Estimation of Structure and Physical Relations among Multi-modal
Sensor Variables for Musculoskeletal Robotic Arm
Kentaro Harada1 and Yuichi Kobayashi2
Abstract— Autonomous robots that work in the same environment as humans must operate safely and adapt to handle
various tools and deal with partial malfunctions. We propose
an approach for estimating the robot structure and apply
this approach for building a controller of dynamic motions.
The robot structure is estimated by evaluating the mutual
information (MI) among the sensor variables. Variables withhigh values of MI are edge-connected and the controller is
automatically constructed based on the estimated structure.
The proposed approach can accommodate changes in the robot
parameters and dynamic motions. We verify the proposed
method by using a simulator of a musculoskeletal arm driventhat is driven by artificial muscle for mechanical safety.

I. I NTRODUCTION
Autonomous robots ysed for housework and nursing carehave been attracting much attention. It is preferred thatthose robots have mechanical safety for surroundings andadaptivity to handle various tools and to overcome their
partial malfunctions. For mechanical safety, soft material(e.g., [1]) and elastic actuators (e.g., [2], [3], [4]) have beendeveloped, and many attempts have been made to enhance
the robots’ ability to adapt to changes of robot environmentand robot body itself.
Machine learning by approximating the robot dynamics
has been applied to control the robot arm (e.g., [5], [6]).
These approaches enable robots to adapt to unknown dynamics. However, one shortcoming of this approaches is thatthe robots cannot effectively adapt to partial changes such as
tool use and malfunction, because the learning process has
to restart from scratch. Thus, learning will be more effective
if the robots can utilize information about property of thesystem that is valid even though dynamics is changed.
From the perspective of learning unknown tools, several approaches have been proposed [7], [8], [9]. These
approaches realize acquisition of tool properties based on
robots observation and experience, but regard tool attachments as a factor that is not a part of the learning. If alearning model includes tool attachment and desorption, it
will be more generally applicable and will not require humanintervention.
Understanding the structure of a robot is an importantbuilding block for realizing a seamless learning frameworkthat is adaptive for both of tool use and partial malfunction.
1

andKentaro Harada, Graduate school of integrated
technology,
Shizuoka
University,
Hamamatsu,

scienceJapan

harada.kentaro.16@shizuoka.ac.jp
2
Yuichi
Kobayashi,
gineering,
Shizuoka

Department
University,ofMechanical
EnHamamatsu,
Japankobayashi.yuichi@shizuoka.ac.jpଶଶ, 

ସ

ଵ



ଶ

ଷ
ଵ



Fig. 1. A model of a musculoskeletal arm.

Fig. 2.

ଵ
Variables of arm robot

Simultaneous motion of a robot and an object was used tobuild a chain of controllable parts in the robot in [10]. This
realizes a unified method for motion generation to avoid
obstacles, push objects, and use tools. Furthermore, learningof the kinematic structure of a robot arm using a Bayesian
network was proposed in [11]. It has been shown that thesystem can adapt to the lack of observations and observationnoise. However, a common shortcoming of these approaches[10], [11] is that they only deal with kinematic relations
among observed variables and hence their application isrestricted to quasi-static motion.
In this study, we present an approach for understanding
the robot structure and for building controller for dynamic
motion of robot. In the proposed approach, the relations
among sensor variables are evaluated using mutual information (MI). The relations between sensor variables with highMI are approximated using observation. These relations areused for building the controller based on a chain-construction
algorithm.
We consider the musculoskeletal arm robot shown in
Fig. 1. The artificial muscle is for the safe of the robot
because of its elasticity. We verify the proposed method inapplications to tendon-driven musculoskeletal arm to show
its applicability.
II. P ROBLEM D EFINITION
A. Structure of the arm robot
We discuss the control of the musculoskeletal arm robot
shown in Fig. 1. This robot arm has two joints with threelinks and the base link is fixed. Each of the two joints
is actuated by two artificial muscles. The coiled polymer
actuator (CPA) [4] is the model of the artificial muscle andthe latter responds to heat by contracting. This actuator isgenerally heated by passing electrical current through wires.

