Speed Adaptation for a Robot Walking with a Human
Emma Sviestins

Noriaki Mitsunaga

Takayuki Kanda

Royal Institute of Technology
S-100 44 Stockholm
SwedenATR IRC Laboratories
2-2-2 Hikaridai Keihanna
Science City, Kyoto
619-0288 JapanATR IRC Laboratories

emmasv@kth.se

kanda@atr.jp

mitunaga@atr.jp
Norihiro Hagita
Hiroshi Ishiguro
Osaka University
2-1 Yamadaoka Suita, Osaka
565-0871 JapanATR IRC Laboratories

hagita@atr.jp

ishiguro@ams.eng.osakau.ac.jp
ABSTRACT1.

We have taken steps towards developing a method that enables an interactive humanoid robot to adapt its speed toa walking human that it is moving together with. This isdifficult because the human is simultaneously adapting to
the robot. From a case study in human-human walking interaction we established a hypothesis about how to read ahuman’s speed preference based on a relationship between
humans’ walking speed and their relative position in the direction of walking. We conducted two experiments to verify
this hypothesis: one with two humans walking together, andone with a human subject walking with a humanoid robot,
Robovie-IV. For 11 out of 15 subjects who walked with therobot, the results were consistent with the speed-position relationship of the hypothesis. We also conducted a preferred
speed estimation experiment for six of the subjects. All ofthem were satisfied with one or more of the speeds that ouralgorithm estimated and four of them answered one of the
speeds as the best one if the algorithm was allowed to give
three options. In the paper, we also discuss the difficulties
and possibilities that we learned from this preliminary trial.

Over the past several years many humanoid robots thatcan make sophisticated human-like expressions have beendeveloped. Several research works have demonstrated useof human-like body properties for natural human-robot interaction, such as facial expression [1], head orientation [11],and body position [16]. We believe that humanoid robots
will be suitable for our research on “communication robots”
that behave as peer-partners to support daily human activities based on advanced interaction capabilities [8]. In addition to providing physical support, these robots will supply
support through communication, for instance guiding theway to some destination.
Adaptation and learning is considered an important research direction in human-robot interaction. For instance,
Breazeal et al. developed a robot that is capable of learningfrom a human collaborative partner [2]. Suga et al. proposeda possibility of tracking preferred repertory of interaction bydirect feedback from a human using an evolutionary learning method [14]. Mitsunaga et al. demonstrated that aninteractive robot is capable of adjusting distance and timing of the interaction to the interacting human by reading
discomfort signals that are subconsciously emitted by thehuman [10].
In this paper, we focus on the situation where a communication robot is moving together with a walking human.
There are many applications for a robot moving together
with a human, such as a museum guide [3, 4, 7] or an assistant [6]. Navigation of a robot in the presence of humans isoften studied [13, 15]. Personal space and distance among
humans and robots are considered important [5, 12]. However, not much previous research has been conducted on an
adaptation mechanism for a robot during walking.
There are three parameters to consider for adaptation during walking: movement speed, parallel distance (the distance in parallel with the moving direction), and side distance (the distance vertical to the direction of moving) (Fig. 1).
Of these, movement speed is most important since if the distance is wrong the human can adjust it by him-/herself but
if the speed is wrong the human will have to put up with itin order to walk together with the robot. This is especially

Categories and Subject Descriptors
H.5.2 [Information Interfaces and Presentation]: User
Interfaces—Interaction Styles; I.2.9 [Artificial Intelligence]:
Robotics

General Terms
Design, Human Factors

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349

INTRODUCTION

Distance

Laser range sensors

A

Preferred distancec) side distancemeasurement areaa) moving speed

O

O

B
b) parallel distancePreferred speed range

Speed

Figure 2: The experiment setup. ’E’ and ’S’ markthe experimenter and the subject respectively andthe boxes represent the range sensors placed on tables. The experimenter and the subject moved backand forth in the measurement area.

