Learning Object-Manipulation Verbs for Human-Robot
Communication
Komei Sugiura
1

Kyoto University
2
ATR Spoken Language Communication
Research Laboratories
2-2-2 Hikaridai, Seika, Soraku
Kyoto 619-0288, Japan

komei.sugiura@atr.jp
ABSTRACTThis paper proposes a machine learning method for mapping
object-manipulation verbs with sensory inputs and motor
outputs that are grounded in the real world. The method
learns motion concepts demonstrated by a user and generates a sequence of motions, using reference-point-dependent
probability models. Four components, needed to learn objectmanipulation verbs, are estimated from camera images; (1)a trajector and landmark, which are the objects of transitive
verbs; (2) a reference point; (3) an intrinsic coordinate system; and (4) parameters of the motion’s probabilistic model.
The motion concepts are learned using hidden Markov models (HMMs). In the motion generation phase, our method
then combines HMMs to generate trajectories to accomplish
goal-oriented tasks. Results from simulation experiments inwhich our method generates motion by combining learned
motion primitives are shown.

Categories and Subject Descriptors
I.2.6 [Artiﬁcial Intelligence]: Learning—Language Acquisition, Concept Learning; I.2.9 [Artiﬁcial Intelligence]:
Robotics—Operator interfaces

General Terms
Algorithms, Languages

1

Naoto Iwahashi

National Institute of Information andCommunications Technology
2
ATR Spoken Language Communication
Research Laboratories
2-2-2 Hikaridai, Seika, Soraku
Kyoto 619-0288, Japannaoto.iwahashi@atr.jp
system, however the referent of a symbol may diﬀer fromperson to person. Let us take an example of conversation at
home, “Put the dishes in the cupboard”. To make a machine
accomplish this task, ﬁrst the recognition of “the cupboard”,
which is speciﬁc to the home, must be successful. The desired motion also depends on the size and shape of the dishes,
as well as those of the cupboard and whether it has a door.
Therefore, adaptation to both the user and the environmentis necessary. Studies have begun to focus on machine learning methods that map symbols to motion and/or objects[7,4].
The main advantage of mapping symbols to motion is asfollows: The machine can break down the given task into
learned motion primitives and then present the planned motions, in a way easy for the user to understand. This is asigniﬁcant safety feature because if the machine can informthe user of the planned motions before executing them, theuser can decide in advance whether they are safe.
In this paper, we propose a method that learns verbs andgenerates motion. With our method, probabilistic models
are learned from visual inputs, and motion is generated using
the learned probabilistic models. Figure 1 shows an example of the method’s application. The robot has multimodal
interfaces such as a camera and a microphone.

Keywords
human-robot interaction, motion generation, HMM

1. INTRODUCTION
To communicate with humans through natural language in a
typical environment, machines need to use mechanism mapping symbols with related information in both linguistic andnon-linguistic contexts. While it is sometimes believed thatsuch mappings are ﬁxed within a certain natural language

Figure 1: Human-robot interaction
The rest of this paper is organized as follows. Section 2 ﬁrst

states the problem we try to solve, brieﬂy reviews related
work, and introduces out method. It then describes the motion learning/generation method in detail. Section 3 shows
the results of simulation experiments in which our method
generated motion by combining learned motion primitives.
Section 4 discusses problems and possible applications with
our method. Then, Section 5 concludes the paper.

2. METHOD
2.1 Reference-Point-Dependent Motion Primitives
How can we teach motion concepts to a robot? To makethe question clear, we consider a situation in which the user
teaches a verb by uttering it and showing the motion toa robot equipped with multimodal input devices (camera,
microphone, etc). The question, therefore, is how the robot
can learn and generate motion, and also map it to speech.
Clustering manipulation trajectories and mapping them toa verb are not suﬃcient for verb learning if the trajectories
are considered only in the camera coordinate system. For
simplicity, we assume that the mapping between the camera
coordinate system and the world coordinate system is given,and that the user’s utterance is accurately recognized. Let
us take the example shown in Figure 2. The ﬁgure depicts acamera image, in which the user is placing the green puppet
on the box. In the ﬁgure, the dotted line represents the
trajectory. The trajectory itself is meaningless, though, if
the position of the box has changed.

