse in a movement timing task. In the range of motion and movement time task conditions, peak force, initial rate of force, and force duration were manipulated either independently or in combination across a range of parameter values. The findings showed that (a) impulse variability is predicted well by the elaboration of the isometric force variability scaling functions of L. G. Carlton, K. H. Kim, Y. T. Liu, and K. M. Newell (1993) to movement, and (b) the movement spatial and temporal outcome variability are complementary and well predicted by an equation treating the variance of force and time in Newton's 2nd law as independent random variables. Collectively, the findings suggest that movement outcome variability is the product of a coherent space-time function that is driven by the nonlinear scaling of the force-time properties of the initial impulse.     

Speed-Accuracy Characteristics of Saccadic Eye Movements

Speed-accuracy trade-off characteristic of horizontal saccadic eye movements were examined in this study. Unlike limb movements, saccadic eye movements are preprogrammed, unidimensional, and do not involve target impact. Hence, they provide an optimal test of the impulse variability account of the speed-accuracy trade-off in rapid movements. Subjects were required to alternately look at two target lights as fast and as accurately as possible for a period of 10 s. Target lights subtended angles of 5,10,15, and 20°. By restricting target distances to less than 20° of arc, the speed-accuracy relation was examined for single horizontal saccadic movements of the eye. Movement of the dominant eye was tracked with an infra-red eye monitoring device. Fifty saccadic movements of the eye were recorded for each target distance and used to compute the average amplitude, duration, and velocity of eye movements, as well as, movement endpoint variability. An increase in both average velocity and movement endpoint variability with increasing movement amplitude was found. This, together with the unique features of the eye movement system, support the impulse variability account of the speed-accuracy trade-off in rapid movements.     

Parameter value switching in discrete and continuous aiming movements

The effect of practice variations on spatial and temporal accuracy was investigated in both discrete and continuous aiming movements in the preferred hand of college-aged participants (N=25). In a completely within-subject design, participants made rapid reversal movements with a lightweight lever in the sagittal plane, practicing 20 degrees and 60 degrees movements in repeated (same distance) and alternating (switching between 20 degrees and 60 degrees) conditions. Movements were also made one at a time (discretely) or in sequences of 20 movements (continuously). Spatial constant error, spatial variable error, spatial overall error, the coefficient of variation, movement time, and the relative timing were calculated for each set of 20 movements and analyzed by within-subject analyses of variance. Movements in the repeated conditions for both discrete and continuous movements were more accurate and consistent compared to the alternating condition where the short movements were overshot and the long movements were undershot. Discrete movements were more spatially and temporally variable than continuous movements. The discrete and continuous movements showed different relative timing patterns, suggesting that the temporal structure of the motor program is affected by task characteristics.     

Control over speeded actions: a common processing locus for micro- and macro-trade-offs?

Cognitive control processes associated with long- and short-term adjustments of human behaviour have attracted much interest recently. It is still unclear, however, whether the mechanisms underlying these adjustments share a common locus within the chain of stimulus-response processing. In order to address this issue, the present study employed a speed-accuracy instruction producing a macro-trade-off, whereas micro-trade-off was studied by means of posterror slowing in reaction time (RT). Participants performed a spatially compatible or incompatible four-stimuli-to-two-response alternative choice RT task. Reliable variations in micro-and macro-trade-off as well as effects of spatial compatibility were found in RT and error rate. Most importantly, posterror slowing was larger when instruction stressed accuracy rather than speed, an effect being independent of spatial compatibility. Because the influence of speed-accuracy instruction and posterror slowing on performance was strongest for response alternations, together present findings suggest that the mechanisms underlying micro- and macro-trade-offs have one common locus at the level of motor processing. Additional influences of macro-trade-off on premotoric processing are likely.     

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.     

Learning the pedalo locomotion task

The authors examined the learning function of a multiple biomechanical degrees of freedom coordination task. Four adult participants practiced the pedalo locomotion task for 350 trials over 7 days. On the basis of the Cauchy theorem, the authors applied a movement pattern difference score that provides a measure of convergence to a fixed point as the criterion for quantifying learning. The findings showed a significant reduction of the movement pattern difference score over practice. Neither an exponential (0.11) nor a power law (0.10) function accommodated a large percentage of the variance of the pattern difference measure on individual learning functions, but the respective fits were higher, although not different, for movement time (.57, .55). Principal components analysis showed a decrease of components over practice; the analysis also showed that 3-5 components were required to accommodate 90% of the variance of the whole-body motion at the end of the final practice session. Those findings on the learning functions for movement and outcome scores are discussed in relation to the redundancy of the biomechanical system in moving to a dynamical stable fixed point in this task.     

