Exp Brain Res (1999) 127:259–269
© Springer-Verlag 1999
R E S E A R C H A RT I C L E
Neil E. Berthier · Rachel K. Clifton
Daniel D. McCall · Daniel J. Robin
Proximodistal structure of early reaching in human infants
Received: 27 July 1998 / Accepted: 26 March 1999
Abstract Nine infants were tested, at the age of onset of
reaching, seated on their parent’s lap and reaching for a
small plastic toy. Kinematic analysis revealed that infants largely used shoulder and torso rotation to move
their hands to the toy. Many changes in hand direction
were observed during reaching, with later direction
changes correcting for earlier directional errors. Approximately half of the infants started many reaches by bringing their hands backward or upward to a starting location
that was similar across reaches. Individual infants often
achieved highly similar peak speeds across their reaches.
These results support the hypothesis that infants reduce
the complexity of movement by using a limited number
of degrees-of-freedom, which could simplify and accelerate the learning process. The proximodistal direction
of maturation of the neural and muscular systems appears to restrict arm and hand movement in a way that
simplifies learning to reach.
Key words Human infant · Motor development ·
Reaching
Introduction
The ability of human infants to reach for and retrieve objects in their environment develops slowly over the first
two years of life. Infants progress from a crude ability to
direct hand movements toward targets at birth (von Hofsten 1982; Ennouri and Bloch 1996), to successful
touching and grasping objects at around four months,
and then to using pincer grasps on small objects at about
12–18 months of age (e.g., White et al. 1964; Touwen
1976).
Functionally, infants face two significant problems in
learning to reach. First, they must transport the hand to
N.E. Berthier (✉) · R.K. Clifton · D.D. McCall · D.J. Robin
Department of Psychology, Tobin Hall,
University of Massachusetts, Amherst, MA 01003, USA,
e-mail: [email protected],
Fax: +1-413-545-0535
the vicinity of the target object. Second, they must conform the hand to the object in order to perform a grasp.
Both of these problems are formidable because of the
dynamic complexity of the arm and because of the relative immaturity of the infant’s neuromuscular systems.
Several investigators (von Hofsten 1993; Thelen et al.
1993; Berthier 1996) have suggested that infants find solutions to these problems through an interactive search
or discovery process. While interactive learning has the
advantage of not requiring solutions to be completely
pre-specified by the genes, it has the disadvantage of requiring the learner to search through a very large space
of possibilities to find correct solutions (the “degrees-offreedom problem”, Bernstein 1967). If infants use interactive learning to discover effective ways of reaching,
we have yet to determine how infants reduce search
complexity to find good solutions in a reasonable time.
The current paper suggests that the pattern of nervoussystem development initially constrains reaching movements so as to substantially reduce the space in which
possible solutions are searched for.
One important fact of neural development that might
appropriately limit the kinematics of infant reaching is
the proximodistal nature of development. Development
of the neural systems controlling the trunk and the proximal arm occurs before that of the distal arm. The corticospinal tract is not functional at birth, but develops extensively over the first year, leading to a gradual development of the infant’s ability to control the distal musculature of the arm and hand (Kuypers 1981; Armand et al.
1997; Olivier et al. 1997; White et al. 1964). If young infants predominately use the musculature of the proximal
arm and trunk in reaching, the learning problem would
become much simpler with the reduction in the functional degrees-of-freedom of the arm.
The current study examined the kinematics of reaching in nine infants at the age at which they first successfully moved their hands to targets presented in their
workspace. We reasoned that, at this age, where infants
have poor hand control, any restrictions that neural maturation places on search or any strategies that an infant
260
uses to reduce the difficulty of the learning task would
be especially observable.
kinematics of reaching at this age have been found in previous analyses of this data (McCall et al. 1994).
Kinematic data analysis and computational methods
Materials and methods
Subjects
Nine infants participated as subjects in the current experiment. All
infants were the result of full-term pregnancies. The data reported
here are from a larger longitudinal study that required parents and
children to make repeated weekly visits to the laboratory. All infants were in good health on the day of testing and received a
small gift for each experimental visit (usually a small toy or
book). The experimental procedure was reviewed and approved by
the institutional human-subjects committee and was performed in
accordance with the ethical standards laid down in the 1964 Declaration of Helsinki. Informed consent was obtained from the infants’ parents.
Equipment and procedure
Infants were seated on one of their parent’s laps at each session.
The parent was asked to hold their infant firmly around the hips to
support the infant and allow for free movement of the infant’s
arms. The parent was further asked to refrain from attempting to
influence the infant in any way.
The infants reached for a colorful plastic toy (Sesame Street’s
Big Bird, 7 cm length). The toy was attached to a rattle and held
by an experimenter, who sat facing the infant. At the beginning of
each trial, the presenter attracted the attention of the infant to the
toy and slowly brought it forward to a position 15–25 cm away
from the infant while shaking the rattle to produce sound. To encourage use of the right hand, the toy was presented approximately 30° in the horizontal plane to the right.
