The breakdown of Fitts’ law in rapid, reciprocal aiming movements

Experimental Brain Research, 2006

An aiming task was used to identify the processes whereby the motor system adapted a repetitive aiming action to systematic changes in ID (ID = log 2 (2A/W), Fitts in J Exp Psychol 47:381-391, 1954) within a single trial. Task ID was scaled in a trial by moving the outside edge of two stationary targets to produce nine diVerent target IDs in a trail. The ID within a trial was scaled in one of two directions: (1) an increasing ID condition, starting with an ID = 3.07 and ending with an ID = 5.91; and (2) a decreasing ID condition, starting with an ID = 5.91 and ending with an ID = 3.07. An index of movement harmonicity (Guiard in Acta Psychol 82:139-159, 1993) revealed that the repetitive aiming action was harmonic in nature when task ID was 3.07, and consisted of a series of discrete segments when task ID was 5.91. This Wnding provides evidence for the existence of discrete and cyclical units of action that are irreducible and that may be employed independently to assemble longer continuous actions. The scaling of ID within a trial promoted a transition in repetitive aiming motions assembled from discrete and cyclical units of action. A variety of kinematic measures (e.g., movement harmonicity, time spent accelerating the limb) revealed a critical ID (ID c ) region (4.01-4.91) separating aiming motions governed by the diVerent units of action. Enhancement of Xuctuations before the transition were found in the movement harmonicity data and in the distance traveled to peak velocity data, with variability in these measures highest in the ID c region. The enhancement of Xuctuations indicates that loss of stability in the limb's motion acted as a key mechanism underlying the transition between units of action. The loss of stability was associated with the transition from cyclical to discrete actions and with the transition from discrete to cyclical actions. The transition between units of action may be conceptualized as a transition from a limit cycle attractor (cyclical unit of action) to a shift between two Wxedpoint attractors (discrete unit of action) when ID was increased, with the transition occurring in the opposite direction when ID was decreased.

Neuroscience Letters, 2006

Previous studies suggested that the advantage in speed accuracy trade-off of cyclic over discrete aiming tasks with the upper limbs may be associated with the operation of spinal neural oscillators, as in locomotion. Similar to the locomotor rhythm that is fairly robust and can accommodate changes in loading or stride length, we predicted that cyclic aiming tasks would be equally resistant to changes in load or amplitude, thereby preserving the advantage over discrete tasks. To test the hypothesis, cyclic and discrete aiming movements were performed with and without loading of the hand. Furthermore a "complex" condition was introduced in which the distance between the targets that the participants moved to alternated between 2.5 and 5 cm. In all cases, two target sizes were used to test spatial accuracy and to be able to calculate the Index of Performance (IP). Findings revealed that even though part of the advantage of the cyclic over the discrete regime was lost during the complex movement pattern and with addition of weight, the former remained superior to the latter. Furthermore, adding weight did not change the oscillation frequency in the cyclic movements. It is concluded that the superiority of cyclic movements over discrete ones is fairly robust, consistent with the high degree of flexibility that is typically observed in neural oscillators. (B.C.M. Smits-Engelsman), [email protected] (S.P. Swinnen), [email protected] (J. Duysens).

Lecture Notes in Computer Science, 2009

Various methods and measures have been developed to assess the quality of input devices and interaction techniques. One approach to investigating the performance of input devices and interaction techniques is to focus on the quality of the produced movements. The current paper proposes a new method of analyzing goal-directed movements by dividing them into meaningful phases. In addition to the proposed analysis method a selection of measures is suggested to assess different aspects of rapidly aimed movements. In order to evaluate the added value of the proposed analysis method an experiment has been conducted to compare two input devices (mouse versus stylus with tablet) with respect to their performance on a multi-directional pointing task. The results show that the analysis into several phases reveals clear differences in the movement strategy.

Acta Psychologica, 1997

The time required to program a movement response (reaction time) has been found to be directly related to the accuracy requirements of the response as well as to the number of movement segments comprising the response. However, since many of the experiments which have manipulated response complexity have concurrently manipulated the amplitude of the entire movement, it was not possible to determine which of these factors was responsible for the change in reaction time. The main purpose of the present experiment was to determine whether the time required to program a limb movement was affected by response complexity, by movement amplitude, by target size, or by some combination of these factors. Subjects made forearm extension and extension-flexion movements of varying amplitudes in the horizontal plane, to targets of varying sizes. The kinematic properties of these movements were also investigated to determine whether these movements were exclusively programmed prior to movement initiation or whether some form of on-line control occurred during the execution of the movement. Pre-motor reaction time was found to be dependent upon response amplitude and total movement duration more than it was on response complexity or target size. In addition, subjects adopted on-line control when the amplitude of the movement was increased and when the terminal target size was decreased.

Journal of Experimental Psychology: Human Perception and Performance, 2000

A series of 8 experiments examined the phenomenon that a rapid aimed hand movement is executed faster when it is performed as a single, isolated movement than when it is followed by a second movement (the 1-target advantage). Three new accounts of this effect are proposed and tested: the eye movement hypothesis, the target uncertainty hypothesis, and the movement integration hypothesis. Data are reported that corroborate the 3rd hypothesis, but not the first 2 hypotheses. According to the movement integration hypothesis, the first movement in a series is slowed because control of the second movement may overlap with execution of the first. It is shown that manipulations of target size and movement direction mediate this process and determine the presence and absence of the 1-target advantage. Possible neurophysiologicai mechanisms and implications for motor control theory are discussed.

