Achieving Different Levels of Adaptability for Human–Robot
Collaboration Utilizing a Neuro-Dynamical System
Yuxi Li1 , Shingo Murata1 , Hiroaki Arie1 , Tetsuya Ogata2 , and Shigeki Sugano1
Abstract— Collaborative robots are expected to acquire adequate planning ability when achieving complex tasks such as
cooking and cleaning with humans in dynamically changing
daily-life environment. To fulfill adequate planning, three levels of adaptability—motion modification, action selection, andturn-taking—should be considered. This study demonstrates
that a single hierarchically organized neuro-dynamical systemcalled multiple timescale recurrent neural network (MTRNN)
can achieve these levels of adaptability by utilizing the socalled multiple timescale property. The system is implemented
in a humanoid robot and the robot is required to collaborate
with a human partner by sharing a specific task underdynamically changing environment. Experimental results showthat in both learned and unlearned situations, the robot cangenerate adequate behaviors against different situations, andthe aforementioned levels of adaptability can be realized by asingle system.

I. I NTRODUCTION
Collaborative robots situated in daily-life environment are
required to perform tasks with spatiotemporal complexity
involving humans. The complexity in such human–robot
collaboration consists of two aspects, temporal complexityof the task and spatial complexity of the environment. A
typical example of task collaboration with spatiotemporalcomplexity is collaborative cooking. Consider a situation
where a human and a robot are working in a shared space toaccomplish a common final goal–cooking a soup. This goalconsists of multiple subtasks (e.g. washing, cutting, and boiling) to be accomplished sequentially. Temporal complexity
is the characteristic of tasks consisting of many sequential
subtasks. The spatial complexity of an environment arises
from variability and uncertainty in the shared environment,such as object positions and physical and interpersonal
constrains from the collaborator [1]. Task collaboration requires mechanisms to maintain multi-step task sequences andadaptability to spatial variations through acquired experience.
Adequate planning is essential for collaborative robots todeal with both temporal and spatial variations during collaboration. When considering humanoid robots engaging incomplex tasks with humans in home environment, adequate
This work was supported in part by CREST, JST; a MEXT Grant-in-Aid
for Scientific Research on Innovative Areas “Constructive Developmental
Science” (24119003); a JSPS Grant-in-Aid for Scientific Research (S)(25220005); a JSPS Grant-in-Aid for Young Scientists (A) (16H05878); andthe “Fundamental Study for Intelligent Machine to Coexist with Nature”
program of the Research Institute for Science and Engineering, Waseda
University, Japan.
1 Yuxi Li, Shingo Murata, Hiroaki Arie, and Shigeki Sugano are with the
Department of Modern Mechanical Engineering, Waseda University, Tokyo,
Japan.
2 Tetsuya Ogata is with the Department of Intermedia Art and Science,
Waseda University, Tokyo, Japan.

(1) Motion modification"(How to do)!

(2) Action selection"(What to do)!

(3) Turn taking"(Who should do)!

Fig. 1. Different levels of adaptability. (1) Motion modification requires
agents to consider how to do one action. (2) Action selection requires agentsto consider what action should be done. (3) Turn taking requires agents toconsider who should do the action.

