to other evidence according to which acquisition of these two aspects of motor timing involves different learning mechanisms. Whereas relative timing gained from imme-diately preceding haptic demonstration, but revealed no practice-related improvement in the presence of haptic guidance, the opposite pattern of results was found for the shape error. this finding is consistent with the claim that haptic demonstration is particularly efficient with respect to relative timing, but not with respect to spatial movement characteristics.
haptic guidance is a time-honored procedure to support motor learning, which has been studied for about a century (cf. holding and Macrae 1964). Its advantages have gener-ally been seen in providing the learner with the feeling of the correct movement and in preventing the risks that can be associated with the production of unskilled movements. Recent developments in robotics have led to a plethora of robotic devices for haptic guidance (Marchal-crespo and Reinkensmeyer 2009). the primary target is rehabilitation (e.g., Kahn et al. 2006; Prange et al. 2006; Reinkensmeyer et al. 2004; takahashi et al. 2007). however, haptic guid-ance by robotic devices has also been explored for motor learning of healthy individuals (cf. Reinkensmeyer and Pat-ton 2009, for review). Overall, the evidence of benefits as compared with other types of practice is quite mixed.
Regarding the learning of novel visuomotor transforma-tions, practice with haptic guidance added to visual feed-back resulted in poorer learning of a visuomotor rotation
Abstract haptic guidance has been shown to have both facilitatory and interfering effects on motor learning. Inter-fering effects have been hypothesized to result from the particular dynamic environment, which supports a passive role of the learner, and they should be attenuated by fad-ing guidance. Facilitatory effects, in particular for dynamic movement characteristics, have been hypothesized to result from the high-quality information provided by haptic dem-onstration. If haptic demonstration provides particularly precise information about target movements, the motor system’s need for such information should more likely increase in the course of motor learning, in which case growing guidance should be more beneficial for learning. We contrasted fading and growing guidance in the course of learning a spatio-temporal motor pattern. to stimulate an active role of the learner, practice trials consisted of three phases, a visual demonstration of the target movement, a guided reproduction, and a reproduction without haptic guidance. Performance was assessed in terms of variable duration errors, relative-timing errors, variable path-length errors, and shape errors. Motor learning with growing and fading guidance turned out to be largely equivalent, so that the notion of an increasing optimal precision of haptic demonstrations, which matches a demand of increasingly precise information on the target movement, found no sup-port. Duration errors declined only with fading, but not with growing guidance. Relative timing revealed a benefit of immediately preceding haptic demonstration, but learn-ing was not different between the two practice protocols. this contrast between absolute and relative timing adds
h. heuer (*) · J. lüttgen IfaDo - leibniz Research centre for Working Environment and human Factors, ardeystraße 67, 44139 Dortmund, Germanye-mail: [email protected]
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than practice without haptic guidance (heuer and Rapp 2011; Van asseldonk et al. 2009). Even when haptic-guid-ance trials were mixed with active-movement trials, the demonstration of the correct movements in the guided tri-als produced no benefits (heuer and Rapp 2012). the det-rimental effects of haptic guidance survived a change of the task instruction from learning a visuomotor rotation to learning to make movements at an angle to the visual tar-gets (heuer and Rapp 2014); in these two tasks, the correct movements for each target were identical.
When the learning of spatio-temporal trajectories was tested rather than the learning of only spatial movement features, primarily dynamic or temporal movement charac-teristics profited, but not spatial ones (Feygin et al. 2002; lüttgen and heuer 2012a). For tasks such as handwriting, in which temporal characteristics are tightly interrelated with spatial ones, the enhancement of motor timing can also result in a benefit for spatial movement features (e.g., Basteris et al. 2012). In general, many instances of facili-tative effects of haptic guidance on motor learning seem to involve dynamic movement characteristics (e.g., Blu-teau et al. 2008; Grindlay 2008; lüttgen and heuer 2012b, 2013; Marchal-crespo and Reinkensmeyer 2008; Marchal-crespo et al. 2013; Milot et al. 2010).
In addition to possible long-term learning effects, the benefits of haptic guidance for motor timing are immediate. For example, lüttgen and heuer (2013) found an imme-diate benefit of haptic guidance on the relative timing of discrete circle drawing. however, with repeated cycles of demonstration and reproduction of the target movement, there was no cumulative advantage of haptic-guidance practice. thus, an immediate benefit of a haptic demonstra-tion on the production of a movement is not necessarily fol-lowed by a cumulative, longer-term benefit.
the findings of costs and benefits of haptic guidance with respect to motor learning suggest a combination of facilitating and interfering mechanisms. Facilitating mech-anisms seem to dominate with respect to temporal move-ment characteristics, whereas interfering mechanisms seem to dominate with respect to spatial movement characteris-tics. the balance of facilitating and interfering mechanisms should depend on further characteristics of the motor task and on the conditions of learning.
