Spatial Memory and Path Integration Studied by Self-Driven Passive
Linear Displacement. I. Basic Properties
I. ISRAËL, R. GRASSO, P. GEORGES-FRANÇOIS, T. TSUZUKU, AND A. BERTHOZ
Laboratoire de Physiologie de la Perception et de l’Action, Centre National de la Recherche Scientifique,
Collège de France, 75005 Paris, France
Israël, I., R. Grasso, P. Georges-François, T. Tsuzuku, and
A. Berthoz. Spatial memory and path integration studied by selfdriven passive linear displacement. I. Basic properties. J. Neurophysiol. 77: 3180 – 3192, 1997. According to path integration, the
brain is able to compute the distance of a traveled path. In this
research we applied our previously reported method for studying
memory of linear distance, a crucial mechanism in path integration; our method is based on the overt reconstruction of a passive
transport. Passive transport is a special case of navigation in
which no active control is performed. Blindfolded subjects were
first asked to travel 2 m forward, in darkness, by driving with a
joystick the robot on which they were seated. The results show
that all subjects but two undershot this distance, i.e., overestimated their own displacement. Then, subjects were submitted to
a passive linear forward displacement along 2, 4, 6, 8, or 10 m,
and had to reproduce the same distance, still blindfolded. The
results show that the distance of the stimulus was accurately
reproduced, as well as stimulus duration, peak velocity, and velocity profile. In this first condition, the imposed velocity profile
was triangular and therefore stimulus distance and duration were
correlated. In a second condition, it was shown that distance was
correctly reproduced also when the information about stimulus
duration was kept constant. Here, different velocity profiles were
used as stimuli, and most subjects also reproduced the velocity
profile. Statistical analyses indicated that distance was not reproduced as a consequence of duration, peak velocity, or velocity
profile reproduction, but was uniquely correlated to stimulus distance. The previous hypothesis of a double integration of the
otolith signal to provide a distance estimate can explain our results. There was a large discrepancy between the accuracy with
which the subjects matched the velocity profiles and that of distance reproduction. It follows that, whereas the dynamics of passive motion are stored and available to further use, distance is
independently estimated. It is concluded that vestibular and somatosensory signals excited by passive transport can be used to
build a dynamic as well as a static representation of the traveled
path. We found a close quantitative similarity between the present
findings on distance reproduction and those obtained from active
locomotion experiments in which the same paradigm was used.
This resemblance suggests that the two types of navigation tasks
draw on common physiological processes and extends the relevance of our results to naturally occurring path integration.
INTRODUCTION
Idiothetic signals (Mittelstaedt and Mittelstaedt 1973) are
the sensory signals generated by the displacement of a subject: optic flow, proprioception, efference copies, and inertial
signals. Mittelstaedt and Mittelstaedt (1980, 1982) hypothesized the use of these idiothetic signals for spatial orientation
in the ‘‘path integration’’ process. Through path integration
the position of a moving subject is continuously updated
with respect to the starting point, and therefore the subject
is able to compute the homing direction at any time. Recent
studies in humans (Bloomberg et al. 1991; Glasauer et al.
1994; Israël and Berthoz 1989; Klatzky et al. 1990; Loomis
et al. 1993; Mittelstaedt and Glasauer 1991; Thomson 1983)
have shown that subjects can indeed estimate the traveled
path solely from self-generated information, i.e., without external signals (visual or acoustic landmarks).
Mittelstaedt and Mittelstaedt (1980) and Etienne et al.
(1988) found that rodents could correctly home after passive
rotations in darkness, but not after passive linear displacements. Although in a more recent study, Mittelstaedt and
Glasauer (1991) showed that linear inertial forces imposed
to active homing trajectories are taken into account by rodents, the former results did cast some doubt on the use of
linear inertial information in the path integration process.
However, passive linear displacement estimation in humans
has been studied with a number of different paradigms—
through verbal estimates (Guedry and Harris 1963), saccadic eye movements (Israël and Berthoz 1989), or buttonpushing responses (Israël et al. 1993; Mittelstaedt and Glasauer 1991) —and all of these studies showed that the amplitude of passive linear motion can be correctly estimated.
Although formal models of path integration have been
proposed (see Benhamou and Séguinot 1995; Maurer and
Séguinot 1995 for critical reviews), with or without distance
estimation, the neural mechanisms involved in the process
are still to be clarified. Spatial memory plays a key role here
inasmuch as an internal coding of the distance and direction
of the perceived motion has to be built and stored by the
brain.
In a preliminary report (Berthoz et al. 1995) we provided
qualitative evidence about the type of memory encoding of
simple whole body passive linear displacements in darkness.
Subjects required to reproduce the distance of an imposed
passive motion also reproduced its velocity profile. This implies that all the spatiotemporal properties of movement are
stored and that reproduction is based on the dynamic comparison of the incoming sensory input with the stored one.
However, such a process does not exclude the possibility that
static parameters of motion may also be either independently
stored or retrieved from spatial memory.
In the present paper, we examine in more detail, with
quantitative methods, the performance of the subjects in this
task and suggest an additional hypothesis that extends previous theories of path integration.
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METHODS
Experimental setup
A mobile robot, the Robuter (Robosoft SA, Bayonne, France),
with a race car seat fixed on it was used for this experiment (Fig.
