- Email: [email protected]
The visual control of ball interception during human locomotion
Neuroscience Letters 334 (2002) 13–16 www.elsevier.com/locate/neulet
The visual control of ball interception during human locomotion A. Chardenon a, G. Montagne a,*, M.J. Buekers b, M. Laurent a a Faculty of Sport Science, Movement and Perception Laboratory, Marseille, France Faculty of Physical Education and Physiotherapy, Motor Learning Laboratory, Leuven, Belgium
b
Received 17 May 2002; received in revised form 2 September 2002; accepted 2 September 2002
Abstract According to the required velocity model, on-line modulations of movement acceleration are performed on the basis of an optically specified difference between required and current behavior. Can this model account for observed displacement regulations in an interceptive task requiring locomotive displacements? In the present study, a virtual reality setup was coupled to a treadmill. Subjects walking on the treadmill were required to intercept a virtual ball approaching at eye-level by adjusting their velocity, if necessary. While the required velocity model could partially account for displacement regulation late in the interception, it was ineffective to explain early regulations. The possible use of a bearing angle strategy to control displacement regulation and the possible degree of complimentarity of these strategies are discussed. q 2002 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Perception-action coupling; Locomotion; Law of control; Bearing angle strategy; Goal-directed action
Intercepting or avoiding a moving object is one of the most complex abilities characterizing the human perceptivo-motor repertoire. It requires on-line movement regulations, based on instantaneously available information, to accommodate to a future event [9]. This is the case when driving a car, when moving through a crowd, or when intercepting a moving ball. While the information substrate possibly used in this kind of task has received special attention [10,14], very few integrative models exist which describe not only the information but also how the information is used in the control process. The required velocity model [1,2,13] constitutes a rather isolated attempt to bridge the gap between perception and action. According to this model, on-line modulations of movement acceleration are performed on the basis of an optically specified difference between required and current behavior (Eq. 1). This continuous updating of the movement with respect to current information [15] guarantees success. In one study [13] a one-handed catching task was used in which the hand was constrained to move along a single lateral direction while the angle of approach of the ball * Corresponding author. Universite´ de la Me´diterrane´e, Faculte´ des Sciences du Sport, UMR Mouvement et Perception, 163 Avenue de Luminy CP 910, 13288 Marseille Ce´dex 9, France. Tel.: 133-49-1172273; fax: 133-49-1172252 E-mail address: [email protected] (G. Montagne).
was varied. In this model, the required behavior corresponds to a required hand velocity expressed by the ratio between the current lateral distance separating the hand from the ball and the time remaining before the ball reaches the movement axis (Eq. 2) (see [5] for an optical specification of this ratio). The current behavior corresponds to the actual velocity of the hand. Y Y X YY 2 aXreq 2 bXcur
Y Xreq ¼
Xb 2 Xh TC
ð1Þ
ð2Þ
Y where X YY is hand acceleration, Xreq is the required velocity, Y Xcur is the current velocity, Xb is the current lateral ball position, Xh is the current hand position, TC is the time remaining before the ball reaches the movement axis and a and b are constants. According to this model, all the subject has to do is to adjust hand acceleration to cancel the difference between required and current behavior. Recently this model received empirical validation [11,12]. In these two experiments the subjects were asked to intercept moving objects while various parameters were manipulated, e.g. angle of approach, ball speed, duration of presentation. The results show adaptations of hand kinematics that match the predictions made on the basis of the
0304-3940/02/$ - see front matter q 2002 Elsevier Science Ireland Ltd. All rights reserved. PII: S03 04 - 394 0( 0 2) 01 00 0- 5
14
A. Chardenon et al. / Neuroscience Letters 334 (2002) 13–16
Fig. 1. Bird’s eye view of the interceptive task. The subject intercepts a moving ball with the head by producing the necessary displacement regulations. The required velocity takes into account the distance separating the current position of the subject from the current projection of the ball on the axis of displacement (Yb 2 Ys) and the current time remaining before the ball reaches the axis (TC). The bearing angle b is also represented.
