Exp Brain Res (2008) 190:99–103 DOI 10.1007/s00221-008-1497-3
RESEARCH NOTE
Perceptual influences on Fitts’ law A. J. Kovacs Æ J. J. Buchanan Æ C. H. Shea
Received: 10 April 2008 / Accepted: 8 July 2008 / Published online: 23 July 2008 Ó Springer-Verlag 2008
Abstract The linear relationship between movement time (MT) and index of difficulty (ID) for Fitts’ type tasks has proven ubiquitous over the last 50+ years. A reciprocal aiming task (IDs 3, 4.5, 6) was used to determine if an enlarged visual display (visual angle 5.1°, 7.4°, or 13.3°) would alter this relationship. With ID = 6, a condition typically associated with discrete action control, the largest visual display (13.3°) allowed the motor system to exploit features of cyclical action control, e.g., shorter dwell times, more harmonic motion, less time decelerating the limb. The large visual display resulted in a quadratic relationship between MT and ID. For the IDs of 3 and 4.5, the visual displays did not alter the underlying control processes. The results are discussed in terms of the preference of the motor system to assemble movements from harmonic basis functions when salient visual information is provided. Keywords Perceptual-motor processes Rapid aiming Coordination dynamics
Introduction In many voluntary motor skills, speed is typically traded off for accuracy as the difficulty of the task increases. Reciprocal and discrete aiming tasks, often referred to as Fitts’ tasks (Fitts 1954; Fitts and Peterson 1964), have been used to study the control processes governing the speedaccuracy trade-off in rapid aiming movements. Fitts developed an index of difficulty (ID = log2 (2A/W)) to A. J. Kovacs J. J. Buchanan C. H. Shea (&) Department of Health and Kinesiology, Texas A&M University, College Station, TX 77843-4243, USA e-mail:
[email protected]
capture the interactive effect of movement amplitude (A) and target width (W) on movement time (MT). In Fitts’ (1954) seminal work and in a large number of experiments conducted over the last 50 years, one consistent finding has been that MT scales linearly with increasing ID, a ubiquitous relationship which has come to be known as ‘‘Fitts’ Law.’’ Thus, factors that alter this lawful relationship are of great interest to movement scientists. With regard to the speed-accuracy trade-off in rapid aiming, research over the past 30 years has focused on identifying kinematic markers in the aiming trajectory in an attempt to develop more refined models of the speed accuracy tradeoff. For example, in the 1980s and 1990s discrete aiming tasks were used to develop models whereby corrective sub-movements were linked together to insure accuracy (Crossman and Goodeve 1983; Meyer et al. 1988; Plamondon and Alimi 1997). Research from the 1990s and the current decade have used reciprocal aiming tasks to develop models of the non-linear changes in the kinematics of the aiming trajectory as a function of ID, with emphasis placed on clarifying differences in discrete and cyclical actions (Adam et al. 1993; Guiard 1993, 1997; Mottet and Bootsma 1999; Mourik and Beek 2004). In reciprocal aiming tasks, a critical ID value (IDc & 4.44) (Guiard 1997) associated with significant non-linear changes in the kinematics of the aiming trajectory has been identified. With IDs smaller than the IDc, accuracy constraints are minimal and the system exploits stored mechanical energy during limb reversal resulting in relatively short constant dwell times (20–40 ms) across IDs (Adam and Paas 1996; Buchanan et al. 2003; Buchanan et al. 2006). Within this lower ID range, limb motion is harmonic with movement harmonicity values between 0.9 and 1 (H = 1, pure harmonic motion; H = 0, inharmonic motion) and time spent decelerating the limb increases
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from around 45 to 55% of total MT as ID increases from 2 up to the IDc (Buchanan et al. 2006). With IDs larger than the IDc, dwell times increase linearly (Adam and Paas 1996; Buchanan et al. 2006), movement harmonicity drops abruptly and remains between 0 and 0.2 (Guiard 1997; Buchanan et al. 2006), and the proportion of time spent decelerating the limb remains constant at around 60% of MT as ID increases (Buchanan et al. 2004; Buchanan et al. 2006). The greater proportion of time spent decelerating the limb has been linked to feedback processing to insure accuracy (Buchanan et al. 2003, 2004, 2006), and the longer dwell times have been linked to the dissipation of stored muscle energy in order to slow limb reversal (Adam et al. 1993; Adam and Paas 1996; Guiard 1997). In many aiming experiments, the visual–spatial coordinates of the target are isomorphic with the movement constraints, i.e., the visual angle of the target/amplitude configuration scales with the movement constraints defined by ID. As discussed, under such isomorphic conditions the MT/ID relationship is linear, whereas changes in the kinematics of the limb’s trajectory are non-linear. The primary purpose of the present study was to determine what impact a non-isomorphic relationship between the visual display and the limb’s movement would have on the linear and non-linear characteristics of the aiming action as a function of ID. Specifically, we propose that an enlarged visual display will have a larger impact on the kinematics of aiming with ID[IDc than with ID\IDc. The reasoning for our hypothesis is that for IDs \ IDc the perceptionaction system is operating maximally with regard to exploiting limb dynamics during the reversal (Adam et al. 1993; Guiard 1997). For IDs [ IDc, the enlarged visual display will reduce the accuracy constraint on a perceptual level, allowing the system to more readily exploit the limb dynamics during reversal.