planning in the context of human–robot collaboration can berealized by three levels of adaptability shown in Fig. 1: (1)motion-level adaptability (motion modification), (2) actionlevel adaptability (action selection), and (3) role-level adaptability (turn-taking). Motion modification requires agents tosolve “how to do” problems by modifying arm trajectories
when small scale changes happen. Action selection requires
agents to solve “what to do” problems by selecting thesuitable arm to perform an action when middle scale changes
around the body happen. Turn-taking requires agents tosolve “who should do” problems by correctly understanding
collaborator intentions and actions and taking their own turnat an appropriate time when large scale changes of roleswitching between agents happen [2], [3].
Previous studies have investigated robotic adaptability tospatiotemporal complexity. Regarding (1) motion modification, in a study of a dynamical system with a Gaussian
mixture model using a single-arm robot, Khansari et al. [4]showed that the system allows the robot to achieve a singlestep task in different environments by modifying motion trajectories through a set of previous demonstrations. Anotherstudy conducted by Maeda et al. [5], demonstrated that a
mixture model based on probabilistic movement primitives
can realize motion modification in a task requiring multiple
human–robot interactions. Regarding (2) action selection,
Hawkins et al. [6] developed a probabilistic model andinference mechanism that permits a robot to infer current
states and choose appropriate actions in human–robot collaboration tasks. In a study of a system based on dynamical
movement primitives, Lioutikov et al. [7] enabled a dual-arm
robot to achieve motion modification and action selection
in multi-step bimanual manipulation tasks. Regarding (3)turn-taking, Calinon et al. [8] and Sheng et al. [9] focusedon collaborative table-lifting tasks between a human and arobot. The robot was able to adapt its behavior to humansubjects who changed their role (leader or follower) during
the collaboration. A simulation study conducted by Awano
et al. [10] showed that a robot can determine its action andtiming during an object arrangement task in collaboration
with a human.
To achieve collaborative tasks with spatiotemporal complexity, each agent should acquire comprehensive adaptability to variances. However, most past studies have only
focused on one or two particular aspects of the aforementioned levels, instead of considering their comprehensive
integration. In addition, several models were required tointegrate levels of adaptability, and their seamless integrationand communication is difficult [11]. We therefore consider
the integration of different levels of adaptability into a single
model.
A hierarchically organized neuro-dynamical system calleda multiple timescale recurrent neural network (MTRNN) [12]is well-known for its ability to self-organize functional
hierarchies by utilizing its multiple timescale properties.
This ability is speculated to contribute to the acquisitionof multilevel adaptability. Thanks to the multiple timescale
property, MTRNNs can deal with sequential tasks.
Previous studies regarding robot learning with MTRNN
have demonstrated its ability of motion modification [12],action selection and turn-taking [13]. However, as far as
we know, no studies have succeeded in achieving turntaking in which robots become a “leader” of interactions
and in integrating these different levels of adaptability. We
believe that MTRNN has a potential to realize these aspects
and the present study tackles this issue. A humanoid robot
implemented with MTRNN was required to collaborate witha human partner for sequential tasks among environmental
changes. Experimental results show that the single system can successfully achieve multilevel adaptability during
human–robot collaboration.
II. C OMPUTATIONAL M ODEL
A. Overview of MTRNN
MTRNN is a derivation of the so-called continuous-time
RNN (CTRNN), whose contextual neural units are modeledby a leaky-integrator neuron with a single time constant.
As shown in Fig. 2, our MTRNN consists of two groupsof context layers according to their timescale, which isdetermined by a set time constant. One is a fast context layer
with a small time constant (i.e., a lower level) representing
action primitives, whose activity changes quickly over the
short term. The other is a slow context layer with a large
time constant (i.e., a higher level) representing the sequenceof the primitives, whose activity changes slowly over thelong term. Thanks to the levels of information processing
by the multiple timescale property, an MTRNN can selforganize its function hierarchy, allowing it to solve sequential
tasks by combining primitives into sequences. To maintaintask information for achieving a given task under different
environmental situations, we introduce a static vector called
the parametric bias (PB) [14] that is directly connected tothe slow context layer and is utilized as the highest-level

representation of task sequences. Note that unlike otherstudies utilizing the modification of PB value to achieve
behavior adaptation, in this study, we gave constraints on
the PB. To achieve adaptation under different situations, PB
stayed static to maintain one shared task information under
different situations during collaboration.
Adequate planning can be achieved through two information pathways in the system. These pathways integrate
both PB information representing a task sequence and sensory inputs representing the current environmental situation.
One is a top-down pathway starting from the highest-level
representation of PB and ending at the lowest-level sensory
predictions through the slow and fast context layers. The
other is a bottom-up pathway starting from sensory inputs tothe slow context layer through the fast context layer.
The following subsections describe the forward dynamics
and the learning method of network parameters.
B. Forward Dynamics
The forward dynamics of the internal state of the ith(s)neuron at time step t corresponding to the sth sequence ut,iis updated in accordance with (s)(i ∈ IP ), ut−1,i










1
1
(s)
(s)


u
+
1
−

∑ wi j xt, j
τi t−1,i τi j∈I

I
!
(s)
ut,i =(s)(s)
+ ∑ wi j pt, j + ∑ wi j ct−1, j + bi
(i ∈ IF ∪ IS ),



j∈IP
j∈IF ∪IS







(s)