Figure 1: The relationship between walking speed
and parallel distance according to our hypothesis.
important if the robot is meant to act as a social partnerin the daily life of people. However, a problem for a robot
trying to adapt its speed to a human is that, just as two
humans walking together adjust their speed to each other,
speed adaptation in a human-robot situation might be mutual. That is to say, a robot trying to adapt its speed to ahuman must take into consideration that the human mightsimultaneously be adapting to the robot. This complicatesthe matter as it is not safe for the robot to merely try tokeep the same speed as the human, which could be achieved
with a simple control algorithm. For instance, if the robot
starts out slowly the human might start walking at a slow
pace so as not to leave the robot behind, which would resultin the robot keeping its slow speed. Conversely, if the robot
moves fast the human might hurry to keep up, and if thehuman succeeds in keeping an even pace with the robot itwill keep moving at that speed even if the human is moving
faster than what is comfortable for him/her.
To overcome this problem it is necessary to find some signal that tells whether the speed people are currently keeping is comfortable for them or not. By studying humans
walking together we have found a hypothetical relationshipbetween walking speed and relative position in the direction of walking that could give information about a person’strue preference. We verify our hypothesis by conducting anexperiment with two humans walking together. Then we
conduct a similar experiment with a human and a robot,
and finally we try a simple speed estimation algorithm.

2.

3.

SPEED ADAPTATION ALGORITHM

To adapt to a human’s preference a robot first needs togather some speed-position information by moving at different speeds and observing the human’s changes in position.
We propose an off-line preferred speed estimation algorithm
for adapting to a human’s preference:
1. The robot walks with a human in n moving speeds
vi and measures relative distance di to gather speedposition information,
2. sorts the (vi , di ) data points on increasing speed andcalculates the gradient of the relative distance to the
speed change,si = 4di /4vi = (di+1 − di )/(vi+1 − vi ),3. normalizes the si by the largest negative gradient sj ,e.g., Si = si /|sj |,4. estimates the preferred speed from the middle of the
speed range where the gradient Si is near to 0 (−Tmin ≤Si ≤ Tmax ), where Tmin and Tmax > 0.
If there is a short interval with positive derivative at thelowest speeds the algorithm will exclude this range. The
reason for this is that some subjects had shown a behaviorof stopping and waiting for the robot when it was moving
too slowly, which is outside of our hypothesis.

SIGNAL FROM HUMAN

By studying people walking together we found that people
seem to have a range of walking speeds with which they
are comfortable. On the other hand, they seem to want tokeep some particular position in the walking direction withrespect to the person they are walking together with: somelike to walk a little distance ahead or behind while others
prefer to walk side by side. People seem to keep this position,
unless the other person’s speed is much too fast or too slow.
This leads us to the idea that people will keep their preferred
relative position as long as the walking speed is within theirpreferred range; when the speed is outside that range therelative position will change even though the person might
still be keeping up with the other person. We sketch this
proposed relationship in Fig. 1.

4.

HUMAN-HUMAN EXPERIMENT

To confirm our ideas of how humans signal discomfort
with the walking speed, we set up an experiment with two
persons walking together, one of which was the experimenter.

4.1

Experiment setup

In this experiment the experimenter and a subject walked
together back and forth along a stretch of corridor. (Fig. 2)
Measurements of the persons’ positions were taken using two
SICK LMS-200 laser range sensors, placed approximately
15 meters apart at each end of the experiment area, at aheight of 1.1 m above the floor. The data acquired while
the persons were less than three meters from one of theends of the experiment area was discarded to avoid taking
position measurements while the persons were slowing down
and turning around.

350

4.2

Subjects and procedure
Table 1: Approximate parameter values for thehuman-human experiment. Relative position denotes the relative position in the direction of walking of the subject to the experimenter. +100 meansthat the subject walked 100 mm ahead of the experimenter.
Lap no.
Lap no.
Rel. pos. Speed(subject 1-6) (subject 7-12)[mm][mm/s]
1
6
0
2
7
+100
3
8
+500
4
9
-100
5
10
-500
6
1
1000
7
2
800
8
3
600
9
4
400
10
5
300

The experiment was conducted with 12 subjects, 7 maleand 5 female, with an average age of 21 years. We chosean intern at ATR (male, 23 years old, and 173 cm tall) as
the experimenter. The experimenter had practice to keep
his speeds or relative distance to the other for two days (1.5hours per day). His speed accuracy was in range of ±100[mm/s]. He kept the relative distance by watching the partner’s heel. Real walking speeds and distances were measured
by the laser range sensors. Each subject received instructions by an experiment assistant and were told that theywould be participating in an experiment together with another subject, who would pose arithmetic problems for themto solve while walking. The assistant and the “other subject”, who was in fact the experimenter, demonstrated theprocedure by walking one lap. The purpose of making the
subjects think that the experimenter was another subject
was to make them feel that they were walking with a personof equal status, since we believed that this would be the best
condition for mutual interaction. The experiment consistedof two parts:
1. Gathering speed-position data:
The experimenter varied speed and distance as shownin Table 1; each parameter value was tested during
one “lap”: walking from one end to the other andback. The distance covered in one lap is about 20 meters excluding the areas for slowing down and turning.
The subject was given two subsequent tasks to perform
while walking. Both tasks consisted of solving arithmetic problems read by the experimenter; the tasks
differed only in the level of difficulty of the problems.
During each task the experimenter cycled through allparameter values in Table 1 once. The main purposeof the tasks was to provide a controlled form of interaction between experimenter and subject since wewanted to simulate a situation of talking while walking together. The purpose of having two tasks withdifferent levels of difficulty was to find out if people’s
preference change when they are working on a difficult
task. This is not treated in this paper, however.