Infants were videotaped throughout the session at 30 frames/s
with an infrared camera (Panasonic WV1800) placed to the right
of the infant for a side view of the reaches. In addition to the videotape, the reaches were monitored using an Optotrak motion
analysis system (Northern Digital). This system consists of three
infrared cameras that generate estimates of a marker’s position in
three-dimensional coordinates. In the current experiments, four infrared-emitting diodes (IREDs) were used as markers. The Optotrak system estimated the positions of these markers at a rate of
100 Hz. Position data were acquired during 10–20 s trials. Two
IREDs were taped on the back of the infant’s right hand, one just
proximal to the joint of the index finger and one on the ulnar surface just proximal to the joint of the little finger. Two IREDs were
used on the hand in order to keep at least one in camera view if the
infant rotated his or her hand during the reach. Infants of this age
are not bothered by the IREDs and tend to ignore them once they
are in place. One IRED was also placed on the apex of the infant’s
shoulder, and one on the lateral edge of infant’s elbow. The Optotrak cameras were placed above and to the right of the infants.
The video camera output was fed through a date-timer (For-A)
and into a videocassette recorder (Panasonic Model 1950) and a
video monitor (Sony Model 1271). The Optotrak system and the
date-timer were triggered simultaneously by a second experimenter in order to time-lock the IRED data with the video-recorded behavior for later scoring. The second experimenter was seated out
of view and observed the infant on the video monitor.
The present study was part of a larger study investigating the
use of vision in the service of reaching. Three levels of illumination, but with sound always available, were presented: (1) trials
with full-illumination of the room; (2) trials with the room in complete darkness, but using a luminescent Big Bird; and (3) trials
with the room in complete darkness using a Big Bird that was not
visible, but was sounding through the use of a rattle. Infants made
twice as many reaches in the fully-lighted and luminescent conditions than in the sounding condition. No condition effects on the
Videotapes were first examined for any significant movement of
the hand (defined as movements of more than 2–4 cm in length)
that was made in the presence of the goal object. We defined a
reach as a forward movement of the hand towards the goal object
that was accompanied by the attention of the infant towards the
goal object, usually visual attention, and by the viewer’s judgment
that the infant was, in fact, attempting to reach for the toy, not
simply batting at it or touching it incidentally in a movement towards the mouth, body, or contralateral hand. We found 78 movements that were defined as reaches, 15 movements that were primarily backward and or upward movements of the hand, 8 movements to the mouth, 4 ”back and forth” movements, and 2 complex, undefined movements.
Reach onset was defined as the point in time when the hand
started to move forward towards the goal object. Backward, upward, or other preparatory movements before forward movement
were analyzed and are discussed below, but were not considered
part of the reach itself. These preparatory movements were easy to
score because they often involved large movements, such as an
upward movement from the infant’s thigh to their shoulder. The
end of the reach was defined by the time of contact. If the infant
did not make contact with the toy, the end of the reach was defined by a speed minimum in the forward extent of the reach. Because of the detailed analysis of the data, and in contrast to our
and others’ earlier work (Thelen et al. 1993), we required that
Optotrak data for a reach to be complete and not have any missing
values.
The data obtained from the Optotrak system are estimates of
the true IRED position at the time of the sample. The dynamic
programming method of Busby and Trujillo (1985) was used to
estimate the position, speed, and acceleration of the hand. The algorithm assumes that the marker is a point moving through space
and computes a smooth path based on a minimal input control. We
used the criteria suggested by Busby and Trujillo for selecting the
parameter B and used B=1×10–11 (Milner and Ijaz 1990; Berthier
1996). While direct comparisons are difficult because of the algorithm, the data reported here are similarly smoothed to traditional
low-pass filtering with a cutoff frequency of 30–50 Hz.
As we and others have found, young infants reach toward targets using multiple accelerations and decelerations of the hand.
We analyzed the amplitude of these individual peaks to determine
if there were any dependencies in the peak amplitudes. To determine the time of a speed peak, we smoothed the speed data with a
three-point moving average filter. We then defined peaks as times
when the two previous samples of the smoothed speed function
had positive slopes and the two succeeding samples of the
smoothed speed function had negative slopes. The times and amplitudes of these speed peaks were then noted.
Principal component analysis was performed with custom software using the CLAPACK routines. Because of the distributions
of the underlying measures in the current report, we used median,
ranges, and other non-parametric statistics to describe the data.
Results
Data were obtained from nine infants at weekly intervals, starting when the infants were a median age of 11
weeks. We operationally defined the age of reach onset
as the laboratory session where the infant attempted to
reach for the goal object three or more times and where
the infant showed continued reaching on subsequent testing sessions. Table 1 shows the age of first testing, age
of reach onset, the number of reaches before onset, the
261
Table 1 Number of reaches
by infant
Infant
1st Test
(age in weeks)
Reach Onset
(age in weeks)
Reaches
Before
Total
Reaches
Optotrak
Reaches
Contacts
A
B
C
D
E
F
G
H
I
Total
8
15
11
13
11
9
15
10
11
13
16
16
17
18
18
18
17
14
0
1
1
1
10
2
0
4
1
20
8
4
4
8
9
13
11
10
11
78
2
2
1
6
9
10
2
8
7
47
0
2
0
6
8
8
2
1
7
34
number of reaches for the session of onset, the number
of these reaches with Optotrak data, and the number of
contacts for the onset session for each infant. Onset was
sudden for most infants, with eight of the infants reaching no more than four times on the weeks before onset.