1A). In this device, two motor wheels driven by two 300-W DC
permanent magnet independent motors ensure propulsion of a 120kg maximal mass at a maximal linear velocity of 1.2 m/s, with a
maximal acceleration of 1 m/s 2 . Steering is obtained by controlling
the relative speed of the two driving wheels. The robot can be
controlled by a remote microcomputer (PC) through wireless modems, or by a joystick connected to the robot itself. The joystick
controls the robot’s linear velocity in steps of 0.05 m/s (robot
velocity directly proportional to joystick angle) with a delay of
0.2 s. Such a delay originates from the hardware and software
implementation of the joystick mode control of robot motion and
is not due to the mechanical inertia of the robot mass. Positioning
accuracy and linearity of trajectory is ensured by proportional inte-
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gral derivative control loops employing optical encoding of position (resolution of 1 mm and 0.01 s) and a trajectory generation
and control system operating at 250 Hz. Odometry (position on
the X-axis and timing) was recorded by the robot during motion
at a 50-Hz sampling rate (Fig. 1B).
The subject was secured with three safety belts onto the seat
of the robot ( Fig. 1 A ) . The subject’s head was restrained by a
cushioned support mounted onto the seat to impede head translations and yaw rotations; a bite bar prevented pitch movements.
The subjects wore headphones relaying a wideband noise
( ‘‘pink’’ noise ) to prevent perception of external acoustic cues,
and a pair of goggles with blacked-out lenses to suppress visual
information.
The joystick, which subjects held in the hands, was set ( software configuration ) for the whole experiment so as to allow only
linear movements of the robot, forward or backward along the
X-axis. All stimuli delivered by the PC were linear displacements
forward along the X-axis ( as in natural locomotion ) . The experiment was performed within a corridor 1.9 m wide and 50 m long.
FIG . 1. A: subject is seated on robot, with black goggles, headphones, and bite bar in place, and is using joystick. Two modems (1 at top of robot seat and the other
close to microcomputer) can also be seen. B: stimulus and
response position for trial of 10-m distance and 1-m/s peak
velocity in 1st (triangular velocity) condition for 15 subjects. C: stimulus and response velocity for trials in B
(derivation after 5-Hz low-pass filtering of position
traces). D–F: some examples of stimulus and response
velocity in a previous test in which subjects had to reproduce velocity of stimulus.
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In a preliminary experiment (Georges-François and Israël, unpublished observations) we checked whether the subjects could
satisfactorily control the robot by manipulating the joystick. We
asked five naive subjects to reproduce, while blindfolded, the velocity profile of a linear passive transport to which subjects had been
submitted. Some recordings from this experiment are shown in Fig.
1, D–F. By the use of different velocity profiles it was observed
qualitatively that the task was apparently rather simple for the
subjects. In some cases the reproduction was strikingly accurate
(Fig. 1, D–F). We emphasize that this control test was performed
with subjects other than those included in the present study.
Experimental procedure
Fifteen healthy volunteers, with ages ranging from 20 to 50 yr
and with no history of vestibular disorder, gave their informed
consent to take part in the experiment, which was approved by the
local ethical committee.
The subject first learned to manipulate the joystick by driving
the robot freely in the corridor, with visual and auditory cues
available. After Ç5 min of training, which was sufficient for the
subject to feel confident with the apparatus, headphones and black
goggles were put on.
CALIBRATION. The preliminary phase of the experiment, called
‘‘calibration,’’ was performed for several reasons: we wished 1)
to force subjects to pay attention to the amplitude of displacement
rather than to other contingent factors such as duration or peak
velocity; 2) to avoid effects due to uncertainty in controlling a
nonfamiliar, although relatively slow, transport vehicle in darkness;
and 3) to obtain information about subjects’ ability to estimate
distance of passive transport. The subjects were requested to drive
the robot a distance of exactly 2 m in complete darkness. The
experimenter then told the subject the exact distance just traveled,
and another attempt was made. This exercise was repeated until
the response was stabilized at Ç2 m, but a minimum of 10 trials
was imposed even when apparently not necessary.
CONDITION 1: TRIANGULAR VELOCITY PROFILE. The subject
was passively randomly displaced along 2, 4, 6, 8, or 10 m with
the headphones and the black goggles on. Velocity profiles of
most stimuli (13 of 16) were triangular, i.e., with equal values of
accelerations and decelerations in the range of 0.06–0.5 m/s 2 .
Peak velocity ranged from 0.6 to 1 m/s (Table 1). This profile
was chosen to produce a continuous stimulation of the otoliths by
linear acceleration. Three stimuli with constant velocity profiles
(0.4, 0.6, and 0.8 m/s) were also applied over distances of 4, 6,
TABLE
1.
Triangular velocity condition stimuli
Velocity
Profile
Distance,
m
Peak Velocity,
m/s
Acceleration,
m/s2
Duration,
s
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Triangle
Constant
Constant
Constant
2
2
2
4
4
4
6
6
8
8
10
10
10
4
6
8
1
0.8
0.6
1
0.8
0.6
1
0.6
1
0.8
1
0.9
0.8
0.6
0.4
0.8
0.5
0.32
0.18
0.25
0.16
0.09
0.167
0.06
0.125
0.08
0.1
0.135
0.064
0.8
0.8
0.8
4
5
6.67
8
10
13.33
12
20
16
20
20
16
25
7.24
15.68
10.9
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and 8 m, with acceleration and deceleration at 0.8 m/s 2 . In contrast
with the triangular profile, this provided only brief stimulation of
the otoliths at the beginning and at the end of the trajectories.
About 10 s after the end of the imposed displacement (stimulus),
the subject was required to reproduce as accurately as possible the
distance traveled, controlling the robot with the joystick (response). The paradigm is illustrated in Fig. 1, B and C.
The whole test included 13 trials with triangular velocity profiles
and 3 trials with constant velocity profiles. The order of these 16
trials was randomly changed for the different subjects.
CONDITION 2: CONSTANT DURATION PROFILES. In the first condition, the total distance and duration of the passive transport were
not independent. Therefore, to prevent the subjects from using the
duration of transport as a cue to reproduce distance, we devised a
second condition in which different velocity profiles of same duration (16 s) for all distances were used.