Figure 2: An example of camera images. The user
is manipulating the green puppet. The dotted line
represents the trajectory of the manipulation.

a secondary focus and a trajector is characterized with respect to a landmark. In cognitive linguistics, words representing spatial relationships such as “away” and “left of”
are described as the relationship between a trajector anda landmark[5]. A method based on recurrent neural networks is proposed in [8], but this method is ineﬀective when
the position of objects has changed. Inamura et al. developed a motion learning/generation method based on hidden
Markov models (HMMs)[3]. However, their method deals
with only intransitive verbs, such as “run” and “walk”, andis thus not applicable to object-manipulation verbs.
In contrast, our method estimates four components, which
are necessary for learning object-manipulation verbs, fromcamera images. The components are (1) the trajector andlandmark, (2) the reference point, (3) the intrinsic coordinate system, and (4) the parameters of the motion’s probabilistic model. Let us consider two examples “raise” and“move-closer” (Figure 3). We can reasonably assume thatthe reference point of “raise” is the trajector’s center of mass.
The intrinsic coordinate system can be a Cartesian coordinate system, as shown in the left-hand ﬁgure. In the caseof “move-closer”, another type of intrinsic coordinate system
is necessary. In this case, the x-axis of the coordinate system passes through the centers of mass of the trajector andthe landmark. As explained in the following subsection, we
think there are several types of intrinsic coordinate systems.

Figure 3: Relationship between trajector/landmark,a reference point, and an intrinsic coordinate system. The spheres, ellipsoids, and box represent objects, and the arrows represent the axes of the intrinsic coordinate systems. Left: “raise”. The small
sphere is the trajector, and the reference point is its
center. The x-axis of the intrinsic coordinate system
is horizontal. Right: “move-closer”. The directionof the x-axis is toward the trajector from the landmark.

2.2
On the other hand, if we consider a coordinate system with
its center at the box, we are able to cluster the trajectories in
the coordinate system and map them to a verb. We call sucha coordinate system an intrinsic coordinate system. The
origin of an intrinsic coordinate system is called the reference
point. Note that the origin of the intrinsic coordinate systemchanges as the position of the box changes.
Regier investigated a model describing the spatial relationship between two objects[6]. He proposed to model verbs
as the time evolution of the spatial relationship between a
trajector and a landmark. Here, a trajector is deﬁned asa participant (object) that is focused on. A landmark has

Motion Learning by Reference-PointDependent Probabilistic Models

Consider that N kinds of learning data are given for a verb.
Let Vi denote the ith learning data. Vi consists of the motion
information of the trajector, Yi , and the set of positions ofstatic objects, O i , as follows:
Vi = (Yi , O i ),Yi = {y i (0), y i (1), ..., y i (Ti )},23
xi (t)y i (t) = 4ẋi (t)5 ,ẍi (t)(1)(2)

where Yi is a time series of vectors yi (t). Here, yi (t) is
composed of position xi (t), velocity ẋi (t), and acceleration

ẍi (t). For simplicity, we omit index i when the context is
clear.
We assume that there are several types of intrinsic coordinate system, and these are given by the designer. We denotethe type of coordinate system by C. From the estimation of
C and the reference point r, we obtain the intrinsic coordinate system in the ith data. The candidate set of reference
points is denoted by R. The set of positions of static objects,
O, has to be included in R, since those objects are the candidates of the landmark. We also include the ﬁrst positionof the trajector, x(0), in R so that we can describe a motion
concept which is dependent only on the object’s trajectory.
Additionaly, the center of the camera image, xcenter , is put
in R to describe motion concepts that are independent on
the positions of objects. Therefore,
R = {O, x(0), xcenter } , {r 1 , r 2 , ..., r M }.