Mechanisms that produce detrimental effects of haptic guidance are at least of two kinds. First, haptic guidance creates a particular dynamic environment during prac-tice to which the motor system adapts (cf. Novakovic and sanguineti 2011). In tests without haptic guidance, afteref-fects of this adaptation interfere with performance. second, the dynamic environment created by haptic guidance can induce a rather passive role of the motor system: it reduces the demands of active preparation and control of the move-ments. a reduction in such demands, for example, has been
invoked to account for the contextual interference effect, the poorer learning (but better performance) with task rep-etitions than with mixtures of different task variants (cf. Magill and hall 1990).
a straightforward means to avoid the detrimental effects of haptic guidance is fading as performance improves. thereby, adaptation to the unusual dynamic environment should be washed out gradually, and an active role of the learner should be gradually encouraged or even enforced. Fading is a particular instance of the more general principle of assistance as needed. this type of assistance has been rather well studied for rehabilitation (e.g., casadio et al. 2009; Emken et al. 2007; Vergaro et al. 2010). Fading guid-ance has also been applied to the motor learning of healthy adults (e.g., chen and agrawal 2013; Marchal-crespo et al. 2013; Marchal-crespo et al. 2010). typically, the fading of guidance involves the decline of supportive forces from trial to trial. however, a different type of fading, in which the proportion of supported trials is reduced, has similar effects (cf. Winstein et al. 1994).
Facilitative mechanisms of haptic guidance are related to the demonstration of the target movement, that is, to the processing of the respective proprioceptive informa-tion. During demonstration, the learner can be passive, so that movements are driven by the guiding forces only, but the learner can also be active in combination with stronger or weaker external forces that support the precision of the movement, but do not enforce it. With respect to the dem-onstration of the target movement, learning with haptic guidance appears similar to observational learning where the target movement is demonstrated visually.
the very fact that benefits of haptic guidance accrue primarily for dynamic movement characteristics has been taken to suggest that these profit more from propriocep-tive target information than from visual target information, whereas for spatial movement characteristics this is just the opposite (lüttgen and heuer 2012a, 2013; Marchal-crespo et al. 2013). Beyond the findings on haptic guidance, how-ever, we are not aware of systematic comparisons of hap-tic and visual demonstrations of temporal movement char-acteristics. Findings on the visual and auditory pacing of rhythmic finger tapping (e.g., Merchant et al. 2008) suggest that visual demonstration of temporal movement character-istics is comparatively poor, at least poorer than auditory demonstration. In addition, Jäncke et al. (2000) identified different brain structures activated by rhythmic tapping with visual and auditory pacing. they noted that the brain structures activated by the auditory-pacing task suggest an internal control of the motor timing that is closely matched to the external pacing, whereas the brain structures acti-vated by the visual-pacing task suggest a continued dependence on the external pacing, without a correspond-ing internal rhythm being generated. In more general terms,
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different types of external timing signals have tighter or less tight links to motor timing. Perhaps, the link between proprioceptive and motor timing is particularly tight, at least tighter than the link between visual and motor timing.
the notion that dynamic characteristics of the target movement are particularly efficiently communicated by haptic demonstration can be taken to suggest that growing guidance might be even more beneficial than fading guid-ance. By growing guidance, we refer to an increase in sup-portive forces in the course of practice. the hypothesis of superior learning with growing guidance appears far-fetched at first glance because it is at variance with the broadly accepted advantages of fading guidance. Of course, poten-tial benefits of a less precise haptic guidance early in prac-tice and a more precise guidance later on could be masked by the costs that accrue because participants adapt to the particular dynamic environment and adopt a passive role in movement preparation and control. however, such costs should be reduced or even be abolished by mixing guided trials with unguided active reproductions of the target move-ment (cf. Winstein et al. 1994). In the present study, we employed this measure to unmask a possible advantage of growing over fading guidance. More precisely, in each prac-tice trial, the spatio-temporal pattern of the target movement was presented visually first, thereafter it was produced with haptic guidance that faded or grew from trial to trial, and finally it was produced without guidance.
there are at least three considerations, which suggest that the hypothesis of better motor learning with growing guidance than with fading guidance is worthy of test. all of them converge on the notion that in the course of learn-ing, the motor system demands progressively more precise information on the target movement, as it is provided by growing guidance. First, a popular broad conception of motor learning (Fitts 1964; Fitts and Posner 1967) posits an initial cognitive phase in which the basic task require-ments are learned. For example, a simple spatio-temporal target pattern as in the present study could become repre-sented cognitively as “move the hand inward with a rapid strong excursion to the right, followed by an oscillation with smaller amplitude, a leftward drift, and a frequency which is fast-slow-fast.” the acquisition of such a rep-resentation, which captures qualitative characteristics of the target movement, does not require precise quantitative information. however, precise information should become essential later in practice as the reproductions of the target movement become more precise.
second, some studies show that the learning of spatio-temporal motor patterns progresses from global character-istics to details. More formally, the acquisition of spatio-temporal patterns has been conceptualized as a progression from low-frequency Fourier components to high-frequency components, analogous to a sequential Fourier synthesis
(Franks and Wilberg 1982; Marteniuk and Romanow 1983), though this kind of progression has not invariantly been found (e.g., stanley and Franks 1990). Whereas the learning of low-frequency components should not require precise information on the target pattern, the learning of high-frequency components should. the reason is that low-frequency components can be demonstrated even with noisy timing information, whereas the demonstration of high-frequency components and thus of the details of the target pattern requires higher temporal precision.
