Motor Control & Sensory Integration

352 J. P. Wann & S. K. Rushton viewpoint was adjusted in real-time such that the tower always remained in the centre of the display. This prevented the participants performing the task in the way proposed by LleweUyn (1971), by centering the tower within the display. The tower was placed at virtual infinity so that the rotational component of flow produced by viewpoint rotation was negligible. The participants travelled for 150m and had 30secs in which to steer online with the target. During this period the display changed in response to their active steering and was presented at 24 frames/s. To accomplish the task participants had to adjust their heading to bring it, and the FRO, coincident with the tower and the centre of the screen. In contrast to the experiments of Warren et al, however, this task requires the active adjustment of heading (and FRO) rather than its passive perception. What order of flow information is necessary to accomplish this task? This can be examined by introducing similar manipulations to those used by Warren et al (1991) in a passive judgement task: If each dot appears in frame N, moves in accord with the observers ego motion to frame N+I, but then disappears, then it can be said that it had a frame life of 2 (2FL) . \"lifts in turn provides the observer with first-order velocity information about the instantaneous direction and speed of ego motion. An extension of the dot life to 3 frames (3FL), provides the observer with higher order motion components, such as change of speed and change of direction, as well as additional velocity information from correlations across non-consecutive frames. Both 2FL and 3FL contained some degree of noise contamination due to 2-frame or 3-frame flow lines, that either start or finish in frame N, and hence do not have a spatially correlated dot in frame N-1 or N+I, respectively. To balance for this factor we introduced a condition where 50% of the dots had permanent status and 50% had a frame life of 1 (pure noise). This latter condition has the same average signal/noise ratio as 2FL and a lower ratio than 3FL. To allow direct comparison with the angular offset at the start of each trial, we took the lateral (X) and forward (Z) displacement at the end of each trial and calculated the angle subtended with respect to the axes defined by the start and tower position: Of = tan \"1 L Z f - Z s (2)

Virtual Environments in Perception-Action Research 353 where subscripts s and f denote the positions at the start and finish of each trial respectively. This measure provides an indication of the degree to which participants had compensated for their initial heading error, but it is different from the directional heading of the tower at the end of each trial. Analysis of this performance measure indicated that all subjects could use the flow field information to substantially reduce their heading error, but there was a significant effect of the display conditions, (F[3, 105] = 39.72, p<.001), and some evidence of an interaction across participant, (F[12, 105] = 1.872, p = 0.057, with Huynh-Feldt corrections). Table 1 Mean unsigned heading error (degrees) after the completion of 30 seconds of active steering towards a target tower. WSE is the mean within-subject standard error across trials. Participant P1 P2 173 P4 P5 M e a n WSE Dot Disvlav 1.65 1.34 3.66 2.4 1.65 2.14 0.69 .,. ,, Permanent 50% Perm. 10.20 2.55 7.62 6.92 2.18 5.89 1.43 3FL 14.57 4.64 11.02 16.01 10.02 11.25 2.12 2FL 18.64 7.52 23.67 18.34 14.08 16.45 3.10 The results presented in Table 1 illustrate that although all participants were able to reduce their heading error in the Permanent condition, none of them approached the 1.2~ accuracy demonstrated by the subjects of Warren et al (1988) in a passive judgement task. It is also evident that the addition of noise to the display (50% Perm.) decreased steering performance, and in contrast to the results of Warren et al (1991) the 3FL and 2FL conditions completely undermined active steering performance. The poor performance of our participants under the latter conditions underscores an important principle in the presentation of VE displays. To make this study a replication of the Warren et al experiments we used a similar display device, which was a conventional computer monitor subtending a visual angle 38~ While this may be appropriate for the task of passively judging the side to which an observer is heading, it would seem to be insufficient to

354 J.P. Wann & S.K. Rushton support active steering. There are important differences between the passive judgements required by Warren et al and an active control task. In the former the participants may accumulate information over the duration of a trial to arrive at a \"best guess\" for the 2 choice paradigm (left or right of the targe0. In active steering, flow lines need to be detected from moment to moment, and the consequences of each steering action must be discerned within the environment. It is not surprising therefore that active steering is inaccurate when the optical array is only presented to a relatively small area of the visual field and there are strong proximal cues from the screen that weaken the illusion of egomotion. These reservations are supported by a further experiment where we presented participants with a 100~ field of view (back-projection) display, that was angled to allow the surface texture to \"flow\" close to the participants' feet, therefore providing a much stronger impression of \"immersion\" within a moving display. In this case subjects were able to steer to within a mean heading error of 1.5~ with skill ranging across 6 participants from 0.6~ to 2.7~ Rushton & Le~, submitted). Furthermore the level of steering skill was maintained across the noise and 3FL manipulations, although 2FL resulted in a significant decrease in performance. Hence we would judge that the results presented in Table 1 stress the importance of providing an ecologically appropriate field of view for active tasks and that the recreation of a suitable VE for perceptual-motor research requires consideration beyond the computation of appropriate graphics. Display devices that are adequate for psychophysical studies (e.g. Roydon, Banks & Crowell, 1992; Warren & Hannon, 1988; Warren et al, 1988, 1991) may not translate well to interactive simulation. Although conventional desktop computer displays have been the workhorse of perceptual psychology, their usefulness in the area of VE simulation is questionable. 3. SHORTCOMINGS OF VIRTUAL ENVIRONMENTS 3.1 The binocular optic array In general the re-creation of a VE requires a display device that can provide the user with the information upon which they would rely in a natural context. Because we have a binocular visual system, binocular cues may be a primary source of information for some tasks. It has been outlined in section 1.1 that stereoscopic information can be provided by

Virtual Environments in Perception-Action Research 355 a dual channel large screen projection or a head-mounted display (HMD: Figure 1). The appeal of a HMD is that it can be made head-responsive and allow the user to scan the display through 360~ using natural head and body movements. The basic HMD design was prototyped by Sutherland (1968) and has since been copied by a number of manufacturers based on the assumption that \"if we place two-dimensional images on the observer's retinas, we can create the illusion that he is seeing a three-dimensional object\" (Sutherland, 1968, p.758). This statement appears correct, but we would modify it by stating that an illusion of a 3-D objects can be produced, but 3-D space can not be rendered with integrity from dual 2-D images. There are problems that arise from using 2- D image sources to represent a range of disparity increment equivalent to a 3-D word which an observer then selectively views. Problems arise from the monocular-focal and binocular-vergence responses that occur in natural visual environments. Binocular regard of visual objects in near space (e.g., 50cm) and far space (>2m) requires differing degrees of ocular convergence. This would normally be accompanied by focusing upon the object of interest. The screen images of a HMD, however, can only be seen in focus by accommodating to a fixed distance (the virtual image plane: Figure 1). Accommodation and convergence are cross-linked so that one will tend to influence the other (Judge & Miles, 1985). This natural coupling of accommodation and convergence becomes problematic as the user begins to sample the VE environment and may lead to symptoms of visual stress during prolonged viewing (Mon-Williams, Wann& Rushton, 1993; Wann, Mon-Williams & Rushton, in press). A simple solution is to move toward monoscopic(single-channel) HMDs which do not appear to produce related symptoms (Rushton, Mon-Williams &Wann, 1994). The issue, however, is whether stereo depth cues are important for a specific application. In natural settings stereo-disparity cues are clearly used for depth judgements in near space. Although kinetic depth cues can make observers in a cinema flinch as an object looms on the screen, they cannot make the object appear to project forward from the screen. A monoscopic display system will always have difficulty in presenting close working images for manual interaction tasks. The results reported in section 2, coupled with the results of Judge & Bradford (1988) also suggest that disparity information will influence interceptive timing.

356 J.P. Wann & S.K. Rushton 3.2 The virtual haptic array The recreation of the haptic sensations that arise from an observer interacting with a visually specified virtual object presents a considerable challenge. If the VE presents a visual structure on the same scale as the observers natural environment, then there should be congruence between the virtual visual space and the actors intrinsic kinaesthetic space: For example if an observer sees a virtual coffee cup that appears to be 50cm away, then reaching to a position that feels as though it is 50cm away from the body, should result in an appropriate motion of a virtual, visual hand, or the cup. It is of course possible to change the visual-proprioceptive mapping and have an observer able to reach across a virtual room to pick up a desk. The learning curve for large scale visual-propdoceptive re-mapping provides an interesting area for future study. Problems arise, however, when it is necessary to provide additional haptic feedback from the virtual environment, as might be required for manipulation tasks. There have been several technical approaches to this problem which we will not discuss in detail: Researchers have piloted inflating gloves, vibratory actuators and exo-skeletons to try and provide feedback of contact forces and haptic properties. To date there are no satisfactory solutions and the options seem to be either over-simplification or over-engineering. There is also a perceptual problem hindering the development of technical solutions: Our knowledge base of mapping from simple stimulus variables to perceptions such as rough, smooth, gritty, metallic, wooden is less extensive than the equivalent for visual perception. While progress is being made with specific haptic displays, the ability to computational specify general properties such as mass, density and surface material for haptic perception, lags well behind the rapid gains in computer graphics. 4. CONCLUSIONS The potential of the VE setting for perceptual-motor experimentation is enormous. Because the display is purely the result of computation, it can be scaled through computational algorithms and changed in non-veddical ways from moment to moment. In tasks where vision can be assumed to be the primary source of information, there is scope for the re-analysis of many experimental tasks. This chapter has presented examples of the perception of impending collision and of locomotor heading. Broader application of VEs in locomotor control can be made to navigation and cognitive mapping of

Virtual Environments in Perception-ActionResearch 357 environmental geography; judgement of locomotor distance (Laurent & Thomson, 1988), and perception of affordances for action (Warren, 1984). VEs also provide an ideal tool to refine tile rather contrived tasks used to examine visual-proprioceptive mapping (Wann, 1991) and proprioceptive stability (Wann& Ibrahim, 1992). Their use for studying behaviours such as grasping and manipulation may be constrained by the problems of haptic displays (section 3.2), although they still provide avenues to examine sub- components of these behaviours, such as pointing (Prablanc et al, 1979) and have been used to explore cortical activation during the perception of reaching (Decety et al, 1994). Additionally, the ability to fashion the environment in which an actor learns and controls their movement may have application to rehabilitation of motor disorders (Wann & TumbuU, 1993). REFERENCES Bruno, N.E., & Cutting, J.E. (1988). Minimodularity and the perception of layout. Journal of Experimental Psychology: General 117, 161-170 Cruz-Neira, C., Sandin, D.J., & Defanti, T.A. (1993). Surround-screen projection-based virtual reality: The design and implementation of the CAVE. Computer Graphics, 135-142 Cutting, J.E. (1986). Perception with an Eyefor Motion. Cambridge, MA: MIT Decety, J., Perani, D., Jeannerod, M., Bettinardi, V., Tadary, B., Woods, R., Mazziotta, J.C., & Fazio, F. (1994). Mapping motor representations with positron emission tomography. Nature, 371,600-602. DeLucia, P. R., & Warren, R. (1994). Pictorial and motion-based depth information during active control of self-motion: Size- arrival effects on collision avoidance. Journal of Experimental Psychology: Human Perception and Performance, 20, 783- 798. Denier van der Gon, J.J., & Thuring, J.Ph. (1965). The guiding of human writing movements. Kybernetik, 2, 145-148. Elliott, D., Zuberec, S., & Milgram, P. (1994). The effects of periodic visual occlusion on ball catching. Journal of Motor Behavior, 26, 113-122.