(3)

Let Ck (mi ) Yi denote the trajectory in the intrinsic coordinate system Ck (mi ), where k and mi are the type of thecoordinate system and the index of the reference point in
Ck (mi ), respectively. Henceforth parameters in a coordinate
system are written in a similar manner. Now, the optimal k,
the optimal set of reference points, m, and the optimal parameters of a probabilistic model, λ, are searched for using
the following maximum likelihood criterion:(λ̂, k̂, m̂) = argmax
λ,k,m= argmax
λ,k,m

N
X

log P (Yi |mi , Ri , k, λ),(4)log P (Ck (mi ) Yi ; λ),

(5)

i=1
N
X
i=1

where ˆ· represents estimation.
The number of candidateQ
solution of k is generally smaller
than that of m, which is N
i=1 mi . Therefore, we ﬁrst ﬁx k
and obtain the following equation from Equation (5).
(Ck λ̂, Ck m̂) = argmax
λ,m

N
X

log P (Ck (mi ) Yi |λ, k)

(6)

i=1

It is not practical to solve this equation because of its computational complexity. Therefore, for constraint relaxation,
we approximate the above discrete optimization problem bya continuous optimization problem:
"M
#
N
i
X
X
Ck
Ck
Ck (mi )( λ̂, ŵ) = argmax
log
wi,m P (Yi |λ, k)
λ,w

i=1

m=1

(7)
where
Mi
X

wi,m = 1(i = 1, 2, . . . , N ),m=1

w i = {wi,1 , wi,2 , . . . , wi,Mi }w = {w 1 , w 2 , . . . , w N }Here, wi,m denotes the weight to select the reference point
m in the learning data Vi . Thus we can think of Ck m as
hidden parameters. We can solve Equation (7) eﬃciently
by applying an EM algorithm[1]. [2] gives the solution to

Equation (7) for the case where an HMM is used as theprobabilistic model. The optimal k is obtained by solving
the following equation.
#
"M
N
i
X
X
Ck
Ck (mi )Ck(8)k̂ = argmax
logŵi,m P (Yi | λ̂)
k

i=1

m=1

These learned HMMs are used for motion generation. Tokuda
et al. has proposed a method that generates the maximum
likelihood trajectory from HMMs[9].

2.3Motion Generation by Combining Transformed HMMs

In motion learning, a verb is learned from multiple scene
data. On the other hand, the scene is ﬁxed in motion generation. Our proposed method deals with the following two
types of motion generation:(a) Target Instruction
The user requests that the robot move an object to agoal. Inputs from the user are the object ID and goal
position xG . The proposed method then outputs a sequence of verb-landmark pairs, (v, m 0 ). The method
also outputs a trajectory, Y, to the goal from the initial position of the object. The method searches forboth the optimal sequence of verb-landmark pairs andthe optimal trajectory according to likelihood criteria.
In other words, it decomposes this goal-oriented task
into the verb-landmark sequence with the maximum
likelihood. For example, if the user wants to put object A above object B, the estimated sequence would
be composed of two verbs: “put-on A B” and “raise A”.
(b) Explicit Instruction
The user requests the robot to move an object according to his instruction. The instruction consists of a sequence of motions. Inputs from the user are the object
ID and a sequence of verb-landmark pairs. The proposed method estimates the optimal trajectory that
accomplishes the sequence. The output trajectory is
optimal in terms of likelihood.
In each case, the generated motion is composed of one ormore motion primitives taught by the user. A novel methodthat combines the probabilistic models for generating a composite trajectory is described below.
The main point of our method is the transformation of an intrinsic coordinate system of reference-point-dependent HMMs.
Although trajectory generation based on HMMs has been
widely investigated in the ﬁeld of speech synthesis, those
HMMs do not have to be transformed since they share thesame coordinate system (Figure 4). It is therefore possible
to combine two HMMs by simply aligning them temporally.
However, it is impossible to combine two reference-pointdependent HMMs in such a way. Figure 5 illustrates an example of combining two reference-point-dependent HMMs.
To combine HMMs corresponding to “raise” and “move-closer”,
each of the HMM output probability distributions needs tobe transformed since it represents a distribution on a coordinate system intrinsic to each motion primitive.