The other infant made nine attempts at 11 and 12 weeksof-age, but failed to reach on succeeding weeks until he
made one attempt at 17 weeks-of-age. In this paper, we
limit our analyses to reaches made on the week of reach
onset.
Of the 78 reaches made by the infants during the
week of onset, 47 had complete and unobstructed position data from the Optotrack motion analysis system. Of
these 47 reaches with complete data, 34 were successful
in that the infant brought their hand in contact with the
goal object, and 13 were unsuccessful in that the infant
failed to make contact with the toy.
Shoulder motion and shoulder-hand distances during
reaching
In the current experiment, infants sat upright in their parent’s lap with no restrictions placed on their movements.
This allowed the infants to use any combination of trunk,
shoulder, and arm movements to move the hand to the
goal object. In order to assess the contribution of shoulder motion to hand movement, we computed the distance
the shoulder marker traveled and the change in the distance between the hand and shoulder markers during
reaching. Elbow angle is an inverse cosine function of
the hand-shoulder distance, but cannot be accurately
computed for the current data because of the unrestricted
motion of the infant’s arm and the location of our Optotrak markers.
Time series of hand-shoulder distances were then
plotted for each infant. Figure 1 shows hand-shoulder
distance time series for the ten reaches of infant F. If the
elbow was extending during a reach, the time series
should be increasing; if it is flexing during a reach, the
time series should be decreasing. Eight of infant F’s time
series were either predominantly decreasing or level, indicating slight flexion or no movement about the elbow.
Two of infant F’s time series show increases, indicating
significant elbow extension during the reach. These two
Fig. 1 Hand-shoulder distance during reaches of infant F
reaches with elbow extension were unusual in that only
one other reach from another infant was observed with
an increase of this magnitude.
In order to assess the degree of change in the handshoulder distances during reaching, we computed the
range in the hand-shoulder distances for each reach. The
range was the maximum hand-shoulder distance minus
the minimum hand-shoulder distance of a particular
reach. These maxima and minima did not necessarily occur at the beginning or end of the reach. The minimum
was then subtracted from the maximum to give the range
of hand-shoulder distances for each reach. This latter
number is an index of the amount of elbow extension
and flexion during the reach.
The median range of hand-shoulder distances for all
infants was 1.55 cm, with individual medians for those
infants with more than two reaches of 2.21, 0.83, 2.77,
1.60, and 0.13 cm for infants D, E, F, H, and I, respectively. There were three reaches where the range was
greater than 5.0 cm; one from infant C (range=10.4 cm),
and two from infant F (range=8.2 and 9.5 cm). The three
reaches where the range was greater than 5.0 cm were all
reaches where the arm was partially flexed at the beginning of the reach. The hand-shoulder distances at the beginning of the reach for these three were between 7.0
and 9.0 cm, while the hand-shoulder distances at the beginning of the reach for all other reaches were between
9.0 to 17.5 cm. The fact that hand-shoulder distance
changed only 1–2 cm on the vast majority of reaches in-
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Fig. 2 Scatterplot of the distance traveled by the shoulder
infrared-emitting marker
(IRED) and the distance traveled by the hand marker for
each reach of infants A–I. The
line on the plot has a slope of
one
dicates that very little elbow flexion or extension was
observed on a typical reach.
The observed lack of elbow flexion and extension
during reaching indicates that the hand could be largely
moved to the goal object either by rotation of the shoulder or trunk, or by forward translation of the shoulder
from abdominal flexion. To investigate these possibilities, we compared the amount of shoulder translation
with the amount of hand translation for each reach. We
assumed that kinematic motion is described by a chain of
rotatory degrees-of-freedom connected by rigid links.
We analyzed the situation of a rigid two-link chain moving in a parasagittal plane, where the first link connects
the hip and shoulder and the second connects the shoulder and hand (with the elbow fixed), with lengths l1 and
l2, respectively. For pure hip flexion, the distance traveled by the shoulder for a change of θ radians at the hip
is l1θ. If the hip, shoulder, and hand all lie on the same
line, the distance traveled by the hand is (l1+l2)θ. Therefore, if the infant’s hand is fully extended straight above
the shoulder with shoulder angle π, the ratio of hand to
shoulder movement is (l1+l2)/l1. If the two links are the
same length, as they approximately are for infants of this
age, the ratio of hand to shoulder movement would be
2.0. As the shoulder flexes and the shoulder angle decreases from π, the ratio of hand to shoulder movement
decreases and reaches 1.0 when both the hand and shoulder lie on a circle of radius l1. Further decreases in shoulder angle will cause the hand-shoulder movement ratio
to approach zero when the hand is at the center of rotation of the hip. This analysis suggests that hand movements caused primarily by forward rotation of the hip
will result in hand-shoulder distance ratios of 2.0 or less
and, often, in hand-shoulder distance ratios approaching
1.0. Hand-shoulder distance ratios of much greater than
2.0 would suggest that hand movement is caused primarily by shoulder rotation or by rotation about the vertical
axis of the torso.
