0306-4522/90 $3.00 + 0.00 Pergamon Press plc 0 1990 IBRO
Neuroscience Vol. 35, No. 2, pp. 365-374, 1990 Printed in Great Britain
THE EFFECT OF ACCURACY CONSTRAINTS ON THREE-DIMENSIONAL MOVEMENT KINEMATICS and M. M. IJAZ$
T. E. MILNER*t
*Department of Brain and Cognitive Sciences, and #Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. Abstract-The kinematics of three-dimensional arm movements were recorded during a task in which subjects were required to place a peg in a hole. The accuracy constraint was varied by using holes of different diameters. If the diameter of the hole was large relative to the diameter of the peg, the tangential velocity profile of hand trajectories was relatively symmetric and bell-shaped, but it became increasingly asymmetric as the diameter of the hole was reduced. Peak tangential velocity decreased, overall movement duration increased and the proportion of the movement spent in deceleration increased systematically. The shape of the accelerative phase of the velocity profile showed little dependence on hole diameter, but the deceierative phase became increasingly irregular as the hole diameter was reduced. This irregularity was attributed to submov~ents corresponding to small changes in the direction of the hand path. On the other hand, deliberately slowing the movement in the absence of a strict accuracy constraint induced a change in the velocity profile which produced irregularity in both the accelerative and decelerative phases of the movement. The results of our experiments are consistent with the idea that movements requiring extreme accuracy and other slow movements are composed of a series of submovemen~. In the case of movements requiring accuracy these submovements may represent corrective actions that are taken throughout the course of the movement.
Recent interest in the three-dimensional kinematics of human arm movements has focused on the possibility of elucidating the ~derl~ng neural control mecha-
nisms and of imitating human behavior in robots. In both contexts considerable importance must be placed on the principles that are employed when accuracy is paramount. Multi-joint, point-to-point arm movements have often been treated as single segments that can be characterized by the velocity profiles of the joints or the endpoint (hand or wrist).“1i*‘8 Although these velocity profiles are typically bell-shaped and symmetric about the midpoint, it has been shown that they can become asymmetric when the final location of the movement must be precisely controlled.‘4*‘9 This as~met~ occurs as the decelerative phase becomes relatively longer than the accelerative phase,6J4,20Jl
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Since Woodworth,2’ a number of investigators have presented evidence that movements requiring precision consist of a sequence of several discrete submovements: an initial phase which covers most of the distance, followed by corrective movements~‘A~~~~i3*20 The submovemen~ have been inferred from irregularities in the hand path or velocity and acceleration profiles. iPresent
address: Institut de readantation
Centre de recherche, 6300 Dar&ton
de Montreal. Avenue, Man:
t&al, Ou&ee. Canada H3S 2I4. IRED, infrared light-emitting diode; TRACK, Telemetered Real-time Aquisiton and Computation of Kinematics.
Abbreoiari&:
Soechting19 investigated the effects of accuracy constraints in the transverse, vertical and horizontal directions. He found that the initial phase of the movement was highly stereotyped and relatively independent of target size. The initial phase of movements to a smaller target had a slightly longer duration (5-g%), but the shape of the velocity profile was similar to that of movements to a larger target. However, the overall movement time to the smaller target was about 15% longer because the final approach to the smaller target consisted of a long period of maintained low velocity. This final approach phase was not analysed in detail, although it was reported that it varied considerably from trial to trial. It is during this final phase that adjustments are likely to be made in aligning the hand with the target and therefore it bears close scrutiny, particularly on a trial by trial basis. MacKenzie et aL’4 investigated the effect of movement amplitude and target size on the velocity profile of a stylus used in a discrete tapping task. Their conclusions were based on the analysis of average movement profiles. They found that target size determined the relative amount of time spent in acceleration and deceleration; the smaller the target the more time spent in deceleration. They also concluded that target size alone had no effect on peak velocity. This latter conclusion is somewhat surprising since movements to larger targets are generally faster and are presumably made at higher peak velocities than movements to smaller targets. These observations do not accord with the findings of Langolf et ~1.~~who
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found that velocity of the overall motion slowed as target size decreased. To date, attempts to model precision movements have been concerned primarily with the derivation of a relation between target size, movement distance and movement time.8~‘5~‘6~‘7 These models have not been concerned with detailed kinematic features of the hand path or the tangential velocity profile of the hand. Our aim has been to develop a model that can account for these kinematic details of precision movements. To this end we have undertaken a systematic study of the effect of target size, as well as movement amplitude on movement kinematics. We have examined movements on a trial by trial basis, carefully analysing both the three-dimensional paths and the velocity profiles. By using a high resolution tracking system we have been able to identify features in the final approach of the hand to the target which are consistent with the existence of submovements.
Eight normal subjects (six male and two female) particpated in the study. Subjects were right-handed and ranged in age from 19 to 31 years. Kinematic data were acquired using a system for Telemetered Real-time Acquisition and Computation of Kinematics (TRACK) developed at the MIT Biomechanics and Human Rehabilitation Laboratory. This is an optical tracking system which uses cameras with infrared sensitive detectors (Selspot I) to record the instantaneous positions of up to 30 infrared light-emitting diodes (IREDs) that are activated sequentially.2 The TRACK software computes the three-dimensional spatial location of individual IREDs. The accuracy can be improved by fixing several IREDs to a rigid surface and providing the TRACK software with information about the geometry of the IREDs. This is done by matching the recorded positions of ail the IREDs with the information about their geometrical relationship to each other and then minimizing the error.’ IRED positions were sampled at 315Hz. Three-dimensional positions were computed off-line using TRACK software. The TRACK coordinate system was oriented so that the X- and Z-axes formed a horizontal plane while the Y-axis pointed in the vertical direction. The three-dimensional spatial data were filtered and differentiated using an algorithm based on dynamic programing.’ The magnitude of the resultant velocity vector (with components along all three orthogonal axes) was then calculated. This velocity will be referred to as the tangential velocity. Each subject was instrumented with four rigid IRED arrays, located respectively on the hand, the wrist, the upper arm and the shouider. The arrays consisted of four to six IREDs mounted in lightweight, plexiglass frames which had been painted flat black to minimize infrared reflections. Elastic straps with Velcro fasteners were placed around the shoulder, upper arm and wrist to serve as anchors for three of the arrays. The fourth array was secured to a tight-fitting, fingerless glove (Fig. 1). Only the data acquired from the IRED array mounted on the subject’s hand will be discussed in this paper, although the conclusions apply equally to data obtained from the forearm array. The subject was comfortably seated in a chair facing a board which had been drilled with four holes: 50.8, 25.4, 17.5 and 11.1 mm diameter. The subject held a short plexiglass peg (120.6 mm long and 9.5 mm in diameter) with a pencil grip in the right hand. Before i~tiating a movement the subject pressed the back of the peg against a contact switch made from a small leaf spring. When the subject
and M. M.