The mean vector of the jth HMM is transformed by thefollowing equation:Wµy (j, s)
02C

j= GW Cj @4

31 2W
3µx (j, s) − Cj µx (j, 1)µx (j − 1, Sj−1 )Cj
5A + 45,µẋ (j, s)0
Cj0µẍ (j, s)(12)(j = 1, 2, ..., D)

W

Figure 4: Schematic of the combination of two motion primitives.

An advantage of transforming intrinsic coordinate systems
is the smoothness in composite trajectories. In our method,
velocity and acceleration data are used for learning as wellas position data. For safety reasons, changes in the velocity
and acceleration data should be continuous. It is therefore
important to obtain smooth trajectories of ẋ and ẍ whencombining two HMMs. Let us consider a case in which verbs
dependent only on velocity information such as “throw” areto be combined. If two HMMs were simply aligned to generate the composite trajectory, the velocity changes might bediscontinuous in this case. On the other hand, our method,which is described in detail below, generates a smooth trajectory.
Let Λ denote a sequence of HMM parameters that represents a sequence of verb-landmark pairs. Λ is a D-tuple
HMM parameters that are transformed from learned HMM
parameters:WΛ = ( W λ1 , W λ2 , . . . , W λD )(9)

λj = FW Cj (λj )(10)where FW Cj denotes a transformation from the jth intrinsic
coordinate system Cj to the world coordinate system, andCj is deﬁned as Cj , Ckj (mj ). We use a single Gaussian
for each dimension of the output probability distributions of
the HMMs. The transformation FW Cj is performed in twostages. First, the mean vectors in λj is transformed, andthen the variance vectors is trandformed.
The mean and variance vectors at state s of the jth HMM
are represented as
23µx (j, s)µy (j, s) = 4µẋ (j, s)5 ,µẍ (j, s)

32 2
σx (j, s)σy 2 (j, s) = 4σẋ 2 (j, s)5 , (11)σẍ 2 (j, s)(j = 1, 2, ..., D,

s = 1, 2, ..., Sj )That is, the mean vector µy (j, s) consists of mean position
vector µx (j, s), mean velocity vector µẋ (j, s), and mean acceleration vector µẍ (j, s). Similarly, variation vector σy 2 (j, s)
consists of position, velocity, and acceleration vectors, σx 2 (j, s),σẋ 2 (j, s) and σẍ 2 (j, s).

µx (0, S0 ) = xS

(13)

Here, GW Cj denotes an aﬃne transformation from the intrinsic coordinate system of the jth motion primitive, Cj ,to the world coordinate system, W . Also, xS denotes theinitial position of the trajector.
Next, the variance vectors are transformed:
W

σy 2 (j, s)
8C
j
σy 2 (j, s) 2
>
>
3
>
<
W
σx 2 (j − 1, Sj−1 )= Cj 26
7>
σy (j, s) + 4
0
5
>
>
:
0

if r j ∈ O,
otherwise(14)(j = 1, 2, ..., D)
whereW

σx 2 (0, S0 ) = 0

(15)

W

(16)

2

σx (1, 1) = 0

Here, O denotes the set of static objects’ positions. Equation (14) adds the position variance of the (j − 1)th HMM
to that of the (j − 1)th HMM if the type of coordinate system intrinsic to the jth motion primitive does not dependon any landmark. Hence, our method combines two HMMs
smoothly.
From Equations (12), (13), and (16), we obtain W µx (1, 1) =xS and W σx 2 (1, 1) = 0; consequently, the composite trajectory starts exactly at xS where its likelihood is at a maximum.
In the target instruction mode, all candidate motion sequences (sequences of verb-landmark pairs) are generated.
Here, the number of combined HMMs, D, is a constant. D
works as a search depth parameter. The maximum likelihood trajectory and motion sequence are then estimatedunder the constraint on start and goal positions.
(Ŷ, v̂, m̂ 0 ) = argmax log P (Y|xS , xG , v, m 0 ),Y,v,m 0(17)

where Ŷ denotes the estimated maximum likelihood trajectory, Λ̂ denotes the estimated maximum likelihood motion sequence, and m 0 represents the sequence of mj . The
method explained in [9] gives the maximum likelihood trajectory from Λ. Therefore, we obtain the solution to Equation (17) by applying this method to all candidate sequences.
On the other hand, in the direct instruction mode, the user
inputs a motion sequence, therefore only the maximum likelihood trajectory is searched for under the constraint on thegoal position.
0Ŷ = argmax log P (Y|xS , v, m )Y(18)

We obtain the solution by following [9] as well.