Figure 2 shows a scatterplot of the distance traveled
by the shoulder versus the distance traveled by the hand
for all of the infants’ reaches. Each letter on the plot refers to a particular reach from that infant, and the plotted
line is the expected hand movement for pure forward
translations of the shoulder. The mean ratio of handshoulder movement was 4.06 with a range of 1.2 to 8.2,
indicating that in most cases hand movement was largely
the result of shoulder or torso rotation.
The result that hand-shoulder distance is relatively
constant during reaching and that the hand is primarily
moving because of shoulder rotation suggest that the infants’ hand movements can be viewed as movements on
a sphere centered at the shoulder. Spinplots of the hand
and shoulder markers confirm this suggestion. If the radius of the sphere is large relative to the extent of hand
movement, hand movements should be well-fit by a
plane that is approximately tangent to the sphere. This
suggestion implies that the first two principal components in a principal component analysis of the hand positions should account for a large proportion of the variance of the data and offers the possibility that planar representations of the hand data using the first two principal
components will be accurate representations of the infants’ hand movements.
To explore these possibilities, principal component
analysis was performed separately on the hand position
data for each of the reaches. Analyses of the reaches
showed that the first principal component accounted for
a median of 94.2% (range 68%–99%) of the variance
and the first two principal components accounted for a
median of 99.6% (range 92%–99.9%) of the variance.
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Fig. 3 Hand paths for two reaches of infant G projected onto the
plane defined by the first two principal components. The starting
positions of the hand for the reaches are given by S1 and S2 with
the end positions unmarked. The first two principal components
account for 98.8% of the variance of these two reaches
The data strongly support the hypothesis that hand
movement is essentially planar for individual reaches,
but a separate question is the degree to which the infants
move their hands on a similar plane across reaches. This
possibility can be assessed by performing principal component analysis on the aggregated hand position data
across trials for each infant. Principal component analysis performed across trials for each infant indicated that
the median proportion of variance accounted for by the
first component was 69% (range 59%–93%), and the
median proportion of variance accounted for by the first
two components was 95% (range 90%–99.9%). This relatively good fit suggests that a given infant’s reaches can
be meaningfully presented by plotting the infant’s hand
points on the plane defined by the first two principal
components. Figure 3 shows the hand positions for the
two reaches from infant G on the plane defined by the
first two principal components. The plane in this plot accounts for 98.8% of the variance of hand movement.
Other kinematic features of initial reaching
Starting location
Inspection of Fig. 3 suggests the possibility that infants
were starting the forward motion of their reaches from
similar initial positions and not from a large number of
starting locations. In order to investigate this possibility,
videotapes of reaches were examined to determine what
behavior immediately preceded reach onset. We found
that reaching was often preceded by movements that either elevated the hand or moved the hand back to the infant’s side. Of the nine infants, four never showed these
backward or elevatory movements, but five infants often
did. Infants A, E, F, H, and I showed these movements
on 1 of 2, 4 of 9, 6 of 10, 5 of 8, and 4 of 7 trials, respectively.
The previous analysis indicates that infants were often moving their hands back or up, but does not indicate
whether these movements moved the hands to similar
starting locations. In order to assess this possibility, matrices of the distances between the observed starting locations were computed. For each infant with N reaches
there were [N(N-1)]/2 pairwise distances between starting locations. The median pairwise distances between
starting locations for infants D, E, F, H, and I was 9.2,
5.2, 11.8, 6.5, and 8.9 cm, respectively (infants with
more than two reaches). Because one would not expect
all of an infant’s starting locations to be similar, the 25percentile of the pairwise distances might be a better
measure of the closeness of starting locations. The infants’ 25-percentiles were 7.3, 3.4, 7.4, 4.4, and 6.7 cm,
respectively, for infants D, E, F, H, and I. It is notable
that the two infants with the smallest distances between
starting locations, infants E and H, were two of the infants that moved their hands back or up before reaching.
Speed and distance dependencies
Young infants reach in a series of accelerations and decelerations of the hand (von Hofsten 1979). When hand
speed is plotted as a function of time, each of these accelerations and decelerations defines a segment of the
reach that is approximately bell shaped (see, e.g., Figs. 5
and 6). Two types of dependencies have been observed
in the amplitude of these speed peaks. First, Robin et al.
(1996) showed that the serial correlation between the
amplitude of one speed peak and the next in a sequence
was 0.86 over all their infants. The serial correlations between speed peaks for the current infants with over ten
data points were 0.51, 0.12, 0.28, 0.06, and 0.84 for infants D, E, F, G, and H, respectively. These correlations
are substantially lower than that seen in older infants.
The second dependency in speed of reaching observed in the adult literature is the highly positive correlation between target distance or distance-to-go and
hand-speed. We computed the correlation between handspeed peak amplitude and distance-to-go and found relatively weak correlations. For infants with over ten data
points, the correlations were –0.05, –0.11, 0.00, –0.09,
0.38, and 0.72 for infants D, E, F, G, H, and I, respectively. In sum, only infant I showed substantial serial dependency of speed peak amplitudes or of speed and distance-to-go, features that are normally observed in older
infants and adults.