(i ∈ IO ), ∑ wi j ct, j + bi
j∈IF

(1)
where II , IF , IS , IP , and IO are the neuron index sets for the
input, fast context, slow context, PB, and output units, τi is
the time constant of the ith context unit (τF or τS ), wi j is the(s)weight of the connection from the jth to the ith neuron, ct, j(s)

is the activation value of the jth context neuron, xt, j is thejth external input, and bi is the bias of the ith neuron.
In this study, the weight wi j was set to zero, whichindicated disconnection, in a case where i ∈ IS ∧ j ∈ II andi ∈ IS ∧ j ∈ IP for the connection constrains. Note that not
only the multiple timescale property, but also the connection
constrains on the information flow are essential for selforganizing the functional hierarchy [15]. From (1), the PB
units can be regarded as a particular case of the context
neurons, whose time constant is a infinite value. Certain
values were set to the PB units in order to represent different(s)task sequence. The value of the initial state u0,i of the fastand slow context neurons were set to zero, which indicateda neutral state regardless of the sequence s.
(s)
The respective activation values of the PB unit pt,i , the
(s)

(s)

context unit ct,i , and the output unit yt,i are calculated by

Activity of each context layer	

Top-down	
MTRNN	⌧S

PB 	Static	Slow	

Slow 	Fast	⌧F

Fast 	
Input	

Time step	

Output	Bottom-up	Task sequence	
Sequence of primitives	
Primitive 1	
Primitive 2	

Fig. 2. System structure. MTRNN consists of two groups of context layers according to their timescale. One is a fast context layer (i.e., a lower level)
representing action primitives, whose activity changes quickly over the short term. The other is a slow context layer (i.e., a higher level) representing thesequence of the primitives, whose activity changes slowly over the long term. A static vector called the PB units is connected with the slow context layer
and is utilized as the highest-level representation of task sequences.

NAO robot	

using the nonlinear function tanh(·) as follows:
pt,i = tanh(ut,i )(s)(i ∈ IP ),

(2)

(s)
(s)
ct,i = tanh(ut,i )(s)(s)
yt,i = tanh(ut,i )(i ∈ IF ∪ IS ),(3)(i ∈ IO ).

(4)

(s)

C. Learning Method
The network training (optimization of parameters) of
MTRNN is based on the mean squared error minimization
using the gradient decent method. Suppose that S target
sequences are given, each of which consists of Ŷ (s) =(s) T (s)(ŷyt )t=1
, where s is the index of the sequences and the T (s) isthe length of the sequence. In this situation, the error function
E is given by
(s)

E=

1T
(s)
(s)
∑ ∑ ∑ (yt,i − ŷt,i )2 ,2 t=1i∈IO s∈IS

(5)

(s)

where ŷt,i is the ith value (training data) at time step t of the
sth target sequence Ŷ (s) . The network parameters including
weights wi j and biases bi are optimized to minimize the meansquared error in an off-line manner by utilizing the gradientdecent method with back-propagation through time (BPTT).
III. E XPERIMENTAL SETUP
A. Task Design
To achieve complex collaborative tasks in an actual environment, the fundamental aspects of human–robot task
collaboration should be investigated first. By considering
the temporal and spatial characteristics of complex task
collaboration, we simplified actual collaborative tasks (suchas cooking meals) to a sequential task collaboration of bell
hitting between a human and a humanoid robot (NAO;

Human’s hand	Fig. 3. Experiment environment. One NAO robot, two bells with blue andred colors and one green glove for the human hand were used.

Aldebaran) under dynamically changing environment. Notethat both the human and the robot were set as bell hitter(executor).
As shown in Fig. 3, the experiment utilized a red bell, a
blue bell, and a green glove for the human hand use. One
bell was located on the left or right side in front of the robot,
and the other was located in front of the human. Hereinafter,these positional relationships between the two bells are calledcases, and the total number of the cases were four (two bellcolors (blue, red) × two sides of robot (left, right)). In eachcase, a bell was placed on one of three fixed positions (bellposition 1, bell position 2, and bell position 3) around one
hand of the robot, and the other on a fixed position in front of
the human (Fig. 4). Two collaborative task sequences were
performed, repeating a BBBR (B: hit blue bell; R: hit redbell) sequence, and repeating a RRRB sequence.
B. Training data
For training data, we first guided the robot’s arms to hit
bells and defined 6 primitive movements each of which wasfor the six bell positions (three for the left and three forRobot	Right arm	1	2	

B B B R …!

Left arm	
1	

3	

2	

Task 1: !

…!

3	

R R R B …!
Task 2: !
Human	…!