Finally, the third consideration refers to the discrepancy between the target movement and its reproduction. accord-ing to the notion of optimal challenge points (Guadagnoli and lee 2004), there is an optimal discrepancy: With a too low discrepancy, there is only little information that could be used for learning, and with a too high discrep-ancy, there should be an excess of information that over-loads the information-processing capabilities of the learner. the notion of optimal challenge points has been invoked to account for the benefits of fading guidance (e.g., Marchal-crespo et al. 2013). haptic guidance reduces the discrep-ancy between movement production and target movement by way of reducing the difficulty of the task, and fading guidance serves to maintain a sufficient discrepancy as performance improves in the course of practice. however, with sequences of guided and unguided movements, as in the present study, the situation may be different. there is not only a discrepancy between the target movement and its guided reproduction, but also a discrepancy between the guided and the unguided reproduction. With fading guid-ance, this discrepancy is quite strong early in practice and vanishes later on. With growing guidance, in contrast, the discrepancy between guided movements and reproductions is smaller than with fading guidance early in practice, but larger late in practice. this more intermediate discrepancy might be a better approximation to the optimal challenge point so that, to the extent that the discrepancy is relevant for learning, growing guidance would be advantageous.
taken together, these considerations suggest the hypoth-esis that more precise haptic information on the target movement later in the course of practice, as it is provided by growing guidance, might facilitate learning in compari-son with precise haptic information early in the course of practice, as it is provided by fading guidance. to test this hypothesis, we compared the learning of the spatio-tem-poral characteristics of a target movement with fading and growing haptic guidance. the target movement was the same as used by lüttgen and heuer (2012a), for which haptic demonstration—as compared with visual demon-stration—was beneficial for learning temporal movement characteristics. In the present study, in each practice trial, the target movement was visually presented first (visual demonstration), then reproduced with haptic guidance
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(haptic demonstration), and finally reproduced without any guidance. In one of the two groups of the participants, hap-tic guidance during the haptic demonstration faded in the course of practice, in the other group it grew.
Methods
Participants
Participants were assigned in turn to two experimental groups, the fading-guidance group and the growing-guid-ance group. In the fading-guidance group, there were 14 female and 6 male participants, aged 20–30 years. In the growing-guidance group, there were 11 female and 6 male participants, aged 20–27 years. For five additional partici-pants, the experiment was not finished because of techni-cal problems or because the participants failed to appear for the second session of the experiment. the data of two addi-tional participants of the growing-guidance group were not included because too many guided movements were exces-sively long or because of excessive variability of move-ment duration in a test block of trials (see below). all par-ticipants gave signed informed consent before the start of the experiment that was done in accordance with the ethical standards laid down in the Declaration of helsinki 1964.
apparatus
the apparatus was basically the same as used by lüttgen and heuer (2012a). a digitizer (Wacom Intuos 4), a robotic device (Phantom Premium 1.5 a, sensable technologies), and a monitor (Iiyama Vision Master Pro 451) were placed on a table. the monitor was in a somewhat raised posi-tion so that the view of the screen was not obstructed by the Phantom, which was placed between the digitizer and the monitor. the final link of the robot arm was custom-made. It carried a hole into which the tip of the digitizer pen was inserted. the pen was held by a rubber ring inside the wall of the hole, so that it could be tilted freely in all directions. For movements in the horizontal plane, it was rigidly linked to the robot arm. Participants held the pen with a tripod grip. to avoid injuries in case of software fail-ures and uncontrolled movements of the robot arm, there was a safety barrier between it and the participant. the position of the tip of the digitizer pen was sampled with 100 samples/s. Positions on the digitizer were mapped 1:1 to positions on the monitor.
task and experimental conditions
Participants had to learn a two-dimensional target move-ment as shown in Figure 2. It was constructed in four steps.
First, the x–y coordinates of start, end, and five reversal positions were defined. second, these seven points were concatenated by segments of sine functions. third, the sequence of x–y coordinates was transformed into posi-tion–time curves x(iΔt) and y(iΔt) for a total duration of 5 s, Δt = 10 ms, i = 1, …, n, n = 500. Fourth, the time axes of the position–time curves were nonlinearly trans-formed such that the initial and final parts were speeded up and the central part of the pattern slowed down. such a nonlinear transformation of the time axis of an otherwise roughly regular amplitude-modulated oscillation serves to make the reproduction of the target movement difficult, in particular the reproduction of its timing (cf. heuer and schmidt 1988).
Each practice trial consisted of three phases. In the first phase, the target movement was demonstrated visually by way of a marker that moved downward on the monitor with the horizontal excursions corresponding to the x positions of the target pattern. In the second phase, the target move-ment was demonstrated haptically. Participants had been instructed to reproduce the visually presented target move-ment, for which they would be supported by the robot arm. the support would be strong (weak) early in practice and become weaker (stronger) later on. they were guided along the correct path with the correct timing by a moving point attractor. the force toward the correct position depended on the distance d (in mm) of the recorded position of the digitizer pen from the correct position, F = k · d, with an upper limit of 5 N. across the 80 practice trials of the fad-ing-guidance group, the stiffness parameter k declined from .5 N/mm in the first trial to 0 N/mm in trial 80 in equal steps of .006329 N/mm, whereas in the growing-guidance group, k increased from 0 to .5 N/mm with the same step size. Finally, in the third phase of each practice trial, partic-ipants had to reproduce the target movement without haptic guidance.
the force driving the hand to the correct position at each point in time was proportional to the distance from that position, and there was no velocity-dependent modula-tion. however, when the robot arm was connected with the handheld pen, the damping was sufficient to avoid vibra-tions. the linear increase and decline of the stiffness was a pragmatic choice. For fading guidance, an initially rapid decline that reaches an asymptote—roughly proportional to the decline of errors during practice—is more common. however, as practice curves tend to be different for differ-ent performance measures, which are nonlinearly related to each other, an exact proportionality of guidance to different measures of performance is impossible. For the purpose of the present study, the dynamics of fading are not critically important, but the contrast with growing guidance matters. therefore, we chose simple linear functions for the decline and increase in stiffness.