Modulation in amplitude of peak speed
Visual inspection of hand-speed profiles for individual
infants suggests that the amplitudes of speed peaks did
not vary continuously, but appeared to cluster at particular amplitudes. Figure 4 shows the distribution of ampli-
264
were 7.0, 15.0, 20.5, 10.5, and 12.0 mm/s, respectively.
While the differences between the data and the Monte
Carlo simulations are modest, they are surprisingly large,
given that the Monte Carlo data were drawn from distributions defined by the mean and standard deviation of
the actual data and, thus, any differences likely reflect
differences in the spacing of the data. In sum, four of the
five infants that had sufficient data for analysis showed
evidence that speed amplitudes were not randomly distributed throughout the possible range, but tended to
cluster about specific values.
Lighting condition
Fig. 4 The distribution of the amplitudes of hand-speed peaks for
each infant (initials)
tudes of hand-speed peaks for each subject. There are
clear differences in overall hand-speed among subjects,
but there appear to be clusters of hand-speed peaks
around particular values. For example, infant E appears
to have a cluster of amplitudes around 300 mm/s.
The visual impression from Fig. 4 is of clustering, but
it is possible that such clustering might normally be observed in a sample of size n from an appropriate distribution. In order to provide some measure of how expected
such clustering would be, we performed Monte Carlo
simulations. Inspection of Fig. 4 suggests that peak
speeds are not distributed normally. Use of normal probability plots and tests of normality confirm this impression. For the infants with sufficient data, infants D–H,
logarithmic transformation of the data of Fig. 4 normalizes the data as assessed by normal probability plots and
tests of normality.
Monte Carlo trials were then performed for each infant with N random draws from a log normal distribution
with mean x– and standard deviation σ, where N is the
number of speed peaks observed for that infant and
x– the sample mean and σ the sample standard deviation
of the log transformed data for that particular infant. For
each set of N speed peaks drawn, differences in peak
speed were computed in the ordered sequence of amplitudes. The median difference was computed for this random sample. We repeated this process to obtain 1000
samples for each infant, each sample described by its
sample median. We then computed the grand median
over these 1000 samples for each infant and compared it
with the observed median in our experimental data.
These Monte Carlo simulations resulted in grand medians of 7.5, 17.8, 17.9, 13.0, and 15.2 mm/s for infants D,
E, F, G, and H, respectively. Four of five median differences in the actual data were lower than the grand median differences in the Monte Carlo simulations, indicating
that the actual data were more closely clustered than
would be expected from random draws from a log normal distribution. Median differences from the actual data
Infants were approximately half as likely to reach in
sounding-object trials than in glowing-object or fullylight trials, with 21 reaches overall in fully-light, 18 in
glowing-object, and 8 in sounding-object trials. Only infants D, E, H, and I reached in all three conditions. In the
weeks previous to the data described in the current paper, i.e., pre-onset, infants were approximately equally
likely to reach in the three lighting conditions.
In order to determine whether lighting condition had
an effect on the use of the shoulder, a Friedman two-way
analysis of variance was performed on the hand-shoulder
distance data from infants D, E, H, and I. The Friedman
test indicated that hand-shoulder distance did not vary
significantly with lighting condition (P=0.27).
The effect of lighting condition on the amplitudes of
the speed peaks was also investigated using a Friedman
two-way analysis of variance. The Friedman test on the
data from infants D, E, H, and I showed that speed-peak
amplitude did not vary with lighting condition (P=1.0).
Changes in hand direction during reaching
As noted above, the major feature of reaching in our data
is the relative constancy of the hand-shoulder distance
during reaching. The data suggest that infants’ hands
move towards the goal object largely by traveling on the
surface of a sphere defined by the hand-shoulder distance. This suggests that a simple, yet veridical, model
of initial reaching dynamics might be a spherical, two
degree-of-freedom pendulum.
While detailed analysis of this hypothesis is beyond
the scope of the present work, dampened oscillation similar to an underdamped spherical pendulum was observed in our data. Figure 5 shows the hand-speed profile
and hand position plot for a step change in hand position
for infant C. This was not part of a reach, but a movement of the hand from the infant’s side to the infant’s
front. The movement was largely a shoulder rotation and
shows a two-dimensional dampened oscillation of the
hand about the end point of the movement.
The dampened oscillations of Fig. 5 were not seen
during actual reaching, a result that may be due to the
fact that the hand movement of Fig. 5 is very fast com-
265
Fig. 5 Hand-speed profile (above) and hand-position plot (below)
for a step change in hand position due to rotation of the shoulder.
The position plot is based on the first two principal components
and the start of the movement is to the right
pared with actual reaches (compare its peak speed with
the distribution of peaks speeds in Fig. 4). Rapid reaching sometimes led to movements of the hand, which
seemed to be the result of uncontrolled intersegmental
dynamics. For example, Fig. 6 shows a reach of infant C
that was not typical of the infants’ reaches because of its
large elbow extension and high speed, but that does illustrate uncontrolled dynamic effects during reaching. This
reach did not lead to contact with the goal object, but resulted in hyperextension of the elbow with bouncing of
the whole arm. Examination of the video tape indicated
that the hyperextension and bouncing would likely not
have occurred if the hand had made contact with the goal
object.
