2012 IEEE International Conference on Robotics and Automation
RiverCentre, Saint Paul, Minnesota, USA
May 14-18, 2012

Extraction of Latent Kinematic Relationships Between Human Users
and Assistive Robots
Jun Morimoto, Tomoyuki Noda and Sang-Ho Hyon
Abstract— In this study, we propose a control method formovement assistive robots using measured signals from humanusers. Some of the wearable assistive robots have mechanismsthat can be adjusted to human kinematics (e.g., adjustable link
length). However, since the human body has a complicated joint
structure, it is generally difficult to design an assistive robot
which mechanically well fits human users. We focus on thedevelopment of a control algorithm to generate corresponding
movements of wearable assistive robots to that of human users
even when the kinematic structures of the assistive robot and thehuman user are different. We first extract the latent kinematic
relationship between a human user and the assistive robot.
The extracted relationship is then used to control the assistive
robot by converting human behavior into the corresponding
joint angle trajectories of the robot. The proposed approach isevaluated by a simulated robot model and our newly developed
exoskeleton robot.

I. INTRODUCTION
Assistive robots for patients and elderly people are seen
as an important research topic in robotics; particularly
movement assisting devices that have a wide variety of
applications including rehabilitation. Therefore, developmentof movement assistive robots is becoming popular [1], [2],[3], [4], [5], [6], [7]. Hitherto, however, most of the works
have focused on the development of hardware devices, while
the software needed to control a movement assistive robot
has not been intensively studied.
A significant difference in the requirements for controllinga movement assistive robot as opposed to other types ofrobots is that the robot needs to interact continuously andphysically with humans. From a hardware development pointof view, preparing adjustable mechanisms that can adapt tothe size of the human user is important to coordinate properly
the physical interaction between the robot and the humanuser. However, since a human’s joint structure is complicated,
it is generally difficult to design an assistive robot whichmechanically well fits human users.
In this study, we propose a control method for movement
assistive robots using measured signals from the human user.
First, while the user is wearing the movement assistive robot,
J. Morimoto is with the Department of Brain Robot Interface, ATR
Computational Neuroscience Labs, 2-2-2 Hikaridai, Seikacho, Sorakugun,
Kyoto, JAPAN. xmorimo@atr.jp
T. Noda is with the Department of Brain Robot Interface, ATR Computational Neuroscience Labs, 2-2-2 Hikaridai, Seikacho, Sorakugun, Kyoto,
JAPAN. t noda@atr.jp
S. Hyon is with the Department of Brain Robot Interface, ATR
Computational Neuroscience Labs, 2-2-2 Hikaridai, Seikacho, Sorakugun, Kyoto, JAPAN, and with Faculty of Science and Engineering,
Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, Shiga, JAPAN.

gen@fc.ritsumei.ac.jp
978-1-4673-1404-6/12/$31.00 ©2012 IEEE

we simultaneously measure the joint angle trajectories of thehuman user and those of the robot. Next, we ascertain the
kinematic relationship between user and robot movements.
To extract the latent kinematic relationship, we use canonicalcorrelation analysis (CCA) [8]. Since the human body has acomplicated joint structure and cannot be tightly fixed to amovement assistive robot, finding the analytical kinematic
relationship is difficult. Therefore, we propose extracting
this relationship directly from the acquired data. However,a problem with finding the kinematic relationship is thatboth the human body and the movement assistive robot have
many degrees of freedom. Thus, the number of parameters
needed to represent the relationship between such systems
with high-degrees of freedom can be large. On the other
hand, human joint movements can be highly correlated(synergistic [9]) for a particular behavior. In this case, theestimated parameters may be overfitted for the acquired
data and the generalization performance of the extracted
relationship would be significantly worse. To cope withthis overfitting problem, we propose using an ARD (autorelevance determination) approach [10]. More specifically,
we use variational Bayesian canonical correlation analysis(VB-CCA) [11]. In this framework, we can select the correct
number of dimensions to describe the relationship between
a human user and the movement assistive robot from theacquired data.
In addition to finding the kinematic relationship, we propose using an electromyography (EMG) signal to control the
movement assistive robot through the extracted kinematic
relationship. The EMG signal can be used as a feedforward
signal to control the movement assistive robot, while agoniometer attached to the human body is used for feedback
control.
We evaluate how the combined system can be used to control a movement assistive robot using a simulated assistive
robot model together with our newly develop exoskeleton
robot (ATR eXoskeleton Robot, or XoR for short) (see also
Fig. 1)[12].
II. E XTRACTION OF L ATENT K INEMATIC
R ELATIONSHIPSIn this section, we introduce a method to extract the latentkinematic relationship through finding a shared state space
between a human user and an assistive robot (see also Fig.
2). To extract the kinematic relationship, we apply canonicalcorrelation analysis (CCA) to the simultaneously acquired
movement data from the human user and the assistive robot.
Throughout this paper, we define that the vector x denotes3909the projections, the optimization problem can be rewrittenas:max wxT Σxy wy(2)wx ,wywxT Σxx wx = 1,