To travel distances from 2 to 10 m in the same amount of time,
different velocity profiles could be used. We chose a rectangular
velocity profile (constant velocity), a trapezoid profile, and a triangular profile (Table 2). The theoretical output signal generated by
the otoliths (Ormsby and Young 1977) corresponding to each profile is shown in Fig. 2. With the triangular profile it was not possible
to travel the 2- and 10-m stimuli in 16 s, given the limited velocity
range of the robot: the durations were 13.33 and 20 s for the 2and 10-m stimuli, respectively.
We used the same instructions as in the first condition, and the
subjects (7 who also participated in the triangular velocity condition, and 2 additional subjects) reproduced the five distances with
the three velocity profiles (i.e., 15 trials) presented in completely
random order.
Data analysis
Inspired by a two-dimensional cross-correlation analysis, a method was developed to
provide an index of resemblance between the stimulus and response
velocity profiles. Our aim was to obtain a comparison of shapes
regardless of errors in distance, duration, or peak velocity reproduction. The first step in the procedure was a normalization of the
time scales of both stimulus and response profiles, separately, from
0 to 100%. The number of samples of the profiles was reduced to
100 by averaging adjacent points. Because the number of points
constituting a profile initially ranged from 1,000 to 2,000, it follows
that from 10 to 20 adjacent points were averaged; this corresponds
to a cutoff frequency of 5–10 Hz for a moving average filter.
Because the profiles were previously filtered at 5 Hz to eliminate
high-frequency, low-amplitude noise, this additional filtering did
not markedly alter the relevant characteristics of the signals. Then,
all of the normalized trials from the same subject or from the same
stimulus were averaged, so as to reduce noise/random variability
stemming from the manipulation of the joystick. Finally, the root
mean square (RMS) of the differences between the averaged stimulus and response velocity profiles was taken as a quantitative index
of mutual resemblance.
REPRODUCTION OF VELOCITY PROFILES.
Appropriate analysis of variance (ANOVA) designs were used to compare the data from individual trials
between different conditions, with either response total magnitude
(distance or duration) or algebraic error (response 0 stimulus) as
dependent variables. The relative error (response 0 stimulus)/
stimulus was used to quantify overall accuracy. Linear regressions
of individual trials were performed to quantify the stimulus-response relationship from the subjects. A probability level of 0.05
was considered significant. Multiple regression analysis was performed to estimate the relative importance of the respective stimulus parameters in determining the response.
STATISTICAL ANALYSIS.
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TABLE
2.
Constant duration condition stimuli
Velocity
Profile
Distance,
m
Peak Velocity,
m/s
Acceleration,
m/s2
Duration,
s
Rectangle
Rectangle
Rectangle
Rectangle
Rectangle
Trapezoid
Trapezoid
Trapezoid
Trapezoid
Trapezoid
Triangle
Triangle
Triangle
Triangle
Triangle
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
0.130
0.258
0.387
0.517
0.651
0.161
0.362
0.546
0.730
0.917
0.300
0.500
0.750
1
1
0.2
0.5
0.8
1
1
0.045
0.073
0.109
0.145
0.180
0.045
0.062
0.093
0.125
0.100
16
16
16
16
16
16
16
16
16
16
13.333
16
16
16
20
RESULTS
Calibration
The average traveled distance of the very first trial of the
calibration test was 1.55 m, i.e., this first trial induced on
average a 22.5% undershoot error with respect to the required 2-m distance, and interindividual variability was
{0.52 (SD) m. The distance was much closer to 2 m (1.90
m, i.e., 5% undershoot error) and the interindividual SD was
lower ( {0.31 m) at the end (the 10th trial) of this preliminary exercise. It can be seen (Fig. 3) that a plateau in performance was already reached by the fifth trial (1.95 { 0.27
m, mean { SE), and successive trials exhibited about the
same error. The difference between the 1st and the 10th trial
distance was significant [F(1,14) Å 5.44, P Å 0.035], as
was the difference between the 1st and the 5th trials
[F(1,14) Å 6.63, P Å 0.022]. The difference was also significant between the 1st trial and each of the trials after the
5th, whereas there was no significant difference between the
5th and the 10th trials.
Triangular velocity condition
Subjects were able to reproduce
the distances (Fig. 4) with an average overall accuracy of
25% (SD of the pooled relative errors, n Å 232). The linear
regression between stimulus and response distance was calculated for each subject with all the 16 trials (an example
is shown in Fig. 4B). Regressions from the individual subjects are presented in Fig. 4A, inset. The average of the
individual regression lines (Table 3) is shown in Fig. 4A,
together with the means and SEs of the reproduced distances.
The correlation coefficient r was highly significant for all
subjects (P õ 0.0001).
The reproduction of the shortest distance (2 m) led to a
slight overshoot (2.31 { 0.12 m), whereas that of the longer
distances exhibited an undershoot (9.21 { 0.33 m for the
10-m stimulus).
Finally, there was no significant difference in the reproduction of the distance between the trials with triangular
velocity profiles and those at constant velocity.
DURATION REPRODUCTION. As mentioned in METHODS, with
the triangular velocity profile, stimulus duration and stimulus
distance were interdependent. Therefore the duration of the
stimulus could provide some information assisting its reproduction. Indeed, the subjects also reproduced the duration
of the stimulus (Fig. 5, Table 3), although the instruction
was to reproduce the distance. The value of r was highly
DISTANCE REPRODUCTION.
FIG . 2. Otolith response to acceleration profiles of 2nd condition, simulated with the use of the transfer function developed
by Ormsby and Young (1977). Dashed lines: result of simulation (MOD). Solid lines: input signal. Thin lines: data from
‘‘artificial’’ (ideal) profiles (ART). Heavier lines: data recorded and derivated from robot odometry (REC) after 3-Hz lowpass filtering. All 3 profiles generated a 6-m distance.