model. For example, in a ball-catching experiment [12], it was shown that the cancellation of the difference between required and current behavior occurred on average 300 ms before contact and was maintained until contact. Moreover, if the subject’s hand was initially placed in the correct position to catch the ball (i.e. no movement necessary), movements away from this position occurred as soon as a lateral hand–ball distance was created, followed by reversal movements back to the correct position. These results argue for the validity of the model under consideration, nevertheless they call for a few remarks. First of all, they were obtained using a task in which hand movements were mechanically constrained to one direction. While this added constraint can be justified insofar as it allows a more easy test of the model, it remains to be seen if the model applies to other, more realistic tasks. It is also worth mentioning that in the three previously cited studies [11,12,13], the movement times were between 1 s and 1.5 s. Consequently, one can ask if the same model can account for movement regulation when the interceptive task involves a larger time scale (around 8 s in the present experiment). The present study was designed to explore the utility of the required velocity model for a longer time frame with a different task. Subjects were asked to move (locomotion displacement) in a specified direction (along the Y-axis) and to intercept with their head a virtual moving ball crossing their displacement axis. The required velocity model can be simply reformulated by expressing both required and produced behavior along the Y direction (Fig. 1). Eight subjects with normal or corrected to normal vision
participated in the present study. Informed consent was obtained prior to testing. The experimental set-up consisted of a virtual environment (Silicon Graphics) coupled to a treadmill (Gymroll). Subjects walked on the treadmill 0.6 m in front of the screen (3 £ 2.3 m) on which the virtual scene was projected. The virtual scene consisted of an approaching ball (0.2 m diameter) and a textured floor. Displacements of the virtual environment were directly proportional to the displacements of the subject on the treadmill. Ball path kinematics were collected by the Silicon Graphics system (100 Hz) and subjects’ displacement kinematics were registered by an optical encoder positioned on the treadmill (100 Hz). The synchronization of the two systems allowed the computation of all displacements (ball and subject) in the same coordinate system. This setup was chosen for obvious reasons: the task constraints are easy to manipulate while natural movement regulation behavior is maintained [4]. Subjects were required to intercept the ball approaching along a rectilinear path (26.568 with respect to subjects’ displacement axis) with a constant velocity (1.26 m s 21) along a horizontal plane going through the head. The interception point was computed at the beginning of each trial on the basis of subjects’ initial velocity (mean velocity 0.81 m s 21, SD 0.057 m s 21), while the time taken by the ball to cross subjects’ displacement axis was kept invariant (7.5 s). Subjects performed the experimental task in three conditions: no change, acceleration and deceleration. In the no change condition, no velocity adjustments were required. In the other two conditions subjects had to either accelerate, or decelerate to intercept the ball. More precisely, in the acceleration and deceleration conditions, if the subject kept his velocity unchanged he would have been one meter short or ahead of the interception point, respectively. Subjects performed ten trials per condition, the order of conditions was randomized across all trials. Subjects received immediate performance feedback after each trial: a green (success) or red (failure) square projected in the center of the screen. A successful trial was one where the distance between the center of the ball and the center of the subject’s head was at most ^2 cm when the ball crossed the subject’s displacement axis. Current error was computed every 10 ms during each trial and represents the error that would result if the current velocity had been kept invariant. Consequently, a current error that tends towards zero implies effective regulation of velocity. Performance measures were percentage of successful trials and the time-course of inter-trial variability of both velocity and current error (i.e. each half second during the last 6 s before contact). An increase in velocity variability indicates velocity regulations. In the assumption that these velocity regulations are effective, they should be accompanied by a decrease in current error variability. For the required velocity model analysis, the fit of the model to the recorded data was examined using multiple linear regression on each trial. The analyses were based on Eq. 1 and tested the extent to which acceleration depends upon the
A. Chardenon et al. / Neuroscience Letters 334 (2002) 13–16
Fig. 2. Time course of both mean displacement velocity and current error profiles with the associated variability (error bars) in the acceleration condition (diamond), the no change condition (square) and the deceleration condition (triangle). The analyses reveal an initial increase in velocity variability 5 s before contact and a second increase 1.5 s before contact together with a decrease in the current error variability from 5 s before contact.
Fig. 3. Mean bearing angle profiles for every successive 0.5 s interval from 6 s until 1 s before contact, and their associated variability. The analyses reveal that the bearing angle is kept constant in the first part of the trial. Bearing angle only changes in the last 2 s before contact.