IIAZ
moved the peg forward to place it in one of the holes, the switch opened and triggered the data collection. The target board was positioned so that its surface was parallel to the YZ-plane of the TRACK coordinate system. The trir-rner switch and target hole were aligned along the X-axis of%he TRACK coordinate system. The trieaer switch could be repositioned to vary the distance between the initial position and target hole along the X-axis. The origin of our coordinate system was chosen to coincide with the position of the geometrical center of the hand IRED array at the onset of movement. Each target hole was instrumented with a contact switch. On some trials the data sampling trigger was also used to trigger an oscilloscope sweep. When the peg contacted the switch in the target hole a pulse was generated and its onset was used to accurately measure movement duration. Subjects were instructed to prepare to initiate a movement by holding the back of the peg against the trigger switch. They were free to initiate the movement at their leisure. The objective was to place the peg into the target hole as quickly as possible without touching the surface of the target board. Any movement in which the peg first touched the board before entering the target hole was classified as an unsuccessful trial. Subjects were instructed to make one continuous movement. This was done to avoid the possibility of having the subject break the task up into several discrete subtasks. For most movements the trigger switch was positioned so that the subject had to make a movement of approximately 20cm in order to place the peg in the target hole. At least two successful trials were recorded for movements to each target hole for each subject. In addition, a third successful trial to each of the two smaller target holes and two unsuccessful trials to the smallest target hole were recorded. For the smallest target hole, the trigger switch was also positioned for an 8 cm movement and three successful triats were recorded. Finally, subjects were instructed to deliberately prolong the movement to the largest target hole by controlling the movement duration. We recorded two movements for each of the following movem~t durations: 500,750 and 1000 ms. RESULTS
Tu~gent~ul velocity profiles The tangential velocity profiles of movements made to each of the four targets by one subject are compared in Fig. 2. Qualitative features of the velocity profiles were similar for all subjects. They become increasingly asymmetric as the diameter of the target hole decreased. The asymmetry was due to a prolonged phase of deceleration and low velocity as the target was approached. Total movement duration increased and peak velocity decreased in conjunction with the increased asymmetry. In addition to the increased asymmetry of movements made to smaller targets, it is also apparent that the veIocity profiles become more irregular. These irregularities may result from secondary movements (submovements) which become more numerous as the constraint on accuracy becomes more stringent. There is evidence for such submovements in the hand paths, as well. Hand paths The hand paths of the movements of Fig. 2 are compared in Fig. 3. The hand paths have been
Accuracy
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Fig. 1. Experimental apparatus showing target board and instrumented subject. Infrared LED arrays were fastened to the hand, forearm, upper arm and shoulder. The subject is positioned ready to initiate the task. projected onto a plane which is parallel to the plane of the target board (YZ-plane). The motion occurring in this plane brings the peg into alignment with the target hole. Although we did not actually monitor motion of the peg, we can infer that motion of the hand is tightly linked with motion of the peg since the peg was held in a firm grip by the fingers. Changes in direction appear during all movements, but tend to occur more frequently when movements are made to the smaller target holes. Such abrupt changes in direction are likely the consequence of corrective submovements which serve to compensate for misalignment of the peg and target hole. When the hand paths are viewed along the X-axis (projections onto the XY- and XZ-planes) the movements to the larger target holes appear to be smooth and relatively linear (Figs 4 and 5). However, there are some rather abrupt changes in direction toward the end of the movements to the two smaller targets. We have taken a movement to the smallest target and used arrows to indicate corresponding points in time along the tangential vetocity profile and the hand path projected onto the YZ-plane as shown in Fig. 6. Inflections in the velocity profile occur with a similar frequency to changes in the direction of the
hand path. Such inflections could result from superimposing secondary movements (submovements) with a primary initial movement. Primary moveme~f We observed that from movement onset to peak tangential velocity, the velocity profile was usually quite smooth and similar in shape for movements to all targets. This provides evidence for the deployment of a large initial movement to cover most of the distance to the target. We postulate that this primary movement has a velocity profile of the same basic shape for all movements, but that its magnitude and duration can be scaled. Scaling would be done according to the following principle. As the target becomes smaller the magnitude of the velocity profile decreases and its duration increases. This would provide more time during which to take corrective action by slowing down the approach to the target. We would also expect to see a reduction in peak velocity, although not necessarily duration, if the distance to the target was decreased. To test these hypotheses we took the tangential velocity profiles for each subject, aligned them on peak velocity and normalized them by scaling them
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primary movement duration was also graded according to target size, increasing as target size decreased, again in agreement with our hypothesis. Finally, we found a reduction in peak velocity by approximately half when the distance to the smallest target was reduced from 20 to 8 cm. However, note that the time from movement onset to peak velocity and the total movement duration were reduced by less than 30%. Sow movements A number of earlier studies of multi-joint arm movements had found that tangential velocity profiles were usually quite symmetric. However, the movements which they examined were generally much faster than those in which we observed marked asymmetry. In order to determine whether the asymmetry resulted from the constraint on accuracy or whether it might simply be due to the speed of the movem~t, we asked subjects to make slow move-
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ments to the largest target. We had them prolong their movements so that they would arrive at the target approximately 500,750 or 1000 ms after movement onset. Figure 8 shows a typical tangential velocity profile. We observed no consistent asymmetry in the movements, although the velocity profiles became much more irregular than the fastest movements to the same target (Fig. 2). The irregula~ty is probably the result of a series of superimposed, overlapping submovements, but because the accuracy constraint is now one of timing rather than positioning, the overall organization is somewhat different. There are now irregularities in the initial phase of the movement, preceding peak tangential velocity. This suggests that unlike the task where speed and accuracy were paramount, the earliest submovements may now have smaller amplitudes than later ones.