subject towyT Σyy wy = 1.

This problem can be solved by finding eigenvectors for ageneralized eigenvalue problem






wx
Σxx 0
wx
0
Σxy
.
=ρ
wy
0
Σyy
Σyx 0
wy
(3)
B. Variational CCA
Fig. 1. Our newly developed eXoskeleton Robot (XoR)[12]. Height: 1.5
m, Weight: 30 kg. XoR has ten degrees of freedom and six active joints.
Each active joint uses a hybrid actuator composed of air muscle and anelectric motor. XoR is designed to assist lower-limb movements in humans.

The probabilistic model of CCA was proposed in [13].
This model assumes that the two observed random vectors
x and y are generated from the same latent vector z:

Wx z + η x
Wy z + η y ,

(4)
(5)

P (z)
P (η x )= N (z|0, Im ),= N (η x |0, Σx ),

(6)
(7)

P (η y )= N (η y |0, Σy ).

(8)

x =
y =
where z ∈ Z ⊂ Rm andFig. 2. Extracting the latent kinematic relationship through finding theshared state space between a human user and an assistive robot.

the state of the human user and the vector y denotes the stateof the assistive robot.
A. Canonical Correlation Analysis (CCA)
Here, we briefly introduce canonical correlation analysis(CCA) [8], which can be used to extract the latent relationship between two random vectors.
We consider two random vectors x and y, where the statevector of one observation is denoted by x ∈ X ⊂ R dx
and the state vector of the other observation is denoted byy ∈ Y ⊂ Rdy . CCA derives directions wx and wy suchthat the correlation between two projected random variables
wx x and wy y is maximized.
Thus, CCA can be formulated as an optimization problem
in which the objective function is defined as
wxT Σxy wy
ρ = max .
wx ,wywxT Σxx wx wyT Σyy wy(1)where ρ is the correlation between projected values of bothobservations on canonical vectors, and Σ is the covariance.
Since the solution of (1) is not affected by any rescaling of

Im is an m-dimensional identity matrix, Σ x and Σy arecovariance matrices.
We generally do not know how many latent variables, i.e.,
the number of elements m in the latent vector z, are involvedin explaining the two observed random vectors. The easiest
way to determine the number of canonical correlations is
simply to use the same number of dimensions as that ofan observed vector with a smaller number of elements.
However, if the true number of canonical correlations issmaller than the assumed number of dimensions, the standard
CCA model can be overfitted for a particular set of sample
data.
On the other hand, using this probabilistic CCA model, we
can introduce a sparse prior to the model so that the number of canonical correlations can be automatically selected
through a hierarchical Bayesian framework. This corresponds
to ARD. To do this, we use the variational CCA proposed in[11]. Figure 3 shows a graphical model of the probabilistic
CCA with a hierarchical Bayesian framework.
The joint distribution of the probabilistic CCA can begiven as (see Fig. 3)
P (x, y, z, Θ)=P (x|z, Wx , Σx )P (y|z, Wy , Σy )P (z)P (Θ),(9)
where the joint distribution of the parameters is:
P (Θ)=P (Wx |αx )P (Wy |αy )P (αx )P (αy )P (Σx )P (Σy ).
(10)

3910

and the selected distribution Q(z, Θ) as
KL(Q||P ) = ln P (x, y) − L(Q),(19)

where the KL divergence is defined as
P (z, Θ|x, z)dzdΘ.
KL(Q||P ) = − Q(z, Θ) ln
Q(z, Θ)Fig. 3. Probabilistic CCA model with a hierarchical Bayesian framework.
The shading of variables x and y implies that these variables can beobserved (see also [14]). The rectangle labeled with N indicates that there
are N observations. z is the latent variable. Wx and Wy are weightmatrices. Σx and Σy are covariances of the random vectors x and y,
respectively. αx and αy determine the covariance of the weight matrices.