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potentiometer (sampled at 200 Hz) attached to the horizontal lever. Participants were seated on a height adjustable chair with the horizontal eye line corresponding with the midway point between two targets projected onto a screen (Fig. 1a). Vision of the right-arm was occluded by a foamboard placed 20 cm above the table top, however, the potentiometer signal was provided as on-line visual feedback in the form of a cursor that represented the flexionextension motion of the elbow. The cursor and two targets were generated with customized software and displayed with a projector mounted above the participant. Movement amplitude was fixed at 32° and three target widths (8°, 2.83°, 1°) were used to create three ID conditions, ID = 3, ID = 4.5, and ID = 6, that spanned the IDc. The coordinates used to project the targets and movement information subtended visual angles of 5.1°, 7.4°, and 13.3°. The 5.1° display represented the approximate visual angle required for participants to view their own movements on the table top, and thus, is referred to as the ‘‘small’’ display. The medium (7.4°) and large (13.3°) visual displays were an enlargement of the amplitude/target dimensions while holding the time dimension constant. Thus, the ID calculated from the projected displays matched that of the actual movement requirements on the table top. The participants’ moved the horizontal lever back and forth so that the cursor on the wall moved between four lines that defined the two targets. Each participant performed three consecutive 15 s trials for each of the nine combinations of ID (3, 4.5, and 6) and display (5.1°, 7.4°, and 13.3°) for a total of 27 trials with the ID 9 Display presentation randomized. Participants were informed to move as fast as possible and reverse their movement within the targets. A 15 s rest interval followed every trial.
Measures and data reduction Method
Participants and procedures Nine right-handed undergraduate students (six females and three males) volunteered to participate in the experiment after reading and signing a consent form approved by the IRB for the ethical treatment of experimental participants. Each participant received class credit. Participants sat at a table with their forearm resting on a horizontal lever that limited elbow motion to flexionextension in the horizontal plane. Elbow flexion moved the lever toward the body and elbow extension moved the lever away from the body, with elbow motion recorded by a
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All data reduction was performed using MATLAB. The potentiometer signal representing the limb’s displacement was filtered (Butterworth, cutoff frequency 10 Hz). Velocity and acceleration signals were computed with each signal filtered (Butterworth, 10 Hz) before performing the next differentiation. All dependent measures were computed on a half-cycle basis with each half cycle representing a different movement direction (extension or flexion). Movement onset and offset was determined with reference to 5% of peak velocity within a given half-cycle. From onset and offset points, movement time was defined in two ways (MT1 and MT2). MT1 was defined as the difference between onset and offset within the same half cycle (MT = onseti-offseti). This method is typical for experiments that separate MT from dwell time. MT2 was determined as the time from onset in one half cycle to onset
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Fig. 1 a Illustration of the top view of the participant and apparatus. Group means plotted as a function of ID and visual angle: b MT1, c MT2, d dwell time, e acceleration and deceleration time, f time to peak velocity (%), g harmonicity, and h functional target width (STD). Means for ID = 6 with different letters are significantly different
in the next half cycle and produces an average MT consistent with dividing the number of cycles completed by the total trial time, in line with Fitts’ original calculation (Fitts 1954). Dwell time was defined as the difference between the onset of one cycle and the offset of the previous cycle (DT = onseti+1-offseti). Acceleration time was defined as the time from movement onset to peak velocity and deceleration time was taken as the time from peak velocity to movement offset. Time windows between a pair of zero crossings in the displacement trace were defined in order to compute an index of movement harmonicity (H) (Guiard 1993, 1997). When an inflection occurred in the acceleration trace within this window, H was computed as the ratio of minimum to maximum acceleration. When a single peak occurred in the acceleration trace within this window the
value of H was set to 1. If the acceleration trace crossed from positive to negative (or vice versa) within this window, the value of H was set to 0. In addition, two measures were determined based on movement endpoint; constant and variable error. Constant error, a measure of endpoint bias, was calculated as the within subject mean difference between movement (reversal) endpoint and the center of the target. Variable error, also referred to as effective target width, was the within subject standard deviation of the signed constant errors. Mean MT1, MT2, dwell time, acceleration time, deceleration time, time to peak velocity (%), harmonicity, constant error, and variable error were analyzed in ID (3, 4.5, 6) 9 Display (normal, medium, large) 9 Movement direction (flexion, extension) ANOVAs with repeated
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measures on all factors. Effect size (gp2) is reported for each significant F value. Duncan’s multiple range tests and simple main effects analysis were performed when appropriate (a = 0.05). The variable movement direction failed to reach significance in any of the reported ANOVAs.