15
velocity differential. The values of the two parameters of Eq. 1 (i.e. a and b) were not set a priori but corresponded to the values that led to the better fit. The validity of the model was assessed by looking at the average percentage of the total variance explained by the model. An initial ANOVA showed that the percentage of successful trials was not affected by experimental condition (Fð2;14Þ ¼ 1:125, P . 0:05). Subjects’ success rate was 61% in all three conditions (acceleration, deceleration and no change). This relatively poor success rate should not be too surprising as it is the result of the particularly stringent success criterion characterizing the task (spatial window: 4 cm, temporal window: around 30 ms). Subsequent ANOVAs were conducted on all trials (i.e. successful trials and failures, n ¼ 240). Velocity and current error variability profiles indicated an initial increase in the velocity variability 5 s before contact and a second increase 1.5 s before contact (Fð11;77Þ ¼ 34:085, P , 0:001) together with a decrease in the current error variability 5 s before contact onward (Fð11;77Þ ¼ 53:646, P , 0:001) (Fig. 2). These results reveal effective velocity regulations occurring very early in each trial. The required velocity model analysis was conducted over the 240 trials. Multiple linear regressions were performed over six temporal ranges: 6 s before contact onward, 5 s before contact onward,..., 1 s before contact. These analyses showed that the percentage of total variance (R 2 £ 100) explained by the model during the last 6 s of the task was an inverse function of the remaining time (8.5%, 9.5%, 11%, 14.5%, 25% and 46% for the time periods 6, 5, 4,..., 1 s before contact, respectively). An analysis of variance performed on the data after Z-transformation revealed an increase of the Z values 3 s before contact onward (Fð5;35Þ ¼ 261:294, P , 0:001). Hence, the required velocity model only predicts the observed kinematics in the vicinity of contact, accounting for (at best) 46% of the variance and cannot account for early velocity regulations (i.e., at 5 s before contact). This rather weak percentage of variance explained by the model could also highlight the need in future modeling work to integrate in some way a noise term in order to account for the inter trial variability inherent to the production of such behavior. An additional analysis was performed in order to see whether an alternative strategy of maintaining a constant bearing angle [3] could explain the observed early velocity regulations. Bearing angle is the angle subtended at the point of observation by the current position of the ball and the direction of displacement (Fig. 1). Linear regression analyses were performed for each trial (n ¼ 30) performed by a representative subject on the time-course of the bearing angle from the beginning of the trial until 2 s before contact. If the bearing angle strategy had been used, the regression analyses should have zero gradient. The analyses revealed, for each trial, variations of the bearing angle across time (P , 0:05 and mean R 2 values 0.73). Nevertheless, the slopes were not statistically different from zero
16
A. Chardenon et al. / Neuroscience Letters 334 (2002) 13–16
(tð1;29Þ ¼ 22:024, P . 0:05)(mean value 20.0009, SD 0.0025). Thus, the bearing angle strategy can explain the early velocity regulations. It is worth noting that one can not exclude that this strategy was also used to produce late velocity regulations. In fact the large bearing angle variations in the last second before contact (Fig. 3) could express small spatio-temporal errors that get magnified at small distances when plotted in term of bearing angle. The present study was designed to test the applicability of the required velocity model over a longer timescale than in previous studies. The percentage of variance explained by the model is slightly lower than the one obtained in unimanual interceptive tasks [12] (46% vs. 55%). Our data show that this model has the potential to explain part of the velocity regulations occurring late in the task. Conversely, the first part of our analysis also reveals the existence of visually driven velocity regulations early in the task, which the required velocity model cannot explain. For these regulations, a simple strategy based on maintaining a constant bearing angle is adequate. It should be noted that we do not want to exclude the possible involvement of this strategy in producing late regulations. However the present data do not permit us to provide an answer to take a clear position in this matter. This study does not support the required velocity model as a generic model for the control of interceptive tasks. Conversely it allowed us to identify a simple bearing angle strategy as a suitable mechanism to perform the ball interception task (see Refs. [7,8] for a similar result in a goal-directed cycling task). However, it remains to be seen if the produced regulations can be explained by the use of a single control mechanism based on the bearing angle, or if they necessitate two mechanisms to effectuate separate control of velocity regulations early and late in the task. Note that, contrary to the bearing angle strategy, the required velocity model is based (partly) on the use of expansion information [5]. Given the task constraints (ball diameter 0.2 m, combined velocity of the ball and the subject: 2 m s 21, subject-ball distance: 15 m) the expansion velocity of the ball at the beginning of the trial (0.05 8 s 21) is below the perceptual threshold (0.08 8 s 21) [6]. This could explain why subjects would use a bearing angle strategy initially and then could opt for a required velocity strategy when the expansion pattern is easily perceptible, i.e. at the end of the trial. A simple way to test the two hypotheses would consist in manipulating the expansion information during the last seconds before contact. The use of a bearing angle strategy should not suffer from this manipulation. The present study illustrates the adaptive capacity of the perceptual-motor mechanisms underlying goal-directed
locomotion. Rather than emphasizing the (real) limits of the required velocity model we prefer to keep in mind the diversity of the mechanisms available. Discovering the range of action of these mechanisms and eventually how these mechanisms cooperate offers a very interesting challenge for future work.