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FIG . 3. Calibration. Performance of subjects during calibration test: average and SE for all 15 subjects shown with respect
to trial number.
significant for each subject (P õ 0.0001, except for 1: subject EC obtained P õ 0.0013). Only subject EC displayed
a ‘‘step strategy,’’ i.e., with joystick manipulations of short
duration and displacement at high velocity; this subject was
nevertheless as accurate as the others in reproducing distance.
The duration of the shortest stimulus (4 s) was reproduced
with an overshoot (4.60 { 0.32 s), and the longest (25 s)
with an undershoot (21.27 { 1.0 s).
VELOCITY REPRODUCTION. There was no correlation between stimulus peak velocity and distance, and therefore
stimulus peak velocity could not be of any help for the
subjects to reproduce the distance. However, most subjects
did reproduce stimulus peak velocity. The value of r was
significant for all subjects (P õ 0.01) but four (subjects
LC, EC, II, and MB). The average determination coefficient
(Table 3) was therefore lower than that of distance and
duration.
In the constant velocity trials the subjects exceeded the
plateau velocity significantly more than the peak velocity in
the triangular profile trials [F(1,14) Å 9.66, P õ 0.008],
by 0.12 { 0.03 m/s compared with 00.04 { 0.04 m/s in
the triangular trials.
INTERDEPENDENCE AMONG DISTANCE, DURATION, AND VELOCITY. To examine whether stimulus duration or peak veloc-
ity had been used by the subjects to reproduce distance,
we applied a multiple regression analysis to our data, with
reproduced distance as the dependent variable and stimulus
distance, duration, and peak velocity as independent variables. The results indicate that the response distance can
only be attributed to the stimulus distance (Table 4A), and
neither to stimulus duration nor peak velocity. The response
is correlated with stimulus duration (Table 4A), but this
correlation results from the existing correlation between
stimulus distance and duration.
The same question can be asked about the reproduction
FIG . 4. Distance reproduction (1st condition). A: average ( – – – ) of all individual lines of 15 subjects, and average {
SE of each reproduced distance. Average determination coefficient r 2 was 0.85. Inset: individual regression lines between
stimulus and response distance for 15 subjects. B: responses of subject BJ, with corresponding regression line ( – – – ).
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TABLE
3.
Linear regressions: R Å A∗S / B, triangular
velocity
Variable
A
B
r2
n
Distance, m
Duration, s
Peak velocity, m/s
0.86
0.74
0.63
0.62
2.05
0.28
0.85 { 0.02
0.78 { 0.02
0.45 { 0.07
15
15
15
r 2 values are means { SE. Linear regressions on the reproduction of
distance, duration, and peak velocity, in the triangular velocity condition.
n is sample size.
of duration: was duration reproduced as a consequence of
distance reproduction, or was it reproduced per se-, by the
subjects ? The results of the multiple regression, with reproduced duration as dependent variable, indicate that duration
was reproduced mainly because of stimulus duration, and
there was a significant contribution of stimulus distance (Table 4B).
VELOCITY PROFILE. Whereas the peak velocity was not a
relevant parameter for judging and reproducing distance,
subjects frequently reproduced the stimulus velocity profile
(Fig. 1C). Only subject LC produced very asymmetric triangular profiles, whereas subject EC systematically used a rectangular velocity profile, reaching the maximal velocity of
the robot on short duration. Subjects II and MB exhibited
variable combinations of velocity profiles. Nevertheless, distance reproduction was not markedly different from that of
the other subjects, who produced mostly triangular responses.
Constant duration condition
The multiple regression analysis applied on the triangular
velocity profile trials allowed us to establish that duration
was not the main cue used by the subjects. Furthermore,
there was some indication that subjects also reproduced the
velocity profile of the passive transport. We then designed
a second condition with another set of stimuli, characterized
by three velocity profiles of identical duration (Table 2).
We wanted to check whether duration was indeed not necessary to reproduce the corresponding distance, and whether
subjects would also reproduce velocity profiles when they
are not triangular.
DISTANCE REPRODUCTION. As expected, although stimulus
duration was not a valid predictor of its distance, subjects
did reproduce the imposed distance (Fig. 6) as well as in
the first condition: overall accuracy (as measured by the SD
of the relative error) was 35% (n Å 132), with 25% (n Å
44) for the triangular profile, 28% for the trapezoid profile,
and 47% for the rectangular profile. The average of the
individual regression lines (each line computed on the basis
of 5 measures) for each velocity profile as well as for all
three pooled profiles (15 measures; Fig. 6A) is given in
Table 5. For the rectangular profile, r was significant for all
subjects but subject EC. The determination coefficient (r 2 )
obtained from the rectangular profile was lower than that
resulting from the other profiles, but a two-factor repeatedmeasures ANOVA (profile type 1 distance) on the reproduced distance showed no effect [F(2,16) Å 0.67, P Å 0.52]
or interaction [F(8,64) Å 0.62, P Å 0.75] due to the velocity
profile.
The mean regression for the seven subjects who had also
participated in the first condition was basically not different
from that obtained in the triangular velocity condition. A
two-factor within-subjects ANOVA (condition 1 distance)
on the reproduced distance showed no effect of the condition
[F(1,6) Å 2.62, P Å 0.16] or interaction [F(4,24) Å 1.79,
P Å 0.16].
DURATION REPRODUCTION. In this condition stimulus duration did not vary and the average response duration was very
close to that of the stimulus: 14.14 { 1.21 s (n Å 132).