DISCUSSION
Velocity profile shape
Our results clearly demonstrate that increasing requirements for accuracy produce an increasingly marked asymmetry in the tangential velocity profile. The decebrative phase of the motion is prolonged. The initial segment of the movement, up to and including the velocity peak, has a characteristically stereotyped shape for each subject. However, the peak velocity of this initial segment decreases and its duration increases as the requirements for accuracy become more stringent. Analysis of the three-dimensional hand paths has shown that there are changes in direction which correspond to inflections in the tangential velocity profile. From this we derive support for the view that final position accuracy is achieved by superimposing upon a primary move-
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series of submovements that are used in error correction. It is well known that movement duration increases as the target becomes smaller.9,2’ Our observations regarding the effects of accuracy on movement trajectories are consistent with a number of other studies.6*8*‘9*20 Our findings suggest that all subjects employed a common strategy. This consisted of a primary initial movement whose peak velocity and duration were controlled in such a way as to increase the time spent in approaching the target as the target became smaller. Woodworthzl made a similar observation when subjects were permitted to move relatively slowly in a task requiring considerable precision. The rationale behind such a strategy could be two-fold. Firstly, as the constraint on accuracy becomes more stringent, a greater number of corrective movements may be necessary to align the peg with the target hole. Secondly, if the arm is moving
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too fast, it may be difficult to make a small, precise correction because the inertia of the arm will tend to determine direction of motion. Thus, it would be desirable to keep tangential velocity low and prolong the time spent in the proximity of the target. Our observations support the findings of Langolf et aLi3 that when target tolerances are reduced, the whole movement becomes slower, that is, peak velocity decreases and movement duration increases. This contrasts with the conclusions of MacKenzie et cd.14 that target size had no effect on peak velocity. Although their task was slightly different (a Fitts’ tapping task with a stylus), the movement amplitude and range of indices of difficulty were similar. It is possible that they would have seen an effect had they separately analysed the horizontal and vertical velocity components. In their task there was no constraint on accuracy along the vertical axis whereas we had constraints on accuracy along all three axes of
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Fig. 6. Tangential velocity profile for a movement to the smallest target hole. Inset: hand path in the YZ-plane. The numbered arrows denote the velocity and position at corresponding times during the movement.
motion. One might expect an accuracy constraint along one axis of motion to have little effect on peak velocity in an orthogonal direction where there is no accuracy constraint.” Thus, if in a Fitts’ tapping task the velocity component in the vertical direction dominated the velocity component in the horizontal direction then the difference in the peak resultant (tangential) velocity might not change significantly even though the requirements for accuracy increased along the horizontal direction. Another factor cont~buting to the failure of MacKenzie ef ~1.‘~to find a change in peak velocity with target size may have been that in the Fitts’ tapping task there is no need for the subject to precisely regulate deceleration of the arm since the movement can be terminated by impact of the stylus with the target. In our task, on the other hand, it was necessary for the subject to regulate deceleration
TIME Fig. 7. Tangential velocity profiles of movements made to all targets by one subject. Profiles have been normalized with respect to peak velocity and scaled in duration to align on movement onset and peak velocity.
during movement termination since we did not permit impact with the target board. Unlike other studies of multi-joint arm movements3*” we found that in our task, the tangential velocity profiles were similar in shape (congruent) only over the initial segment of the movement. So~h~ng19 made similar observations, although he was able to demonstrate congruency over a greater proportion of the movement. Because irregularities in the velocity profile often appeared soon after peak velocity in our task, it was rarely possible to see congruency beyond the velocity peak. We attribute this difference to the fact that the accuracy constraint in our task was considerably more stringent than in these previous studies. Error correction Carlton and Meyer ef a1.l6 provided evidence for discrete corrective responses which appeared as auxilliary movements initiated when the velocity of the initial movement segment had almost reached zero. The velocity profiles of most of the movements which we recorded show evidence of secondary movements superimposed on the primary movement, often very soon after peak velocity is reached. This suggests to us that corrective responses are already occurring while the velocity is still high. There are often two or more of these secondary movements, suggesting further that overall accuracy is being assessed and corrective action taken periodically throughout the movement. Our findings are also supported by the work of MacKenzie et a1.j4 who reported that local peaks and valleys during the decelerative phase of tangential velocity profiles became particularly evident as the target was reduced in size. They also took this as evidence for “multiple inputs for trajectory control”, i.e. secondary movements.