Results The visual displays had minimal influence on limb kinematics for the IDs of 3 and 4.5, but when combined with an ID of 6 the large visual display altered the linear MT/ID relationship and the non-linear features of other kinematic variables. In the MT1 and MT2 data sets (Fig. 1b, c), significant effects of ID, Fs(2,16) = 63.87, g2p = 0.89, and 40.47, g2p = 0.89, ps \ 0.001, and Display, Fs(2,16) = 23.76, g2p = 0.74, and 14.67, g2p = 0.78, ps \ 0.001, and significant ID 9 Display interactions, Fs(4,32) = 5.85, g2p = 0.42, and 11.82, g2p = 0.74, ps \ 0.001 were found. No significant differences were detected across visuals angles for IDs 3 and 4.5. With ID = 6, post-hoc tests revealed that increases in visual angle were associated with a significant shortening of MT1 and MT2. Regression analysis of MT1 and MT2 found significant linear trends (ps \ 0.001) for the small (R2adj = 0.72 and 0.76, respectively), medium (R2adj = 0.76 and 0.78, respectively), and large (R2adj = 0.62 and 0.62, respectively) displays across IDs. A significant quadratic trend, however, was only found in MT1 and MT2 as a function of the large visual display (R2adj = 0.71 and 0.72, respectively, ps \ 0.01). Main effects of ID, F(2,16) = 109.37, gp2 = 0.93, p \ 0.001, and Display, F(2,16) = 3.64, g2p = 0.31, p\0.01, and an ID 9 Display interaction, F(4,32) = 2.88, g2p = 0.19, p\ 0.01, were found in the dwell time data (Fig. 1d). Tests of the interaction did not reveal any differences as a function of visual display for IDs 3 and 4.5. Post-hoc tests revealed that dwell times were significantly different between the large and small display with ID = 6. The analysis of the deceleration time data indicated main effects of ID, F(2,16) = 45.94, g2p = 85, p\0.001, and Display, F(2,16) = 34.76, g2p = 0.81, p \ 0.01, and a significant interaction of ID 9 Display, F(4,32) = 7.03 g2p = 0.46, p \ 0.001 (Fig. 1e). For the IDs of 3 and 4.5, no significant differences between visual displays were found. With ID = 6, post-hoc tests revealed that the absolute time spent decelerating the limb decreased with each increase in visual angle. A main effect of ID was revealed in the acceleration time data set, F(2,16) = 100.50, g2p = 0.92, p \ 0.001) with less time spent accelerating the limb with ID = 3 compared to the IDs of 4.5 and 6. Even though the absolute time spent in acceleration did not reveal an interaction between visual display and ID, the
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analysis of the time spent accelerating the limb as a percentage of MT1 (time to peak velocity (%), Fig. 1f) indicated a significant interaction of ID 9 Display, F(4,32) = 3.15, g2p = 0.28, p \ 0.01. Post-hoc tests failed to detect differences across displays for IDs 3 and 4.5. With ID = 6, post-hoc tests revealed that each increase in visual angle was associated with an increase in the percentage of total MT1 needed to reach peak velocity. The main effects of ID, F(2,16) = 17.77, g2p = 0.69, p \ 0.001, and display, F(2,16) = 12.3, g2p = 0.84, p \ 0.001) were also significant in the proportional data. The analysis of the harmonicity data yielded main effects of ID, F(2,16) = 62.96, g2p = 0.88, p \ 0.001, and Display, F(2,16) = 24.14, g2p = 0.75, p \ 0.01, and a significant interaction of ID 9 Display, F(4,32) = 8.7, g2p = 0.38, p \ 0.001 (Fig. 1g). No significant differences between visual displays were found for IDs 3 and 4.5. Post-hoc tests revealed that each increase in visual angle with ID = 6 was associated with an increase in movement harmonicity. The analysis of constant error failed to detect any main or interactive effects. However, the analysis of variable error (Fig. 1h) detected a main effect of ID, F(2,32) = 85.49, g2p = 0.92, p\0.01, and an ID 9 Display interaction, F(4,32) = 3.91, g2p = 0.29, p \ 0.05. Post-hoc tests failed to detect differences across displays for IDs 3 and 4.5. With ID = 6, post-hoc tests revealed that an increase in visual angle from the small to large display resulted in an increase in endpoint variability.