The effects of temporal-precision and time-minimization constraints on the spatial and temporal accuracy of aimed hand movements

Discrete aimed hand movements, made by subjects given temporal-accuracy and time-minimization task instructions, were compared. Movements in the temporal-accuracy task were made to a point target with a goal movement time of 400 ms. A circular target then was manufactured that incorporated the measured spatial errors from the temporal-accuracy task, and subjects attempted to contact the target with a minimum movement time and without missing the circular target (time-minimization task instructions). This procedure resulted in equal movement amplitude and approximately equal spatial accuracy for the two task instructions. Movements under the time-minimization instructions were completed rapidly (M = 307 ms) without target misses, and tended to be made up of two submovements. In contrast, movements under temporal-accuracy instructions were made more slowly (M = 397 ms), matching the goal movement time, and were typically characterized by a single submovement. These data support the hypothesis that movement times, at a fixed movement amplitude versus target width ratio, decrease as the number of submovements increases, and that movements produced under temporal-accuracy and time-minimization have different control characteristics. These control differences are related to the linear and logarithmic speed-accuracy relations observed for temporal-accuracy and time-minimization tasks, respectively.     

Speed-accuracy tradeoff and information processing dynamics

For a long time, it has been known that one can tradeoff accuracy for speed in (presumably) any task. The range over which one can obtain substantial speed-accuracy tradeoff varies from 150 msec in some very simple perceptual tasks to 1,000 msec in some recognition memory tasks and presumably even longer in more complex cognitive tasks. Obtaining an entire speed-accuracy tradeoff function provides much greater knowledge concerning information processing dynamics than is obtained by a reaction- time experiment, which yields the equivalent of a single point on this function. For this and other reasons, speed-accuracy tradeoff studies are often preferable to reaction-time studies of the dynamics of perceptual, memory, and cognitive processes. Methods of obtaining speed-accuracy tradeoff functions include: instructions, payoffs, deadlines, bands, response signals (with blocked and mixed designs), and partitioning of reaction time. A combination of the mixed-design signal method supplemented by partitioning of reaction times appears to be the optimal method.     

Combined visual illusion effects on the perceived index of difficulty and movement outcomes in discrete and continuous fitts’ tapping

The speed-accuracy trade-off is a fundamental movement problem that has been extensively investigated. It has been established that the speed at which one can move to tap targets depends on how large the targets are and how far they are apart. These spatial properties of the targets can be quantified by the index of difficulty (ID). Two visual illusions are known to affect the perception of target size and movement amplitude: the Ebbinghaus illusion and Muller-Lyer illusion. We created visual images that combined these two visual illusions to manipulate the perceived ID, and then examined people’s visual perception of the targets in illusory context as well as their performance in tapping those targets in both discrete and continuous manners. The findings revealed that the combined visual illusions affected the perceived ID similarly in both discrete and continuous judgment conditions. However, the movement outcomes were affected by the combined visual illusions according to the tapping mode. In discrete tapping, the combined visual illusions affected both movement accuracy and movement amplitude such that the effective ID resembled the perceived ID. In continuous tapping, none of the movement outcomes were affected by the combined visual illusions. Participants tapped the targets with higher speed and accuracy in all visual conditions. Based on these findings, we concluded that distinct visual-motor control mechanisms were responsible for execution of discrete and continuous Fitts’ tapping. Although discrete tapping relies on allocentric information (object-centered) to plan for action, continuous tapping relies on egocentric information (self-centered) to control for action. The planning-control model for rapid aiming movements is supported.     

Accommodation to increased accuracy demands by the right and left hands

This study was designed to identify the phase of rapid aimed movements responsible for hand differences in motor skill, and to evaluate potential differences between the hands in accommodating to greater accuracy demands. In both experiments, an accelerometer mounted on a stylus allowed key changes in acceleration to be used to partition the movement into phases. In Experiment 1, slower left hand movement times were attributable primarily to a terminal homing-in phase, especially as target size decreased. Since error rates varied as a function of hand and target size, speed-accuracy trade-offs may have occurred. Experiment 2 rigidly controlled error rate and confirmed the major hand difference to occur in the latter phase of the movement where error correction is presumed. Although less pronounced, adjustments were made in the earlier movement phases as well. Accommodation to greater accuracy demands involved moving the stylus closer to the target before decelerating to engage in error correction. This adjustment to gain enhanced precision was more pronounced in the left hand.     

Learning to optimize speed, accuracy, and energy expenditure: a framework for understanding speed-accuracy relations in goal-directed aiming

Over the last century, investigators have developed a number of models to explain the relation between speed and accuracy in target-directed manual aiming. The models vary in the extent to which they stress the importance of feedforward processes and the online use of sensory information (see D. Elliott, W. F. Helsen, & R. Chua, 2001, for a recent review). A common feature of those models is that the role of practice in optimizing speed, accuracy, and energy expenditure in goal-directed aiming is either ignored or minimized. The authors present a theoretical framework for understanding speed-accuracy tradeoffs that takes into account the strategic, trial-to-trial behavior of the performer. The strategic behavior enables individuals to maximize movement speed while minimizing error and energy expenditure.