[1] Bootsma, R.J., Fayt, V., Zaal, F.T.J.M. and Laurent, M., On the information-based regulation of movement: things Wann (1996) may want to consider, J. Exp. Psychol. Hum. Percept. Perform., 23 (1997) 1282–1289. [2] Bootsma, R.J., Ecological movement principles and how much information matters, In A.A. Post, J.R. Pijpers, P. Bosch and M.S.J. Boschker (Eds.), Models in Human Movement Science, Print Partners Ipskamp, Enschede, 1998, pp. 51–63. [3] Cutting, J.E., Vishton, P.M. and Braren, P.A., How we avoid collisions with stationnary and moving obstacles, Psychol. Rev., 102 (1995) 627–651. [4] De Rugy, A., Montagne, G., Buekers, M.J. and Laurent, M., The study of locomotor pointing in virtual reality: the validation of a test set-up, Behav. Res. Meth. Ins., C, 32 (2000) 215–220. [5] Laurent, M., Montagne, G. and Durey, A., Binocular invariants in interceptive tasks: a directed perception approach, Perception, 25 (1996) 1437–1450. [6] Lee, D.N., A theory of visual control of braking based on information about time-to-collision, Perception, 5 (1976) 437–459. [7] Lenoir, M., Musch, E., Janssens, M., Thiery, E. and Uyttenhove, J., Intercepting moving objects during self-motion, J. Mot. Behav., 31 (1999) 55–67. [8] Lenoir, M., Savelsbergh, G.J., Musch, E., Thiery, E., Uyttenhove, J. and Janssens, M., Intercepting moving objects during self-motion: effect of environmental changes, Res. Q. Exerc. Sport, 70 (1999) 349–360. [9] McBeath, M.K., Shaffer, D.M. and Kaiser, M.K., How baseball outfielders determine where to run to catch fly balls, Science, 268 (1995) 569–572. [10] McLeod, P. and Dienes, Z., Running to catch the ball, Nature, 362 (1993) 23. [11] Montagne, G., Laurent, M., Durey, A. and Bootsma, R.J., Movement reversals in ball catching, Exp. Brain Res., 129 (1999) 87–92. [12] Montagne, G., Fraisse, F., Ripoll, H. and Laurent, M., Perception-action coupling in interceptive task: first order temporal relation as an input variable, Hum. Movement Sci., 19 (2000) 59–72. [13] Peper, C.E., Bootsma, R.J., Mestre, D.R. and Bakker, F.C., Catching balls: how to get the hand to the right place at the right time, J. Exp. Psychol. Hum. Percept. Perform., 20 (1994) 591–612. [14] Savelsbergh, G.J.P., Whiting, H.T.A. and Bootsma, R.J., ‘Grasping’ tau, J. Exp. Psychol. Hum. Percept. Perform., 31 (1991) 1655–1663. [15] Warren, W.H., Visually controlled locomotion: 40 years later, Ecol. Psychol., 10 (1998) 177–219.