TABLE I

Structure Estimatorଵ  ୲ୟ୰୥ୣ୲ேSENSOR VARIABLESθ̇ [rad/s]

d1 ∈ R2

τ [N/m]d7 ∈ R2ẋ [m/s]d2 ∈ R2

L̇ [m/s]

d8 ∈ R4

θ [rad]d3 ∈ RL [m]d9 ∈ Rx [m]d4 ∈ RL̈ [m/s ]d10 ∈ R4θ̈ [rad/s2 ]d5 ∈ R2F [N]d11 ∈ R4ẍ [m/s2 ]d6 ∈ R2

T [◦ C]d12 ∈ R4

2
2

2

ଶ

4

ହ
ସ  

ଷ
Evaluator

ଵ , … , ଵଶ 

However, in this case, we use the temperature of muscles tocontrol the robot for simplicity.
The sensor variables are listed in TABLE. I. x, θ, L,
τ , F and T denote the position of the end-effector, theangle of each joint, the muscular length, the torque appliedat the joints and muscular force, and the temperature ofeach muscle, respectively. Noise is not added on each sensor
variable. These sensors are configured redundantly assumingthat the robot is designed for robustness. The arrangementof the variables on the robot arm is shown in Fig. 2.
It is assumed that the physical meaning of each sensor
variable is unknown to the robot except for the timederivative information among the same sensor values (e.g.,
relations among θ, θ̇, and θ̈). This implies that the mechanical structure of the robot is also unknown. Additionally,
the parameters related to the dynamics of the robot arm are
unknown. Therefore, each sensor variable, which is writtensuch as x, θ, is treated as vectors d1 , d2 . The control inputof the robot system is known (in this case, µ = d12 = T ).
d1 = θ̇ and d3 = θ are also known as the state variables.
The robot system aims to generate a controller that realizes adesired value of the end-effector position dtarget = d4 = x.
Thus, the task for the robot is to achieve dd4 = ddes .
B. Robot arm dynamics
The dynamics of the robot arm is described as follows:
M (θ)θ̈ + C(θ, θ̇) + g(θ) = τ ,Controller(1)

where M (θ) and C(θ, θ̇) denote the inertia matrix and amatrix including the centrifugal force, Coriolis force andfriction, respectively. The gravity term g(θ) is zero because
the motion of the robot arm is assumed in the horizontal
plane.
The relation between the control input µ = ∆T and torqueτ is described as follows:
F =A∆T + K∆L + C L̇(2)

τ =GT (θ)F ,(3)

where A=diag(a1 , . . . , a4 )[N/℃], K=
diag(k1 , . . . , k4 )[N/m], C = diag(c1 , . . . , c4 )[N/m·s],∆T [℃] and ∆L[m] denote the thermal, elastic, anddamping constants, the temperature change, and thedisplacement of muscular length from ordinary length,
respectively. G(θ) Is the Jacobian matrix that shows theFig. 3.


Robot

Overview of the operation

relation between muscle length and joint angle defined asfollows:
L̇ = G(θ)θ̇, G(θ) ∈ R4×2 .
(4)The arm is actuated by the muscular temperature ∆T . The
CPA will be torn off if it is excessively heated; therefore,∆Ti , i = 1, · · · , 4 is constrained so that T i does not exceed
the maximum temperature, which is 200 ◦ C in this case.
III. L EARNING C ONTROL I NCLUDING S TRUCTURE
E STIMATIONA. Overview of the structure estimation and control
To achieve the reaching action under the condition of
unknown structure, we propose an automatic construction ofa controller based on identifying the dependency among thevariables. The overview of the proposed process is shown in
Fig. 3.
First, the robot collects data from the sensor variables
by moving randomly. The structure is estimated from thecollected samples using the MI and a path-finding method.
A controller is generated based on the estimated structure.
The position control starts after the controller is generated.
The generated controller is evaluated and updated online
using the collected samples of the sensor variables. If thecontroller does not achieve the target, it is abandoned and a
new controller is generated.
B. Least squares mutual information
Mutual Information (MI) is a measurement of the dependency among pairs of random variables which provides
estimates of the decreasing randomness of a variable byobserving another variable. Different types of MI are definedby [12]. In this study, an approximate value of the squaredloss MI (SMI) by least squares MI (LSMI) [13] is usedbecause SMI has moderate sensibility for dependency anddoes not require adjustable parameters. The definition of SMI
I(x, y) between two random variables x and y is given asଵ  ୲ୟ୰୥ୣ୲

∫∫I(x, y) =p(x)p(y)(r(x, y) − 1)2 dxdyp(x, y)r(x, y) =,p(x)p(y)ଶ(7)I(x, y) =0 ⇔ p(x, y) = p(x)p(y).