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Accuracy and movement kinematics Table 1. Mean values and standard deviations of movement amplitude, peak tangential velocity and total movement duration Target size (mm)
Distance (cm)
Peak velocity (m/s)
50.8 25.4 17.5 11.1 11.1
20.7 + 1.2 20.1 f 1.1 20.0 & 1.4 19.7 + 1.3 8.2 f 0.1
1.05 * 0.20 0.73 + 0.18 0.59 &-0.08 0.50+0.12 0.26 f 0.04
Because the task of placing the peg in the smallest hole was very difficult, subjects were often unsuccessful. However, there was no obvious difference in the general appearance of tangential velocity profiles between successful and unsuccessful attempts to place the peg in the hole, indicating that subjects used the same strategy regardless of outcome. It is quite likely that the skill required to consistently succeed in quickly placing the peg in the hole can only be acquired through considerable practice, much like playing darts for example. What we have observed is probably a general strategy used in learning to be fast and accurate. Had we not insisted on speed and continuity of movement, we expect that our subjects would have chosen to break the motion into smaller discontinuous segments which would have allowed more sensory processing time and thereby guaranteed them of a higher success ratio. Hening et al.” have shown that the accuracy of subjects’ responses decreases when the time between appearance of a target and movement initiation is reduced. This is analogous to the reduction in sensory processing time that would occur in our task with an increase in the speed of movement to the target hole.
We examined movements on a trial by trial basis because the initial errors are very likely random in nature, and since corrective actions must be tailored individually to each movement, much of the detail
Time to peak (ms) 160&24 192&46 213&48 2405 100 169&31
Duration (ms)
n
383 &82 525rt: 109 617+94 971&279 713+205
20 20 28 53 25
would have been lost by averaging. It is clear that corrective actions take place as the target is approached. These corrective actions appear as abrupt changes in direction of the hand path. When a comparison is made between movements to targets of different sizes it is evident that these changes in direction are more numero~ for the smaller targets. The amplitude of these corrections is small which implies that the initial movement segment must already be quite accurate. It is not surprising therefore, that the corrective responses may not be seen if requirements for accuracy are not stringent or if the resolution of the recording apparatus is too low. One must exercise caution in using only hand path data to infer the existence or non-existence of submovements. Submovements could occur without producing a change in hand path direction. However, they would then be evident in the tangential velocity profile. At the other extreme, changes in curvature of the hand path could occur even in the absence of submovements. Flash” has modeled multi-joint movement trajectories which consist of a single primary movement with no submovements. She has shown that for certain movement directions musculoskeietal dynamics alone are sufficient to produce significant curvature in the hand path. However, in this case she predicts no inflections in the ~ngential velocity profile so once again velocity profile would be a better
5e ”
Target Size 50.8 mm
Fig. 8. Tangential velocity profile of a prolonged movement to the largest target hole. The subject was instructed to prolong the movement so that its duration would be approximately 1OOOms.Inset: hand path in the YZ-plane.
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T. E. MILNER and M. M. I~AZ
indicator of submovements than hand path. Abrupt changes in hand path direction should be considered as supporting evidence though, since Flash’s model predicts only smooth changes in direction. Submovement struteg) When subjects were required to deliberately prolong their movements to the largest target hole, irregularities in the tangential velocity profile appeared throughout the movement, beginning during the accelerative phase. Taken together with evidence from changes in direction of the hand path this suggests that these movements also consisted of a series of superimposed submovements. In this case it is unlikely that the submovements reflect a strategy for error correction. A more plausible rationale is that they are related to the regulation of movement duration. It may be difficult to generate a single motor command with a duration as long as 1000 ms because of higher frequency periodic behavior within the central nervous system. Thus, a movement with a duration of IOOOms may be approximated by an overlapping sequence of submovements at shorter intervals which are superimposed upon one another.
CONCLUSIONS
The results of our experiments are consistent with the idea that a tangential velocity profile can be scaled in amplitude and duration according to the requirements of a task.“i’ However, when accuracy is required additional secondary movements may be superimposed on an initial primary movement. These secondary movements could be delayed with respect to one another, beginning with a large submovement and followed by a series of smaller ones. A similar principle can be used to account for the shape of velocity profiles recorded when the subjects were asked to regulate movement duration to the largest target. However, in this case the initial submovement need not have the largest amplitude.
Acknowledgements-This work was supported by a fellowship to T.M. from the Alberta Heritage Foundation for Medical Research and a fellowship to MI. from the
Harvard/MIT Division of Health Sciences and T~hnotogy, Medical Engin~ring-M~i~i Physics Program. We wish to thank Professor Robert Mann for having made available the facilities of the MIT Biomechanics and Human Rehabilitation Laboratory.
REFERENCES
1. Annett J., Golby C. W. and Kay H. (1958) The measurement of elements in an assembly task-the information output of the human motor system. Q. .JI exp. Psychol. 19, 1--l I. 2. Antonsson E. K. (1982) A three-dimensional kinematic acquisition and inter~~~~l dynamic analysis system for human motion. Ph.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge. 3. Atkeson C. G. and Hollerbach J. M. (1985) Kinematic features of unrestrained vertical arm movements, J. Neurosci. 5, 23182330. 4. Beggs W. D. A. and Howarth C. I. (1970) Movement control in a repetitive motor task. ?ciature 225, 752-753. 5. Busby H. R. and Trujillo D. M. (1985) Numerical experiments with a new differentiation filter. J. biomech. Eq. 107, 293-299. 6. Carlton L. G. (1980) Movement control characteristics of aiming responses. Ergonomics 23, 1019-1032. 7. Conati F. C. (1977) Real-time measurement of three-dimensional multiple rigid body motion. SM. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA. 8. Crossman E. R. F. W. and Goodeve P. J. (1983) Feedback control of hand-movement and Fitts’ law. Q. Jtexp. Psychol. 35A, 251-278. Original work presented at the meeting of the Experimental Psychology Society, Oxford, U.K., July 1963. 9. Fitts P. M. (1954) The information capacity of the human motor system in controlling the amplitude of movement. J. exp. Psychol. 47, 381-391. IO. Flash T. (1987) The control of hand equilibrium trajectories in multi-joint arm movements. Biol. Cybern. 57, 257-274. 11. Flash T. and Hogan N. (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 5, 168881703. 12. Hening W., Favilla M. and Ghez C. (1988) Trajectory control in targeted force impulses: gradual specification of response amplitude. Expl Brain Res. 71, 116-128. 13. Langolf G. D., Chaffin D. B. and Foulke J. A. (1976) An investigation of Fitts’ law using a wide range of movement amplitudes. J. Moror. Behav. 8, 113-128. 14. MacKenzie C. L., Marteniuk R. G., Dugas C., Liske D. and Eickmeier B. (1987) Three-dimensional movement trajectories in Fitts’ task: implications for control. Q, JI. exp. Psychol. 39A, 629-647. 15. Mever D. E.. Smith K. E. and Wright C. E. (1982) Models for the speed and accuracy of aimed movements. Psycho/. Re;. 89, 4491482. 16. Meyer D. I?., Abrams R. A,, Kornblum S., Wright C. E. and Smith K. E. (1988) Optimaiity in human motor oerformance: ideal control of rapid aimed movements. PsvchoL Rev. 95, 340-370. 17. Schmidt R. A., Zelaznik H., Hawkins B., Frank J. S. and Quinn J. T. Jr (1979) Motor-output variability: a theory for the accuracy of rapid motor acts. Psychol. Rev. 86, 415-449. 18. Soechting 1. F. and Lacquaniti F. (1981) Invariant characteristics of a pointing movement in man. J. Neurosci. 1, 710-720. 19. Soechting J. F. (1984) Effect of target size on spatiat and temporal characteristics of a pointing movement in man. Expl Brain Res. 169, l-12.