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Design and procedure
In a dimly lit and quiet room, participants were seated at the table on which the digitizer, the Phantom, and the mon-itor were placed. they wore earphones that shielded them from any residual auditory stimuli such as the drawing noise, and that served to present tones. after the instruction had been read, three familiarization trials were performed. the target movement in these trials had a circular path and a variable tangential velocity. this target movement was presented, first, visually and, second, haptically. thereafter, it had to be reproduced. across the three familiarization tri-als, the stiffness of guidance increased, being k = .05, .25, and .5 N/mm.
the experimental protocol is illustrated in Fig. 1. Prac-tice was organized in 8 blocks of 10 trials each, with breaks of 30 s between blocks. ten minutes after the end of prac-tice, a test block of 10 trials (immediate test) followed, in which the target movement had to be reproduced without preceding visual or haptic demonstration. In a second ses-sion about 24 h later, a delayed test followed, consisting again of one block of 10 trials without visual or haptic demonstration.
Each practice trial consisted of three phases, which were indicated by a text at the right lower edge of the monitor, saying (in German) “demonstration” (“Demonstration”), “with guidance” (“mit Unterstützung”), or “without guid-ance” (“ohne Unterstützung”). the first phase of a practice trial (visual demonstration) started when the participant had been in the start position for 2 s. the start position was marked by a cyan outline circle of 7 mm diameter. the position of the digitizer pen was indicated by a cursor, a filled green circle of 5 mm diameter. When the green cur-sor had been moved to the start position, the cyan outline circle was filled. two seconds later, the filled cyan marker started the visual demonstration of the target movement. Following a waiting period of 500 ms after the end of the demonstration, the start circle re-appeared and the haptic demonstration began 2 s after the participant had entered the start position again. Its beginning was signalled by a short tone presented via the headphones. at the same time, the filled cyan circle was replaced by the green cursor, which remained visible during the guided movement. the end of the guided movement was also signalled by a short tone. It was defined by distances below .2 mm between
successively sampled positions for 500 ms. Finally, after another waiting period of 500 ms and another 2 s of the cursor in the start position, the tone signalled the time to reproduce the movement pattern without haptic guidance. the green cursor remained visible during the unguided reproduction. the end of the movement was defined in the same way as in the second phase of a practice trial.
Immediately after the unguided reproduction, knowledge of the results was provided for 3 s. the target path (green) was presented together with the path of the reproduction (yellow) and a number between 0 and 100, which indicated the accuracy of timing. this number was 100 times the cor-relation between the resultant velocity signals of the target movement and the reproduction, with the reproduction hav-ing been scaled to the duration of the target movement.
In the test blocks 10 min after the practice period (immediate test) and on the next day (delayed test), only reproductions without guidance, corresponding to the third phase of practice trials, were performed. there was neither a visual nor a haptic demonstration, and after the end of each reproduction, no knowledge of the results was provided.
Data analysis
We analyzed the guided and unguided reproductions of the target movement. the position–time curves were low-pass filtered (fourth-order Butterworth, 8 hz, dual-pass). For each movement, the tangential velocity was computed (two-point central-difference algorithm) and filtered again. start and end of each movement were defined by velocity exceeding 65 mm/s in a forward scan and 80 mm/s in a backward scan; these thresholds were chosen because they were close to the initial and final velocities of the target movement.
Both the guided and unguided reproductions of the target movement were screened for irregularities. trials were discarded from further analysis when at least one of the following criteria was satisfied: (1) the duration of the recorded movement was shorter than 2 s or longer than 10 s, (2) velocity was so low that the thresholds for the start or the end of the movement were not reached, (3) the duration of a guided reproduction deviated 500 ms or more from the duration of the target pattern. the data of one participant of the growing-guidance group were not
Fig. 1 Experimental procedure. Eight blocks of 10 practice trials each were followed by an immediate and a delayed test
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included in the analyses because 63 % of the trials were considered invalid. More specifically, the guided reproduc-tions deviated in 71 % of the practice trials by more than 500 ms from the target duration. thus, haptic demonstra-tion in general was quite inaccurate. For the remaining par-ticipants, the percentage of discarded trials was 3.9 %, with individual percentages ranging between 1.0 and 9.0 %.
For each of the guided and unguided movements per-formed by the participants, we focussed on four dependent variables to which we refer as duration error, path-length error, relative-timing error, and shape error. two of these variables measured dynamic or temporal movement charac-teristics—duration error and relative-timing error, whereas the other two variables measured spatial movement char-acteristics—path-length error and shape error. One of the two variables of each type assessed overall scaling
errors—duration error and path-length error, whereas the other of the two variables of each type assessed errors that persist even when duration and size are scaled to be the same for the target movement and its reproduction.