There was no significant difference between the duration
errors for the three profiles. The average error was
01.41 { 0.93 s (n Å 9) with the rectangular velocity profile,
00.65 { 0.84 s with the trapezoid profile, and 02.17 {
FIG . 5. Duration reproduction. A: individual regression lines between stimulus and response duration for 15 subjects. B:
responses of subject BJ with corresponding regression line.
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TABLE
4.
Multiple regression on distance reproduction and duration reproduction in the triangular velocity condition
F(3,228) Å 278.53 P õ 0.0001
Stimulus
r
B
P
Variable
Distance, m
Duration, s
Velocity, m/s
Response, m
0.92
00.03
00.08
0.0001
0.348
0.879
Distance
Duration
Velocity
Response
1.00
0.87
1.00
0.25
00.04
1.00
0.89
0.75
0.23
1.00
A. Distance reproduction
Distance (m)
Duration (s)
Velocity (m/s)
F(3,228) Å 148.93 P õ 0.0001
Stimulus
r
B
P
Variable
Distance, m
Duration, s
Velocity, m/s
Response, s
0.38
0.57
01.15
0.032
0.0001
0.41
Distance
Duration
Velocity
Response
1.00
0.87
1.00
0.25
00.04
1.00
0.74
0.81
00.02
1.00
B. Duration reproduction
Distance (m)
Duration (s)
Velocity (m/s)
0.63 s with the triangular profile: response duration was
shorter than stimulus duration in all cases.
Subject EC again exhibited a shorter response than the
other subjects: mean duration error for subject EC was 07.40
s, whereas the error of the six remaining subjects was
00.52 { 0.36 s; the difference was larger than in the first
condition ( 04.91 s for subject EC vs. 00.59 { 0.76 s for
the 6 remaining subjects). Subject EC apparently applied
the step strategy with still more conviction when deprived of
temporal information correlated to distance, without losing
accuracy in fulfilling the task.
VELOCITY REPRODUCTION. In this condition, in which stimulus duration and distance were not correlated, stimulus maximal velocity could have been used to provide some information about distance. Stimulus peak velocity and distance of
the five trials were indeed strongly interdependent for all
velocity profiles.
This may have been a reason why there was a significant
correlation between stimulus and response peak velocity, in
all subjects but two, in all profiles (P õ 0.03): subject EC
had a nonsignificant correlation of stimulus-response peak
velocity in all three profiles, and another subject (PG)
showed a nonsignificant correlation for both the rectangular
and trapezoidal profiles. Table 5 indicates the average regression line between stimulus and response peak velocity for
all subjects.
Subject EC displayed the greatest peak velocity error
(0.73 m/s, vs. 0.02 { 0.03 m/s for the 6 other subjects).
With a multiple regression analysis, following the same
procedure as in the triangular velocity condition, it was found
that distance was again the most important predictor of distance reproduction [F(3,129) Å 149.93, P õ 0.0001]. The
value of r was significant for stimulus peak velocity (0.74) and
for stimulus distance (0.88), but not for duration, as expected.
FIG . 6. Distance reproduction (2nd condition). A: average ( – – – ) of all individual lines of top left inset, and average
and SE of each reproduced distance. Top left inset: individual regression lines between stimulus and response distance of 3
profiles pooled (n Å 15) for 9 subjects. Bottom right inset: average regression lines between stimulus and response distance
for 3 profiles. B: responses of subject BJ with corresponding regression line.
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TABLE
5.
Linear regressions: R Å A∗S / B, constant duration
Velocity Profile
Variable
A
B
Rectangular
Trapezoid
Triangular
Pooled
Rectangular
Trapezoid
Triangular
Pooled
Distance
Distance
Distance
Distance
Peak velocity
Peak velocity
Peak velocity
Peak velocity
0.93
0.97
0.99
0.95
0.88
0.85
0.90
0.80
1.05
0.60
0.34
0.73
0.26
0.19
0.12
0.24
r2
0.86
0.89
0.94
0.84
0.87
0.81
0.89
0.79
{
{
{
{
{
{
{
{
n
0.04
0.03
0.02
0.04
0.04
0.10
0.05
0.08
9
9
9
9
9
9
9
9
r 2 values are means { SE. Distance values in m, peak velocity in m/s.
Linear regressions on the reproduction of distance and peak velocity in the
constant duration condition. n is sample size.
VELOCITY PROFILE. Subjects reproduced the velocity profile
of the stimuli more closely for longer distances (Fig. 7A).
A global overshoot at the onset of the reproduction can be
seen, principally in the triangular profiles. This was probably
due to the relatively long delay of the joystick control
(0.2 s).
We then applied the method called ‘‘normalization’’ (Fig.
7B) to quantify our visual inspection. The RMS errors of
the differences reproduction-stimulus appear in Table 6. A
one-factor repeated-measures ANOVA revealed a significant
difference among the three values [F(2,8) Å 5.61, P Å
0.014], and a Student-Newman-Keuls post hoc comparison
confirmed that the RMS error of the triangular profile was
greater than that of the trapezoid and rectangular profiles,
but the errors of the latter two were not significantly different
from one another. Therefore in general the subjects reproduced the rectangular and trapezoid profiles more accurately
than the triangular one. However, two subjects (EC and PG)
exhibited a larger error with the rectangular than with the
triangular profile, and two other subjects (EM and RG) exhibited a larger error with the rectangular than with the trapezoid profile.
Finally, to test whether an accurate reproduction of velocity profiles was sufficient for an equivalently accurate reproduction of distance, we compared the velocity profile error
(RMS) with the reproduced distance error, and found no
significant correlation [F(1,13) Å 0.93, P ú 0.1]. This suggests that the velocity profile and the distance were independently reproduced.