The visual control of ball interception during human locomotion A. Chardenon a, G. Montagne a,*, M.J. Buekers b, M. Laurent a a Faculty of Sport Science, Movement and Perception Laboratory, Marseille, France Faculty of Physical Education and Physiotherapy, Motor Learning Laboratory, Leuven, Belgium
b
Received 17 May 2002; received in revised form 2 September 2002; accepted 2 September 2002
Abstract According to the required velocity model, on-line modulations of movement acceleration are performed on the basis of an optically specified difference between required and current behavior. Can this model account for observed displacement regulations in an interceptive task requiring locomotive displacements? In the present study, a virtual reality setup was coupled to a treadmill. Subjects walking on the treadmill were required to intercept a virtual ball approaching at eye-level by adjusting their velocity, if necessary. While the required velocity model could partially account for displacement regulation late in the interception, it was ineffective to explain early regulations. The possible use of a bearing angle strategy to control displacement regulation and the possible degree of complimentarity of these strategies are discussed. q 2002 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Perception-action coupling; Locomotion; Law of control; Bearing angle strategy; Goal-directed action
Intercepting or avoiding a moving object is one of the most complex abilities characterizing the human perceptivo-motor repertoire. It requires on-line movement regulations, based on instantaneously available information, to accommodate to a future event [9]. This is the case when driving a car, when moving through a crowd, or when intercepting a moving ball. While the information substrate possibly used in this kind of task has received special attention [10,14], very few integrative models exist which describe not only the information but also how the information is used in the control process. The required velocity model [1,2,13] constitutes a rather isolated attempt to bridge the gap between perception and action. According to this model, on-line modulations of movement acceleration are performed on the basis of an optically specified difference between required and current behavior (Eq. 1). This continuous updating of the movement with respect to current information [15] guarantees success. In one study [13] a one-handed catching task was used in which the hand was constrained to move along a single lateral direction while the angle of approach of the ball * Corresponding author. Universite´ de la Me´diterrane´e, Faculte´ des Sciences du Sport, UMR Mouvement et Perception, 163 Avenue de Luminy CP 910, 13288 Marseille Ce´dex 9, France. Tel.: 133-49-1172273; fax: 133-49-1172252 E-mail address: [email protected] (G. Montagne).
was varied. In this model, the required behavior corresponds to a required hand velocity expressed by the ratio between the current lateral distance separating the hand from the ball and the time remaining before the ball reaches the movement axis (Eq. 2) (see [5] for an optical specification of this ratio). The current behavior corresponds to the actual velocity of the hand. Y Y X YY 2 aXreq 2 bXcur
Y Xreq ¼
Xb 2 Xh TC
ð1Þ
ð2Þ
Y where X YY is hand acceleration, Xreq is the required velocity, Y Xcur is the current velocity, Xb is the current lateral ball position, Xh is the current hand position, TC is the time remaining before the ball reaches the movement axis and a and b are constants. According to this model, all the subject has to do is to adjust hand acceleration to cancel the difference between required and current behavior. Recently this model received empirical validation [11,12]. In these two experiments the subjects were asked to intercept moving objects while various parameters were manipulated, e.g. angle of approach, ball speed, duration of presentation. The results show adaptations of hand kinematics that match the predictions made on the basis of the
0304-3940/02/$ - see front matter q 2002 Elsevier Science Ireland Ltd. All rights reserved. PII: S03 04 - 394 0( 0 2) 01 00 0- 5
14
A. Chardenon et al. / Neuroscience Letters 334 (2002) 13–16
Fig. 1. Bird’s eye view of the interceptive task. The subject intercepts a moving ball with the head by producing the necessary displacement regulations. The required velocity takes into account the distance separating the current position of the subject from the current projection of the ball on the axis of displacement (Yb 2 Ys) and the current time remaining before the ball reaches the axis (TC). The bearing angle b is also represented.