(B: hit blue bell, R: hit red bell)	

Fig. 4. Bell positions and task sequences. Regarding bell positions, onebell was placed in three of the fixed positions (bell position 1, bell position
2, and bell position 3) around one hand of the robot, and the other bell was
located in a fixed position in front of the human. Two collaborative bell
hitting task sequences were designed in experiments. One is BBBR task:
repeating a BBBR (B: hit blue bell, R: hit red bell) sequence. The other is
RRRB task: repeating a RRRB sequence.

the right side of the robot). During task collaboration withthe human, one of these defined primitives was called forthe robot’s action generation. Data for two task sequences(BBBR task and RRRB task) in the aforementioned fourcases with three considered bell positions around one handof the robot were collected three times. Therefore the wholedataset consisted of 2 × 4 × 3 × 3 = 72 training data.
For each robot arm, four degrees of freedom including
shoulder pitch, shoulder roll, elbow yaw, and elbow roll wereconsidered. The centers of gravity (x position and y positionof the colored area from an image) and the area ratios (can be
regarded as distance or depth) with respect to red, green, andblue area were extracted from an image captured by a camera(originally mounted on the robot) for visual information.
Both the vision and arm joint angle values in training data
were scaled between −0.8 and 0.8. An example of training
data for the BBBR task sequence collaboration with the blue
bell located in the bell position 1 on the robot’s right side isshown in Fig. 5. Note that we did not include any switchingamong situations or bell positions in each training data.
C. Parameter setting
MTRNN training was conducted offline using all collected
data. The number of the fast context, slow context, and PB
units were, respectively, NF = 100, NS = 10, and NP = 2. The
time constants for the fast and slow context units were τF = 2
and τS = 50. The parameters were optimized for 500,000
times.
D. Testing method
Three levels of adaptability were tested during one sharedtask sequence (BBBR task or RRRB task) collaboration
between a human and the robot. For (1) motion modification,different situations were considered by slightly changing bell
positions around one of the robot’s hands. The robot was
expected to adapt to such small scale changes by modifying
its arm joint trajectories according to the new position. For(2) action selection, different situations were considered bychanging bell positions between both of the robot’s hands.
The robot was expected to adapt to such middle scaleFig. 5.
An example of training data. Here, the BBBR task sequencecollaboration with the blue bell located in the bell position 1 on the robot’s
right side is shown. The top row shows the x, y positions and the colored area
ratios of the blue and red bells. Note that there are no situational changes
in training data. The middle row shows the corresponding information of
the green glove for the human hand use. The bottom row shows the arm
joint angles of both left and right arms of the robot.