Discussion The most prominent finding in rapid aiming studies has been the ubiquitous linear relationship between MT and ID, with MTs getting longer as ID increases. In the current experiment, the small and medium visual displays did not alter the linear relationship between MT and ID. However, the large display introduced a strong quadratic trend into the MT/ID relationship for both MT measures. In conclusion, the large visual angle produced an exception to Fitts’ law. Why the violation in Fitts’ law with the large visual display? The lawfulness (i.e., linear slope of MT/ID) of the speed-accuracy tradeoff revealed in rapid aiming actions has been suggested to emerge from harmonic basis functions (non-linear oscillator) that are tailored by boundary conditions and task constraints (spatial accuracy requirements) (Kelso 1992). Theoretical work has shown that discrete and rhythmic actions may emerge from the same dynamical system (non-linear oscillator) based on initial parameter values (Scho¨ner 1990; Jirsa and Kelso 2004). Experimental work has shown that discrete and repetitive aiming actions have unique kinematic signatures (Guiard 1997; Mourik and Beek 2004), and that repetitive aiming
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can be composed of discrete individual segments or continuous cyclical actions as a function of a critical ID boundary (Guiard 1997; Buchanan et al. 2006). Thus, Fitts’ law was violated because the large visual angle with ID = 6 reduced the spatial accuracy constraint such that the motor system parameterized the aiming action in a manner more consistent with a cyclical action with ID B IDc, than as a series of discrete segments for ID C IDc. Evidence for the parameterization of the aiming action based on a smaller ID compared to the actual ID comes from three main findings. First, the large display and ID = 6 condition produced harmonicity values[0.5, consistent with research linking such harmonicity values to cyclical aiming actions that typically occur for IDs \ IDc (Guiard 1997; Buchanan et al. 2006). Moreover, the visual displays had no impact with ID = 3 (\IDc), consistent with recent findings suggesting that cyclical actions are more efficient than discrete actions (Smits-Engelsman et al. 2006). Second, dwell times for the large display with ID = 6 were reduced to values near those reported for the IDc (Buchanan et al. 2006), suggesting that the motor system was able to exploit stored mechanical energy during limb reversal, making the motion more cyclical. Third, the time spent decelerating the limb was reduced significantly from the small to large display with ID = 6, with an accompanying increase in the proportional time to peak velocity from 33% for the small display to 44% for the large display, again a shift in values to ones consistent with the IDc (Buchanan et al. 2006). Reduced deceleration and dwell times are thought to suggest reduced reliance on feedback based corrections to achieve the required accuracy demands (Buchanan et al. 2004, 2006). However, it must be noted that a considerable amount of MT was still devoted to the deceleration phase in the ID = 6 compared to the ID = 3 condition with the large visual display; implying that feedback was essential in allowing the violation in Fitts’ law to occur. Adam et al. (2006) have also recently demonstrated a perceptual based violation of Fitts’ law. When a target was presented in a row of targets versus as an independent target, a shorter MT only occurred for the farthest target (ID = 5.25) in the row. This shows that perceptual context can influence motor performance under certain conditions. Over 30 years ago, Langolf et al. (1976) found substantial reductions in MT for finger and wrist movements compared to arm movements for IDs [ 4. The standard textbook interpretation of this result is that the wrist and fingers can produce more precise movements. However, the finger and wrist trials were viewed under a 7 power microscope while the arm movements were produced without enhanced vision. It is entirely possible that the shorter MTs for the higher IDs for the finger and wrist movements resulted from the perceptual display rather than differences in limb precision. Thus, the bottom line is that salient perceptual
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information (Mechsner et al. 2001) that reduces accuracy constraints can allow the motor system to exploit more efficient modes of control, in the current case harmonic basis functions (Kelso 1992), that lead to improved performance, i.e., shorter MTs without a decrease in accuracy.
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