358 J. P. Warm & S. K. Rushton Ellis, S., et al, (1992). Research Directions in Virtual Environments. Report of an NSF Invitational Workshop, Univ. N. Carolina, March 1992. Computer Graphics, 26, (3), 153-177. Held, R., & Freedman, S. (1963). Plasticity in human sensorimotor control. Science, 142, 455-462. Held, R., & Gottlieb, N. (1958). Technique for studying adaptation to disarranged hand eye coordination. Perception & Motor Skills, 8, 83-86. Hubbard, M. (1994). Simulating sensitive dynamic control of a bobsled. Proc. of Mathematics & Computers in Sport, July 1994. Bond Univ. Australia. 1-6. Jeannerod, M. (1981). Intersegmental coordination during reaching at natural visual objects. In J. Long & A.D. Baddeley (Eds) Attention & Performance (pp. 153-168). Hillsdale, N.J: Erlbaum. Judge, S.J., & Bradford, C.M. (1988). Adaptation to telestereoscopic viewing measured by one-handed ball-catching performance. Perception, 17, 783-802 Judge, S.J., & Miles, F.A. (1985). Changes in the coupling between accommodation and vergence eye movements (the stimulus AC/A ratio) induced in human subjects by altering the effective interocular separation. Perception, 14, 617-629. Kaiser, M.K., & Mowafy, L. (1993). Optical specification of time-to- passage: Observer's sensitivity to global tau. Journal of Experimental Psychology: Human Perception and Performance, 19, 1028-1040 Laurent, M., & Thomson, J.A. (1988). The role of visual information in control of a constrained locomotor task. Journal of Motor Behavior, 20, 17-37. Lee, D.N. (1976). A theory of visual control of braking based on information about time- to-collision. Perception, 5, 437- 459 Llewellyn, K.R. (1971). Visual guidance of locomotion. Journal of Experimental Psychology, 91,245-261. Mcleod, R.W., & Ross, H.E., (1983). Optic-flow and cognitive factors in time-to- collision estimates. Perception, 12, 417-423. Mon-Williams, M., Wann, J. & Rushton, S. (1993). Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display. Ophthalmic and Physiological Optics, 13, 387-391 Nakayama, K. (1994). James J. Gibson - An appreciation. Psychological Review, 101, 329-335.

Virtual Environments in Perception-ActionResearch 359 Prablanc, C., Echallier, J.F., Komilis, E., & Jeannerod, M. (1979). Optimal response of eye and hand motor systems in pointing at a visual target. I. Spatio-temporal characteristics of eye and hand movements and their relationships when varying the amount of visual information. Biological Cybernetics, 35, 113-124. Regan, D., & Beverley, K.I. (1979). Binocular and monocular stimuli for motion in depth: Changing-disparity and changing-size feed the same motion-in-depth stage. Vision Research, 19, 1331-1342. Regan, D., & Hamstra, S.J. (1993). Dissociation of discrimination thresholds for time to contact and for rate of angular expansion. Vision Research, 33, 447-462. Roydon, C.S., Banks, M.S., & Crowell, J.A. (1992). The perception of heading during eye movements. Nature, 360, 583-585. Rushton S., Mon-Williams, M., & Warm, J.P. (1994). No evidence of visual deficits following the use of a new generation head-mounted display. Displays, 12, 234-245. Savelsbergh, G.J.P., Whiting, H.T.A., & Bootsma, R.J. (1991). Grasping tau. Journal of Experimental Psychology: Human Perception and Performance, 17, 315-322. Savelsbergh, G.J.P., Whiting, H.T.A., Pijpers, J.R., & van Santvoord, A.A.M. (1993). The visual guidance of catching. Experimental Brain Research, 93, 148-156. Schiff, W., & Oldak, R. (1990). Accuracy of judging time-to-arrival: Effects of modality, trajectory, and gender. Journal of Experimental Psychology: Human Perception and Performance, 16, 303-316. Sharp, R.H., & Whiting, H.T.A. (1974). Exposed and occluded duration effects in a ball- catching skill. Journal of Motor Behavior, 3, 139-147. Sutherland, I.E. (1968). A head-mounted three dimensional display. Fall Joint Computer Conference, 33, 757-764. Tresilian, J.R. (1991). Empirical and theoretical issues in the perception of time to contact. Journal of Experimental Psychology: Human Perception and Performance, 17, 865-876. Van Den Berg, A.V. (1992). Robustness of perception of heading from optic flow. Vision Research, 32, 1285-1296. Wann, J.P. (1991). The integrity of visual-propriocepdve mapping in Cerebral Palsy. Neuropsychologia, 29, 1095-1106

360 J.P. Warm& S.K. Rushton Warm, J.P., & Ibrahim, S. (1992). Does proprioception drift? Experimental Brain Research, 91,162-166. Warm, J.P., Mon-Williams, M., & Rushton, S.K. (in press). Natural problems in the perception of stereoscopic virtual environments. VisionResearch. Wann, J.P., & Rushton, S.K. (in press). Grasping the impossible: Stereoscopically presented virtual balls. In B. Bardy, R. Bootsma & Y. Guiard (Eds.), Proceedings of the 8th International Conference on Event Perception and Action. July, 1995, Marseilles, France. Wann, J.P., Rushton, S.K., & Lee, D.N. (in press). Can you control where you are heading when you are looking at where you want to go? In B. Bardy, R. Bootsma, & Y. Gtflard (Eds.), Proceedings of the 8th International Conference on Event Peerception andAction. July, 1995, Marseilles, France. Wann J.P., & Turnbull, J. (1993). Motor Skill Learning In Cerebral Palsy: Movement, Action and Computer EnhanceATherapy. BaiUiere's Clinical Neurology, 2, 15-28 Warren, W.H. (1984). Perceiving affordances: Visual guidance of stair climbing. Journal of Experimental Psychology: Human Perception & Performance, 10, 683-703 Warren, W.H. (1988). Action modes and laws of control for the visual guidance of action. In O. Meijer & K. Roth (Eds.), Movement Behavior: The motor-action controversy (pp. 339-379). Amsterdam: North Holland. Warren, W.H., & D.J. Hannon, D.J. (1988). Direction of self-motion is perceived from optical flow. Nature, 336, 162-163. Warren, W.H., Blackwell, A.W., Kurtz, K.J., Hatsopoulos, N.G., & Kalish, M.L. (1991). On the sufficiency of the velocity field for the perception of heading. Biological Cybernetics, 65, 311-320. Warren, W.H., Morris, M.W., & Kalish, M.L. (1988). Perception of translational heading from optic flow. Journal of Experimental Psychology: Human Perception & Performance, 14, 646-660. Whiting, H.T.A. (1968). Training in a continuous ball throwing and catching task. Ergonomics, 13, 445-454.

Motor Control and Sensory Motor Integration\" Issues and Directions 361 D.J. Glencross and J.P. Piek (Editors) 9 1995 Elsevier Science B.V. All fights reserved. Chapter 14 TRAJECTORY MODIFICATIONS IN RF_.~PONSE TO SUPERSEDING STEP STIMULI N.C. Barrett School of Psychology, Curtin University of Technology, Perth, Western Australia, 6001, Australia. R.T. Kane Department of Psychology, University of Western Australia, Nedlands, Western Australia, 6907, Australia. The present paper examines one-dimensional and two-dimensional double-step tracking responses across the manual and oculomotor control systems. Initial double-step responses are characterized by i) a corrective reaction time that increases as a function of the determinant time interval (D) between the onset of a second step and the initiation of a response, and ii) an amplitude or angle of the initial response that varies as a function of D across an amplitude transition function. The modification to the amplitude of an initial step response occurs at shorter Ds for target steps in opposite directions than for steps in the same direction. For two-dimensional step-tracking, the initial angle is modified at the outset of the response and is independent of the interstimulus interval between target steps. The corrective response is characterized by its accuracy with respect to the final target position and can display a peak velocity that is threefold that of an equivalent single-step response. These results are discussed in relation to models that predict either i) that the initial portion of the initial response should be equivalent to a single-step response to the first target step position, or ii) that the initial response is determined by the temporal integration of both target step positions. 1. INTRODUCTION The ability to rapidly update visuo-spatial error information is a crucial requirement for the control of aiming movements. The present paper discusses trajectory modifications during a step-tracking task for which the superseding target displacement occurs specifically during the reaction time to the initial target step. Amendments to the trajectory of responses to double-step stimuli, as a function of when the second step occurs during the initial reaction time, have been well documented for both the saccadic (e.g., Aslin & Shea, 1987; Becker & Jtirgens, 1975, 1979; Deubel, Wolfe & Hauske, 1984; van Asten, Gielen & Winkel, 1988) as well as manual (e.g., Barrett & Glencross,