20 Taylor F. V. and Birmingham H. P. (1948) Studies of tracking behavior. II. The acceleration pattern of quick manual corrective responses. J. exp. Psychol. 38, 783-795. 21 Woodworth R. S. (1899) The accuracy of voluntary movement. Psychof. Rev. 3, L-114. (Accepted 18 November 1989)
Neuroscience Vol. 35, No. 2, pp. 365-374, 1990 Printed in Great Britain
THE EFFECT OF ACCURACY CONSTRAINTS ON THREE-DIMENSIONAL MOVEMENT KINEMATICS and M. M. IJAZ$
T. E. MILNER*t
*Department of Brain and Cognitive Sciences, and #Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. Abstract-The kinematics of three-dimensional arm movements were recorded during a task in which subjects were required to place a peg in a hole. The accuracy constraint was varied by using holes of different diameters. If the diameter of the hole was large relative to the diameter of the peg, the tangential velocity profile of hand trajectories was relatively symmetric and bell-shaped, but it became increasingly asymmetric as the diameter of the hole was reduced. Peak tangential velocity decreased, overall movement duration increased and the proportion of the movement spent in deceleration increased systematically. The shape of the accelerative phase of the velocity profile showed little dependence on hole diameter, but the deceierative phase became increasingly irregular as the hole diameter was reduced. This irregularity was attributed to submov~ents corresponding to small changes in the direction of the hand path. On the other hand, deliberately slowing the movement in the absence of a strict accuracy constraint induced a change in the velocity profile which produced irregularity in both the accelerative and decelerative phases of the movement. The results of our experiments are consistent with the idea that movements requiring extreme accuracy and other slow movements are composed of a series of submovemen~. In the case of movements requiring accuracy these submovements may represent corrective actions that are taken throughout the course of the movement.
Recent interest in the three-dimensional kinematics of human arm movements has focused on the possibility of elucidating the ~derl~ng neural control mecha-
nisms and of imitating human behavior in robots. In both contexts considerable importance must be placed on the principles that are employed when accuracy is paramount. Multi-joint, point-to-point arm movements have often been treated as single segments that can be characterized by the velocity profiles of the joints or the endpoint (hand or wrist).“1i*‘8 Although these velocity profiles are typically bell-shaped and symmetric about the midpoint, it has been shown that they can become asymmetric when the final location of the movement must be precisely controlled.‘4*‘9 This as~met~ occurs as the decelerative phase becomes relatively longer than the accelerative phase,6J4,20Jl
-
-
Since Woodworth,2’ a number of investigators have presented evidence that movements requiring precision consist of a sequence of several discrete submovements: an initial phase which covers most of the distance, followed by corrective movements~‘A~~~~i3*20 The submovemen~ have been inferred from irregularities in the hand path or velocity and acceleration profiles. iPresent
address: Institut de readantation
Centre de recherche, 6300 Dar&ton
de Montreal. Avenue, Man:
t&al, Ou&ee. Canada H3S 2I4. IRED, infrared light-emitting diode; TRACK, Telemetered Real-time Aquisiton and Computation of Kinematics.
Abbreoiari&:
Soechting19 investigated the effects of accuracy constraints in the transverse, vertical and horizontal directions. He found that the initial phase of the movement was highly stereotyped and relatively independent of target size. The initial phase of movements to a smaller target had a slightly longer duration (5-g%), but the shape of the velocity profile was similar to that of movements to a larger target. However, the overall movement time to the smaller target was about 15% longer because the final approach to the smaller target consisted of a long period of maintained low velocity. This final approach phase was not analysed in detail, although it was reported that it varied considerably from trial to trial. It is during this final phase that adjustments are likely to be made in aligning the hand with the target and therefore it bears close scrutiny, particularly on a trial by trial basis. MacKenzie et aL’4 investigated the effect of movement amplitude and target size on the velocity profile of a stylus used in a discrete tapping task. Their conclusions were based on the analysis of average movement profiles. They found that target size determined the relative amount of time spent in acceleration and deceleration; the smaller the target the more time spent in deceleration. They also concluded that target size alone had no effect on peak velocity. This latter conclusion is somewhat surprising since movements to larger targets are generally faster and are presumably made at higher peak velocities than movements to smaller targets. These observations do not accord with the findings of Langolf et ~1.~~who
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found that velocity of the overall motion slowed as target size decreased. To date, attempts to model precision movements have been concerned primarily with the derivation of a relation between target size, movement distance and movement time.8~‘5~‘6~‘7 These models have not been concerned with detailed kinematic features of the hand path or the tangential velocity profile of the hand. Our aim has been to develop a model that can account for these kinematic details of precision movements. To this end we have undertaken a systematic study of the effect of target size, as well as movement amplitude on movement kinematics. We have examined movements on a trial by trial basis, carefully analysing both the three-dimensional paths and the velocity profiles. By using a high resolution tracking system we have been able to identify features in the final approach of the hand to the target which are consistent with the existence of submovements.