the computation of the dependent variables is illus-trated in Fig. 2. the low-pass filtered position–time curves x(t) and y(t) are shown in the leftmost column of graphs (Graph 1b, c) together with the movement path (Graph 1a). Duration error was defined as the difference between the duration of the reproduction and the target movement. In the example of Fig. 2, the duration error was −400 ms, that is, the reproduction (dotted lines in Graph 1b, c of Fig. 2) ended 400 ms before the target movement (continuous lines in Graph 1b, c of Fig. 2). Both for the target movement and each reproduction, path lengths were computed by way of summing the distances between successively sampled
Fig. 2 Illustration of the analysis of individual trials. Graphs 1a, b, and c show the path (x–y) and the position–time curves x(t) and y(t) of the filtered target movement (continuous line) and its reproduction (dotted line). Graphs 2a, b, and c show the same data after scaling the duration and the path length of the reproduction to the duration and path length, respectively, of the target movement and after align-
ing the means of the x and y positions. Graph 3a shows the same paths as Graph 2a, with lines connecting the positions matched by dynamic time warping; in graph 3b the temporal shifts between the matched positions are shown, and in graph 3c the distances between the matched positions
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positions. Path-length error was the difference between the path lengths of the reproduction and the target move-ment. In the example of Fig. 2, the path-length error was 15.3 mm, that is, the path of the reproduction (dotted line in Graph 1a of Fig. 2) was 15.3 mm longer than the target path (continuous line in Graph 1a of Fig. 2).
after the determination of the temporal and spatial scaling errors, both the durations and path lengths of the reproductions were scaled to be identical to the duration and path length of the target movement. For this purpose, the units of the time axis and the distances between succes-sive samples of the reproductions were proportionally com-pressed or expanded. In addition, the x and y positions were expressed as deviations from their means so that systematic spatial offsets between the movement paths were removed. the resulting movement paths and position–time curves are shown in the middle column of Fig. 2 (Graph 2a, b, and c).
to obtain the measures of temporal and spatial errors of the reproductions after scaling them to the duration and path length of the target movement, we used dynamic time warping. this is a method that has been developed primar-ily for speech recognition (e.g., Rabiner et al. 1978). It is now in rather widespread use for the comparison of time series, though it is not common for the analysis of kin-ematic data. Basic principles and several variants of the method are described in many publications (e.g., Di Brina et al. 2008; Keogh and Ratanamahatana 2005). We used MatlaB function dtw (http://www.mathworks.com/matlabcentral/fileexchange/6516-dynamic-time-warping; down-loaded July 4, 2013), which was only slightly modified as described below.
the essence of dynamic time warping is a local scaling of the time axis by the criterion of minimizing the total dis-tance between two time series. We applied the procedure after global (proportional) scaling. thus, the variations of the local scaling represent the deviations from the correct relative timing of the reproductions. the procedure starts with a matrix of the distances between all positions of the target movement and all positions of the reproduction. For the computation of this matrix of distances between sam-ples of two-dimensional time series, we modified the Mat-laB function dtw, which otherwise computes distances between samples of unidimensional time series. Based on these distances, a warping path (or matching path) is deter-mined that assigns indices (and thus times) of the one time series to indices (and thus times) of the other time series. this process has to satisfy certain constraints. In our case, these were (1) the boundary condition (the warping path starts with assigning the first elements of the two time series and ends with assigning the last elements), (2) the continuity condition (no index in any of the two time series is skipped), and (3) the monotonicity condition (indices of both time series do not decline).
the results of the dynamic time warping are illustrated in the right column of graphs in Fig. 2. In Graph 3a, the normalized paths of the target movement and the reproduc-tion are shown (as in Graph 2a), with additional lines that link matched positions of the two curves as specified by the warping path (more precisely, its 1., 11., 21., … ele-ment). Graph 3b of Figure 2 shows the local time shifts Δt. these are the differences between the indices of the matched positions of the two time series as specified by the warping path, multiplied by the sampling interval and thus expressed in ms. (In using this unit, we take the rescaled reproduction to be “really” of the same length as the target movement. alternatively, the local time shifts can also be expressed as proportion of the movement duration by divid-ing them by the total target duration of 5,000 ms.) Graph 3c of Figure 2, finally, shows the remaining distances Δp between the matched positions. (again, the unit mm—in a strict sense—holds only for the target pattern and can be transformed to a proportional deviation by dividing it by the path length of the target movement of 239 mm.) We defined the relative-timing error by the standard deviation of the local time shifts Δt shown in Graph 3b of Fig. 2. In the example, it was 388 ms. the shape error was defined as the mean of the remaining deviations Δp shown in Graph 3c of Fig. 2; for the example, it was 6.6 mm. (For the normalized time series before dynamic time warping, as shown in the middle column of Fig. 2, the mean deviation of the positions of the reproduction from those of the target movement was 23.4 mm).
the four dependent variables, computed for guided and unguided reproductions of each trial, were pooled for each block of trials. For both duration errors and path-length errors, we computed the interquartile range; thus, for each block, we report variable errors of duration and path length. For the relative-timing error and shape error, we computed the median. We used interquartile ranges and medians rather than standard deviations and means because of their higher robustness against outliers that had passed the quite relaxed criteria used in screening for irregularities of the data. Nonetheless, there was one participant of the growing-guidance group with a (variable) duration error of 4,860 ms in the immediate test, which deviated from the mean of all participants in that test by more than 5 standard deviations. all data of this participant were neglected in the analyses.
the dependent variables computed for each block of tri-als were subjected to aNOVas and planned contrasts as specified in the “Results” section. Degrees of freedom were Greenhouse–Geisser corrected when appropriate, but we report the uncorrected degrees of freedom together with the Greenhouse–Geisser epsilon. In a final step, which sum-marizes the results for the unguided movements, we esti-mated learning, immediate benefits of haptic guidance, and
forgetting in the two practice conditions for the different dependent variables by means of linear regression analyses.