362 N. C. Barrett & R. T. Kane 1988; Georgopoulos, Kalaska & Massey, 1981; Gielen, van den Heuvel, Dernier van der Gon, 1984; Gottsdanker, 1967, 1973; Kerr, 1993; Van Sonderen, Denier van der Gon & Gielen, 1988) control systems. An ongoing theoretical debate (e.g., Gottsdanker, 1967) has focused on whether the initial response to double-step stimuli is directed towards the location of the first target or whether the amended trajectory is already specified in the central commands that initiate the displacement of the response unit. The control processes underlying responses to double-step stimuli may be inferred by comparing the response parameters of double-step responses to those of single-step responses. In particular, the present paper focuses on four parameters that characterise responses to double-step stimuli: The corrective reaction time, the modified trajectory, the peak velocity of the corrective response for transitional responses, and the accuracy of the corrective response. The parameters are examined in the next section followed by an examination in section 4 of the control principles that underlie trajectory modifications to double-step stimuli. 2. CHARACTERISTICS OF RESPONSES TO DOUBLE STEP STIMULI Response parameters depend on the location of the second target position relative to the initial step position. In one dimensional tracking - where the tracking is from left to fight or vice versa - stimulus patterns fall into four categories. These have been labeled by Becker and Jiirgens (1979) as: Staircase (SC) stimuli, pulse overshoot (PO) stimuli, pulse undershoot (PU) stimuli, ans symmetrical pulse (SP) stimuli. SC stimuli refer to successive steps in the same direction. The other stimulus categories refer to successive steps in opposing directions: For PO stimuli, the final target position is located on the side of the homebase opposite to the initial step position; for PU stimuli, the final target position is located between the homebase and the initial target position; for SP stimuli, the second target step brings the target back to the homebase. For a circular arrangement of targets around a central target, step-tracking in two dimensions is possible. For this type of display, the step pattern can be described in two dimensions - e.g., near-center-left or center-right-far.

Superseding Step Stimuli 363 2.1 The Corrective Reaction Time The corrective reaction time - i.e., the time that elapses between the onset of a second target step and the modification of an initial step response - has traditionally aroused much interest with reports that it might be equivalent to the initial reaction time (e.g., Georgopoulos et al., 1981; Gielen et al., 1984; Gottsdanker, 1966, 1973; Van Sonderen et al., 1988; Soechting & Lacquaniti, 1983). These reports were of interest because they suggested that responses to superseding stimuli made with the same response unit (both stimuli are responded to with the fight ann) are immune to a psychological refractory period (PRP). When separate response units are used, however, a PRP phenomenon has consistently been reported (e.g., Bertelson, 1966). Delayed corrective reaction times compared to control reaction times have nevertheless been reported. Georgopoulos et al. (1981), for example, noted that when the stimulus crossed the homebase - a PO stimulus pattern - at very short interstimulus intervals (ISis) of 50 msec, corrective reaction times averaged 59 msec longer than reaction times to single-steps of the target. More extensive delays have been reported in those studies that have considered response parameters as a function of the determinant time interval, rather than the ISI. The determinant time interval (henceforth referred to as D) is the interval between the onset of the second target step and the initiation of a response. At the same ISI a wide range of Ds is possible. As a result any delays to the corrective reaction time that may be a function of D will be averaged-out when the analysis focuses on the ISI. Kerr (1993) noted that corrective reaction time is lengthened as a function of the D for PO and SC stimuli. For the oculomotor system corrective reaction time did not reach a minimum until about 90-100 msec prior to a saccade. For arm movements the minimum corrective reaction time occurred at a D of approximately 50 msec. Depending on the stimulus pattern, maximum corrective reaction times were observed to be in the order of 400 msec for both the oculomotor (saccadic) and manual control systems. Long delays, particularly at large Ds, have also been reported for PU stimuli (e.g., Barrett & Glencross, 1988). Minimum corrective reactive reaction times were noted for Ds of 80-120 msec. Movement time is one variable that may account for the different delays in the corrective reaction time reported in the literature, since movement time might play a role in determining the onset of the corrective response. Whereas the control movement time used in the Georgopoulos et al (1981) study was 400 msec, the control movement time

364 N.C. Barrett & R.T. Kane for Barrett & Glencross (1988) was 150 msec. Moreover, estimates of the corrective reaction time vary according to its assumed offset: Shorter estimates are obtained when the offset corresponds to the onset of deceleration; when the offset corresponds to a change in the initial response, minimal delays have been reported; when the offset corresponds to the onset of the corrective response, more extensive delays have been reported. The nature of the delays in the corrective reaction time merits further investigation. Kerr (1993) argues that they are consistent with a serial 'bottleneck' in the processing of visuo-motor information. He argues that visual information appears to be continuously updated during the early stages of response preparation and therefore there will be alterations to the initial response amplitude. However, the corrective response itself must await the completion of any ongoing computations associated with the initial response amplitude. As a result there will be a PRP between the initial and corrective motor responses. Implicit in Kerr's (1993) argument is the notion of a temporal integration of step stimuli. The feasibility of this approach is addressed in a subsequent section. 2.2 The Modified Trajectory In a double-step tracking situation subjects often do not produce a response that goes to the initial step position before effecting a response to the superseding target step. Whether a modification is made - and indeed the nature of modification - depends on the particular stimulus pattern as well as the control system involved. For both the manual and oculomotor control systems, the literature concurs that the minimum D at which an amendment is possible is longest for SC stimuli. Becker and Jiirgens (1975, 1979) observed that saccadic responses to SC stimuli were more likely to go initially to the first target location at which point a corrective saccade was initiated to the final target position. In addition, the magnitude of the D at which a modification is first observed was longest for SC stimuli than for the other stimulus patterns: 200 msec for SC stimuli, 172 msec for PO stimuli, 122 msec for SP stimuli, and 81 msec for PU stimuli. For PU stimuli, the minimum D of 81 msec for PU stimuli at which an amendment to the response amplitude is first observed corresponds well with estimates for the manual control system (e.g., Barrett & Glencross, 1988). Kerr (1993) estimates the minimum D for manual responses to SC stimuli to be 135 msec and for PO stimuli to be 67 msec. Though these estimates differ somewhat across the manual and oculomotor

Superseding Step Stimuli 365 control systems, it is interesting to note that for both control systems the longest minimum D is observed for SC stimuli. For both the manual and the oculomotor control systems then, the literature concurs that the minimum D at which a trajectory modification is possible is longest for SC stimuli. This suggests that it is easier to halt or reduce the amplitude of an ongoing movement than it is to increase its amplitude. In contrast, for a second step occuring after the initiation of the response, increasing the amplitude of the response has been shown to be achieved more readily than decreasing the amplitude (e.g. Barrett & Glencross, 1989). These researchers argued that once a motor program is initiated, it is easier to reorganise an already existing motor program than to select a new program. A similar principle may account for adjustments to other movement parameters. The reaction time to a stimulus indicating that a movement should be sped-up is shorter than one indicating that the movement be slowed down (e.g., Vince & Welford, 1967). On the other hand, Piek, Glencross, Barrett and Love (1993) found no difference in the organizational time to either increase or decrease the force of a tap in a sequence of taps. When presented with a crossed PO stimulus pattern, the subject wRl sometimes produce a response directly to the second target step location - a direction opposite to that specified by the initial target step. For saccadic responses to PO stimuli, a movement directly to the final target step position may (Becker & Jiirgens, 1979) or may not (e.g., Kerr, 1993) be associated with a lengthened initial reaction time. Direct movements to the second target location are not typically reported for manual responses to PO stimuli, although equivalent types of manual responses have been observed (e.g., Schmidt & Gordon, 1977). These researchers were interested in single- step tracking responses to stimuli presented either to the left or fight of a homebase position. They 'fooled' subjects into believing that on certain trials the single target step would be in a particular direction; the actual step, however, was in the opposite direction. In this situation, an incorrectly anticipated single-step response is equivalent to a double- step PO trial: An initial response is generated to a first 'anticipated' target step and the subject must then respond to a second 'actual' target step on the opposite side of the homebase. Six of the 8 subjects initiated a response in the wrong direction, halted the response, and then produced a response to the required target location. The two subjects who produced a response directly to the target, did so with a lengthened reaction time - 404 msec on average.

366 N.C. Barrett & R.T. Kane F'mal position responses similar to those investigated by Schmidt and Gordon (1977) have been shown to be associated with a suppression of eleetromyographic activity prior to limb displacement (e.g., Morris, 1981). This is consistent with the notion that PO responses directly to the final target position result from a cancellation of ongoing processes associated with the decision to produce responses to the initial target step position. Once the response decision has been cancelled, processes associated with a response in the corm~t direction are initiated. Transition-free responses directly to the final step position are relatively rare. Typically the response will either go to the initial step position or to some intermediate position between the first and second step positions. Georgopoulos et al (1981), for example, noted a gradual transition of trajectory amplitudes between the f'wst step position and the homebase for crossed PO step stimuli. Under these circumstances, the amplitude of the initial response for both the manual and oculomotor control systems has been shown to vary as a function of the ISI (e.g., Georgopoulos et al, 1981) as well as D (e.g., Becker & Jiirgens, 1979). Becker and Jiirgens (1979) considered oculomotor response parameters as a function of D. They proposed that their results could be understood in terms of an amplitude transition function (ATF). Examples of amplitude transition functions from Becker and Jtirgens' (1979) data are illustrated in Figure 1. Figure 1 plots amplitude transition functions for different types of stimulus pattern. The amplitude of the first saccade (~b1) is plotted as a function of D. Consider, for example, responses to PU stimuli that involve target steps in opposite directions but on the same side of the homebase. At short Ds (i.e., long ISis) the initial saccade covered the entire amplitude to the initial target step position; this type of response is referred to as an initial amplitude response (IAR). The IAR was then followed by a corrective saccade to the final step position. At a very long Ds (i.e., short ISis) a single saccade was initiated that jumped immediately to the final target position; this type of response is referred to as a final amplitude response (FAR). Intermediate values D were associated with saccadic responses with an amplitude between the first and second step positions; this type of response is referred to as an intermediate amplitude responses 0MAR). IARs and FARs have also been observed as a function of D for manual responses (e.g., Gielen et al., 1984). Figure 1 shows that very