Figure 3: Case matched with the hypothesis: The
speed-position relation and the preferred speed ofsubject 4 under hard math task. This graph supports our hypothesis.

2. Measuring preferred speed interval:
To find out the subject’s preferred speed interval, we
asked the subject to raise a blue or orange flag if thewalking speed was too fast or too slow, respectively.
The experimenter and the subject walked a total offour laps, two with the easy math task and two withthe difficult one. The experimenter changed his walking speed in steps as above from 600 mm/s to 1000
mm/s in the first half of each lap, and from 600 mm/s
to 300 mm/s in the second half.

4.3

Results

Due to technical problems we were only able to use datafrom Step 1 from 15 of the 24 (12 subjects × 2 tasks) experiments. 10 of the 15 speed-distance relation graphs giveindications that our hypothesis is correct. Figs. 3 and 4
show such examples. In the figure, ‘slow’ and ‘fast’ lines
indicate the average speed during the time span the subject
held up the ‘slow’ and ‘fast’ flags respectively. For somesubjects there are several ‘slow’ or ‘fast’ lines since subjects
often raised flags at different speeds since they were unsure

Figure 4: Case matched with the hypothesis: The
speed-position relation and the preferred speed ofsubject 3 under hard math task.

351

Figure 6: Overview of Robovie-IV. It has two powered wheels, two laser range sensors, and so on.

Figure 5: Case that did not match with the hypothesis: The speed-position relation and the preferred
speed of subject 5 under hard math task.
whether current speed was comfortable or too fast/slow. As
shown in Fig. 3, we consider subject 4, difficult task a successful case since the graph has the expected shape withplateau and negative slope. Fig. 4, subject 3, difficult task
also shows a graph that has roughly the right shape, thoughlacking a well-defined plateau and not being quite consistent with the subject’s flagged speed preference. Part of thecause is that the preffered speed range is much narower thanallowable range which they raised flags.
Meanwhile, the other five of 15 graphs did not fit with the
hypothetical model. As shown in Fig. 5, subject 5, difficult
task represents an unsuccessful case: the graph does nothave the expected shape.

5.

Figure 7: Robovie-IV, wearing his experiment hat,is walking along with a human

HUMAN-ROBOT EXPERIMENT

to be registered by the range sensors it was fitted with acylindrical paper hat as can be seen in Fig. 7.
For people to perceive the robot as an interactive partnerit should display some kind of interactive behavior. For thispurpose, the robot gives the subject arithmetic problems asin the human-human experiment, to create a form of conversation. Additionally, the robot turns its head to look at the
subject when it is speaking, as well as occasionally between
utterances.
During the experiments the robot moved back and forth
between the range sensors. At each end it would slow down,turn around and speed up again. During this time no measurements were taken.

To test the results indicated by the human-human experiment in a human-robot situation we set up an experiment similar to the human-human experiment where a robot“walks” together with a human while moving at a different
speeds while the distance of the human to the robot is measured. We also tried out a simple offline speed estimation
algorithm.