DISCUSSION
A passive displacement can be represented in static as
well as in dynamic terms. That is to say that we could
refer to an experienced travel either as a 10-m, 10-s linear
displacement or as a motion at a gradually increasing speed
followed by a deceleration up to a stop. These two representations might coexist in short-term memory or, alternatively,
only one might be stored. In this latter case, if the dynamic
representation is the one available, static estimates could be
derived by reprocessing it. On the other hand, motion dynamics would be lost if only static parameters are stored.
In this paper we applied our recently developed method
for studying the memory of traveled linear distance, which
is based on the overt reconstruction of a passive transport
(Berthoz et al. 1995), to address the relationship between
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motion perception and path integration. Blindfolded subjects
were asked to reproduce the perceived distance of a linear
passive displacement by directing another passive motion.
The results show that 1) the distance of the passive travel
was reproduced; 2) this was accompanied by the reproduction of the stimulus duration, peak velocity, and velocity
profile; and 3) distance was reproduced even when stimulus
duration was kept constant. This latter finding and the statistical analysis of the results suggested that distance was reproduced per se, and not as a consequence of duration, peak
velocity, or velocity profile reproduction. Therefore the present study provides evidence that both a static and a dynamic
representation of passive motion are stored in memory.
The reproduction experiment was preceded by a calibration task that is discussed before the main findings are addressed.
Calibration task
In this initial experiment, subjects were asked to drive the
robot in darkness over a 2-m linear path with the joystick.
Klatzky et al. (1990) used the same distance to ‘‘train’’
their subjects in an experiment on locomotion. It is indeed
reasonable to assume that humans should have some meaningful representation of such a short length. The results
showed that all subjects but two undershot this distance (i.e.,
subjects overestimated their own self-traveled distance) by
22% in the first trial with an interindividual variability
ú25%. Such a considerable undershoot and variability suggest that either subjects have a very variable representation
of the required length, or the vestibular and somatosensory
inputs are not calibrated to correspond to a metrical representation of distance.
A similar undershoot was observed by Israël et al. (1993)
in another linear displacement task. Subjects, blindfolded
and with ears plugged, sitting on a sled that moved along
the X-axis, had to push a button when they thought that the
sled passed a previously seen target (the distance here was
2.4 m): the button was pushed at 1.57 { 0.37 m during
the displacement. Despite methodological differences (the
displacement was passive and not self controlled; the task
was goal directed and not amplitude coded; and the expected
response was at 2.4 m, not 2.0 m), the error is quantitatively
similar. Because the target was seen by the subjects in this
former experiment, the previous hypothesis of a variable
metrical representation of the 2-m length is weakened. Another explanation can be suggested for both cases: in the
former experiment the undershoot was explained as a consequence of a double integration over time of otolith discharge,
including the initial overshoot that is induced by an acceleration step (see Berthoz and Droulez 1982 for a review). It
is possible that such a process occurred also in the present
experiment.
The calibration experiment, theoretically, has no consequence on the performance in the reproduction task other
than the expected one, i.e., that of polarizing subjects’ attention on the distance of the displacement on the robot.
Reproduction task
REPRODUCTION OF DISTANCE. The present work brought
contrasting evidence about the mechanisms of distance per-
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TABLE
6.
Velocity profile reproduction
Velocity Profile
RMS Error
n
Rectangular
Trapezoid
Triangular
10.1 { 2.23
9.2 { 0.73
17.6 { 1.97
9
9
9
Root mean square (RMS) error values are means { SE. Constant duration
condition. n is sample size.
ception because 1) the strategy selected by most subjects to
reproduce distance (the assigned task) was to reproduce
the velocity profile, i.e., the spatiotemporal dynamics of the
passive transport, but 2) regression analyses indicated that
distance reproduction was not correlated with the accuracy
of duration, peak velocity, or velocity profile reproduction.
Thus the results suggest that whereas the dynamics of passive motion are stored and available to further use, total
distance is probably independently estimated.
Possibly, subjects reproduced the dynamic characteristics
of the passive transport because the self-controlled transport
was not goal directed but amplitude coded, and the task itself
was ambiguous because ‘‘distance’’ is a static parameter,
whereas the word ‘‘reproduction’’ can implicitly denote a
dynamic task. Also, the joystick did not control the displacement magnitude but the robot speed, which might have induced subjects to work with dynamics. Moreover, the subjects might have felt that retrieving the dynamic properties
of the displacement could help fulfill the requested task. It
must be underscored that this was not the only possible
strategy, because one subject (EC) systematically used a
rectangular velocity profile, of short duration and high peak
velocity, which resulted nevertheless in an accurate reproduction of the distance.
It might also be argued that the observed independence
in distance reproduction does not necessarily imply that an
accurate, independent, static internal estimate of total path
length was produced and memorized: distance is processed
3189
twice in each trial, and thus even in the case in which processing was highly nonlinear or biased or totally uncalibrated, the result for reproduction would still be correct
should the same processing apply to the passive and the
active phase of displacement. An alternative explanation of
the results of the statistical analyses could be that distance
was independently reproduced as a consequence of some
peculiar feature of the actively controlled transport phase,
dissociating path length from motion dynamics (e.g., noise).
The results from subject EC, the evidence from previous
experiments (Glasauer et al. 1994; Israël et al. 1993; Mittelstaedt and Glasauer 1991), and the relative accuracy in total
distance reproduction do not favor, in our opinion, this last
hypothesis. Subject EC must have retained or reconstructed
some internal static estimate of the imposed path and disregarded the dynamic information in the reproduction task.