model. For example, in a ball-catching experiment [12], it was shown that the cancellation of the difference between required and current behavior occurred on average 300 ms before contact and was maintained until contact. Moreover, if the subject’s hand was initially placed in the correct position to catch the ball (i.e. no movement necessary), movements away from this position occurred as soon as a lateral hand–ball distance was created, followed by reversal movements back to the correct position. These results argue for the validity of the model under consideration, nevertheless they call for a few remarks. First of all, they were obtained using a task in which hand movements were mechanically constrained to one direction. While this added constraint can be justified insofar as it allows a more easy test of the model, it remains to be seen if the model applies to other, more realistic tasks. It is also worth mentioning that in the three previously cited studies [11,12,13], the movement times were between 1 s and 1.5 s. Consequently, one can ask if the same model can account for movement regulation when the interceptive task involves a larger time scale (around 8 s in the present experiment). The present study was designed to explore the utility of the required velocity model for a longer time frame with a different task. Subjects were asked to move (locomotion displacement) in a specified direction (along the Y-axis) and to intercept with their head a virtual moving ball crossing their displacement axis. The required velocity model can be simply reformulated by expressing both required and produced behavior along the Y direction (Fig. 1). Eight subjects with normal or corrected to normal vision
participated in the present study. Informed consent was obtained prior to testing. The experimental set-up consisted of a virtual environment (Silicon Graphics) coupled to a treadmill (Gymroll). Subjects walked on the treadmill 0.6 m in front of the screen (3 £ 2.3 m) on which the virtual scene was projected. The virtual scene consisted of an approaching ball (0.2 m diameter) and a textured floor. Displacements of the virtual environment were directly proportional to the displacements of the subject on the treadmill. Ball path kinematics were collected by the Silicon Graphics system (100 Hz) and subjects’ displacement kinematics were registered by an optical encoder positioned on the treadmill (100 Hz). The synchronization of the two systems allowed the computation of all displacements (ball and subject) in the same coordinate system. This setup was chosen for obvious reasons: the task constraints are easy to manipulate while natural movement regulation behavior is maintained [4]. Subjects were required to intercept the ball approaching along a rectilinear path (26.568 with respect to subjects’ displacement axis) with a constant velocity (1.26 m s 21) along a horizontal plane going through the head. The interception point was computed at the beginning of each trial on the basis of subjects’ initial velocity (mean velocity 0.81 m s 21, SD 0.057 m s 21), while the time taken by the ball to cross subjects’ displacement axis was kept invariant (7.5 s). Subjects performed the experimental task in three conditions: no change, acceleration and deceleration. In the no change condition, no velocity adjustments were required. In the other two conditions subjects had to either accelerate, or decelerate to intercept the ball. More precisely, in the acceleration and deceleration conditions, if the subject kept his velocity unchanged he would have been one meter short or ahead of the interception point, respectively. Subjects performed ten trials per condition, the order of conditions was randomized across all trials. Subjects received immediate performance feedback after each trial: a green (success) or red (failure) square projected in the center of the screen. A successful trial was one where the distance between the center of the ball and the center of the subject’s head was at most ^2 cm when the ball crossed the subject’s displacement axis. Current error was computed every 10 ms during each trial and represents the error that would result if the current velocity had been kept invariant. Consequently, a current error that tends towards zero implies effective regulation of velocity. Performance measures were percentage of successful trials and the time-course of inter-trial variability of both velocity and current error (i.e. each half second during the last 6 s before contact). An increase in velocity variability indicates velocity regulations. In the assumption that these velocity regulations are effective, they should be accompanied by a decrease in current error variability. For the required velocity model analysis, the fit of the model to the recorded data was examined using multiple linear regression on each trial. The analyses were based on Eq. 1 and tested the extent to which acceleration depends upon the
A. Chardenon et al. / Neuroscience Letters 334 (2002) 13–16
Fig. 2. Time course of both mean displacement velocity and current error profiles with the associated variability (error bars) in the acceleration condition (diamond), the no change condition (square) and the deceleration condition (triangle). The analyses reveal an initial increase in velocity variability 5 s before contact and a second increase 1.5 s before contact together with a decrease in the current error variability from 5 s before contact.
Fig. 3. Mean bearing angle profiles for every successive 0.5 s interval from 6 s until 1 s before contact, and their associated variability. The analyses reveal that the bearing angle is kept constant in the first part of the trial. Bearing angle only changes in the last 2 s before contact.