changes around its arms by selecting the suitable arm for
performing the action. For (3) turn-taking, different situations
were considered by changing bell positions between thehuman and the robot. The robot was expected to adapt tosuch large scale changes between the agents by correctly
taking its own turn and acting on the bell.
IV. R ESULTS
We implemented the trained MTRNN in the NAO robot forcollaboration with the human in an actual environment, andtested the three levels of adaptability by changing the situations as described above. In both BBBR task and RRRB task
collaboration, the robot was able to reproduce learned behaviors for all learned situations. For the situational changes
among learned and unlearned cases with novel bell positions,the robot also successfully generated adequate behaviors
against situational changes through learned experience.
Figure 6 shows an example of the testing results for system
adaptability during the BBBR task sequence collaboration
in a dynamically changing environment with the human.
Here, three conditions were tested. The first condition tested
motion modification. The robot first hit the blue bell on its
right side three times and then the human hit the red bell
once. During this action generation, a third agent changed
the bell position on the robot’s side from the bell position
1 (R1 ) to 2 (R2 ), then to a novel position (R123 : the centerof the three learned positions). The second condition tested
action selection, by the third agent moving the bell from therobot’s right side to its left (L3 ). The third condition tested
turn taking, by the third agent switching the blue and red
bells between the robot and the human. In this case, therobot should wait for its turn before hitting the red bell.
Figure 7 (a) shows the bell positions (first panel), human
hand position (second panel), arm joint predictions of therobot (third panel), PB, slow context, and fast context activations (fourth, fifth, and sixth, respectively) during the
aforementioned BBBR task testing. In order to compare thedifference of the context activation with a different task
collaboration, the RRRB task collaboration under the sameenvironmental setting is shown in Fig. 7 (b). In the first
condition, with the slight changes of the bell position in
the robot’s vision, the motion (arm joint angle prediction)
was slightly modified. In the second condition, the robot
successfully adapted to repositioning of the bell positionchanging from the right side to the left side by correctly
selecting the left arm to perform the action. In the third
condition, the robot successfully took turns. After switching
the blue and red between the robot and human, the robot
waited for the ending of the human’s action of hitting bell
three times, then took its turn to hit on the bell in time.
As shown in Fig. 7 (a) and (b), when the robot generated
same or similar actions such as hitting a bell with the rightarm and hitting a bell with the left arm, similar patterns
can be observed in the fast context layer, whose activation
changes rapidly. In contrast, in the slow context layer, theactivation changes gradually. The activation for the sametask sequence collaboration under the different situations
is different. Furthermore, The activation for the different(BBBR and RRRB) task sequence collaboration under thesame environment setting is also different. Regarding theactivation of the PB units, it remains static throughout thetesting process. Changes in the slow context layer exhibit alonger period than those in the fast context layer. The slow
context seems to have the ability to count the number of bellhits during one BBBR or RRRB collaboration. Maintaining
the same value in PB units, which cannot be represented
in the other two context layers, is similar to the ability
to maintain the BBBR or RRRB task sequence during
collaboration in a dynamically changing environment.
In each condition tested above, the two information pathways of the system, namely, top-down task information represented by the PB and bottom-up environmental information
represented by the visual input, played an important role
for achieving different levels of adaptability during the task
collaboration. By receiving the environmental changes fromthe bottom-up pathway and the given task information fromthe top-down pathway, MTRNN can generate output againstchanges based on learned experience. In the first condition,
the robot’s motion (arm joint angle prediction) was slightly
modified by receiving the changes of the bell position around
one of the robot’s hands as visual input. In the second
condition, the robot’s action was selected by receiving thechange of the bell position (the left or right side of therobot). In the last condition, the turn-taking was realized byreceiving the changes of the bell position (the robot or thehuman side).
V. CONCLUSION
In this study, we applied a hierarchically organized neurodynamical system called MTRNN to achieve a human–robot
collaboration. The integration of motion modification, action
selection, and turn-taking was thus successfully achieved
within a single system thanks to its top-down and bottom-up
information pathways.
We trained MTRNN with all considered situations. In
future work, instead of using all situations in the training phase, we will attempt using only some situations forlearning, and the others for testing. In the testing phase,
we will expect the robot to generalize trained situations to
new untrained situations. In order to achieve more real task
collaboration, using color-based centers of gravity to detect
only object positions and human movements is not enoughbecause other visual information like the shape of the objects
is also important for object manipulation. Therefore, insteadof using color-based centers of gravity, we will consider
applying deep learning approach [16] for extracting visualfeatures from raw images.
R EFERENCES[1] G. Pezzulo and H. Dindo, “What should I do next? Using shared
representations to solve interaction problems,” Experimental Brain
Research, vol. 211, no. 3-4, pp. 613–630, 2011.
[2] N. Jarrasse, V. Sanguineti, and E. Burdet, “Slaves no longer: review
on role assignment for human-robot joint motor action,” Adaptive
Behavior, vol. 22, no. 1, pp. 70–82, 2013.
[3] G. Pezzulo, “Shared Representations as Coordination Tools for Interaction,” Review of Philosophy and Psychology, vol. 2, no. 2, pp.
303–333, 2011.
[4] M. Khansari-Zadeh and A. Billard, “Learning Stable Non-Linear
Dynamical Systems with Gaussian Mixture Models,” Transactions on
Robotics, vol. 27, no. 5, pp. 943—-957, 2011.
[5] G. J. Maeda, G. Neumann, M. Ewerton, R. Lioutikov, O. Kroemer,
and J. Peters, “Probabilistic movement primitives for coordination ofmultiple human-robot collaborative tasks,” Autonomous Robots, mar
2016.
[6] K. Hawkins, N. Vo, S. Bansal, and A. Bobick, “Probabilistic
Human Action Prediction and Wait-sensitive Planning for Responsive
Human-robot Collaboration,” International Conference on Humanoid
Robots, pp. 499 – 506, 2013.
[7] R. Lioutikov, O. Kroemer, G. Maeda, and J. Peters, “Learning manipulation by sequencing motor primitives with a Two-Armed robot,”
Advances in Intelligent Systems and Computing, vol. 302, pp. 1601–
1611, 2016.
[8] S. Calinon, P. Evrard, E. Gribovskaya, A. Billard, and A. Kheddar,“Learning collaborative manipulation tasks by demonstration using a
haptic interface,” International Conference on Advanced Robotics, pp.
1–6, 2009.
[9] W. Sheng, A. Thobbi, and Y. Gu, “An Integrated Framework for
Human-Robot Collaborative Manipulation.” IEEE transactions on
cybernetics, vol. 45, no. 10, pp. 2030–2041, 2014.
[10] H. Awano, T. Ogata, S. Nishide, T. Takahashi, K. Komatani, and
H. G. Okuno, “Human-robot cooperation in arrangement of objects
using confidence measure of neuro-dynamical system,” Conference
Proceedings - IEEE International Conference on Systems, Man andCybernetics, pp. 2533–2538, 2010.
[11] H. Chong, A. Tan, and G. Ng, “Integrated cognitive architectures: asurvey,” Artificial Intelligence Review, vol. 28, no. 2, pp. 103–130,
aug 2007.
[12] Y. Yamashita and J. Tani, “Emergence of functional hierarchy ina multiple timescale neural network model: A humanoid robot
experiment,” PLoS Computational Biology, vol. 4, no. 11, p.
e1000220, nov 2008.