Results
Guided movements
the group means of the (variable) duration error, (variable) path-length error, relative-timing error, and shape error of guided movements are shown in Fig. 3. the overall pat-tern was quite uniform. In the fading-guidance group, errors increased across practice blocks, but in the growing-guidance group they declined. Even though the stiffness of guidance declined and increased linearly in the two groups, the variation of the mean errors was clearly nonlinear in that errors increased most strongly as the stiffness of haptic guidance approached zero.
aNOVas with the between-participant factor group and the within-participant factor block of trials revealed signifi-cant interactions of the factors group and block for all four
dependent variables, F(7,245) = 26.7, p < .01, ε = .22, for the duration error, F(7,245) = 42.2, p < .01, ε = .34, for the path-length error, F(7,245) = 71.9, p < .01, ε = .45, for the relative-timing error, and F(7,245) = 135.7, p < .01, ε = .34, for the shape error. Because of the non-linear changes in the errors across blocks of trials in both groups, the means of both groups varied across blocks in a U-shaped form. the main effect of block was significant for all four dependent variables, F(7,245) = 14.2, p < .01, ε = .22, F(7,245) = 23.3, p < .01, ε = .34, F(7,245) = 16.9, p < .01, ε = .45, and F(7,245) = 39.3, p < .01, ε = .34, respectively. For all four error measures, fading-guidance group was slightly superior to growing-guidance group, but this main effect reached statistical significance only for the duration error, F(1,35) = 4.2, p < .05.
the data shown in Fig. 3 are dominated by the effects of fading and growing guidance. however, even for the guided movements, participants had been instructed to reproduce the target movement. therefore, we tested for possible practice effects that might add to the effects of guidance. For this purpose, we analyzed performance in
Fig. 3 Mean variable dura-tion error (a), mean variable path-length error (b), mean relative-timing error (c), and mean shape error (d) of guided movements during practice. Error bars represent standard errors
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the first and last blocks of practice and compared blocks with the same stiffness of guidance, but different levels of practice. the weak-guidance block was the first one in the group with growing guidance, but with fading guid-ance it was the last one. therefore, in this block, practice benefits should result in superior performance of the fad-ing-guidance group. In contrast, the strong-guidance block was the last one with growing guidance and the first one with fading guidance. therefore, practice benefits in this block should result in superior performance of the grow-ing-guidance group. Overall, practice benefits should thus be revealed by better performance of the fading-guidance group in weak-guidance blocks and better performance of the growing-guidance group in strong-guidance blocks. the respective means of the four dependent variables are shown in table 1.
We ran four aNOVas with the between-participant fac-tor group and the within-participant factor stiffness of guid-ance (weak vs. strong guidance). the relevant interaction of these two factors, which indicates a practice benefit in guided trials, turned out to be significant only for the shape error, F(1,35) = 7.5, p < .01. For none of the other depend-ent variables, it approached statistical significance.
Unguided movements
the group means of the duration error, path-length error, relative-timing error, and shape error for the unguided movements in the practice blocks, the immediate test block (10 min after the end of practice), and the delayed test block (on the day following practice) are shown in Fig. 4. Even though the unguided movements themselves were produced under identical conditions in all practice and test trials, they were preceded by a guided movement and a vis-ual demonstration of the target movement in the practice trials, but not in the test trials. Moreover, in the fading-guid-ance group, the strength of guidance declined in the course of practice, whereas it increased in the growing-guidance group. the means shown in Fig. 4 are most likely affected by the preceding guided movements because haptic demon-strations can have immediate effects on reproductions. to take these complications into account, we analyzed the data
by means of a series of contrasts. We focussed on the first and last practice block, the immediate test, and the delayed test—the means are shown in table 2a, and the planned contrasts were based on the mean squares of the aNOVas with 2 groups × 4 blocks of trials.
the first set of contrasts tested learning and forgetting separately for each group and each dependent variable. to test learning, we contrasted performance in the first practice block with performance in the two tests. these contrasts are conservative because performance in the first practice block, but not the tests, could profit from the preceding vis-ual demonstration of the target movement, and in the fad-ing-guidance group from the preceding guided movement. From Fig. 3 and the means of table 2a, it is evident that there was a rather consistent practice effect with only a sin-gle exception: for the duration error, the practice effect was significant for the fading-guidance group, F(1,35) = 15.8, p < .01, but not for the growing-guidance group, F < 1. For all other dependent variables, both groups produced signifi-cant contrasts, F(1,35) = 14.6, p < .01, and F(1,35) = 15.6, p < .01, for the path-length error, F(1,35) = 8.5, p < .01, and F(1,35) = 18.1, p < .01, for the relative-timing error, and F(1,35) = 21.4, p < .01, and F(1,35) = 22.3, p < .01, for the shape error. We repeated these contrasts separately for the immediate and the delayed test and found the same pattern of significant and nonsignificant contrasts for each of the two tests as for both of them. thus, even with the conservative estimates, there was clear evidence of learning the pattern, with the single exception that there was no evi-dence of learning the total duration with growing guidance during practice.