C2 an orthogonal coordinate system with its origin at thelandmark position. The direction of the x-axis is fromthe landmark towards the trajector.
C3 a transformed camera coordinate system with its origin
at the original position of the trajector.
C4 a transformed camera coordinate system with its origin
at the center of the image.
After motion primitives were prepared, we carried out motion generation simulation experiments. Two types of motion experiments were done: for target instruction and for
explicit instruction.

Figure 5: Example of transformation in the combination of two HMMs, “raise” and “move-closer”.
Each dotted circle represents the variation of output probability distributions at each state of a leftto-right HMM. The direction of state transition isindicated by the color darkness. The intrinsic coordinate system of “move-closer” is transformed sothat the x-axis of it passes through both the landmark (the reference point of “move-closer”) and thelast position of the HMM regarding “raise”. The
dotted line represents the composite trajectory.

3. EXPERIMENTS
3.1 Experimental Settings
First, motion primitives to be used in the motion were prepared. All motion primitives were taught by the user ina learning phase beforehand, and they were ﬁxed throughout the motion generation experiments. During the learning
phase, the user taught verbs to the robot by uttering themand demonstrating their trajectories.
In the learning phase, the robot learned the following verbs.
raise, move-closer, move-away, rotate, place-on,
put-down, jump-overIn the target instruction experiment, the user requested thatthe robot move an object in a camera image. The object ID
and a goal point were input, and then the robot output
both a sequence of verb-landmark pairs and a trajectory
to the goal. We used 64 grid points as goal points. The
search depth parameter D was set as D = 3. Therefore,
the estimated motion sequence was composed of up to threemotion primitives.

3.2 Result (A): Target Instruction
The simulation environment is shown in Figure 7. There
were ﬁve objects in the environment (depicted as numberedboxes and circles). Object 1 was used as the trajector. Figure 7 shows examples of maximum likelihood trajectories
output by our method. In the ﬁgure, bracketed pairs represent the estimated sequences of verb-landmark pairs. For
example, <place-on, 2><move-closer, 5> means “place object 1 on object 2, and move object 1 closer to object 5”.
From Figure 7, we can see that our method combined two
motion primitives smoothly rather than independently. Specifically, although <move-away, 2> and <move away, 2><jumpover, 4> share <move-away, 2>, the trajectories do not
overlap each other. This is probably due to the large variation for the last position in the learned probabilistic modelof “move-away”. In other words, part of the trajectory for<move-away, 2> was curved to smoothly combine <moveaway, 2> and <jump-over, 4>, but the likelihood of the resultant trajectory was still high because of its large variance.

3.3
For each verb, the number of learning data was 15.
The verbs were successfully learned in the experiment. Figure 6 shows examples of the recognition results for the learning data. In Figure 6, the thick arrows represent the trajectories of an object manipulated by the user. The thin arrows
show the x- and y-axes of the estimated type of intrinsic coordinate system. The type name is shown at the lower rightof each illustration. The types of intrinsic coordinate system
are deﬁned as follows:
C1 a coordinate system with its origin at the landmark
position. C1 is a transformed camera coordinate system. The x-axis is inverted in case the x-coordinate of
the original position of the trajector is negative after
transformation.