Superseding Step Stimuli 367 large amplitude modifications for saccadic responses to PO stimuli were relatively rare - as they were for manual responses to the same type of stimuli (Kerr, 1993). 30 ~ 9 eQ o ~ 15\" t g' ,b j 9 9 ..-. ~,,- .,..\". SC 9~ i' l 9 ZOO 40o r v', \".: PU ! I 9\"\" OOo oo 9 Io0 ! IS 9 - 400 ZOO 0 ~ ..... \" \"'- \"':\"~ '\" PO 9! tOO \"2, o j- -,- 0I 9 ',,.. 600 / ,t J ii --- [3 / msec -I s\" !.. 200 ~9 - \"~-~= ~;';;~'~- -- Figure 1. Initial response amplitudes (~) as a function of the determinant time interval (D) between the onset of a second target step and the initiation of a saccadic response for staircase (SC), pulse undershoot (PU) and pulse overshoot (PO) stimuli. Each response amplitude is recorded as a dot. The dashed lines represent amplitude transition functions. The horizontal line-segments correspond to the average amplitude of single step responses to the furst (at shorter D's) and final target step positions (at longer D's). An amplitude of 0 corresponds to the homebase. (Reproduced withpermission of Pergamon Press from Becker, W., & Jttrgens, R. (1979). An analysis of the saccadic system by means of double step stimuli. VisionResearch, 19, 967-983. Figure5.) For other stimulus patterns, very large amplitude modifications are frequently observed. Not only are these modifications similar across the manual and oculomotor control systems, but they are correlated across these systems. Kerr (1993) has reported correlations between the initial amplitudes for corresponding saccadic and limb

368 N. C. Barrett & R. T. Kane movements: r = .229 for PO stimuli and r = .658 for SC stimuli. The strength of the relationship across control systems is highest for steps in the same direction. Becker and Jiirgens (1979) fitted an idealized shape of the function relating D to r (see dashed lines in Figure 1). Of particular interest, are the gradual transitions of saccadic amplitudes between the first and second step positions as a function of D. They reflect a time window during the initial reaction time in which a transition between the unamended IARs and the fully-amended FARs are observed. At issue is to what extent this time window reflects processes unique to the initial reaction time. It is interesting to note that although the minimum D at which an amendment may occur can differ substantially across stimulus patterns, the duration of the slope of the function in Becker and Jiirgens' data remained relatively constant. A transitional time window is also suggested by responses to a two-dimensional tracking situation in which targets are arranged around a central target (e.g., Georgopoulos et al; 1981; Flanagan et al., 1992; van Sonderen et al., 1988; van Sonderen & Denier van der Gon, 1991). Georgopoulos et al. (1981) have suggested, however, that separate control principles may govern responses to target steps in one and two dimensions. Figure 2, from the data of van Sonderen et al (1988), describes examples of trajectory modifications in two-dimensional space as a function of ISI. The trajectory modifications are for responses to center-fight-far target steps. Interestingly, at very short ISis (viz, 25msec) the initial movement direction showed signs of modification at its outset. This suggests that there is no relationship between the ISI and the duration of the initial response that remains unaffected by the second stimulus. van Sonderen et al (1988) reported that correlations between the initial response angle and D were greater than correlations between the initial response angle and either the initial reaction time or ISI. These findings support Becker and Jiirgens' (1979) decision to analyse response parameters as a function of D by intimating that effects may be averaged-out if response parameters are considered as a function of ISI.

Single-Step P0 \" P1 P -2 ,,.. ISI 100 msecl~ ISI 75 msec I~ Double-Step P0 \" P1 ISI 50 msec 1~ ISI 25 msec I~ sin les p P2 T/ P0 Figure 2. Movement trajectories to single (top and bottom traces) and double steps of a reproduced in the left side column. At ISI25 and ISI50 ms the trajectory appears to be modi Sonderen, J.F., Denier van der Gon, J.J., & Gielen, C.C.A.M., (1988). Conditions determ location. Experimental Brain Research, 71, 320-328. Figure 2 ).

<_,,,- > ll 11 target at different interstimulus intervals (ISIs). The stimulus patterns are ified at its outset. (. Reproduced with permission of Springer-Verlag.. from van mining early modification of motor programs in response to change in target

370 N. C. Barrett & R. T. Kane Flanagan et al. (1993) compared two-dimensional double-step responses for near- center-left and near-center-fight responses. They looked at the amplitude at which the paths for the two types of responses diverged. They did this for responses produced at both faster-than-preferred rates and preferred rates. The traces reported by Flanagan et al. (1993) for the former type of responses for two subjects (A and C) are reproduced in Figure 3. The point at which the traces diverge for a second step to the right or left of the center step position are indicated by a horizontal bar. The longer the ISI, the greater the amplitude before the responses to the second target step to the left or fight diverged. In view of van Sonderen et al's (1988) observation that initial response angle is correlated more strongly with D than ISI it would be interesting to re-evaluate Flanagan et al's (1993) results as a function of D. 2 0 m s ISI 6 0 m s ISI 1 0 0 m s ISI -\"~~~~ ~,. .... . .... ...::...:. ... .-. . . . . ..!? A \"I I 1 ! I I If f I 9 I I I \"~ f l !t J \"\" I ......... C t \" /\"J- ~! l I If 11! I I1 f I I I I Figure 3. Trajectoriesof responses to double-steps of a target as a function of the interstimulus interval (ISD for two subjects. The responses are produced at a faster than prefmed rate. Dotted lines represent near-center-left target steps. Solid lines represent near-center-right steps. A horizontal bar indicates where the dotted and solid lines diverge. The point of divergence occurs at longer amplitudes the greater the ISI. (Reprintedby permissionof Heldref Publicationsfrom Flanagan, J.R., Ostry, D.Z, & FeMman, A.G. (1993). Control of r modifications in target-directed reaching. Journal of Motor Behaviour, 16, 2-19, Figure 10.)

Superseding Step Stimuli 371 Systematic changes to the initial movement direction need not result from a superseding target shift. Indeed, such changes have been observed in the absence of a superseding target step. van Sonderen and Denier van der Gon (1991) examined the initial movement direction of responses across a wider range of reaction times. They used a technique involving the presentation of an auditory stimulus that has been shown to reduce reaction time. They confirmed previous findings that initial movement direction varies as a function of ISI. An interesting observation is that this relationship holds for single-step responses as well. Changes to the initial movement direction may therefore occur even without target displacement. On the basis of this finding, van Sonderen and Denier van der Gon (1991) argued that the system uses a default direction when target information is not yet available. This strategy adds to the complexity of the stimulus situation when superseding steps of the target are eventually presented. The duration and slope of the transition phase between IARs (i.e., initial amplitude responses) and FARs (i.e., final amplitude responses) may be useful in revealing the control processes underlying trajectory modifications. Becker and Jiirgens (1979) compared the duration of the transition phase across stimulus patterns. They concluded that the transition phase was characterized by a constant duration in the order of 120 msec. If this duration is indeed constant, then it has fundamental implications for how we view the control processes underlying response to double-step stimuli. There is, however, little agreement in the literature concerning the duration and constancy of the transition phase between IARs and FARs. For the oculomotor system, Aslin and Shea (1987) have suggested that the interval may be as short as 20 msec. On the other hand, van Sonderen et al's (1991) estimate of 100 msec for the manual control system is more in line with Becker and Jiirgens' (1979) estimate. Barrett and Glencross (1988) argued that if the duration of the transition phase is constant, then by keeping the amplitude of the initial target step constant and varying the amplitude of the second target step there should be a corresponding change in the slope of the transition phase of the ATF (i.e., amplitude transition function). Using PU stimuli, they noted a relationship between the slope of the ATF and the amplitude of the superseding step. This suggested a time w'mdow of constant duration. The likelihood of a superseding step on any trial, however, was high in this study and their results might merely reflect anticipation.

372 N. C Barrett & R. T. Kane 2.3 Peak Velodty of the Corrective Response For crossed double-step responses Georgopoulos et al. (1981) and Massey, Schwartz and Georgopoulos (1986) have observed large increases in the peak velocity of the corrective response compared to control single-step responses. In some instances, the peak velocity of the corrective response was reported to represent a three-fold increase over the peak velocity for control responses. This increase was observed even at short ISis where the amplitude of the corrective response was equivalent to the amplitude of the control single-step responses. Therefore, as Georgopoulos et al. (1981) point out, it is not simply a matter that the peak velocity has been adjusted to the amplitude of the movement. This is a crucial feature of PO double-step responses and needs to be addressed by models of the control principles underlying trajectory modifications to target displacements. 2.4 Accuracy of the Corrective Response The accuracy of the corrective response has important implications for the information that must be available to the system at the time the corrective response is implemented. For SC stimuli (e.g., Gielen et al., 1984, Kerr, 1993) as well as PO stimuli (e.g., Georgopoulos et al., 1981), the corrective response is accurate with respect to the final target step position. The system achieves this accuracy despite the wide variations in the initial response amplitude. The amplitude of the corrective response does not simply equal the size of the second target step or the distance from the homebase to the final target position. Instead, the corrective response takes into account the differences in the initial response amplitude and consequently the discrepancy between the amended hand position and the final target location. The interval between target steps seems an unlikely candidate as a source of information, since response parameters vary more as a function of D rather than ISI (van Sonderen & Denier van tier Gon, 1991). One possibility is that the system has available to it advance information regarding the initial response amplitude. For this to happen, the information must fLrstly be available in the efferent command and secondly the system must be able to monitor the efference centrally (e.g., Angel, 1976). For an efference copy to be of value, the corrected amplitude must itself be specified in the initial efferent command. On the other hand, if

Superseding Step Stimuli 373 the amplitude of the initial response is irrelevant to the implementation of a corrective response, then the information available in an efference copy is not a crucial consideration. For the manual control system, the forces are modified from movement to movement (e.g., Kelso & Stelmach, 1976). It is unlikely, therefore, that position information is available to the manual control system via an efference copy. The eyeball, however, is propelled by only two sets of muscles and therefore moves under a fairly constant set of forces. The prediction of response amplitude from an efference copy is more feasible (e.g., Guthrie, Porter & Sparks, 1983). 3. CONTROL PRINCIPLES UNDERLYING RESPONSES TO DOUBLE STEP STIMULI Models of response amendments to superseding step stimuli are divided on whether or not the response is initially directed to the first step position. 3.1 The Initial Response as a Function of the Temporal Integration of Stimuli According to Becker and Jiirgens (1979) distinct control processes account for saccadic responses to the initial and final target step positions. First, a decision regarding the direction of the saccade is made over a randomly varying time when mounting excitation in a channel to the left or fight reaches a threshold value. The lengthy reaction times associated with responses to crossed step stimuli which go directly to the final target position for saccadic (e.g., Becker & Jtirgens, 1979) as well as manual (e.g., Schmidt & Gordon, 1977) responses are consistent with the ability of the system to halt processes associated with the decision to produce a movement in the direction of the initial step position. At the same time processing is initiated in a decision channel associated with a movement in the opposite direction. Such amendments to PO stimuli are infrequent and cannot account for amendments of the amplitude or angle of a response across an amplitude transition function. Becker and Jiirgens (1979) further proposed that after the direction decision has been generated, the position error of the eye is signaled to the central decision and computing stage, where it is averaged over a time window of constant duration. At issue however is whether the duration of the transitionphase is indeed constant. Becker and Jiirgens (1979) argue that if a new target location is presented during the time window a weighted