5.1

Setup and robot platform

The physical experiment setup was identical to the setup
in the human-human experiment (Fig. 2) with two SICK
LMS-200 laser range sensors placed 15 meters apart in acorridor, except that the robot took the place of the experimenter.
The robot used throughout this research is the humanoid
robot Robovie-IV [9] (Fig. 6), developed at ATR. It consistsof a humanoid upper body on a differential drive platform
capable of moving at 1 m/s. It is 1 m tall and is equippedwith a variety of sensors such as cameras, microphones andskin sensors. In the experiment, we used two Hokuyo laser
range sensors mounted front and back on the base of therobot for obstacle detection, human tracking for the purpose of gaze meeting, and localization by map matching tostablize the locomotion. Robovie-IV is equipped with an onboard PC with a Pentium-M 2 GHz CPU, running Linux.
It has a speaker and text-to-speech software, enabling it toutter sentences in Japanese. Since the robot was too short

5.2

Subjects and procedure

The experiment was conducted at ATR using 15 subjects:
5 male and 10 female. The average age was 22 years. They
were asked to answer math problems spoken by the robot.
We verified that our hypothesis works in a human-robot
situation with the following procedure:
1. Gathering speed-position data:
The robot cycled through speeds between 300 mm/s
and 1000 mm/s, with a step of 100 mm/s, e.g. 300,
400, ..., 900, 1000, 900, ... , 400 , 300, 400 mm/s,... It ran at each speed for an interval of 4 seconds:
1 second for changing speed and 3 seconds for taking
measurements of the distance to the subject. If the352

end of the measurement area was reached before the 4seconds interval was completed the robot would startover at that speed after turning around. The robot did
a total of 10 laps.
2. Measuring preferred speed:
2a. Best speed: The robot ran laps on constant speeds,
300, 400, 600, 800, and 1000 mm/s which we usedin the human-human experiment (see table 1).
The subject was asked if this speed was comfortable for walking after each lap. We also asked
the subject which speed(s) was the best after the
robot ran all laps. If the subject answered morethan one speed as the best we recorded all ofthem.
2b. Preferred speed interval: The robot cycled
speeds as in “gathering speed-distance data” andthe subject was asked to raise a blue or an orange
flag if the speed was too slow or too fast as inpreferred speed interval measurement in humanhuman experiment.
We evaluated the proposed speed estimation algorithm forthe 6 out of 15 subjects. We ran step 1 as above and fed theresulting speed-position data to the speed estimation algorithm. The output speeds of the algorithm were prepended
to the list of speeds for step 2a as in Table 3 and the experiment was continued as above.

5.3

Table 3: Result for the speed estimation algorithm
in the human-robot experiment. Speeds marked as
best by the subject are shown in bold type. All
speeds are in mm/s.
Subj.
Alg. output
Standard range
s1
s2
s3
300 400 600 800 100013
550 900
800
14
650 850600
500 850600
1516
550 750 950 300
17550 800
800
800
18quality: each data point in these graphs is an average of 2-3
measurements taken during 3 seconds each, whereas the inhuman-human plots each data point is a single measurement
taken during half a lap. In general, we found the graphs fromthe experiment to be fairly consistent with our hypothesis.
We note, however, that for seven out of 15 subjects the graphin step 1 has a plateau at the lowest speeds. We conclude
that this comes from the subject being relatively far aheadof the robot and not wanting to leave him further behind atvery slow speeds. Additionally, we note that two out of 15
graphs in step 1 have a positive slope at the highest speeds,
which is contrary to our expectations.

5.4

Speed estimation results

The results of the speed estimation algorithm are shownin Table 3. The subject and the robot walked laps withspeed(s) estimated by the algorithm (s1, s2, s3) and five
fixed speeds (300 to 1000[mm/s]). In the table, the speed(s)that the subject answered as best are shown in bold type.
We can see that four subjects chose one or more of the estimated speeds as the best one. The subjects 14 and 15
did not choose them as the best speed. However, since theysaid that the estimated speed of 650 and 500[mm/s] are good
speeds for them and their preferred speed 600[mm/s] is close
to the estimated speed, we can say that the algorithm also
successfully estimated the preferred speed for these two subjects.