The sample of reaches from our study are quite different from the above two examples, in that the overall
speed of reaching was much lower. The vast majority of
speed peaks during reaching were less than 600 mm/s,
with infants D and G showing no speed peaks greater
than 400 mm/s (Fig. 4). Given that the effects of arm dynamics increase dramatically with hand speed, it is not
surprising that we could not find other examples of underdampened oscillation during reaching.
We investigated whether the multiple accelerations
and decelerations of the hand might reflect a feedback
control strategy, where later motion in a reach corrects
for early errors. We segmented infant reaching using the
local minima of the speed profile (these segments are often called ”movement units”, von Hofsten 1979). A segment was defined by two minima in the hand-speed profile that occurred sequentially. In order to be counted as
a segment, the minima had to be separated by at least
100 ms. Principal component analysis was then performed on the hand positions of each segment to determine their linearity and planarity. For the 131 segments,
Fig. 6 Hand-speed (above) and hand-position (below) plots for a
reach composed primarily of a forward extension of the elbow.
The hand did not make contact with the goal object. The first two
principal components were used in the position plot and the start
of the movement is to the left
the first principal component accounted for a median of
98.6% (range 74.0%–99.9%) of the variance, and the
first and second principal components accounted for a
median of 99.9% (93.7%–99.99%) of the variance. This
analysis indicates that movement segments were usually
well-approximated by a straight line, with 83% of the
first principal components accounting for over 95% of
the variance in the movement.
Because of the excellent linear fits to the hand movement during a segment, we used the first principal component to define a direction of movement during a segment and computed the directional error of movement
during the segment. The directional error was defined as
the angle between a vector pointing from the hand position at the start of the segment to the target location and
the vector defined by the first principal component. The
distribution of these angular errors was positively
skewed with a median error of 24.9° (range: 1.05–
133.1°; this measure is unsigned).
To answer the question of whether the sequence of
”movement units” is corrective in nature, we compared
the directional heading of the hand on the nth segment
with the heading on the n+1th segment. The directional
headings were given by the first principal component
and the analysis was performed at the hand position at
the end of the nth segment. Figure 7 illustrates the proce-
266
Fig. 7 Bottom Planar projection of the hand positions for a reach
by infant E. The first two principal components account for 99.2%
of the variance. Top The angular analysis for this reach. The hand
moves from the right to the left, starting at the position denoted
”S”. Hand positions at the time of a speed minimum are marked
by the normal lines and the letters A–F. Segments of the reach are
enumerated 1–7. The angular analysis for each point of analysis is
given in the table at the top. Each row of the table gives the location of evaluation, the segments that were evaluated, the angle between the target and the direction of the nth segment, the angle between the target and the direction of the n+1th segment, and the
angular improvement between the segments
dure for a reach performed by infant E. The angular error
for the nth segment was the angle between the direction
to the target at the point of analysis and the direction the
hand would have taken if it had continued in the same
direction as during the nth segment. The angular error for
the n+1th segment was the angle between the hand direction for the n+1th segment at that same point and the target. The angular error for the n+1th segment was then
subtracted from the angular error for the nth segment to
give an estimate of the angular improvement at the evaluation point. If the n+1th segment was corrective and
brought the hand closer to the target, the angular improvement would be positive. Across all infants the median difference between these angles was 38.6° (range,
–97.6–165°, n=112), with 80% of the pairs having positive differences.
Discussion
Our beginning reachers primarily used shoulder and torso rotation to move their hands to targets. The infants’
use of the elbow was minimal. Although this style of
reaching was typical, other ways of reaching were possible, because at least three reaches showed substantial elbow extension. The lack of elbow extension and flexion
was probably the result of co-contraction of the intrinsic
musculature of the arm. Reaching with minimal elbow
extension and flexion results in geometrical constraints
on hand position such that the infants’ hand positions lie
approximately on the surface of a sphere centered at the
shoulder. Because the radius of curvature of this sphere
is large relative to the extent of hand movement, this
style of reaching means that hand positions can be fit
with good accuracy by a plane that is approximately tangent to the sphere.
Two other constraints on movement were observed.
First, approximately half of the infants tended to start
their reaches from approximately the same location in
space, with some infants actively drawing their hands
backward or upward before the start of forward hand
motion. Second, while infants showed a broad range of
reaching speeds, individual infants tended to show speed
peaks around particular values. Other kinematic constraints that might be expected were not observed; infants did not show serial dependencies in speed during
reaching that have been observed in older infants (Robin
et al. 1996), nor did infants show a dependency between
distance-to-go to the target and the speed of reaching.
When reaches were segmented using hand-speed minima, we found that the hand paths for each segment were
largely linear and that later segments of a reach corrected
for the angular errors of preceding segments.