374 N.C. Barrett & R.T. Kane average of the two target positions is then calculated. Accordingly, if the second target step occurs towards the close of the time window the weighted average will correspond to a position close to the initial target position. A second step occuring soon after the onset of the time window will result an amplitude close to the final step position. The later the second step occurs during the time window the more likely it is that the amplitude of the initial response will correspond to the first target position. At the close of the time window the neural pulse generator is triggered, and since the pulsative activity is proportional to the averaged error, a saccade is elicited with an amplitude equivalent to the weighted average of target positions. Within the double-step tracking situation an implication is that the initial saccade will display an amplitude equivalent to a weighted average of all the fixation errors (step positions) occurring during the time window. According to the error averaging hypothesis, the initial response and the corrective response in a double-step situation are programmed and issued as two discrete responses. This is a necessary property of a system that determines response amplitude from the average of error signals. The result of the averaging window will be treated as the correct response until the system is informed otherwise. As a result, IAR and IMAR double-step responses should resemble the profiles of two separate single-step responses with equivalent amplitudes. Since the output of the time window, furthermore, is assumed to be the correct response for the task at hand, a corrective response will not be initiated until the error in the initial response is detected. Error detection is not likely to be a result of a visually based comparison of the resultant initial amplitude to the final target location. If this was the case, the delays to the corrective response would be greater than those predicted by a PRP. Furthermore, the delay before the onset of a corrective response would not vary systematically as a function of D. One possibility is that the error is signalledat via an efference copy. The requirement that the incorrect amplitude of the initial response be signalled via an efference copy, implies that the corrective response will appear one reaction time after the initiation of the response when the efference copy is available for evaluation. The lengthening of the corrective reaction time as a function of D may reflect corrective responses that can not be initiated until signalled by an efference copy. van Sonderen et al. (1988) have discussed how the weighted averaging of target step positions may be achieved via a control system that translates the external location of the target to an internal representation of the target location. They propose a 'WHEN'- and

Superseding Step Stimuli 375 'WHERE'- system. The 'WHERE'- system translates the external target position into an internal representation of the target position and corresponds to Becker & Jtirgens' (1979) averaging window, van Sonderen et al. (1988) account for variations in the initial response amplitude, however, by proposing that this internal representation of the target location shifts gradually from the first to the second target location at a fixed velocity. It is not clear why the internal target should shift instantaneously to the initial target location but gradually between the initial and final locations. The 'WHEN'- system determines the moment at which to pass the 'WHERE' signal on to the motor program generator. The 'WHEN'- system adds additional computational complexity. For Becker & Jiirgens (1979) the averaging time window had a constant duration and after this time the weighted amplitude was passed on to the motor program generator, van Sonderen et al. (1988) argue on the other hand that the 'WHERE'- system has a duration that is not constant but which is determined by a 'WHEN'- system with stochastic properties. By implication the transition phase of the ATF will not have a constant duration. The amplitude of the response will be proportional to the internal position of the target when a decision is made to generate the motor program, van Sonderen et al's (1988) model differs from the error averaging model since the duration of the transition phase of the amplitude transition function is determined by a 'WHEN'- system and therefore need not have a constant duration. The models of Becker and Jtirgens (1979) and van Sonderen et al. (1988) both assume separate control processes to underly the generation of the initial and corrective responses to superseding target steps. The initial response is nevertheless determined by the temporal integration of the step stimuli. Flanagan et al. (1993), on the other hand, argue that similar mechanisms are involved. Flanagan et al's (1993) model is an extension of the ~, model. According to the k model, a system similar to van Sonderen et al's (1988) 'WHERE'-system controls the equilibriurn point of the joint coded in terms of the interplay between agonist and antagonist muscles. Shifts in this equilibrium point result in movements of a proportional amplitude. Within the context of a double-step tracking task: When an initial target is presented there is a shift of the equilibrium point. If another target is presented there is another shift of the equilibrium point. These shifts are assumed to occur without delay.

376 N. C Barrett & R. T. Kane 3.2 Modifications to the Initial Response Following Response Initiation Alternatively, it has been proposed that the initial response to a double-step stimulus is equivalent, at least at its onset, to a single-step response to the initial target position. Modification of the trajectory may be achieved as a result of the superpositioning of paraUel and overlapping motor commands. The superpositioning of two motor programs separated in time implies that a proportion of the initial response, equivalent in duration to the ISI, should resemble a single-step response to the first step position. Often however the response will be modified at its outset (e.g., van Sonderen et al., 1988). Georgopoulos et al. (1981) and Massey et al. (1986) argue that when a superseding step in the opposite direction to the initial target step occurs, the system is able to apply sufficient forces to brake the initial response at which point the corrective movement is implemented as fast as possible. In terms of an amplitude transition function, for initial steps of the same amplitude and second steps of different amplitudes, the slope of the transition phase should remain constant. However, the duration of the time window should be variable since it will be easier to adjust the response for a short amplitude second step than for a large amplitude second step. A consequence of the rapid implementation of a corrective response towards the final target position is the proportionately greater peak velocities noted for the corrective response. Flash and Herds (1991) attempted to account for the kinematic form of double-step tracking responses in terms of the superpositioning of two minimum jerk (i.e., rate of change of acceleration) trajectories, one corresponding to the displacement of the target from the homebase to the initial target location and the other between the two target locations. When both the braking hypothesis and the superposition hypothesis were mathematically model, the predicted velocity profile for the superposition hypothesis was found to provide a closer least-squares fit to actual profiles than did the braking hypothesis. Interestingly, the durations for the superimposed units that were inferred by Flash et al (1992) were found to be very similar to the corresponding single-step movements. On the other hand, Georgopoulos et al. (1981) have observed that superimposed trajectories do not have equivalent durations as their corresponding single- step responses. Indeed, Georgopoulos et al (1981) have reported a three-fold increase in the peak velocity of the corrective response. A major challenge for the minimum-jerk

Superseding Step Stimuli 377 model of Flash and Henis (1991) is to account for the changes to the velocity profiles of corrective double-step responses which have been observed by Georgopoulos et al. (1981). Hoff and Arbib (1993) modeled a sequence of two minimum jerk trajectories rather than overlapping trajectories. In this sense Hoff and Arbib's (1993) model is similar to Flanagan et al's (1993) model since central commands are activated successively. The kinematics of Hoff and Arbib's simulation of Georgopoulos et al's (1981) double-step tracking task were similar to the original data. Of particular interest was that the corrective response displayed a significantly higher peak velocity than for control single- step responses. The ratio of the second peak height to the first was 1.69 which corresponded well to the particular trial they modelled. However they did not model a trial for which a threefold increase in the peak velocity of the corrective response was observed. The ability of minimum jerk models to produce amplitude transitions between IARs and FARs as a function of D, as well as to account for the variability in performance as a function of the stimulus pattern, needs to be evaluated. Minimum jerk models of trajectory formation are essentially kinematic models for which an optimal solution may be derived analytically from specification of movement time, initial homebase location, possible via points and the final target position. Recent attempts have been made to incorporate the dynamic aspects of the motor task into models of trajectory formation. Uno, Kawato and Suzuki (1989) and Hirayama, Kawato and Jordan (1993) have proposed an alternative model, the minimum torque change model, for which the trajectory is derived from the initial, via- and final target positions as well as arm posture and external forces. The ability of the minimum torque change model compared to the minimum-jerk model to describe the trajectories of double-step responses needs to be further evaluated particularly within a three-dimensional step tracking situation. 4. CONCLUSIONS The present chapter has examined the control principles underlying responses to double- step stimuli. For both one-dimensional and two-dimensional tracking these responses have been shown to conform to transition functions which describe how the initial

378 N. C. Barrett & R. T. Kane amplitude or angle of a response varies as a function of a determinant time interval between the onset of the second step stimulus and the initiation of a response. Accounts of the general features of the transition function have proposed either that the initial response is directed towards the first step location and is modified after initiation or that the initial response represents a temporal integration of step positions. These accounts need to be evaluated in relation to changes in the transition function under different stimulus conditions and movement times. Future research needs to address two particular features of the transition function, namely the minimum determinant time interval at which a modification is observed and the duration of the transition between initial and final amplitude responses. Specifically, why should double-steps in the same direction (i.e., SC stimuli) have longer minimum modification Ds than steps in opposite directions (i.e., PO, PU stimuli). Moreover, the conditions under which the duration of the transition phase remains constant needs to be established since the different models evaluated in the present paper make different predictions regarding the time duration of the transition phase. REFERENCES Angel, R.W. (1976). Efference copy in the control of movement. Neurology, 26,1164- 1168. Aslin, R.N., & Shea, S.L. (1987). The amplitude and angle of saccades to double-step target displacements. Vision Research, 27, 1925-1942. Barrett, N.C., & Glencross, D.J. (1988). The double-step analysis of rapid manual aiming movements. Quarterly Journal of Experimental Psychology, 40 A ,299-322. Barrett, N.C., & Glencross, D.J. (1989). Response amendments during manual aiming movements to double-step targets. Acta Psychologica, 70, 205-217. Becker, W., & Jiirgens, R. (1975). Saccadic reactions to double-step stimuli: Evidence for model feedback and continuous information uptake. In G. Lennerstrand & P. Bach-y-Rita (Eds.), Basic mechanisms of ocular motility and their clinical implications (pp. 111-119). Oxford: Pergamon Press. Becker, W., & Jtirgens, R. (1979). An analysis of the saccadic system by means of double-step stimuli. Vision Research, 19,967-983.