Speed-position data gathering results

We plotted the experimental result of speed-position relations of steps 1 and 2a. An experimenter looked at theplotted figures and classified them into three categories: theshape with plateau (matched with the hypothetical model),the shape looked like a flat-negative-slope, and other shapes.
Table 2 shows the classification result. From the table, we
see that the plot of steps 1 and 2a matched with the hypothesis for 11 and 9 subjects respectively.
Figs. 8 through 11 show the speed-position relationshipsof steps 1 and 2a for subjects 8, 16, 15, and 7. The ‘slow’
and ‘fast’ lines indicate the speeds that the subject started
to answer the speeds are slow and fast in step 2a respectively. The ‘best’ line indicates the speed that the subject
selected as best one in step 2a. As in Fig. 8, subject 8’s
speed-position relation for step 1 and step 2a matched withthe hypothesis. However, there are differences in the position where plateaus stay. Subject 16’s relations (Fig. 9)
are another example of a matched case. Here the plateau is
shifted to the right and the negative slope is hidden since
the subject 16’s preferred speed was 950[mm/s].
For subject 15 (Fig.10), we classified the results of step 1
as “flat” and step 2a as “matched”. Subject 15 preferred
600[mm/s] and we see no plateau in step 1. As for step 2a,plateau seems to starting at between 600 and 800[mm/s]
which the robot did not try.
For subject 7 (Fig.11), we classified the results of step 1
as “matched” and step 2a as “flat”. Subject 7 preferred
800[mm/s] and we see slight plateau in step 1. But therelationship changed to “flat” for step 2a.
Overall, the speed-position graphs were closer to our theoretical graph in this experiment than in the human-humanexperiment. We believe that this is a result of better data

6.

DISCUSSION

6.1

How well does human-robot interaction data
fit with the hypothetical model?

It was revealed that for 11 out of 15 subjects the resultsin step 1 were consistent with the hypothesis while for four
subjects they were not. As Figs.8-11 suggest the range ofallowable speeds were somewhat wide. However, the rangeof preferred speed was narrow compared to the resolutionof the data points. Few subject answered more than two
speeds were comfortable in the human-robot experiment.
Then, it was too difficult to show the existence of plateaus
in graphs by fitting mathematical models. It is a future work
to present speeds in higher resolution to subjects and examine detailed speed-distance relationships, especially around
preferred speed.
Also, we found that the relative position changes dependending on how the robot changes its speeds. Contrary
to our expectation, speed-position relationships differed intheir values or shapes for most of the subjects as the Figs. 9,10,353

Table 2: Classification result of the speed-position plots under two conditions; robot changed speed in a lap
and robot kept constant speed in a lap
Robot varied speed(step 1 speed-position relation)with plateau
flat(matched with negative otherthe model)
slope
11
4
0

Robot kept constant speed(step 2a best speed measurement)with plateau
flat
other
(matched with negative otherthe model)
slope
9
5
1

class
changed8

Figure 8: Case matched with the hypothesis: The
speed-position relationship of subject 8. Best indicates the speed that subject answered as the best.
Slow/Fast indicates the starting speed that the subject claimed slow/fast.

Figure 10: Case that step 1 is classified as “flat” andstep 2a as “matched”: The speed-position relationship of subject 15.

Figure 9: Case matched with the hypothesis: The
speed-position relationship of subject 16.
Theplateau can be seen in higher speed range and thenegative slope is hidden.

Figure 11:
Case that step 1 is classified as“matched” and step 2a as “flat”: The speed-position
relationship of subject 7.

354

and 11 show. This indicates the importance of the “datagathering method” or how a robot changes its speed.
In addition, we found that the pattern was not consistent
between variable-speed mode (step 1) and constant-speed
mode (step 2a, Table. 2). When we measured the best speed,
we used the constant-speed mode. As a result, eight subjects’ speed-position pattern in step 2a was changed fromthat of the variable-speed mode (step 1). At the variable
speed (step 1), four subjects was categorized into the flatnegative-slope pattern, which means that we have a difficulty in estimating their preferred speed; at the constant
speed mode (step 2a), two of these four subjects categorized into the with plateau pattern. This implies that there
is a possibility to accurately estimate people’s preference
if a robot appropriately changes its speed pattern between
constant-speed and variable-speed.
Note that eleven subjects were categorized in the withplateau pattern at the variable speed and two of them moved
into the flat-negative-slope pattern at the constant speed.
Thus, it does not mean that the constant speed mode isbetter than the variable speed mode. In fact, the fitness ofthe model is better at the variable speed. This also suggests
a robot to keep changing its speed to adjust its speed to aperson as long as the reaction from the person fits with thewith-plateau model. Probably, people are more consciouswith the current speed when the speed is changed; and if
the speed is constant for a while, they are accustomed to
be at the speed due to humans’ flexibility toward walking
speed.

6.2

Figure 12: The changes of the averaged relative position in one lap (subject 18). Robovie moved in
600[mm/s]. The average is taken at every 4[s]. Thissubject changed her relative position frequently.
Averaged relative position in the lap was -144[mm].