to test forgetting, we contrasted performance in the immediate test with performance in the delayed test. With one exception, there was no reliable decline of performance overnight. the exception was the shape error in the grow-ing-guidance group, F(1,35) = 4.8, p < .05.
the second set of contrasts tested group differences of learning and forgetting. to compare learning between the two groups, we contrasted their mean performance in the immediate and delayed tests, that is, their final per-formance. Performance in the first practice block was neglected in these analyses because it could be different
Table 1 Mean dependent variables for the guided movements with strong and weak guidance in the fading-guidance group and the growing-guidance group
In italics are the means of the last practice blocks (weak guidance in the fading-guidance group, strong guidance in the growing-guidance group)
Fig. 4 Mean variable duration error (a), mean variable path-length error (b), mean relative-timing error (c), and mean shape error (d) of unguided movements during practice, immediate (imm.), and delayed (del.) tests. Error bars represent standard errors
Table 2 (a) Observed means for the unguided movements in the first and last practice block, the immediate test, and the delayed test in the fading-guidance group and the growing-guidance group, (b) predicted means as derived from the regressions of the observed means on the reliable effects (L learning effect, F forgetting effect, S immediate effect of guidance, B initial performance; effects not listed were set to 0)
between the two groups, resulting from the immediate effects of strong guidance, which were tested with the third set of contrasts. to compare forgetting in the two groups, we contrasted the changes from the immediate to the delayed test. None of these contrasts reached statistical sig-nificance, and only one of the learning contrasts and one of the forgetting contrasts approached significance. With respect to learning, we had found a practice effect for the duration error in the fading-guidance group, but not in the growing-guidance group. the contrast between the two groups was almost significant, F(1,35) = 3.6, p = .07. With respect to forgetting, we had found an overnight increase in the shape error after practice with growing, but not with fading guidance. again, the difference between the two groups approached statistical significance, F(1,35) = 3.6, p = .07.
the third set of contrasts tested the presence of immedi-ate benefits of haptic guidance. In the first practice block, performance of the fading-guidance group, but not of the growing-guidance group, could benefit from the immedi-ately preceding accurate guided movements, and in the last practice block performance of the growing-guidance group could profit. thus, immediate benefits of haptic guidance should give rise to interaction contrasts for the four depend-ent variables, showing an advantage of the fading-guidance group in the first practice block, but an advantage of the growing-guidance group in the last block of practice. In addition, immediate benefits of guidance should give rise to a decline of performance from the last practice block to the immediate test in the growing-guidance group, where the last practice block, but not the test, could profit from the immediately preceding guided movements. With the exception of the relative-timing error, these contrasts did not approach statistical significance. For the relative-timing error, the increase from the last practice block to the imme-diate test in the growing-guidance group was significant, F(1,35) = 18.6, p < .01, and so was the interaction con-trast to compare the group differences in the first and last practice block, F(1,35) = 4.7, p < .05. thus, the immediate effect of the preceding haptic guidance was limited to the relative-timing error.
the analyses of the unguided movements revealed learn-ing, forgetting, and immediate benefits of haptic guidance. learning was equally present in both groups for all depend-ent variables, with the exception of the duration error in the growing-guidance group for which learning was absent. Forgetting was absent in both groups for all dependent vari-ables except for the shape error in the growing-guidance group. Finally, an immediate benefit of haptic guidance was seen only for the relative-timing error. It should improve the relative timing after guided movements with strong guidance, that is, in early practice in the fading-guidance group and in late practice in the growing-guidance group.
We used these three components to reproduce the means of table 2a by means of linear regressions. the estimated parameters are given in table 2b together with the pre-dicted means. Except for the duration error, the goodness of fit of the simple model that starts with an initial perfor-mance level (the additive constants of the regressions) and adds changes reflecting learning, forgetting, and immediate benefits in the appropriate conditions is reasonably good.
Discussion
In the present experiment, we compared haptic-guidance practice of a spatio-temporal motor pattern with decreasing and increasing stiffness of guidance. For the same pattern, we have shown benefits of haptic guidance for temporal or dynamic movement characteristics, but not for spatial ones in a previous study (lüttgen and heuer 2012a). Fading guidance is generally seen as a means to boost the benefits of haptic guidance because it should wash out any adap-tation to the particular dynamic environment created by the guiding forces and prevent a purely passive role of the learner. In contrast, possible benefits that could accrue from growing guidance seem not to have been studied thus far. a major reason to expect such benefits is the notion that the motor system learns best when information about the tar-get movement is at first presented in a simplified form, then with increasing precision as learning continues. Growing haptic guidance could conceivably be an effective means to convey this increasingly precise information as learning continues. Of course, possible advantages of growing guid-ance could be masked by adaptation and a progressively passive role of the learner, that is, by those factors that should be overcome by fading practice. to reduce the pos-sible role of such factors, we mixed guided and unguided movements in that in each practice trial, a visual demon-stration of the target movement was followed by a guided reproduction first and an unguided reproduction second. the requirement to reproduce the target pattern actively should prevent a passive stance of the learner (cf. Winstein et al. 1994), and the alternation of guided and unguided movements should prevent (or at least minimize) adapta-tion to the guiding forces that is carried over to unguided movements.