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Motor Control and Sensory Motor Integration: Issues and Directions 383 D.J. Glencross and J.P. Piek (Editors) 9 1995 Elsevier Science B.V. All rights reserved. Chapter 15 LIMITING MOTIONS IN PREHENSION Patricia J. Bate Latrobe University Errol R. Hoffman University of Melbourne An experiment involving reach and grasp of circular cylinders of diameters ranging from 2 to 32 mm, over movement amplitudes of 100 to 400 tmn, showed no effect of the size of the cylinder on the time to reach and grasp. This result was in agreement with that of Zaal and Bootsma (1993) and others but contrary to that of Marteniuk et a1.(1990). The movement time data were linearly related to the square-root of the amplitude of the reach distance, indicating that the movements may have been controlled ballistically (Hoffmann 1981). In a second experiment, rectangular objects were grasped; object widths and depths ranged from 2 to 64 mm and reach distances ranged from 12 to 512 rant These data differentiated two regions in the movement time/amplitude relationship. Interpreting this finding it was proposed that for small movement amplitudes the movement time was controlled by that requiredfor opening of the fingers; for large amplitudes the movement time was a function of the square-root of the amplitude of the movement. This interpretation is consistent with the constant enclosure model of control of prehension (Hoff and Arbib, 1993). Object depth contributed a portion of the variance in movement time only for objects of small depths placed at large distances from the subject. This finding was consistent with that reported by Marteniuk et al. (1990). 1. INTRODUCTION Prehension may be viewed as consisting of two components: transport of the hand to the object (reaching) and manipulation of the object (grasping) (Jeannerod 1981, 1984). Within an information processing framework it has been proposed that these components are controlled by two subsystems organised independently. Extrinsic properties of the object (location) have been argued to control the transport component, and intrinsic properties (size, shape) to guide the grasp component. Function requires that these two systems be coordinated in some way, so that the hand is open before the position of the object in space is gained. The nature of this coordination has been much discussed. More recently several experiments have demonstrated interaction between the two systems (Gentilucci, Chieffi, Scarpa & Castiello, 1992; Paulignan, Jeannerod,

384 P.J. Bate & E.R. HoOinan MacKenzie & Marteniuk, 1991; Paulignan, MacKenzie, Marteniuk & Jeannerod, 1991; Wing, Turton & Fraser, 1986) Several theoretical models address the relationship between coordination of the two components of prehension. Hoff and Arbib (1993) have developed a three component continuous feedback control model explaining the f'mdings of these studies. In this model planned movement duration is used to coordinate transport time with times for preshaping of the hand and enclosure of the object. Marteniuk, Leavitt, MacKenzie and Athenes (1990) and Jeannerod, Paulignan, MacKenzie and Marteniuk (1992) proposed a more general concept of the relationship between the two components as a functional coupling in which the movement goal is encoded as a temporal structure which serves to synchronise kinematic landmarks. This concept is an extension of the idea of central coding of the desired position of the effector system described by Cole and Abbs (1986) to explain the results of their studies in which the end goal of a task was achieved despite perturbation of the contributing components. Bootsma and van Wieringen (1992) argued for a model of integrationbetween the two components in which the precision requirements of the task, which may be partly indicated in intrinsic properties of the object such as size, determine the velocity of the approach of the hand. The present study examined effects of precision requirements on the transport phase of prehension; some of the findings supported predictions of the Hoff and Arbib (1993) model. Effects of object size and shape on movement time were investigated in two studies of prehension. The role of object size as a factor affecting both transport and manipulation components has been much investigated. One of a germinal series of experiments by Jeannerod (1981) found that changing the size of an object between 4 and 7 cm during the transport phase of prehension did not alter any characteristics of the transport component, including the movement duration, in subjects reaching 40 cm without visual feedback from their hand. However, in a more natural study of subjects able to see their ann while reaching, Marteniuk et al.(1990) found that when subjects reached 30 cm for cylinders of diameters that varied between trials from 1-10 cm, duration of the movement decreased with increase of object size. The authors interpreted this finding as a precision effect similar to that previously demonstrated in aiming tasks when target size was reduced (Mackenzie, Marteniuk, Dugas, Liske & Eickmeier, 1987) and also in prehension in relation to object fragility or intended use (Marteniuk, MacKenzie,

Limiting Motions in Prehension 385 Jeannerod, Athene & Dugas, 1987). Interestingly, the same group (Marteniulc et al., 1987), earlier reported a similar study in which no significant effect of object sizes 20 and 40 cm was found on movement time. Zaal and Bootsma (1993) partially replicated Marteniuk et al.'s (1990) study. However, they found no differences in movement times to grasp cylinders of widths 3, 5 or 7 cm. Re-examining Marteniuk et al.'s (1990) data, Zaal and Bootsma (1990) found that the obtained relationship was primarily an effect at the lowest object sizes tested, 1 and 2 cm diameter cylinders. Effects of small object sizes on movement time were investigated by Wallace and Weeks (1988). Subjects reached 23 cm to grasp a dowel of 3 or 25mm diameter. This study did not support the possibility that effects of object size are strong at small object sizes, as it failed to demonstrate a relationship between object size and movement duration. The apparently conflicting findings of these studies may be due to differences in task parameters. Two major differences between these experimental paradigms were the speed of movement and the operations performed on the object after grasping. The aiming literature, and studies of prehension, suggest that either of these factors may cause subjects to change movement strategy and therefore possibly alter the relationship between object size and movement duration. In aiming movements varying movement speed alters the effect of target width on movement duration. Performed at slow speeds, aiming movements usually demonstrate effects of both target width and amplitude on movement time: however, if the movements are performed fast, with movement times of less than 200 ms (approx.), then movement times are independent of target width (Gan & Hoffmann, 1988a). As it has been demonstrated that the trajectories of reaches to grasp stationary objects are similar to those of pointing movements (Carnahan, Goodale & Marteniuk, 1993), it is possible that varying movement speeds may have altered effects of object size on movement time in these studies. It has also been demonstrated in the aiming literature that in sequential movements later components can influence the durations of initial movement components (Gan & Hoffmann 1988b; Hoffmann 1993; Langolf et al. 1976). When the movements were fast it was demonstrated that the time taken for a second or later component was strongly dependent on the amplitude of the preceding component. In slower aiming movements, the duration of a later component was dependent on both the amplitude and

386 P.J. Bate & E.R. Hoffman the target width of the preceding component. Similarly, in prehension, differences in sequential components of tasks have been shown to affect the kinematics of the initial transport phase (Marteniuk et al., 1987). Marteniuk et al. (1987) showed that if subjects were required to fit a disk into a small slot after it had been grasped, movement time to the disk was greater than if the disk was to be thrown into a large receptacle. Both speed of movement and sequential operations varied between the studies investigating effects of object size on the transport component of prehension. A summary of the task parameters of these studies is presented in Table 1. Only one of these studies investigated effects of object size at comfortable movement speeds. Zaal and Bootsmas' (1993) subjects were given no time restrictions, and were requested to pick up a disk between thumb and index finger and to place it on a target halfway back to the starting position. Subjects' movement times were between 842 and 944 ms; their speeds ranged from .32 to .38 metres per second. No effects of object size on movement time were identified by this study. All other reported studies required subjects to move as fast and accurately as possible. Movement times reported in these studies ranged from 242 to 753 ms; movement speeds ranged from .47 to .95 metres per second (Table 1). These values for movement speed are similar to those obtained by Wing, Turton and Fraser (1986) whose subjects were instructed to grasp and lift a dowel under two instruction conditions: (a) no instructions regarding speed (b) as fast and accurately as possible. Two of the studies of fast movements required sequential operations on the object. Marteniuk et al.'s (1990) subjects were required to reach, grasp and lift a cylinder and then replace it on the table top, but no target was specified for this replacement. For 5 of the 6 subjects, a significant negative correlation between movement time and cylinder width was identified. Jeannerod's (1984) subjects reached and grasped the object and carried it to near the starting place. For the two subjects tested under normal visual conditions, no effect of object size on movement time was found. A lesser sequential operation was required by the task of Paulignan, Jeannerod et al. (1991). They grasped and rifted a dowel, but were not required to replace it. Again, this study found no effect of object size on duration of the transport component. Two studies did not require any operation after grasping the object. Wallace and Weeks' (1988) task was to reach and grasp a cylindrical joystick and not to move the joystick

Table 1. Task constraints and performance measures for repo AUTHORS TIME OBJECT MANIPU INSTRUC CONSTRAINT grasp & lif & Bootsma none Circular disk Yes 1993a (!) Zaaland Bootsma none Oblate disk Yes 1993b (D Wallace and AFAAP Dowel Weeks 1988 Yes AFAAP Ellipsoid/ (D| Jeanner~ AFAAP Sphere 1984 Yes Disk @| Martenuik et at. 1987 Yes (!)~9 ~arteniuk AFAAP Disk Yes et al. 1990 (D I'aulignan AFAAP Dowel Yes et al. 1991 (D Use thumb and/'orefinger q) Pla\"ce'in new position | Place on | No constraint on type of grasp | No visual feedback of hand ~

rted studies of effects of object size on transport time in prehension. ULATION OBJECT AMPLITUDE MOVEMENT VELOCITY CTIONS ft place WIDTH (mm) TIME (m/s) (ram) (ms) Yes .... 30 300 842 .36 ~r 50 300 861 .35 70 300 871 .34 Yes 30 300 907 .33 ~.,~ 50 300 944 .32 3O0 913 .33 o~~t r174 70 ~,~~ No 3 230 242-345 .67-.95 ~t 25 230 260-435 .53-.89 t.tJ No 40 400 .53 \"--d 70 400 753 Yes 20 200 425 .47 9 20 400 524 .76 40 200 408 .49 40 400 495 .81 Yes 10-100 300 614-702 .43-.49 No 15 350 549 .64 60 350 556 .63 n' target | Various tolerances for movement of dowel ~9 No requirement to lift object. AFAAP = As fast and accurate as possible.