15
velocity differential. The values of the two parameters of Eq. 1 (i.e. a and b) were not set a priori but corresponded to the values that led to the better fit. The validity of the model was assessed by looking at the average percentage of the total variance explained by the model. An initial ANOVA showed that the percentage of successful trials was not affected by experimental condition (Fð2;14Þ ¼ 1:125, P . 0:05). Subjects’ success rate was 61% in all three conditions (acceleration, deceleration and no change). This relatively poor success rate should not be too surprising as it is the result of the particularly stringent success criterion characterizing the task (spatial window: 4 cm, temporal window: around 30 ms). Subsequent ANOVAs were conducted on all trials (i.e. successful trials and failures, n ¼ 240). Velocity and current error variability profiles indicated an initial increase in the velocity variability 5 s before contact and a second increase 1.5 s before contact (Fð11;77Þ ¼ 34:085, P , 0:001) together with a decrease in the current error variability 5 s before contact onward (Fð11;77Þ ¼ 53:646, P , 0:001) (Fig. 2). These results reveal effective velocity regulations occurring very early in each trial. The required velocity model analysis was conducted over the 240 trials. Multiple linear regressions were performed over six temporal ranges: 6 s before contact onward, 5 s before contact onward,..., 1 s before contact. These analyses showed that the percentage of total variance (R 2 £ 100) explained by the model during the last 6 s of the task was an inverse function of the remaining time (8.5%, 9.5%, 11%, 14.5%, 25% and 46% for the time periods 6, 5, 4,..., 1 s before contact, respectively). An analysis of variance performed on the data after Z-transformation revealed an increase of the Z values 3 s before contact onward (Fð5;35Þ ¼ 261:294, P , 0:001). Hence, the required velocity model only predicts the observed kinematics in the vicinity of contact, accounting for (at best) 46% of the variance and cannot account for early velocity regulations (i.e., at 5 s before contact). This rather weak percentage of variance explained by the model could also highlight the need in future modeling work to integrate in some way a noise term in order to account for the inter trial variability inherent to the production of such behavior. An additional analysis was performed in order to see whether an alternative strategy of maintaining a constant bearing angle [3] could explain the observed early velocity regulations. Bearing angle is the angle subtended at the point of observation by the current position of the ball and the direction of displacement (Fig. 1). Linear regression analyses were performed for each trial (n ¼ 30) performed by a representative subject on the time-course of the bearing angle from the beginning of the trial until 2 s before contact. If the bearing angle strategy had been used, the regression analyses should have zero gradient. The analyses revealed, for each trial, variations of the bearing angle across time (P , 0:05 and mean R 2 values 0.73). Nevertheless, the slopes were not statistically different from zero
16
A. Chardenon et al. / Neuroscience Letters 334 (2002) 13–16
(tð1;29Þ ¼ 22:024, P . 0:05)(mean value 20.0009, SD 0.0025). Thus, the bearing angle strategy can explain the early velocity regulations. It is worth noting that one can not exclude that this strategy was also used to produce late velocity regulations. In fact the large bearing angle variations in the last second before contact (Fig. 3) could express small spatio-temporal errors that get magnified at small distances when plotted in term of bearing angle. The present study was designed to test the applicability of the required velocity model over a longer timescale than in previous studies. The percentage of variance explained by the model is slightly lower than the one obtained in unimanual interceptive tasks [12] (46% vs. 55%). Our data show that this model has the potential to explain part of the velocity regulations occurring late in the task. Conversely, the first part of our analysis also reveals the existence of visually driven velocity regulations early in the task, which the required velocity model cannot explain. For these regulations, a simple strategy based on maintaining a constant bearing angle is adequate. It should be noted that we do not want to exclude the possible involvement of this strategy in producing late regulations. However the present data do not permit us to provide an answer to take a clear position in this matter. This study does not support the required velocity model as a generic model for the control of interceptive tasks. Conversely it allowed us to identify a simple bearing angle strategy as a suitable mechanism to perform the ball interception task (see Refs. [7,8] for a similar result in a goal-directed cycling task). However, it remains to be seen if the produced regulations can be explained by the use of a single control mechanism based on the bearing angle, or if they necessitate two mechanisms to effectuate separate control of velocity regulations early and late in the task. Note that, contrary to the bearing angle strategy, the required velocity model is based (partly) on the use of expansion information [5]. Given the task constraints (ball diameter 0.2 m, combined velocity of the ball and the subject: 2 m s 21, subject-ball distance: 15 m) the expansion velocity of the ball at the beginning of the trial (0.05 8 s 21) is below the perceptual threshold (0.08 8 s 21) [6]. This could explain why subjects would use a bearing angle strategy initially and then could opt for a required velocity strategy when the expansion pattern is easily perceptible, i.e. at the end of the trial. A simple way to test the two hypotheses would consist in manipulating the expansion information during the last seconds before contact. The use of a bearing angle strategy should not suffer from this manipulation. The present study illustrates the adaptive capacity of the perceptual-motor mechanisms underlying goal-directed
locomotion. Rather than emphasizing the (real) limits of the required velocity model we prefer to keep in mind the diversity of the mechanisms available. Discovering the range of action of these mechanisms and eventually how these mechanisms cooperate offers a very interesting challenge for future work.
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