Result (B): Direct Instruction

The direct instruction experiment was carried out in thesame simulation environment. Figure 8 shows two examples
of motion generation: “jump object 1 over object 2, thenput object 1 down, and move object 1 closer to object 4”
and “jump object 2 over object 1, jump object 2 over object
1 again, and then place object 2 on object 5”. The inputs
for the two cases were as follows:(a) trajector = object 1, motion sequence = <jump-over,
2><put-down, no landmark><move-closer, 4>(b) trajector = object 2, motion sequence = <jump-over,
1><jump-over, 1> <place-on, 4>
Figure 8 shows that the three motion primitives were combined smoothly. To examine this result quantitatively, we

C3

C3

C3

C3

C2

C2

C2

C2

C2

C2

C2

C2

"raise""move-closer""move-away"

C3

C3

C3

C3

C1

C1

C1

C1

C3

C3

C3

C3

C1

C1

C1

C1

"rotate"Figure 7: Examples of generated motion for manipulating object 1. Numbered boxes and circles
represent objects. Bracketed pairs represent the estimated sequence of verb-landmark pairs. Speciﬁcally, <place-on, 2><move-closer, 5> means “place
object 1 on object 2, and move object 1 closer toobject 5”.

"place-on""put-down""jump-over"Figure 8: Direct Instruction
Figure 6: Examples of learning data.

plotted the evolution of the position, velocity, and acceleration in case (a) in Figure 9. Figure 9 veriﬁes that the composite trajectory of the velocity and that of the acceleration
were continuous.

4. DISCUSSION
4.1 Problems
Our method has a possibility of generating inappropriate
trajectories leading to object collision. For instance, Figure 7 shows that the trajectory of <move-closer, 2><movecloser, 3> runs through Object 2.
There are at least three solutions to this problem. The ﬁrst is
to select the maximum likelihood sequence of verb-landmark
pairs among which no collision occur. This is the simplest
solution since the positions of all static objects are evident incamera images. Another solution is to change the maximum
trajectory slightly to avoid collisions. The third one is tomodify the output probability density functions of HMMs

by setting them to 0 near the position of obstacles. The last
method, however, will not work if there are many obstaclesin the camera image.
Another problem is that Equation (14) does not consider
the full-covariance matrices, so the rotation of coordinate
systems is ignored. The transformed variance is therefore
thought to be an approximation. One reason these matrices
are not considered is that no trajectory generation method
has been formulated.

4.2

Possible Applications

The proposed method can be applied to motion planning
other than manipulating objects. One example is a mobile
robot that generates a path to a goal set by the user by
combining learned motion primitives and tells them to theuser. Suppose a camera is placed on the ceiling of an ofﬁce and a camera image like Figure 7 is obtained. In thiscase, the robot can decompose an instruction like “go to
the president’s room” into learned motion primitives such as“move-forward” and “move-along”.

Acknowledgments

300
x 200
100

This research was partially supported by the Ministry of
Education, Science, Sports and Culture, Grant-in-Aid for
JSPS Fellows, 18-2972, and by a research grant from the
National Institute of Informatics.

0
200
y 100

6.

0
5

vx 0
-5
5

vy 0
-5

0.1
ax 0
-0.1
0.1
ay 0
-0.1

0

t [msec]

4500

Figure 9: Evolution of position, velocity, acceleration under condition (a) in Figure 8

Another application would be a system to recognize the actions and movements of people within an oﬃce. Wren proposed an HMM-based method for understanding human behavior on a building-wide scale[10].
In the target instruction mode, the proposed method searches
for trajectories that pass through both the start and goal
positions. This is done by computing the likelihood for all
combinations of motion primitives, where the search depth
is a constant. Consider a detection problem in which the
movements of people are recorded. The maximum likelihood verb-landmark sequence is searched for through thefollowing equation:(v̂, m̂ 0 ) = argmax log P (v, m 0 |Y)
v,m 0

(19)

Thus the user’s movement can be described by a combination of learned motion primitives. Furthermore, if the estimation is done with part of the trajectory, the system canpredict the landmark of the motion and help the user. For
example, this could be used in a technique to unlock a door
before the user arrives at it.

5. CONCLUSION
Within environments shared by humans and machines, it
is important that machines be able to report their internal
states to humans in a comprehensive way. For example, it
is critical to the safety of people working around machines,that a robot functioning in the same area be able to tell what
it will do next. In this paper, we have described a methodthat (1) learns motion primitives grounded in real world
actions, and (2) plans a motion sequence to accomplish goaloriented motion by combining learned motions.

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