388 P.J. Bate & E.R. Hoffman outside specified limits. Similarly, Marteniuk et al.'s (1987) subjects reached to grasp a disk. Neither of these studies identified an effect of object size on movement time. In summary, all reported studies investigating effects of object size on duration of a prehension movement, except one (Marteniuk et. al, 1990) failed to identify an effect of object size on movement time. Arbib and colleagues (Arbib, 1981; Arbib, lberall & Lyons, 1985; Hoff & Arbib, 1992; Hoff & Arbib, 1993) have developed the constant enclosure model of the relationship between the transport and grasp components of prehension. This model predicts that transport time will be unaffected by object size unless the planneA transport time is less than the time necessary for the hand to open and close. It is possible that the transport distances in the reported studies Were so long that time to adjust the hand for different object sizes was not the limiting motion. When movement time is sufficiendy large, it can be expected that there is complete overlap in time of these two components: that is, aperture opening is completed within the transport period. In engineering terms, this is expressed as the transport component being the limiting motion (Barnes, 1968). When the distance to be reached is small, the time for aperture adjustment may be greater than that for transport. In this case, the aperture adjustment is the limiting motion. The present study investigated limiting motions in prehension with small movement amplitudes and various object sizes. In order to reduce variability between subjects, and to remain consistent with the majority of studies of aiming movements and prehension, subjects in the present study were asked to move as fast as possible. Objects were fixed to an immovable base to avoid influence of a second component on the movement time. Another possible source of difference in results between studies of prehension is their different accuracy requirements. In aiming tasks the error tolerance is partly expressed in the target width and the pointer size. In a prehension task the error tolerance for placing the hand may be embedded in various parameters: the depth of the object in the direction of movement; the shape of the object; the surface area of the object available for contact by the hand, the surface area of the hand available for contact, and the number of configurations of hand posture available. The purpose of the reach, and movement permitted after contact, may also constrain hand postures. Tolerance has been variously def'med in prehension studies. In the task used by Wallace and Weeks (1988) subjects were required to limit movement of a joystick after

Limiting Motions in Prehension 389 it was grasped, to within a circle the radius of which represented one of three error tolerance conditions. The authors found that movement durations were greater for smaller tolerances. Zaal and Bootsma (1993) modified the amount of surface area of the object available for contact in the direction of transport when subjects reached for cylinders of three different diameters. Consonant with the findings of Wallace and Weeks (1988) they described longer movement times when the surface of the object available for contact was reduced. Bootsma and van Wieringen (1992) also found that the surface area of the object available for contact was a constraint on the transport component of prehension. The studies of Marteniuk et al. (1987, 1990) and Jeannerod (1981, 1984) and Paulignan, Jeannerod et al. (1991) did not report control of tolerances. In the present study, error tolerance was controlled by fixing objects to an immovable base and by controlling the surface area of the object available for contact in the direction of transport and by measuring the surface area of the hand available for contact. In this situation, the error allowable in the direction of movement is not simply the depth of the object in the direction of movement, but is dependent also on the size of the finger pads used in the grasp. This is illustrated in Figure 1 for a small object being grasped between the thumb and index finger. Figure 1. Diagramillustratinggraspof a smallobject, showingthat the effectivetarget toleranceis greaterthan the objectsize and is dependenton the fmgerpad length 'F'. Even though the object is very small, the tolerance in the direction of movement is relatively large as the object could be grasped anywhere within the finger pad area.

390 P.J. Bate & E.R. H o ~ Hoffmann and Sheikh (1991), Drury and Hoffmann (1992) and Hoffmann (in press) have used this concept of effective tolerance to show that Fitts' law applies when the finger is used as a probe, provided that the finger pad size is added to the size of the target. The concept is equally applicable to the case of prehension and, as will be shown later, provides an explanation for movement time being relatively independent of object size. 2. EXPERIMENT 1: M O V E M E N T TIMF~ IN PREHENSION: EFFECTS OF AMPLITUDE AND CYLINDER DIAMETER This experiment was designed to address the conflicting findings of Jeannerod (1981), Marteniuk et al. (1987; 1990), Wallace and Weeks (1988), Paulignan, Jeannerod et al. (1991) and Zaal and Bootsma (1993) regarding the effects of object size on the movement time in prehension of small objects. 2.1. Subjects Ten male engineering students between 19 and 23 years old were paid to participate in this experiment. 2.2. Apparatus Five metal cylinders of diameters 2,4,8,16 and 32mm and height 100 mm were rigidly mounted on a board in a line, 110 mm apart. In parallel to the line of cylinders metal strips were attached to the board at distances of 100, 200 and 400 mm. The strips and cylinders were wired to an electronic timer such that a circuit was completed when a subject touched a metal strip or a cylinder. Tinting commenced when the circuit was broken at the start of the movement and finished when the cylinder was grasped. The electronic timer was accurate to within one ms. 2.3. Procedure Subjects were seated in front of the horizontal board on which were mounted the cylinders and metal strips. The subject started with the thumb and index finger lightly closed and resting on one of the metal strips, directly in front of one of the target cylinders. Subjects were instructed to move as quickly and accurately as possible to grasp a cylinder, using the thumb and index f'mger, and to avoid touching the cylinder

Limiting Motions in Prehension 391 prior to f'mger closure. Movement times were recorded as the time between the fingers leaving the metal strip and closure of the finger and thumb around the cylinder. Subjects were allowed to practice until they could perform the task without error. Five trials of each condition were then recorded. The fifteen conditions comprising five cylinders and three movement amplitudes were presented in random order; a different random order was used for each subject. 2.4. Results and Discussion A mixed-model Analysis of Variance (subjects random) identified a significant main effect of amplitude of transport on movement time (F(2,18)=170; p<.001), but no effect of cylinder diameter or any interaction between amplitude and diameter. Post-hoe tests, using the Newman-Keuls procedure, showed all distances to be significantly different 09<.01). Mean movement times are plotted in Figure 2. Observation of this data suggests a square-root relationship between movement time and amplitude. Such a relationship has been demonstrated for aiming movements of short duration (Gan and Hoffmann, 1988a; Hoffman, 1981). Regression of the mean data in terms of this model gave MT = 77 + 13.4 ~/A; r2 =.98 where MT = movement time is in ms and A = amplitude in mm. Movement Time (ms) 4O0 35O 300 - • • 25O 2OO 150 10 15 2 0 5 Square-root of Movement Amplitude(mm'.5) + D l a m - 2mm ~ D i a m - 4mm [] Dlarn- 8ram • D l a r n - 16mm b Diam - 32ram Figure 2. Resultsof Experiment1 withmovementtimeas a function of squareroot of movementamplitudefor fivecylinderdiameters.

392 P.J. Bate & E.R. Hoffman This finding was considered in terms of Keele's (1968) model of control of aiming movements. In this model a distinction is made between visually controlled and aiming movements made without use of visual feedback i.e. \"ballistic\" movements. This distinction is based on the assumption that visually based corrections of a finite duration are made intermittently after an initial movement which was generated under open loop control (Keele, 1968). If the movement duration is shorter than the duration of a visually based correction, the movement may be entirely open loop generated, or \"ballistic\". Effects of target width are thought to be incorporated in the visual correction phase of a movement; thus, if the movement is too brief, target width is not related to the movement duration. In movements that are long enough to permit visual control, object width and amplitude are linearly related to movement time through Fitts' \"Index of Difficulty\" (Fitts, 1954), defined by: ID = log2(2A/W), where A= amplitude and W= target depth in the direction of transport. When ID < 3.5, the movement time is usually so short the movement is considered to be under open loop control: that is, ballistic. The Indices of Difficulty of the present tasks, when calculated with W as the cylinder diameter, ranged from 2.64 to 8.64 (Table 2); that is, 12 of the 15 depth/amplitude combinations were associated with ID values greater than 4 and hence within the range in which the movement may be visually controlled. Table 2 Uncorrected Indices of Difficulty for tasks of Experiment 1. Cylinder Movement Distance (mm) Diameter (mm) 100 200 400 2 6.64 7.64 8.64 4 5.64 6.64 7.64 8 4.64 5.64 5.64 16 3.64 4.64 4.64 32 2.64 3.64 4.64 However, because the data was well fitted by a ballistic model, the method of calculation of the ID values was reconsidered. As described below, a different method was adopted, which more accurately accounted for the error tolerances of the tasks.

Limiting Motions in Prehension 393 Hoffmann and Sheikh (1991) have shown that in aiming tasks, when the f'mger is used as a probe, because it has a f'mite width it is necessary to substitute an \"effective target tolerance\" for the target width in the calculation of ID. For such tasks the effective target tolerance may be calculated as the finger width plus the target width. For the present task it was possible to grasp the cylinder using any part of the length of the contact surface of the finger and thumb (Figure 1). Thus the \"effective target tolerance\" was derived by adding the finger pad length plus the surface dimension in the direction of transport (the cylinder diameter). The finger pad length of subjects in this experiment was determined by inking the subjects' fingers and having them press lightly on a piece of paper placed between the thumb and index f'mger. The imprint obtained in this manner had a mean length of 20.4 mm with a standard deviation of 2.9 mm. Values of Index of Difficulty (ID) thus calculated ranged from 1.93 to 5.16, with 9 of the 15 values less than 4, and hence within the region where movement may be ballistically controlled (Gan and Hoffmann, 1988a). The lack of an effect of cylinder diameter on movement times also suggested that a ballistic model of control was operating. However, because the object was cylindrical, effects of object depth in the direction of movement (an error tolerance effect) were not separable from effects of object width. An effect of object size in the direction perpendicular to the direction of transport may have been masked by an error tolerance effect. A second study was thus conducted in which effects were separable. 3. EXPERIMENT 2: MOVEMENT TIMES IN REACH AND GRASP: EFFECTS OF TOLERANCE Experiment 1 supported previously reported findings of no effect of object size on the transport component of prehension. The second experiment was designed to further investigate effects of object size. Effects of surface contact length in the direction of transport were controlled separately from effects of surface contact length perpendicular to the direction of transport, with the height being maintained constant at 65 mm in all cases. It was expected that the size perpendicular to the direction of motion would affect the size of the aperture required for grasp and that the size in the direction of motion would affect the final accuracy with which transport must be completed in order to grasp the object.