Eight normal subjects (six male and two female) particpated in the study. Subjects were right-handed and ranged in age from 19 to 31 years. Kinematic data were acquired using a system for Telemetered Real-time Acquisition and Computation of Kinematics (TRACK) developed at the MIT Biomechanics and Human Rehabilitation Laboratory. This is an optical tracking system which uses cameras with infrared sensitive detectors (Selspot I) to record the instantaneous positions of up to 30 infrared light-emitting diodes (IREDs) that are activated sequentially.2 The TRACK software computes the three-dimensional spatial location of individual IREDs. The accuracy can be improved by fixing several IREDs to a rigid surface and providing the TRACK software with information about the geometry of the IREDs. This is done by matching the recorded positions of ail the IREDs with the information about their geometrical relationship to each other and then minimizing the error.’ IRED positions were sampled at 315Hz. Three-dimensional positions were computed off-line using TRACK software. The TRACK coordinate system was oriented so that the X- and Z-axes formed a horizontal plane while the Y-axis pointed in the vertical direction. The three-dimensional spatial data were filtered and differentiated using an algorithm based on dynamic programing.’ The magnitude of the resultant velocity vector (with components along all three orthogonal axes) was then calculated. This velocity will be referred to as the tangential velocity. Each subject was instrumented with four rigid IRED arrays, located respectively on the hand, the wrist, the upper arm and the shouider. The arrays consisted of four to six IREDs mounted in lightweight, plexiglass frames which had been painted flat black to minimize infrared reflections. Elastic straps with Velcro fasteners were placed around the shoulder, upper arm and wrist to serve as anchors for three of the arrays. The fourth array was secured to a tight-fitting, fingerless glove (Fig. 1). Only the data acquired from the IRED array mounted on the subject’s hand will be discussed in this paper, although the conclusions apply equally to data obtained from the forearm array. The subject was comfortably seated in a chair facing a board which had been drilled with four holes: 50.8, 25.4, 17.5 and 11.1 mm diameter. The subject held a short plexiglass peg (120.6 mm long and 9.5 mm in diameter) with a pencil grip in the right hand. Before i~tiating a movement the subject pressed the back of the peg against a contact switch made from a small leaf spring. When the subject
and M. M.
IIAZ
moved the peg forward to place it in one of the holes, the switch opened and triggered the data collection. The target board was positioned so that its surface was parallel to the YZ-plane of the TRACK coordinate system. The trir-rner switch and target hole were aligned along the X-axis of%he TRACK coordinate system. The trieaer switch could be repositioned to vary the distance between the initial position and target hole along the X-axis. The origin of our coordinate system was chosen to coincide with the position of the geometrical center of the hand IRED array at the onset of movement. Each target hole was instrumented with a contact switch. On some trials the data sampling trigger was also used to trigger an oscilloscope sweep. When the peg contacted the switch in the target hole a pulse was generated and its onset was used to accurately measure movement duration. Subjects were instructed to prepare to initiate a movement by holding the back of the peg against the trigger switch. They were free to initiate the movement at their leisure. The objective was to place the peg into the target hole as quickly as possible without touching the surface of the target board. Any movement in which the peg first touched the board before entering the target hole was classified as an unsuccessful trial. Subjects were instructed to make one continuous movement. This was done to avoid the possibility of having the subject break the task up into several discrete subtasks. For most movements the trigger switch was positioned so that the subject had to make a movement of approximately 20cm in order to place the peg in the target hole. At least two successful trials were recorded for movements to each target hole for each subject. In addition, a third successful trial to each of the two smaller target holes and two unsuccessful trials to the smallest target hole were recorded. For the smallest target hole, the trigger switch was also positioned for an 8 cm movement and three successful triats were recorded. Finally, subjects were instructed to deliberately prolong the movement to the largest target hole by controlling the movement duration. We recorded two movements for each of the following movem~t durations: 500,750 and 1000 ms. RESULTS
Tu~gent~ul velocity profiles The tangential velocity profiles of movements made to each of the four targets by one subject are compared in Fig. 2. Qualitative features of the velocity profiles were similar for all subjects. They become increasingly asymmetric as the diameter of the target hole decreased. The asymmetry was due to a prolonged phase of deceleration and low velocity as the target was approached. Total movement duration increased and peak velocity decreased in conjunction with the increased asymmetry. In addition to the increased asymmetry of movements made to smaller targets, it is also apparent that the veIocity profiles become more irregular. These irregularities may result from secondary movements (submovements) which become more numerous as the constraint on accuracy becomes more stringent. There is evidence for such submovements in the hand paths, as well. Hand paths The hand paths of the movements of Fig. 2 are compared in Fig. 3. The hand paths have been
Accuracy
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Fig. 1. Experimental apparatus showing target board and instrumented subject. Infrared LED arrays were fastened to the hand, forearm, upper arm and shoulder. The subject is positioned ready to initiate the task. projected onto a plane which is parallel to the plane of the target board (YZ-plane). The motion occurring in this plane brings the peg into alignment with the target hole. Although we did not actually monitor motion of the peg, we can infer that motion of the hand is tightly linked with motion of the peg since the peg was held in a firm grip by the fingers. Changes in direction appear during all movements, but tend to occur more frequently when movements are made to the smaller target holes. Such abrupt changes in direction are likely the consequence of corrective submovements which serve to compensate for misalignment of the peg and target hole. When the hand paths are viewed along the X-axis (projections onto the XY- and XZ-planes) the movements to the larger target holes appear to be smooth and relatively linear (Figs 4 and 5). However, there are some rather abrupt changes in direction toward the end of the movements to the two smaller targets. We have taken a movement to the smallest target and used arrows to indicate corresponding points in time along the tangential vetocity profile and the hand path projected onto the YZ-plane as shown in Fig. 6. Inflections in the velocity profile occur with a similar frequency to changes in the direction of the