Experimental Brain Research, 2006

Recent studies have shown that the initial impulse associated with goal-directed aiming movements typically brings the limb to a position short of the target. This is because target overshooting is associated with greater temporal and energy costs than target undershooting. Presumably these costs can be expected to vary not only with the muscular forces required to move the limb, but also the gravitational forces inherent in the aiming task. In this study we examined the degree to which primary movement endpoint distributions depend on the direction of the movement with respect to gravity. We hypothesized that the magnitude of an undershoot bias would be greatest for downward movements because target overshooting necessitates a time and energy consuming movement reversal against gravity. Participants completed rapid aiming movements toward targets located above and below, as well as proximal and distal to a central home position. Movements were made both with and without additional mass attached to the limb. Although movement time did not vary with experimental condition, primary movement endpoint distributions were consistent with our predictions. SpeciWcally, both greater undershooting and greater endpoint variability was associated with downward aiming movements. As well, a greater proportion of the overall movement time was spent in the corrective phase of the movement. These results are consistent with models of energy minimization that posit an inherent eYciency of control and hold that movements are organized to minimize movement time and energy expenditure and maximize mechanical advantages.

Psychology and Aging, 1996

Using a cross-sectional design, this study determined the time course of aging effects on rapid discrete and reciprocal aiming movements in men and women. A total of 80 men and 61 women in good health were classified into six age groups (25, 35, 45, 55, 65, and 75 years). The discrete task required participants to make one discrete aiming movement, whereas the reciprocal task required a series of back-and-forth movements. Results indicated for both aiming tasks that greater age was strongly associated with slower movement times. The significant interaction between age and task indicated that the discrete task showed much larger aging effects (54%) than the reciprocal task (25%). This finding is tentatively interpreted in terms of a reduced efficiency of "on-line" control processes.

Experimental Brain Research, 1998

In daily living, we continuously interact with our environment. This environment is rarely stable and living beings show remarkable adaptive capacities. When we reach for an object, it is necessary to localize the position of this object with respect to our own body before programming an adequate arm movement. If the target remains stable, the programmed movement brings the hand near the target. However, what happens when the target suddenly jumps to another position in space? The aim of this work was to investigate how rapid aiming movements are corrected when the target is displaced close to movement onset. Our results reveal that rapid movements can be modified and that the efficiency of trajectory amendments vary according to task (directional or direction/amplitude pointings) and environment (structured or darkness). We were most interested in the specific role played by peripheral and/or central feedback information (efferent copy) in the control of aiming movements. The results suggest that the two types of loops are complementary in movement regulation. However, their predominance varies according to the nature of the task at hand.

Previous research has demonstrated that movement times to the first target in sequential aiming movements are influenced by the properties of subsequent segments. Based on this finding, it has been proposed that individual segments are not controlled independently. The purpose of the current study was to investigate the role of visual feedback in the interaction between movement segments. In contrast to past research in which participants were instructed to minimize movement time, participants were set a criterion movement time and the resulting errors and limb trajectory kinematics were examined under vision and no vision conditions. Similar to single target movements, the results indicated that vision was used within each movement segment to correct errors in the limb trajectory. In mediating the transition between segments, visual feedback from the first movement segment was used to adjust the parameters of the second segment. Hence, increases in variability that occurred from the first to the second target in the no vision condition were curtailed when visual feedback was available. These results are discussed along the lines of the movement constraint and movement integration hypotheses.

Psychological Review, 1988

A stochastic optimized-submovement model is proposed for Pitts' law, the classic logarithmic tradeoff between the duration and spatial precision of rapid aimed movements. According to the model, an aimed movement toward a specified target region involves a primary submovement and an optional secondary corrective submovement. The submovements are assumed to be programmed such that they minimize average total movement time while maintaining a high frequency of target hits. The programming process achieves this minimization by optimally adjusting the average magnitudes and durations of noisy neuromotor force pulses used to generate the submovements. Numerous results from the literature on human motor performance may be explained in these terms. Two new experiments on rapid wrist rotations yield additional support for the stochastic optimizedsubmovement model. Experiment 1 revealed that the mean durations of primary submovements and of secondary submovements, not just average total movement times, conform to a square-root approximation of Pitts' law derived from the model. Also, the spatial endpoints of primary submovements have standard deviations that increase linearly with average primary-submovement velocity, and the average primary-submovement velocity influences the relative frequencies of secondary submovements, as predicted by the model. During Experiment 2, these results were replicated and extended under conditions in which subjects made movements without concurrent visual feedback. This replication suggests that submovement optimization may be a pervasive property of movement production. The present conceptual framework provides insights into principles of motor performance, and it links the study of physical action to research on sensation, perception, and cognition, where psychologists have been concerned for some time about the degree to which mental processes incorporate rational and normative rules.