The kinematics of the development of reaching
Several groups of investigators have performed longitudinal investigations of infant reaching using sophisticated motion analysis systems (von Hofsten 1991; Thelen et
al. 1993; McCall et al. 1994; Konczak and Dichgans
1997; Konczak et al. 1995, 1997). These studies focused
on the straightness, speed, and segmented nature of
reaching and how these features change with age. The
general finding from these studies is that, while beginning infant reaching is characterized by multiple accelerations and decelerations of the hand, experienced infants
reach with much straighter hand paths and with a single
smooth acceleration and deceleration of the hand.
Our purpose in this paper was to quantitatively investigate the control strategies of infants beginning to reach,
and our principal finding was that reaching is largely accomplished using shoulder or torso rotation. Bullinger
(1998; Bullinger and Millan 1993) reported observational data that young infants learning to reach show much
greater usage of the torso than accomplished reachers.
Why have other investigators failed to notice the infant’s
reliance on shoulder and torso movement to move the
hand to targets? Perhaps the most likely answer is that no
other investigators used our measure, hand-shoulder distance, to analyze infant reaching, and that only two other
groups (Thelen et al. 1993; Konczak et al. 1995, 1997;
Konczak and Dichgans 1997) computed a related measure, elbow angle, during reaching. Neither of these other groups reported summary statistics of the amount of
change of elbow angle at the onset of reaching, but Thelen et al. (1993) presented joint-angle plots of their four
infants’ reaches at onset of reaching. Using these jointangle plots (Figs. 1l, 18, 25, and 32 in Thelen et al.
267
1993), we estimated the maximum change in elbow angle for each reach and found median angular changes of
52, 16, 27, and 27°, respectively, for the youngest to oldest infants. It is difficult to precisely compare these angular estimates with our hand-shoulder distance estimates, but they suggest much more elbow usage than our
data.
How can these observations from Thelen et al. (1993)
be reconciled with the current data? One possibility is
that the means of support of the infants, which varied
among the studies, affected the way infants reached. In
the current study, infants sat upright on their parent’s lap
and were supported by the parent holding their infants’
hips. This posture allowed the infants to flex forward at
the hip and to freely rotate the shoulder and torso about
the vertical axis. Thelen et al. (1993), as well as Konczak
et al.’s (1995, 1997; Konczak and Dichgans 1997), supported their infants on a backboard with a strap across
the upper chest that extended to the infant’s axilla. Clearly, such means of support will restrict the infant’s ability
to flex the trunk and to rotate the shoulder and torso. Because the backboard was tilted backward 15 or 50°, infants also had to push their hands up against gravity to
reach the targets. These differences could well have led
to the differences in reach kinematics of the studies.
A second possibility for the observed differences between the present study and those of Thelen et al. (1993)
and Konczak et al. (1995, 1997; Konczak and Dichgans
1997) lies in the ages of the infants at testing. All three
groups studied infants at the onset of reaching, but the
ages of infants in the current study were generally
younger than those of Thelen et al. and Konczak et al.
Our infants started reaching between 13 and 18 weeks,
with seven of the nine infants showing onset between 16
and 18 weeks. Konczak et al.’s infants showed onsets between 20 and 24 weeks-of-age and Thelen et al.’s infants
showed onsets at 12, 15, 21, and 22 weeks.
Because one of our infants, infant E, showed considerable reaching at 11 and 12 weeks of age, we investigated whether this infant showed increased elbow usage
similar to Thelen et al.’s (1993) youngest infant, who
was 12 weeks of age. Kinematic data were available for
eight reaches of this infant at 11 and 12 weeks-of-age.
Hand-shoulder distance ranges were computed as above
and found to be significantly higher than the same infant’s range at 18 weeks (medians of 2.69 cm and
0.83 cm, Mann-Whitney U, P<0.05). While elbow usage
was still only moderate for the young infant E, the data
is certainly in line with that of Thelen et al. (1993).
Chronological age at the onset of reaching might lead
to differences in the kinematics of reaching. The state of
development of the neuromuscular system and its
strength significantly changes from 12 to 24 weeks of
age and perhaps late-onset reachers have neuromuscular
resources and skills that allow them to reach differently
from early-onset reachers. The available data from the
current study and those of Thelen et al. (1993) and
Konczak et al. (1995, 1997; Konczak and Dichgans
1997) follows a pattern of high elbow use in young in-
fants, low elbow use in 15- to 18-week-olds, and moderate elbow use in infants older than 20 weeks. If very
young reachers have very poor control of the intrinsic
arm muscles or are unable to forcefully co-contract about
the elbow, one might observe significant changes in elbow angle during reaching. If infants of intermediate age
have the ability and discover the merits of locking the elbow in reaching, they might predominantly reach using
the shoulder musculature. If late-onset reachers have better control of the intrinsic muscles of the arm, they might
modulate elbow angle during reaching to take advantage
of the increased degrees-of-freedom. While all current
data is consistent with this developmental progression,
confirmation must await detailed studies of infants in the
same laboratory at a variety of ages within the span of
10–24 weeks.
Relationship to neural development
The exact developmental state of the neuromuscular systems of the 12- to 21-week-old human infant is not well
understood. The regressive events of motoneuronal and
neuromuscular development, motoneuron death and the
transition from multiple to single innervation of trunk
and arm muscle fibers, extend to the early postnatal
weeks of life in humans (Jansen and Fladby 1990).