We use the conjugate priors as the prior distribution of theparameters:
P (Wx |αx )

=

dx


N (wxj |0, (diag{αx })−1 ), (11)(20)

Since the marginal log likelihood is only determined by theobserved data (x and y) and is not a function of distribution
Q, maximizing the lower bound L(Q) corresponds to minimizing the KL divergence between the true posterior anddistribution Q. Thus, if we can find an analytically tractable
distribution Q such that we can maximize the lower bound
L(Q), the true posterior P (z, Θ|x, y) can be efficiently
approximated by distribution Q. To do this, we use thefactorized distribution,
Q(z, Θ)=Q(z)Q(Wx )Q(Wy )Q(αx )Q(αy )Q(Σx )Q(Σy ).
(21)
By maximizing the lower bound L(Q), distribution Q canbe derived as follows:jQ(z) = Cz exp ln P (x, y, z, Θ)Q(Θ) ,dy

P (Wy |αx )

=



j
m


N (wyj |0, (diag{αy })−1 ), (12)Γ(αix |a0 , b0i ),(13)

Γ(αiy |a0 , b0i ),(14)

P (Σx )

= W(Σx |K0x , νx0 ),(15)

P (Σy )

= W(Σy |K0y , νy0 ),(16)

P (αx )=i

P (αy )=m

Q(Θi ) = CΘi exp ln P (x, y, z, Θ)Q(z)Q(Θk=i ) ,(23)where Cz and CΘi are normalization constants. The brackets< · >Q represent the expectation with respect to distribution
Q. By considering (4)-(23), we find the factorized distribution Q as follows:iwhere Γ is the Gamma distribution and W is the Wishart
distribution (see [14] for more details). The hyper parameterthat controls the sparseness of the weight vector is represented by α = (α1 , . . . , αm ).
Since integrations to derive the marginal distribution,P (x, y) = P (x, y, z, Θ)dzdΘ,(17)
are analytically intractable, we consider a variational approximation to the true posterior distribution by introducing the
distribution Q(z, Θ). The lower bound of the log marginal
distribution is calculated as follows:
ln P (x, y) = ln P (x, y, z, Θ)dzdΘ
P (x, y, z, Θ)dzdΘ
= ln Q(z, Θ)Q(z, Θ)P (x, y, z, Θ)≥Q(z, Θ) lndzdΘ
Q(z, Θ)= L(Q).
(18)(22)

Q(z) =Q(wxj ) =N (z|µz , Σz ),N (wxj |µjwx , Σjwx ),(24)
j = 1 . . . dx , (25)Q(wyj ) =N (wyj |µjwy , Σjwy ),j = 1 . . . dy , (26)Q(αix )Q(αiy )

Γ(αix |ax , bix ),Γ(αiy |ay , biy ),=i = 1 . . . m,

(27)

i = 1 . . . m,=Q(Σx ) =W(Σx |Kx , νx ),

(28)
(29)

Q(Σy ) =W(Σy |Ky , νy ).

(30)

Then, the update rules for each parameter of the factorized
distribution are given as:



−1
,
(31)
Σz = I + WxT Σx Wx + WyT Σy Wyµkz =Σz xTk Σx  Wx  + ykT Σy  Wy 

3911

,

(32)

k=1, . . . , N, where N denotes the number of samples,νx =νx + N,(33)
νy =νy + N,
Kx =K0x +Ky =K0y +

(34)
N


(xk − Wzk )(xk − Wzk )T

k=1
N


T

(yk − Wzk )(yk − Wzk )k=1

We find that the difference between the log marginal distribution and the lower bound L(Q) can be represented by the
Kullback-Leibler (KL) divergence between the true posteriorTΣjwx =Ndiag < αx > +zk zTk Σj,j
x )
k=1



,

(35)



,

(36)

−1

,

(37)

1

1
2

2

2
2

1.5
3

1.5
3

1
4

1
4

0.5
5

0.5
5

0
6

0
6

−0.5
7

−0.5
7

−1
8

−1
8

−1.5
9

−1.5
9

−2
10

−2
10

1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

Fig. 4. Illustrative example: (left) standard CCA, (right) variational CCA.
In the right figure, sparse projection matrix can be observed.