With both practice regimens, we found motor learning, with one exception, in all four types of errors assessed: timing errors and spatial errors both with respect to over-all scaling of time and amplitude and with respect to local variations of scaling. the exception was the variable dura-tion error for which there was a practice-related improve-ment only with fading, but not with growing guidance. Forgetting from one day to the next day was absent for all dependent variables. But again, there was an exception,
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namely the shape error after practice with growing guid-ance. an immediate benefit of a preceding guided move-ment was found for the relative-timing error only. Finally, for guided movements, for which the errors depended pri-marily on the stiffness of guidance, there was a practice-induced improvement only for the shape error. We shall discuss different implications of these findings in turn.
Overall, the differences between fading-guidance prac-tice and growing-guidance practice were only small. On the one hand, this appears remarkable because there was no clear superiority of fading which is broadly accepted as an important feature of robot-assisted practice. how-ever, in the present study, we had included a design fea-ture supposed to have similar effects as fading guidance, namely the mixture of guided and unguided movements. this measure should have produced those benefits also for growing-guidance practice, which are typically ascribed to fading guidance, namely stimulation of the active role of the learner and prevention of adaptation to the particular dynamic environment of haptic guidance.
On the other hand, the only small differences appear remarkable because the hypothesized benefits of growing guidance were not realized. there are two possible reasons for this, a principled one and a more incidental one. the principled reason is that, as far as motor learning is con-cerned, there is no optimal relation of the precision of tar-get information provided by haptic guidance to the state of the learner, specifically to his changing demands for lower and higher levels of precision. Of course, even if this were true for the limited duration of practice studied, it might be different for practice durations of several days, weeks, or even years.
the more incidental reason for not finding an advan-tage of growing guidance over fading guidance could be related to the linear changes in the stiffness of guidance across practice trials. this had the effect that with grow-ing guidance, the precision of guided movements increased rapidly early in practice, whereas with fading guidance it declined rather late in practice. these variations of the pre-cision of haptic demonstration may have not been optimal for a good and a poor match to the information demands of the learning motor system with growing and fading guid-ance, respectively. (the nonlinear changes in the precision of guided movements, and in particular its strong variation across the lowest levels of stiffness, had the effect that the errors in blocks of unguided trials, where the stiffness was zero, were larger than in the blocks of guided trials with the smallest stiffness, in which the mean stiffness was .028 N/mm, ranging from 0 to .057 N/mm).
the only differences between the two practice groups were found in the variable duration error, which revealed practice benefits only with fading-guidance practice, but not with growing-guidance practice, and in the shape error,
which revealed forgetting after growing-guidance practice, but not after fading-guidance practice. Both these findings indicate selective advantages of fading guidance. however, the mechanisms, which produce these advantages, are not clear. Perhaps, duration is a global movement character-istic that is learned early during practice, similar to other global characteristics of spatio-temporal movement pat-terns (Franks and Wilberg 1982; Marteniuk and Romanow 1983) or complex visuomotor transformations (heuer and sülzenbrück 2012). If this is the case, it should profit from early haptic-guidance precision, but not from late precision.
lüttgen and heuer (2013) had found an immediate ben-efit of haptic guidance of discrete circle drawing (drawing circles with pauses after each circle) on the relative timing of the reproductions that was not accompanied by a cumu-lative learning effect across a series of demonstration–reproduction cycles. In the present study, we found again an immediate effect of precise haptic demonstration on relative timing that was not observed in the other perfor-mance measures. this finding is consistent with the notion that relative-timing control is particularly susceptible to the immediate benefits of haptic guidance. In this respect, rela-tive timing differs from spatial movement characteristics and absolute timing (or total movement duration).
the space-related measure, which is comparable to the relative-timing error of the present study, is the shape error. Whereas the relative-timing error is the only measure that profited from an immediately preceding precise hap-tic demonstration of the target movement, the shape error was the only measure for which we found a learning benefit in guided movements. there, for all measures—except for the shape error—the haptic guidance dominated the preci-sion of the movements and thereby masked the learning benefit that is apparent in the unguided movements. Only with respect to the shape, learning resulted in an excess of precision beyond that provided by the haptic guidance. In particular, for the relative timing, no such excess preci-sion was apparent. this contrast is again consistent with the notion that haptic guidance is more efficient with providing temporal information than with providing spatial informa-tion. Whereas precise relative-timing information by hap-tic guidance enhanced timing accuracy in the immediately following reproductions, spatial precision of guided move-ments had no such effect. Instead of driving learning, the spatial precision of guided movements was enhanced by practice-related improvements.
Whereas the relative-timing error revealed an immediate effect of haptic demonstration and no difference between fading-guidance and growing-guidance practice, the vari-able duration error was differently affected by the two practice regimens and did not profit from an immediately preceding precise haptic demonstration. these discrepant findings for the two types of timing error are consistent
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with other results, which suggest distinct processes of learning for absolute timing and relative timing of spatio-temporal motor patterns. One of the classic variables in the field of motor learning is knowledge of results (KR). somewhat contrary to classical conceptions, salmoni et al. (1984) noted that KR in 100 % of the trials results in bet-ter performance during practice than KR in only a portion of all trials, but that this performance difference tends to be reversed in subsequent tests without KR. later studies (Wulf et al. 1993, 1994) revealed that the reduction in rela-tive KR frequency serves to improve the learning of the rel-ative timing of the target movement, but generally degrades the learning of absolute timing or total duration.
Acknowledgments We thank andreas Volgmann and hanno Muss-mann for software support and sarah Jacob and sarah längler for support in running the experiment.
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