hand path. Such inflections could result from superimposing secondary movements (submovements) with a primary initial movement. Primary moveme~f We observed that from movement onset to peak tangential velocity, the velocity profile was usually quite smooth and similar in shape for movements to all targets. This provides evidence for the deployment of a large initial movement to cover most of the distance to the target. We postulate that this primary movement has a velocity profile of the same basic shape for all movements, but that its magnitude and duration can be scaled. Scaling would be done according to the following principle. As the target becomes smaller the magnitude of the velocity profile decreases and its duration increases. This would provide more time during which to take corrective action by slowing down the approach to the target. We would also expect to see a reduction in peak velocity, although not necessarily duration, if the distance to the target was decreased. To test these hypotheses we took the tangential velocity profiles for each subject, aligned them on peak velocity and normalized them by scaling them
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primary movement duration was also graded according to target size, increasing as target size decreased, again in agreement with our hypothesis. Finally, we found a reduction in peak velocity by approximately half when the distance to the smallest target was reduced from 20 to 8 cm. However, note that the time from movement onset to peak velocity and the total movement duration were reduced by less than 30%. Sow movements A number of earlier studies of multi-joint arm movements had found that tangential velocity profiles were usually quite symmetric. However, the movements which they examined were generally much faster than those in which we observed marked asymmetry. In order to determine whether the asymmetry resulted from the constraint on accuracy or whether it might simply be due to the speed of the movem~t, we asked subjects to make slow move-
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ments to the largest target. We had them prolong their movements so that they would arrive at the target approximately 500,750 or 1000 ms after movement onset. Figure 8 shows a typical tangential velocity profile. We observed no consistent asymmetry in the movements, although the velocity profiles became much more irregular than the fastest movements to the same target (Fig. 2). The irregula~ty is probably the result of a series of superimposed, overlapping submovements, but because the accuracy constraint is now one of timing rather than positioning, the overall organization is somewhat different. There are now irregularities in the initial phase of the movement, preceding peak tangential velocity. This suggests that unlike the task where speed and accuracy were paramount, the earliest submovements may now have smaller amplitudes than later ones.
DISCUSSION
Velocity profile shape
Our results clearly demonstrate that increasing requirements for accuracy produce an increasingly marked asymmetry in the tangential velocity profile. The decebrative phase of the motion is prolonged. The initial segment of the movement, up to and including the velocity peak, has a characteristically stereotyped shape for each subject. However, the peak velocity of this initial segment decreases and its duration increases as the requirements for accuracy become more stringent. Analysis of the three-dimensional hand paths has shown that there are changes in direction which correspond to inflections in the tangential velocity profile. From this we derive support for the view that final position accuracy is achieved by superimposing upon a primary move-
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series of submovements that are used in error correction. It is well known that movement duration increases as the target becomes smaller.9,2’ Our observations regarding the effects of accuracy on movement trajectories are consistent with a number of other studies.6*8*‘9*20 Our findings suggest that all subjects employed a common strategy. This consisted of a primary initial movement whose peak velocity and duration were controlled in such a way as to increase the time spent in approaching the target as the target became smaller. Woodworthzl made a similar observation when subjects were permitted to move relatively slowly in a task requiring considerable precision. The rationale behind such a strategy could be two-fold. Firstly, as the constraint on accuracy becomes more stringent, a greater number of corrective movements may be necessary to align the peg with the target hole. Secondly, if the arm is moving
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too fast, it may be difficult to make a small, precise correction because the inertia of the arm will tend to determine direction of motion. Thus, it would be desirable to keep tangential velocity low and prolong the time spent in the proximity of the target. Our observations support the findings of Langolf et aLi3 that when target tolerances are reduced, the whole movement becomes slower, that is, peak velocity decreases and movement duration increases. This contrasts with the conclusions of MacKenzie et cd.14 that target size had no effect on peak velocity. Although their task was slightly different (a Fitts’ tapping task with a stylus), the movement amplitude and range of indices of difficulty were similar. It is possible that they would have seen an effect had they separately analysed the horizontal and vertical velocity components. In their task there was no constraint on accuracy along the vertical axis whereas we had constraints on accuracy along all three axes of
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Fig. 6. Tangential velocity profile for a movement to the smallest target hole. Inset: hand path in the YZ-plane. The numbered arrows denote the velocity and position at corresponding times during the movement.
motion. One might expect an accuracy constraint along one axis of motion to have little effect on peak velocity in an orthogonal direction where there is no accuracy constraint.” Thus, if in a Fitts’ tapping task the velocity component in the vertical direction dominated the velocity component in the horizontal direction then the difference in the peak resultant (tangential) velocity might not change significantly even though the requirements for accuracy increased along the horizontal direction. Another factor cont~buting to the failure of MacKenzie ef ~1.‘~to find a change in peak velocity with target size may have been that in the Fitts’ tapping task there is no need for the subject to precisely regulate deceleration of the arm since the movement can be terminated by impact of the stylus with the target. In our task, on the other hand, it was necessary for the subject to regulate deceleration
TIME Fig. 7. Tangential velocity profiles of movements made to all targets by one subject. Profiles have been normalized with respect to peak velocity and scaled in duration to align on movement onset and peak velocity.