Σjwy =

−1
N

 j,j

T
diag < αy > +,zk zk Σy )

(38)

k=1

T

dx
N







T
T
, (39)µjwx =Σwx xTk Σjx zk  − zk zTk
wxl Σl,j
x
k=1

l=j

T

dy
N
 





T
T
,(40)µjwy =Σwy ykT Σjy zk  − zk zTk
wyl Σl,jy
k=1

Fig. 5. Simplified simulation models for (left) an exoskeleton robot and(right) a human user. The exoskeleton robot model is composed of threelinks with one slider joint (le ) and two revolve (rotational) joints (θ1e , θ2e ).
The human user model is composed of four links with three revolve joints(θ1s , θ2s , θ3s ).

l=j

dx
ax =a0 +,2dy,ay =a0 +2 i 2||Wx ||
bix =b0i +, 2i 2||Wy ||
biy =b0i +
,
2

(41)

(42)
(43)
(44)

where Σj,j denotes the j-th diagonal element of matrix Σ,Σl,j denotes (l, j) element of matrix Σ, Σ j denotes the j-thcolumn vector of matrix Σ and W i denotes the i-th column
vector of matrix W.
C. Illustrative example
In this section we present an illustrative example of how
CCA and variational CCA work. We consider two observation vectors x ∈ R8 and y ∈ R10 , which are assumed to begenerated from latent vector z ∈ R 3 .
We randomly generated the latent vector z from the normal
distribution in (6). Σ x and Σy in (7) and (8), respectively,
are unit covariance matrix. Each element of the projection
matrices Wx and Wy is also generated from the normal
distribution N (0, 1).
By simply using CCA, we estimate the projection matrices
Wx and Wy as shown in Fig. 4 (left). On the other hand,using variational CCA and as a result of ARD, we can findthe sparse projection matrices as shown in Fig. 4 (right).
III. J OINT ANGLE PREDICTION USING EMG
So far we have focused on the problem of finding thelatent kinematic relationship between the human user andthe assistive robot. In this section, we consider the control
problem that uses the derived kinematic relationship.

As introduced in the previous section, we can find thestate of the assistive robot that corresponds to the state of
the human user through the derived shared state space. Thus,
we can use the corresponding state of the assistive robot as
the desired joint angles and angular velocities to control therobot using a proportional-derivative (PD) controller.
Generally, we need to use higher gains to achieve smaller
tracking errors. However, it is not preferable to use very highgains for the PD controller since a human must wear theassistive robot. To reduce the tracking errors without using
very high gain feedback, we can use predicted desired joint
angles θ and angular velocities θ̇ as the feedforward control
signal. Moreover, the predicted desired joint trajectory isnecessary to assist human behaviors since the robot can startmoving a bit earlier than initiation of a human behavior.
To generate the predicted desired joint angles and angularvelocities, we use the EMG signals of human users [15],[16]. In this study, we use a linear prediction model:x(k + 1) = Ax(k) + Bu(k),(45)
where x = θ, θ̇ and u = (EM G1 , EM G2 , ..., EM Gn ).
Parameters A and B can be derived from the simultaneously
measured joint angles θ, angular velocities θ̇, and EMG data.
Using the linear model is a popular approach for movement
reconstruction (e.g., [17], [18]), and we also empiricallyfind that the linear model is sufficient to reconstruct the
movements considered in this study.
IV. S IMULATION
Here, we consider an assistive robot model, depicted inFig. 5(left) and, a simplified human user model, depicted inFig. 5(right). As shown in Fig. 5, these two models havedifferent kinematic properties. The assistive robot model iscomposed of three links with one slider joint (l e ) and two
revolve (rotational) joints (θ 1e , θ2e ). The human user model iscomposed of four links with three revolve joints (θ 1s , θ2s , θ3s ).