These anatomical events appear to be largely complete
by 12 weeks of age (Gramsbergen et al. 1997), but the
physiological maturation of the motor unit may still be
occurring at the age of testing of our infants (Jansen and
Fladby 1990). This suggests that young infants might be
limited in their ability to select particular arm muscles
during reaching or might be unable to smoothly modulate force during reaching. It is likely that these abilities
might depend on the particular muscles, with the proximal muscles developing before the distal muscle of the
arm. These neural limitations probably contribute to the
jerky and poorly modulated arm movements of our infants.
The brain and spinal systems underlying reaching are
still undergoing significant development when reaching
is first observed. In mammals, the reticulospinal and rubrospinal systems appear to develop first (Cabana and
Martin 1986), followed by the corticospinal tract (Kuypers 1981; Armand et al. 1997; Olivier et al. 1997). Myelination of these systems in human infants proceeds
over the first two years of life (Yakovlev and Lecours
1967). The behavior of infants reflects the maturational
state of these systems. The corticospinal tract has been
implicated in control of the intrinsic muscles of the hand
(Kuypers 1981), and our infants, while able to contact an
object, primarily grasped objects using palmar grasps.
Fully independent use of the fingers in grasping objects
occurs sometime after the infant’s first birthday (White
et al. 1964), which is coincident with substantial maturation of the corticospinal tract.
Hoffman and Strick (1995) have also argued that the
motor cortex and the corticospinal tract are necessary to
268
smoothly combine elementary movements and to smoothly modulate force across muscles. The presence of handspeed minima and maxima during infant reaching and the
lack of a mature corticospinal tract is consistent with their
hypothesis. Again, corticospinal tract maturation occurs
at about the same time the infant reaching shows singlepeaked hand-speed profiles (von Hofsten 1991).
Implications for learning
The principal finding of the current paper, that infants
primarily use the proximal muscles of the arm and torso
in reaching, suggests that the initial learning problem
facing infants is much simpler than previously assumed.
This strategy substantially reduces the number of degrees-of-freedom controlling motion and simplifies
learning by reducing the size of the space that must be
explored for solutions. Essentially, this means that infants are solving a limited version of the Bernstein
(1967) degrees-of-freedom problem by only searching a
sub-space of possible commands. This solution to the degrees-of-freedom problem simplifies the problem facing
the infant to the extent that interactive learning could be
an efficient and rapid means by which infants could
learn to move effectively.
Two other results of the current analysis suggest ways
in which infants limit the size of the space of possible
movements. One is that some infants discover, or are
somehow predisposed by neural maturation, to start their
reaches from a relatively small number of starting locations. A second is that the peak speeds of movement
units cluster about a few values. This restriction in amplitude of movement and in the number of starting locations also reduces the size of the sub-space that is
searched for solutions because the infant is not learning
to move from a large number of arbitrary points in space
with a large number of possible movement amplitudes.
Clearly, this also restricts the power and flexibility of
reaching, but makes control and learning much simpler
for the beginning reacher.
Other features of young infant reaching also simplify
learning, not so much by reducing the size of the search
space, but by increasing the utility of feedback information that is obtained from exploratory movements. Use
of the proximal arm muscles and stiffening of the distal
muscles allows for smoother and more predictable
movements of the hand because the intersegmental forces in the limb are dampened. The effects of particular
motor commands are reliable and similar motor commands result in similar movements. For example, it is
generally not likely that larger shoulder torques will result in longer movements of the hand because of the intersegmental dynamics of the arm. However, it is likely
that larger shoulder torques will result in longer hand
movements when elbow and wrist motion is limited by
co-contraction. This smoothness in the effects of motor
commands may allow the infant to generalize across
movements and develop simple strategies for movement.
The use of the shoulder and torso in reaching also
makes sense in that it separates the learning process into
two phases. First, infants learn to use the proximal muscles to move the hand to the region of the target. Grasp
would be largely accomplished in this early phase by
tactile conformation to the target object. Learning to preorient the hand for grasp during transport using the distal
arm musculature could then occur on top of the movements learned in the first phase. This second phase is
necessary to utilize the full power of the degrees-of-freedom of the arm. This learning process is reminiscent of
Skinnerian shaping procedures, but with neural maturation and not an experimenter providing the constraints
on the task and guiding learning.
One potential drawback of interactive learning is that
it is not very efficient because there are a potentially
large number of commands that must be explored before
any noticeable improvement in movement is observed.
Furthermore, interactive learning is potentially dangerous for the actor when no initial control policy is available and the learner must start to move with random
movements. The effector might be damaged either
through interaction with the environment or by the generation of dangerous internal forces. In the current case,
stiffening of the distal limb provides a basic controller
that both limits dangerous movements of the limbs and
provides a basic strategy for movement, from which the
infant can build on. Presumably, this stiffening of the
limb is largely the result of neural maturation and occurs
from birth.
Acknowledgements This research has been supported by NSF
grants SBR 94-10160 and IRI 97-20345 to the first author and NIH
HD-27714 and NIMH MH-0332 to the second author. The authors
would like to express their gratitude for many helpful comments
from Andrew Barto, André Bullinger, and Michael McCarty.
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