during movement termination since we did not permit impact with the target board. Unlike other studies of multi-joint arm movements3*” we found that in our task, the tangential velocity profiles were similar in shape (congruent) only over the initial segment of the movement. So~h~ng19 made similar observations, although he was able to demonstrate congruency over a greater proportion of the movement. Because irregularities in the velocity profile often appeared soon after peak velocity in our task, it was rarely possible to see congruency beyond the velocity peak. We attribute this difference to the fact that the accuracy constraint in our task was considerably more stringent than in these previous studies. Error correction Carlton and Meyer ef a1.l6 provided evidence for discrete corrective responses which appeared as auxilliary movements initiated when the velocity of the initial movement segment had almost reached zero. The velocity profiles of most of the movements which we recorded show evidence of secondary movements superimposed on the primary movement, often very soon after peak velocity is reached. This suggests to us that corrective responses are already occurring while the velocity is still high. There are often two or more of these secondary movements, suggesting further that overall accuracy is being assessed and corrective action taken periodically throughout the movement. Our findings are also supported by the work of MacKenzie et a1.j4 who reported that local peaks and valleys during the decelerative phase of tangential velocity profiles became particularly evident as the target was reduced in size. They also took this as evidence for “multiple inputs for trajectory control”, i.e. secondary movements.
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Accuracy and movement kinematics Table 1. Mean values and standard deviations of movement amplitude, peak tangential velocity and total movement duration Target size (mm)
Distance (cm)
Peak velocity (m/s)
50.8 25.4 17.5 11.1 11.1
20.7 + 1.2 20.1 f 1.1 20.0 & 1.4 19.7 + 1.3 8.2 f 0.1
1.05 * 0.20 0.73 + 0.18 0.59 &-0.08 0.50+0.12 0.26 f 0.04
Because the task of placing the peg in the smallest hole was very difficult, subjects were often unsuccessful. However, there was no obvious difference in the general appearance of tangential velocity profiles between successful and unsuccessful attempts to place the peg in the hole, indicating that subjects used the same strategy regardless of outcome. It is quite likely that the skill required to consistently succeed in quickly placing the peg in the hole can only be acquired through considerable practice, much like playing darts for example. What we have observed is probably a general strategy used in learning to be fast and accurate. Had we not insisted on speed and continuity of movement, we expect that our subjects would have chosen to break the motion into smaller discontinuous segments which would have allowed more sensory processing time and thereby guaranteed them of a higher success ratio. Hening et al.” have shown that the accuracy of subjects’ responses decreases when the time between appearance of a target and movement initiation is reduced. This is analogous to the reduction in sensory processing time that would occur in our task with an increase in the speed of movement to the target hole.
We examined movements on a trial by trial basis because the initial errors are very likely random in nature, and since corrective actions must be tailored individually to each movement, much of the detail
Time to peak (ms) 160&24 192&46 213&48 2405 100 169&31
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n
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would have been lost by averaging. It is clear that corrective actions take place as the target is approached. These corrective actions appear as abrupt changes in direction of the hand path. When a comparison is made between movements to targets of different sizes it is evident that these changes in direction are more numero~ for the smaller targets. The amplitude of these corrections is small which implies that the initial movement segment must already be quite accurate. It is not surprising therefore, that the corrective responses may not be seen if requirements for accuracy are not stringent or if the resolution of the recording apparatus is too low. One must exercise caution in using only hand path data to infer the existence or non-existence of submovements. Submovements could occur without producing a change in hand path direction. However, they would then be evident in the tangential velocity profile. At the other extreme, changes in curvature of the hand path could occur even in the absence of submovements. Flash” has modeled multi-joint movement trajectories which consist of a single primary movement with no submovements. She has shown that for certain movement directions musculoskeietal dynamics alone are sufficient to produce significant curvature in the hand path. However, in this case she predicts no inflections in the ~ngential velocity profile so once again velocity profile would be a better
5e ”
Target Size 50.8 mm
Fig. 8. Tangential velocity profile of a prolonged movement to the largest target hole. The subject was instructed to prolong the movement so that its duration would be approximately 1OOOms.Inset: hand path in the YZ-plane.
374
T. E. MILNER and M. M. I~AZ
indicator of submovements than hand path. Abrupt changes in hand path direction should be considered as supporting evidence though, since Flash’s model predicts only smooth changes in direction. Submovement struteg) When subjects were required to deliberately prolong their movements to the largest target hole, irregularities in the tangential velocity profile appeared throughout the movement, beginning during the accelerative phase. Taken together with evidence from changes in direction of the hand path this suggests that these movements also consisted of a series of superimposed submovements. In this case it is unlikely that the submovements reflect a strategy for error correction. A more plausible rationale is that they are related to the regulation of movement duration. It may be difficult to generate a single motor command with a duration as long as 1000 ms because of higher frequency periodic behavior within the central nervous system. Thus, a movement with a duration of IOOOms may be approximated by an overlapping sequence of submovements at shorter intervals which are superimposed upon one another.
CONCLUSIONS
The results of our experiments are consistent with the idea that a tangential velocity profile can be scaled in amplitude and duration according to the requirements of a task.“i’ However, when accuracy is required additional secondary movements may be superimposed on an initial primary movement. These secondary movements could be delayed with respect to one another, beginning with a large submovement and followed by a series of smaller ones. A similar principle can be used to account for the shape of velocity profiles recorded when the subjects were asked to regulate movement duration to the largest target. However, in this case the initial submovement need not have the largest amplitude.
Acknowledgements-This work was supported by a fellowship to T.M. from the Alberta Heritage Foundation for Medical Research and a fellowship to MI. from the
Harvard/MIT Division of Health Sciences and T~hnotogy, Medical Engin~ring-M~i~i Physics Program. We wish to thank Professor Robert Mann for having made available the facilities of the MIT Biomechanics and Human Rehabilitation Laboratory.
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