3912

1.5

0.5
0
−0.5
−1
0

Training
Test

0.8
Vertical [m]Horizontal [m]1

Training
Test

1

1Time [s]

1.5

0.6
0.4

0
0

2

0.5

1
Time [s]1.5

ActualEstimated

rad

0.6
0.4

2

2

1

1

0

rad

1
0.8

−1

0.2

ActualEstimated

−2
0
0

0.5

1
Time [s]

1.5

2

0

0
−1

0.5

1
Time [s]1.5

ActualEstimated

−2
2

0

0.5

1
Time [s]1.5

2Fig. 8. Reconstructed joint trajectories (le , θ1e , θ2e ). Estimated trajectories
are almost same as actual.

V. F INDING S HARED S TATE S PACE USING E XOSKELETON
ROBOT

0.2
0.5

be derived analytically from knowledge of the parametersof kinematics models. The plots in Fig. 8 show that theestimated trajectories are almost same as the actual. This
results indicate that the latent kinematic relationship is correctly estimated.

m

In this simulation, we attempt to find the latent kinematic
relationship between the human user and assistive robot
models using variational CCA.
We assume that the user’s feet are attached to the feetof the assistive robot and that the user takes the saddle. In
other words, foot and hip positions are the same for thetwo models. We consider the sinusoidal movements of thehorizontal hip position as shown in Fig. 6.
As depicted in Fig. 5, the state of the assistive robot is y =(le , θ2e , θ3e ) and that of the human user is x = (θ 1s , θ2s , θ3s ).
In this simulation study, we purely focus on the kinematic
relationship and only consider joint angles.
Figure 7 shows the trajectories of the states of the humanuser and the robot as the hip position moves horizontally.

2

Fig. 6. (left) Horizontal and (right) vertical trajectories of hip positions
for training data and test data.

In this section, we consider using our newly developed
exoskeleton assistive robot XoR. XoR is designed to assist
lower-limb movements of humans. XoR has ten degrees of
freedom and six active joints. Each active joint use a hybrid
actuator composed of air muscle and electric motor. By using
the hybrid actuator, we can develop a light weight robot withhigh power actuation [12], [19], [20].
A. Finding shared state space

3.5

4

3

le
θe1

3.5

2.5

θe2

3

1

2

1

0

0.5

−0.5

Fig. 7.
models.

θs3

1.5

0.5

−1
0

θs2

2.5

1.5

[rad]

[m/rad]

2

θs1

0
0.5

1
Time [s]

1.5

2

−0.5
0

0.5

1
Time [s]1.5

2Joint trajectories of (left) exoskeleton and (right) human user

We extract the latent kinematic relationship through finding the shared state space using variational CCA. In thissimulation, by using the ARD property of variational CCA,
we found a two-dimensional latent space with fewer dimensions than the state space of the human user or that of theassistive robot. Moreover, the variational CCA captures thenumber of dimension of the operational 2-D space only fromthe acquired data.
In the variational CCA model, we derive distributions ofweight matrices Wx and Wy , for generating the user state
x and the robot state y, respectively, from the latent state z.
Here we consider using mean matrices of the distirubutions
TW̄x and W̄y , where W̄ = µ1 , µ2 , . . . , µd . The row
vectors of the mean matrices are derived in (39) and (40).
Simultaneously, we can derive the pseudo inverse of themean weight matrix W̄x+ . Thus, we can derive the state of
the assistive robot model y from the human user state x as
y = W̄y W̄x+ x.

First, a human subject rides on the assistive robot andgenerates squat movements. We measure the joint angles
and angular velocities of the human subject and the assistive robot simultaneously using encoders on the robot andgoniometers attached to the human subject.
The state of the human subject x = (θ 1s , θ2s , θ3s ) is the sameas that depicted in Fig. 5(right). The state of the assistive
robot XoR y = (θ1e , θ2e , θ3e ) is illustrated in Fig. 9. Note that
this kinematics model is different from the model presented
in Fig. 5(left. Figure 10 shows the squat movement of theexoskeleton robot XoR. Having found the shared state space
between the human subject and the assistive robot, we derive
the corresponding state of the assistive robot to the humansubject state using (46).
B. Predicting state of human subject using EMG signals
As discussed in Section III, we predict the future stateof the human subject using EMG signals. We measured(46)

In Fig. 8, we compare the estimated trajectory of therobot model using (46) with the actual trajectory that can

Fig. 9. Simulation model of our newly developed exoskeleton robot XoR.