394 P.J. Bate & E.R. Hoffman Experiment 2 also allowed further investigation of the relationship between the two components of prehension, transport and grasp. Movement times were manipulated by varying the amplitude of the transport component in order to change the limiting motions of the task. When movement time is sufficiently large, it can be expected that there is complete overlap in time of these two components: that is, aperture opening is completed within the transport period. In engineering terms, this is expressed as the transport component being the limiting motion (Barnes, 1968). When the distance to be reached is small, the time for aperture adjustment may be greater than that for transport. In this case, the aperture adjustment is the limiting motion. Varying the movement times by varying movement amplitude allowed investigation of these components. 3.1. Subjects 10 male engineering students between 19 and 23 years old participated in this experiment. 3.2. Method This was as for experiment 1. However, objects were rectangular right prisms, allowing independent control of depth (size in direction of transport; 2,6,20,64 mm) and width (size perpendicular to the direction of transport; 2,6,20,64 mm). Amplitudes of movement were derived which it was practical to test in combination with the prism widths. Seventy-six combinations of prism width, depth and movement amplitude were tested (Table 3). Five movements were recorded at each of these amplitudes. The values of amplitude were selected to yield Index of Difficulty values ranging from one to seven, when calculated without the effects of finger pad size. The blank cells in the design shown in Table 3 result from impractical values for the movement amplitude. 3.3. Results and discussion Mean movement time data are presented in Table 4. Movement times are plotted separately for the four prism widths, against the square-root of the amplitude (Figure 3). Inspection of this data shows little effect of depth at any of the prism widths. That is, the size of the prism in the direction of the movement did not greatly affect the movement time.

Limiting Motions in Prehension 395 Table 3 Amplitudes of movements (mm) usedfor each of the prism depths (mm) to obtain given Indices of Difficulty in the direction of movement. Each of these 19 conditions was combined with cylinder widths of 2,6,20 and 64 mm perpendicular to the direction of motion. Cylinder Index of Difficulty Depth (mm) 12 3 456 7 2 - - - 16 32 64 128 6 - 12 24 48 96 192 384 20 20 40 80 160 320 64 64 128 256 512 - Calculation of the Index of Difficulty in the direction of motion using effective target tolerance demonstrated that, as in Experiment 1, many of the tasks were of difficulty levels so low that movement times would lie within the range where ballistic control is likely. IDs varied from -.14 to 4.86; onlY 1 of the 19 ID values tested was greater than 4. Application of the equation for ballistic movements (Hoffmann, 1981) yielded a linear relationship between movement time and square-root of the amplitude, explaining 88% of the variance in the data. This result of little effect of prism depth was similar to the finding of Experiment 1 of no effect of object diameter. Further inspection of these data showed that, particularly for higher prism widths, there appeared to be a break in the linear relationship between the movement time and the square-root of the amplitude at lower levels of amplitude (Figure 3). Table 4 demonstrates that of the sixteen data series representing effects of decreasing amplitude on movement times for different prism widths, six reached minima which were followed by increases in movement times as amplitudes continued to reduce. These increases in movement times tended to occur when prism widths were large, with movements of small amplitude.

396 P.J. Bate & E.R. Hoffman Table 4 Mean movement times (ms)for 10 subjects reaching to grasp in the 76 conditions of prism width (mm), depth (nun) and amplitude of movement (mm) in Experiment 2. Depth Ampl Width (mm) (mm) (mm) 2 6 20 64 2 16 138 159 167 195 2 32 160 174 172 186 2 64 181 184 193 212 2 128 210 251 213 224 6 12 160 187 219 236 6 24 181 175 177 207 6 48 191 201 203 210 6 96 222 221 202 248 6 192 265 276 270 263 6 384 329 321 325 330 20 20 150 162 194 211 20 40 170 178 178 200 20 80 188 194 190 186 20 160 227 221 220 218 20 320 288 299 286 304 64 64 160 175 182 191 64 128 211 216 205 216 64 256 253 242 260 254 64 512 345 342 337 354 This pattern in the data was interpreted in the light of a change in the limiting motion. When the amplitude of the movement was extremely small (less than 25mm) and the prismwidth large, aperture adjustment became the limiting motion, and movement time was increased to allow the aperture to fully open. This interpretation was consistent with observations of subject behaviour. For the smallest amplitudes, subjects were noticed to initially withdraw the hand toward the body. During this time, the finger aperture was increased, prior to movement of the hand toward the prism. It was considered that this phenomenon represented a strategy to allow opening of the hand when the object was large and close. The occurrence of a change in the limiting motion was also supported by the observation that the location of the breakpoint was dependent

Limiting Motions in Prehension 397 on the width of the object; as width increased, so the amplitude at which the break point occurred increased (Figures 3a,b,c,d). Movement time (ms) o Movement time (ms) o 350 350 + (a) Width - 2 mm (b) Width \" 6 mm 300 300 260 4- 260 4- o 200 - m 200 - 150 160 - 4- 4- 90 4- o 4-.~ .~- 100 ,It, 26 100 ii I i 25 0 6 10 16 20 0 6 10 16 20 Square-root of Amplitude (Jmm) Square-root of Amplitude (,/ram) 9 Depth - 2 mm 4- D e p t h - 6 mm 9 Depth - 2 mm + Depth - 6 mm Depth - 20 mm o Depth - 64 mrn Depth - 20 mm o Depth - 64 mm Movement time (ms) o Movement time (ms) 350 350 (c) Width - 20 mm (d) Width 9 64 mm 300 300 260 2 6 0 4- + +9 200 200 + § 6 150 4-.~ 0 150 100 , i ~= 25 100 iii 1 0 5 10 15 20 0 6 10 15 20 Square-root of Amplitude (Jmm) Square-root of Amplitude (Jmm) 9 Depth - 2 mm + Depth - 6 mm 9 Depth - e mm + Depth - 6 mm Depth - 20 mm o Depth - 64 mm ~ Depth - 20 mm o Depth - 64 mm Figure 3. Results of Experiment 2 showing movement time as a function of square root of movement ampfitude. (a) Width = 2ram Co) Width = 6ram (c).Width = 20 mm and (d) Width = 64 ram. Symbols represent Depth values: 9 = 2ram; + = 6ram; * = 20mm; O = 64 mm

398 P.J. Bate & E.R. Hoffman The data were partitioned into two sets: movements in which aperture adjustment was the limiting motion (amplitudes < 25mm), and those in which the transport component limited motion (amplitudes > 90mm). A multiple regression was conducted to examine the relationships between square- root of amplitude, width and depth of the prism, and all interactions between these variables, with movement time. The resulting regression was (including only significant terms), MT = 99.5 + 11.6 ~/A - 0.4 (Depth); r2 =.92 Thus, when the transport component was the limiting motion, the movement time was independent of the width of the prism. There was a small effect of the depth of the prism in the direction of movement; this term accounted for about five percent of the total variance in the movement time data. The null effect of prism width supported the findings of Jeannerod (1981), Zaal and Bootsma (1993), Paulignan (1988), Jeannerod et. al (1991) and Wallace and Weeks (1988). This regression function assumes a linear effect of object depth on movement time. To further investigate the effect of object depth, a single variable regression was conducted on the same data, without including depth as a variable. This regression gave MT = 101 + 10.8 ~/A ; r2 =.88 The movement times predicted from this equation for each value of depth, width and amplitude, were subtracted from the measured times to obtain a residual that contained the effect of object depth. The mean values of the residuals for each depth are shown plotted in Figure 5. Movement times appeared to reduce when prism depths were increased from 6 to 20mm; however, above a depth of 20 mm little effect of increasing prism depth was observable in the data. This result was compared with the data of Marteniuk et al. (1990). Because these authors used cylinders as objects it was possible to interpret their reported object widths as object depths (Figure 6). Comparison of the two data sets (Figures 5 and 6) showed a similar pattern of effects of object depth on movement time. Note that in the present data, and also that of Marteniuk et a1.(1990), these apparent effects of object depth are small, being of the order of 25-60 ms for small object depths and negligible for object depths greater than 20-30 mm.

Limiting Motions in Prehension 399 Examining the data for small amplitude mOvements, where the limiting motion was aperture adjustment, an approximate square-root relationship appeared to exist between movement time and object width (Figure 4). Aperture AdjustmentTime (ms) 200 / // I 150 [3 100 ~ ~~ 0 2 468 Square-root of Cylinder Width (ram'.5) Figure4. Movementtimesas a functionof prism widthfor small transport distances, where the limitingmotion is the time for adjustmentof aperture. The movement times were in conformity with the ballistic equation of Hoffmann (1981) and Hoffmann and Gan (1988), suggesting that the fingers were opened in a ballistic movement in which there is no close control of final accuracy. Residual Movement time (ms) Movement time (ms) 2O 760 15 7~0 10 5 680 0 800 -5 550 -1~I -15 iiiiii 500 ~J J J 120 0 0 20 40 60 eo 100 10 20 30 40 50 60 70 Cylinder Diameter (mm) Object Depth (mini Figure 5. Mean residual movement times Figure 6. Mean movement times for ten trials conducted at each value of prism cylinder diameters (10-100 mm). Data depth (2,6,20,64 nun). from Marteniuk et al., 1990.

400 P.J. Bate & E.R. Hoffman A model describing prehension of close, small objects was developed by combining the findings of ballistic movement of the limb toward the object when transport was the limiting motion, and ballistic opening of the f'mgers when aperture adjustment limited the movement. A diagram of the postulated model is presented in Figure 7. Movement Time Increasing Cylinder Width -/ Square-root of Movement Amplitude Figure7. Proposedmodelfor movementtimeas a functionof object width (perpendicular to the directionof transport) and amplitudeof movement. The model incorporates effects of increasing object widths at small amplitudes. A smaller third study was conducted to illustrate this model with more detailed kinematic measures. 4. EXPERIMENT 3: KINEMATIC DESCRIPTION OF TRANSPORT AND APERTURE COMPONENTS OF REACH TO GRASP IN A SINGLE SUBJECT In Experiments 1 and 2, recording the duration of transport times for the reach and grasp of objects of various sizes and distances from a starting point, led to development of a simple model describing the duration of the transport component of reach and grasp in terms of limiting motions. It was proposed that for movements of amplitude greater than 90 mm the transport component is the limiting motion and that for movements of less than 25mm aperture adjustment is the limiting motion. The third experiment was conducted to illustrate this model by presenting more detailed kinematic information, from both transport and grasp components, during reach to grasp.