Estimating subjects’ preferred speed

As shown in Table 3, our algorithm successfully predictedsubjects’ preferred speed if it was allowed to give three
speeds. The subject who was presented three speeds preferred two of them. The three subjects who were presented
two speeds preferred one of them and one subject preferredboth. If we assume this study as a preliminary trial, thisis a promising result. Since the range of preferred speed isnarrow, the chance rate of making a successful guess is notvery high. Thus, this is unlikely to happen by chance. On
the other hand, the algorithm had difficulty deciding thebest one among three speeds. As discussed in the previous
section, the data did not fully fit the hypothetical model,
which caused erroneous speeds. It is our future work to improve the algorithm so that it will provide the best speedwith better precision.

6.3

Figure 13: The changes of the averaged relative
position in one lap (subject 16). Robovie moved
in 600[mm/s]. The average is taken at every 4[s].
This subject did not changed her relative position
so much as the subject 18 did. Averaged relative
position in the lap was 26[mm].

6.4

Observations

Through this study, we found that adaptation of a robot’s
speed to a human is even more difficult than we originally expected. Here we describe what we have learned that can give
us insight for further studying such an adaptation method.
• People’s preferred walking speed is not fixed, rather, itchanges depending on task and situation. There is alsoa large individual variation. In our case where people
are asked to perform a thinking task, some preferredvery slow speed (400 mm/s) while some preferred fast
speed (more than 900 mm/s). Therefore it is motivated to make a robot that is capable of adjusting its
speed to a person.

Oscillation of human behavior

Furthermore, we analyzed the temporal aspect of the relative position and found that the distance sometimes oscillated. Figure 12 is a plot of relative positions of a subject
and the robot during one lap (about 20m) of the experimentwhen the robot’s speed was constant at 600 mm/s. The subject often changed her position, going in front of and behind
the robot. On the contrary, Figure 13 shows the relative
position of another subject where the robot’s speed was also
at 600 mm/s. This subject did not change her position so
often and kept the distance relatively stably. This indicatesthat the robot may need to observe a person’s reaction toits speed for a certain amount of time.

• Even though a person may at a glance seem to besatisfied with the speed of walking this is not necessarily the case. Although we carefully observed video
recordings we could not find any obvious behavior suchas facial expressions, gestures, rapid change of speed
and distance, and so forth, that might suggest dissatisfaction with the walking speed. This indicates theneed of an active method that tries a variety of speeds
on a human and watches their behavior.

355

• Rather than being drawn from observations of obvious
behavior, our hypothetical model about the relationship between speed and parallel distance is establishedfrom a case study. It fits with 11/15 of human-robot
interaction data in step 1.

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• Observations of a person’s relative position in the direction of walking gives us a better chance of predicting his/her preferred speed, although the fitness of themodel was not so supportive. Note that our preferred
speed estimation algorithm cannot find the best speed
yet; further study will be required before we can use
this technique for real applications.
• A comparison of the graphs from constant versus variable speed mode suggests that adjustment of speed
step might be necessary. It seems that although people might be sensitive to speed changes they are insensitive to small differences between two speeds.
• People’s speed-position pattern changed between thevariable-speed mode and the constant-speed mode. At
the variable-speed mode, 11 out of 15 subjects fit the
hypothetical model; but 4 of them shifted into the flatnegative-slope pattern at the constant speed. Regarding the rest of 4 out of 15 subjects who were categorized in flat-negative-slope pattern at the variablespeed model, 2 of them fit with the hypothetical modelat the constant-speed mode. This suggests that weneed to pay attention to the way a robot indicates its
speed.
• Some people often change his/her position within shortmovements of 20 m (about one lap in our experimentsetting). This suggests that the robot needs to observe
people’s behavior for a certain amount of time.

7.

CONCLUSIONS

We found a relationship between walking speed and relative position which we used to implement a preferred speed
estimation method that successfully found the preferred speed
for all of the six subjects it was tried on and the best speed
for four of them even though the humans were adapting to
the robot. However, not all subjects in our experiments displayed speed-position relationships consistent with our hypothesis. In future work it is important to investigate how
far this method can be extended. It is also important tomake the speed-position data gathering phase as short andsmooth as possible, for example by not exploring more of
the speed range than is necessary so as to avoid making thehuman feel discomfort.

8.

ACKNOWLEDGEMENTS

This research was supported by the Ministry of Internal
Affairs and Communications of Japan.

9.

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[2] C. Breazeal, D. Buchsbaum, J. Gray, D. Gatenby, and
B. Blumberg. Learning from and about others:
Towards using imitation to bootstrap the social

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