3913

Simultaneous acquisition of joint angle data for the exoskeleton robot XoR and the human user.

Fig. 11.

Generated squat movement of the exoskeleton robot model.

0.5
[mV]

In Fig. 13, we evaluated the tracking errors between theactual movement of the robot and the simulated movement of
the robot model. The mean-squared error, when applying thepredicted desired state generated by EMG, was 1.8×10 −3. If
we simply used the current joint angles and angular velocitiesof the human subject, the mean-squared error was 2.1. These
results show the benefit of using the predicted desired statesof human users to control assistive robots.

0
0

2

4

6

8

10

6

8

10

6

8

10

Time [s]
[mV]

0.5
0
0

2

4
Time [s]

[mV]

0.5
0
0

2

4
Time [s]

0
0

2

4

6

8

Hip Joint [rad]

[mV]

0.5

10

Time [s]

0.6

0.6

0.5

0.5

0.4

0.4
Hip Joint [rad]Fig. 10.

0.3
0.2
0.1

−0.1
0

0.2
0.1

0

Fig. 12. EMG signals. Each plot, from top to bottom, shows EMG signalof Quadriceps femoris, Tensor fasciae latate, Gluteus medius, and Tibialis
anterior, respectively.

0.3

0ActualEstimated
2

4Time [s]

6

8

−0.1
0

ActualEstimated
2

4Time [s]68Fig. 13. Comparison of tracking errors at hip joints: (left) with EMG,
(right) without EMG.

activity in four muscles (Quadriceps femoris, Tensor fasciae
latate, Gluteus medius, and Tibialis anterior) (see Fig. 12) topredict the joint angles and angular velocities as in (45). The
measured EMG signals were rectified and low-pass filteredwith 10 Hz cut-off. The input to the linear system in (45)is u = (EM G1 , EM G2 , EM G3 , EM G4 ). The predictedstate is used as the desired input to the PD controller:τi = Kp (θid − θis ) + Kd (θ̇id − θ̇is ),(47)

where τi is the torque output and θ id is the predicted state
for the i-th joint. K p = 1000 and Kd = 100 are the servo
gains.
C. Application to simulated exoskeleton robot model
To evaluate the proposed approach, we applied this control
scheme to the simulated XoR model. We used a dynamical
model for the assistive robot.

VI. CONCLUSIONSIn this study, we extracted the latent kinematic relationships between human users and assistive robots. Using
the extracted relationship, we can efficiently transfer the
movement intention of a human user to the assistive robot
through the derived kinematic relationship.
We evaluated the proposed approach in a simulated environment. We also found the kinematic relationship between ahuman subject and the newly developed exoskeleton assistive
robot XoR. The measured EMG and the extracted kinematic
relationship were used to control the simulated XoR model.
Then, we showed that we were able to control the XoR
model by using the latent kinematic relationship and the
EMG signal. We used the simple linear model to predict
joint angles and angular velocities from EMG data. To cope3914

with wider variety of movements, we may need to use anonlinear model [21]. We empirically figured out that the
selected four muscles were useful for the prediction. As anext step, we will consider to develop an automatic muscle
selection method.
As future studies, we combine the proposed frameworkwith the pattern-generator-based biped locomotion controller [22] to support biped walking movements.
ACKNOWLEDGMENTS
This research is the result of ”Brain Machine Interface
Development” carried out under the Strategic Research Program for Brain Sciences by the Ministry of Education,
Culture, Sports, Science and Technology of Japan. This work
was partially supported by Grant-in-Aid for Scientific Research on Innovative Areas: Prediction and Decision Making
23120004.