BBBR task sequence	
Action selection	

Motion modification	
(1)	

(3)	

(2)	

Novel

	

(4)	

	

R2

	

	

X3
L3

R1

Turn taking	
(5)	

L3

	

	

R123	

Fig. 6. Robot arm actions in the BBBR task collaboration. Here, the BBBR task sequence collaboration under a dynamically changing environment wastested. The robot generated five different actions. (1) The robot hit the blue bell located in the position 1 (R1 ) using the right hand. (2) The robot hit theblue bell located in the position 2 (R2 ) using the right hand. (3) The robot hit the blue bell located in a novel position (R123 : the center of the positions
1, 2, and 3) using the right hand. (4) The robot hit the blue bell located in the bell position 3 (L3 ) using the left hand three times. (5) The robot hit the
red bell located in the bell position 3 (L3 ) using the left hand.
(1)!

(2)!

(3)!

Motion!
modification	

(4)!

(5)!

Action!
selection	

Turn!
taking	Human!
side	

(1)!

(4)!

(5)!

Motion!
modification	

(2)!

(3)!

Action!
selection	

Turn!
taking	

R1	
 R2	
 R123	L	
 L	 L	

Human!
side	

Robot!
side	

L	
R1	
 R2	
 R123	

L	

L	

L	

L	

(a)!

Robot!
side	

L	

L	

(b)!

Fig. 7. Time-series data of visual inputs, arm joint predictions, and context activations in BBBR and RRRB task sequence collaborations. The first andsecond panels show the bell positions (blue: x position of blue bell, red: x position of red bell) and the human hand position (green: y position of green
glove), respectively. The third panels show four (blue: right shoulder pitch, green: right elbow yaw, red: left shoulder pitch, and cyan: left elbow yaw) ofeight dimensional arm joint predictions. The bell positions are also illustrated between the second and third panels. The fourth, fifth, sixth panels show
PB (2 units), slow context (4 of 10 units), and fast context (4 of 100 units) activations, respectively. In both BBBR and RRRB task testing, the testing
positions of bells were same. In the first case, motion modification was tested. In the second case, action selection was tested. In the third case, turn taking
was tested.

[13] T. Yamada, S. Murata, H. Arie, and T. Ogata, “Attractor Representations of Language–behavior Structure in a Recurrent Neural Network
for Human–robot Interaction,” IEEE/RSJ International Conference onIntelligent Robots and Systems (IROS’15), vol. 10, no. July, pp. 4179–
4184, 2015.
[14] J. Tani, “Learning to generate articulated behavior through the bottomup and the top-down interaction processes,” Neural Networks, vol. 16,
no. 1, pp. 11–23, 2003.

[15] S. Murata, Y. Yamashita, H. Arie, T. Ogata, S. Sugano, and J. Tani,“Learning to Perceive the World as Probabilistic or Deterministic
via Interaction With Others: A Neuro-Robotics Experiment,” IEEE
Transactions on Neural Networks and Learning Systems, pp. 1–31,
2015.
[16] K. Noda, H. Arie, Y. Suga, and T. Ogata, “Multimodal integration
learning of robot behavior using deep neural networks,” Robotics andAutonomous Systems, vol. 62, no. 6, pp. 721–736, jun 2014.