REPRODUCTION OF DISTANCE WITH DURATION AND PEAK VELOCITY. The different statistical analyses indicated that no
motion parameter (including the velocity profile) significantly contributed to the accuracy of reproduction of distance. On the other hand, reproduction of duration appeared
secondary to distance. The indication given by this method
was confirmed by the constant duration experiment, in which
the duration of the stimulus was kept constant. Indeed, the
accuracy in reproducing distance was the same as when
duration varied proportionally to distance. Therefore we conclude that distance was not estimated from related magnitudes. This is not surprising, because we have previously
shown (Israël and Berthoz 1989) that the otoliths are necessary to estimate a passive linear whole body displacement
with respect to an earth-fixed memorized visual target, and
to acquire this target with eye saccades.
RANGE EFFECT. Whereas during calibration an undershoot
of the requested 2 m was observed, in the reproduction task
the subjects overshot 2-m trials but undershot larger distances. These distortions in the reproduction task can be
interpreted as a manifestation of the ‘‘range effect,’’ also
FIG . 7. Velocity reproduction (2nd condition). A: all
velocity responses to all trials of all subjects (except subject EC) are shown for each profile and each distance.
Heavy line: stimulus. B: normalized response (velocity
and duration) averaged over all trials of same velocity
profile for 3 subjects (RG, YT, and BJ), mean { SD, with
cumulated velocity error. Dotted line: stimulus. Heavy
line: mean velocity. Thin lines: mean { SD.
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known as ‘‘regression to the mean effect’’ or ‘‘central tendency effect’’ (overshoot of small distances and undershoot
of large distances of a given set) (Poulton 1979; Stevens
and Greenbaum 1966). The effect was observed both for
the reproduced distance and for the duration in the triangular
velocity condition, whereas it almost disappeared in the constant duration condition. Because this effect is characteristic
of judgments of sensory magnitude (Poulton 1979), the subjects might have implicitly estimated both distance and duration, although the instruction was about distance only. The
absence of range effect in the constant duration condition
suggests that this effect can be mainly ascribed to the estimation of duration.
COMPARISON WITH LOCOMOTION EXPERIMENTS. There is a
close resemblance between our results and those obtained
by Loomis et al. ( 1993 ) . In the experiment of Loomis et
al., blindfolded subjects were first led by the experimenter
while walking along a path 2 – 10 m long ( the same distances as in the present experiment ) , and the subjects then
had to reproduce the same distance while blindfolded and
without aid. The reported results are strikingly similar to
the present ones: the 2-m distance was overshot by 0.26 m
( 0.31 { 0.12 m in the present test ) and the 10-m distance
was undershot by 1.02 m ( 0.79 { 0.33 m here ) . This resemblance suggests that there are important parallels between
active locomotion and the self-controlled passive displacement we have used in the present study. It should be noted
that the motion parameters ( speed and acceleration ) selected for passive motion were much in the physiological
range of normal locomotion.
It may thus be suggested that the inertial and proprioceptive signals generated in the present task are processed in a
very similar way as during locomotion when motion-related
information is considered and when motion is self-driven.
The double time integration of the acceleration forces on the
otoliths (Israël et al. 1993) might participate in the updating
of position during motion.
The absence of bias in the stimulus-response relationship
on distance suggests that the same processing of inertial
signals occurred during the passive and the active transport
phase. This is at variance with respect to the results obtained
by Mittelstaedt and Glasauer (1991): those authors found
that subjects passively transported in darkness toward a previously seen target tended to underestimate (in the range of
linear velocity and distance used in the present experiment)
the traveled distance, whereas the opposite happened during
active locomotion. Mittelstaedt and Glasauer proposed the
idea that a leaky path integrator, loaded with the visually
estimated distance, processes incoming inertial signals: the
reference distance is differently included in the processing
during passive transport and active locomotion, respectively.
If we applied the same rule to the present experiment, we
would obtain a large undershoot of reproduced versus imposed distances, which was not the case. The similarity between the passive and active transport phases in our experiment might have caused the same processing of inertial signals to occur in both phases. Because of the important
methodological differences between both experiments (i.e.,
the visually acquired reference distance and the proprioceptive locomotion-related signals of the above quoted experiment), further comparison would be pointless.
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Somatosensory signals could also have contributed to the
estimation process: arthrokinetic information is known to
affect linear self-motion perception (Bles et al. 1995; de
Graaf et al. 1994; Hlavacka et al. 1992). Tactile cues may
complement vestibular information, providing 1) a signal
related to the body linear acceleration (pressure on the back,
visceral shifts, etc.) and 2) a signal generated by robot vibrations. The subjects could have correlated all of these signals
with visually perceived velocity during the very preliminary
training (before the calibration task). However, the training
phase was unlikely to influence the strategy of reproduction,
because the performance of the subjects who participated in
the constant duration condition was not different from that
displayed in the first condition, although no training was
performed before the second condition. Therefore it is highly
improbable that the somatosensory input generated by vibrations (which are peculiarly linked to the robot and ground
characteristics) was calibrated.
The case for the propulsion forces exerted by the motor
during travel is different. It is impossible to dissociate vestibular from somatosensory contribution to motion perception
because the two sensory systems are simultaneously stimulated during the transport. Pressure on the back during acceleration is unavoidably felt in sitting subjects and vibrations
always occur during transport. However, a paraplegic subject
who underwent the triangular velocity test was as good as
normal subjects in reproducing distance (Berthoz et al.
1995). This result does not rule out the participation of
tactile cues to the estimation process, but it confirms the
importance of the otolith signals.
How are the motion dynamics matched during the
reproduction?
An important finding of this (and the previous) work is
that motion dynamics are stored during the passive displacement and played back during the reproduction phase. There
are many ways such a behavior can be modeled. Figure 8
shows a simple schema that summarizes our concept. The
schema is made of two parts: 1) the passive transport phase
and 2) the active transport phase. The actual acceleration
drives the otoliths (and somatosensory system), the output
of which is stored in a dynamic short-term memory. Then
memory feeds a comparator of a negative feedback controller. The block labeled ‘‘robot control’’ represents the feedback gain. The robot acceleration profile provides the input
to the otoliths, whose output is in turn compared with the
memorized input profile. This generates an error signal driving the active reproduction of passive motion dynamics.