[18] P. K. Artemiadis and K. J. Kyrakopoulos, “EMG-Based COntrol of a
Robot Arm Using Low-Dimensional Embeddings,” IEEE Transactions
on Robotics, vol. 26, no. 2, pp. 393–398, 2010.
[19] H. Hisa, Y. Tanaka, and S. Minimisawa, “Rotation Type of Electricand Pneumatic Hybrid Actuator,” in Nihon Kikai Gakkai Nenji Taikai
Koen Ronbunshu (in Japanese), 2007, pp. 311–312.
[20] I. Sardellitti, J. Park, D. Shin, and O. Khatib, “Air muscle controller
design in the distributed macro-mini (DM2) actuation approach,” inIEEE/RSJ International Conference on Intelligent Robots and Systems,
2007, pp. 1822–1827.
[21] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for
Machine Learning. Cambridge, MA: The MIT Press, 2006.
[22] J. Morimoto, G. Endo, J. Nakanish, and G. Cheng, “A Biologically
Inspired Biped Locomotion Strategy for Humanoid Robots: Modulation of Sinusoidal Patterns by a Coupled Oscillator Model,” IEEE
Transaction on Robotics, vol. 24, no. 1, 2007.

R EFERENCES[1] S. Jacobsen, “On the Development of XOS, a Powerful Exoskeletal
Robot,” in 2007 IEEE/RSJ International Conference on Intelligent
Robots and Systems, Plenary Talk, 2007.
[2] H. Kazerooni and A. C. nad R. Steger, “That Which Does Not
Stabilize, Will Only Make Us Stronger,” International Journal of
Robotics Research, vol. 26, no. 1, pp. 75–89, 2007.
[3] K. Suzuki, M. G. Kawamoto, H. Hasegarwa, and Y. Sankai, “Intensionbased walking support for paraplegia patients with Robot Suit HAL,”
Advanced Robotics, vol. 21, no. 12, pp. 1441–1469, 2007.
[4] S. K. Au, P. Dilworth, and H. Herr, “An ankle-foot emulation system
for the study of human walking biomechanics,” in IEEE International
Conference on Robotics and Automation, 2006, pp. 2939–2945.
[5] H. Kobayashi, A. Takamitsu, and T. Hashimoto, “Muscle Suit Development and Factory Application,” International Journal of Automation
Technology, vol. 3, no. 6, pp. 709–715, 2009.
[6] G. Yamamoto and S. Toyama, “Development of Wearable-Agri-RobotMechanism for Agricultural Work,” in IEEE/RSJ International Conference on Intelligent Robots and System, 2009, pp. 5801–5806.
[7] T. Kagawa and Y. Uno, “Gait pattern generation for a power-assist
device of paraplegic gait,” in The 18th IEEE International Symposium
on Robot and Human Interactive Communication, 2009, pp. 633–638.
[8] H. Hotelling, “Relations between two sets of variates,” Biometrika,
vol. 28, pp. 321–377, 1936.
[9] N. A. Bernstein, On Dexterity and Its Development.
New York:
Psychology Press, 1996.
[10] R. M. Neal, “Bayesian Learning for Neural Networks,” in Lecture
Notes in Statistics 118. New York: Springer, 1996.
[11] C. Wang, “Variational Bayesian Approach to Canonical Correlation
Analysis,” IEEE Transaction on Neural Networks, vol. 18, no. 3, pp.
905–910, 2007.
[12] S. Hyon, J. Morimoto, T. Matsubara, T. Noda, and M. Kawato, “XoR:
Hybrid Drive Exoskeleton Robot That Can Balance,” in IEEE/RSJ
International Conference on Intelligent Robots and Systems, 2011.
[13] F. R. Bach and M. I. Jordan, “A probabilistic interppretation of
canonical correlation analysis,” Technical Report of the Departmentof Statistics, University of California, Berkeley, Tech. Rep., 2005.
[14] C. M. Bishop, Pattern Recognition and Machine Learning. NY, USA:
Springer, 2006.
[15] Y. Koike and M. Kawato, “Estimation of dynamic joint torques andtrajectory formation from surface electromyography signals using aneural network model,” Biological Cybernetics, vol. 73, no. 4, pp.
291–300, 1995.
[16] P. Artemiadis and K. Kyriakopoulos, “EMG-based teleoperation of arobot arm in planar catching movements using ARMAX model andtrajectory monitoring techniques,” in IEEE International Conferenceon Robotics and Automation, 2006, pp. 3244–3249.
[17] T. Kitamura, N. Tsujiuchi, and T. Koizumi, “Hand motion estimation
by EMG signals using linear multiple regression models,” in International Conference of IEEE Engineering in Medicine and Biology
Society, 2006, pp. 1339–1342.

3915