The critical point in the schema is the MEMORY box,
because we cannot directly access the internal representation.
The otoliths (and the somatosensory system) provide signals
directly related to linear acceleration, which might allow an
efficient acceleration feedback control to take place. On the
other hand, data from motion perception and eye movement
studies in humans (Lichtenberg et al. 1982; Shelhamer and
Young 1994; Young and Meiry 1968) revealed that integration over time of the otolith-induced neural discharge occurs
over the whole frequency range of the stimuli employed in
the present study, leading to a close relationship between
the perceived and the actual linear velocity (Young 1984).
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FIG . 8. Simple schema of distance reproduction paradigm. Graph labeled ‘‘stimulus’’ includes all dynamic properties of
passive motion. OTOLITHS actually includes all idiothetic signals available in present experiment (i.e., those due to vestibular
and somatosensory systems), and box labeled ‘‘robot control’’ covers all robot and joystick parameters.
On the grounds of these latter findings it can be proposed
that feedback control is carried out on linear speed rather
than acceleration. As mentioned above, a second time integration of sensory input may occur (Israël et al. 1993) and
feedback control could be theoretically performed on instantaneous position. This last possibility corresponds to the true
path integration hypothesis (Mittelstaedt and Mittelstaedt
1982), which is a very attractive one because it would attribute to one and the same process both the static and the
dynamic characteristics of the subjects’ responses. In such
a case, the static estimate of distance would correspond moment by moment to the current stored value of the dynamic
profile and no reprocessing of recorded signals should be
needed.
We must admit that there is no evidence from the results
obtained in the present experiment to favor one formulation
or another. From a mathematical point of view all of them
can solve the experimental task. However, they will imply
substantially different consequences if the first and the second phase of the experiment are dynamically uncoupled. For
example, if control is carried out on instantaneous position,
by constraining the robot speed in the active phase, the reproduction of the displacement distance will not be impaired.
In contrast, gross distance errors will be expected if feedback
is performed on acceleration or speed. Such predictions will
allow testing the above hypothesis.
It is worth noting that the greatest mismatch between the
stimulus and response velocity profile was found for the
triangular profile when compared with the trapezoidal and
rectangular profiles. Because the triangular profile provided
stimulation to the otoliths continuously throughout the displacement, whereas the trapezoidal and rectangular profiles
included segments at constant velocity, this result is surprising. However, it should be noted that reproducing a triangular profile requires more complex motor skill. Subjects had
to continuously increase the tilt of the joystick to achieve a
velocity ramp, despite a critical delay in response time of
the control (0.2 s) and low elasticity in the joystick itself.
But the poor accuracy in triangular velocity reproduction
could also be due to the normalization analysis, which is
particularly severe with this profile because it takes into
account both slope and symmetry. In contrast, the variability
in distance reproduction (SD of relative error) was much
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larger when rectangular rather than triangular profiles were
applied. Trapezoidal profiles induced intermediate accuracy
in distance reproduction. Because in the triangular type of
profile, otoliths are continuously stimulated (Fig. 2), it is
suggested again that otolith signals play a major role in the
perception of distance but a dissociation between dynamic
and static components emerges. This dissociation suggests
an independence between the use of sensory signals for path
length estimation and for the monitoring of active reproduction, as already suggested by regression analysis results.
General remarks
A careful quantitative analysis of the results of the present experiment allows us to conclude that vestibular and
somatosensory signals generated by passive transport can
be used to build a dynamic as well as a static representation
of the traveled path. Recent studies have already provided
some neurophysiological background to understand the
present findings: by transporting monkeys on a robotmounted platform in complete darkness, O’Mara et al.
( 1994 ) found hippocampal neurons responding to linear
motion and others responding to axial rotation; cells belonging to the rat hippocampal formation that code head
direction in space have now long been known ( McNaughton et al. 1983 ) ; changes in rat hippocampal theta activity
correlated to the velocity of angular rotation in the yaw
plane have been demonstrated ( Gavrilov et al. 1996 ) . The
improving description of neural ascending pathways ( Grüsser et al. 1992; Muller et al. 1996 ) bringing multisensory
motion-related information to the cortex led to the identification of computational ( Wan et al. 1994 ) and biological
( McNaughton et al. 1996 ) models of a corticothalamohippocampal navigation system that work by updating position
and direction in space in real time.
Passive transport is a special case of navigation in which
no active control is performed. The qualitative and quantitative similarity between our experimental results and those
obtained in analogous experiments on locomotion (Loomis
et al. 1993) suggests that these two types of navigation tasks
draw on common physiological processes and extend the
relevance of our results to more ecological behaviors of path
integration.
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ISRAËL, GRASSO, GEORGES-FRANÇOIS, TSUZUKU, AND BERTHOZ
We are grateful to A. Treffel for the mechanical adaptation of the Robuter,
and to S. Glasauer for the design of the Robuter-experimenter interface
software.
This work was supported by the Commission of European Communities
programs Esprit Basic Research project 6615 (MUCOM) and Biomed
BMH1-CT94-1133. R. Grasso was supported by the Fondation pour la
Recherche Médicale and the Training and Mobility of Researchers program
of the CEC. T. Tsuzuku was supported by the Fondation Fyssen (France).
Address for reprint requests: I. Israël, Laboratoire de Physiologie de la
Perception et de l’Action, CNRS, Collège de France, 11, place Marcelin
Berthelot, 75005 Paris, France.
Received 17 July 1996; accepted in final form 20 February 1997.
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