(8)

A high SMI suggests that the data in the pairs are highly
dependent.
LSMI calculates an approximate value of SMI by estimating the probability density ratio r(x, y) of (5) which isdifficult to calculate directly. The probability density ratio ismodeled as follows:(9)

where α denotes the optional parameter vector and ϕ denotes
the non-negative basis function vector: α and ϕ have thesame dimensions as sample number of x, y, and ϕ is definedby the cross variation of the candidates. LSMI retrives αaccording to:
(10)
(11)

i,i =11∑
T
ϕ(x, y) ,
d i=1

ହ

High

଺
Cost: ∞

ଶହRe-explore(6)

I(x, y)≧0α̃LSMI =argmin(αT Hα − 2αT h + λαT α)
α
d
∑
1
T
H= 2
ϕ(x, y)ϕ(x, y)d ′Highest costin ሺଵሻ

(5)where I(x, y) denotes the MI between x and y. p(x, y)and p(x)p(y) denote the joint probability density function
and marginal probability density functions of x and y,
respectively. r(x, y) is the probability density ratio. The
characteristic of SMI is described as follows:rα (x, y) = αT ϕ(x, y),ଵ  ୲ୟ୰୥ୣ୲

଺

Cost

follows :ଷସ  

ଷସ  
Low

Chain1:  ሺଵሻ  1,5,2,4 ୘(Failed to control)

Chain2:  ሺଶሻ  1,6,5,2,4 ୘(New chain)

Fig. 4. Example of the resultant dependency graph. Derivative relations
and chain are expressed by broken lines and arrows.

minimum cost path problem [14].
For constructing the controller, Dijkstra’s algorithm is used
to find a chain with large dependencies among the sensor
variables. For this purpose, the dependency information isconverted to cost. Let ζa,b denote the cost between sensor
variables da and db . Costs are defined as follows:
if db is derivative of da0,
if db is integral of daζa,b = ∞,
.
(15)


1
, otherwise
I(da ,db )As described in section II, the relation between sensor
variables is assumed to be known when one variable is atime-the derivative of the other.
(j)
Let c(j) ∈ NP
denote a vector comprising indicesof sensor variables in the chain (j), where P (j) denotes
the number of the edges obtained by the above mentioned
method.
[]Tc(j) = c1 , c2 , . . . , cP
(16)

d

h=

(12)

where λ > 0 is the regularization parameter.
The general solution of (10) is described as follows:α̃LSMI = (H + λI)−1 h.

(13)Using the solution of (13), LSMI is approximated as follows:
˜ y) = α̃T h − 1.
I(x,
LSMI

(14)

If the LSMI value between sensor variables da and db ishigh, it may be possible to infer that da can be controlled
by manipulating the value of db or vice versa. Considering
the both possibilities, chains of controller are constructed as
described in the next section.
C. Structure estimation using LSMI and Dijkstra’s Algorithm
The structure of the robot system is estimated by evaluating dependencies of the sensor variables. The controller isconstructed as a “chain” starting from the derivative of thetarget variable ḋtarget and terminates at the control inputµ based on information of the dependencies. The chain
is obtained using Dijkstra’s algorithm based on the LSMI
values. Dijkstra’s algorithm is a method used solve the

The first and last element of c become the data number ofthe derivative of the target variable and control input: thus,
dc1 = ḋtarget , dcP = µ.
An example of the result is given in Fig. 4. Note that the
number of sensor variables in Fig. 4 is not corresponding to
TABLE I. The controller is generated from the chain by themethod described in III-D. If the generated controller fails
to converge the target variable dtarget to the desired value
ddes , another chain is explored by setting the cost of theedge with the highest value in the current chain to infinity.
In Fig. 4, the re-explored chain c(2) directly connects d1 andd5 , because of the updated cost of infinity and due to owingthat ζ1,5 is the highest in the chain c(1) .
D. Generation of the controller
A controller is created from the constructed chain. For thecontrol, relation between the two variables in the chain c(j)is used. The rule for constructing the controller is describedin Algorithm 1， where the notation of c(j) is omitted
for simplicity. In the algorithm, relation between variables
dci and dci+1 is estimated by the linear approximation
Rci ,ci+1 , where Rci ,ci+1 denotes the matrix of the linear]T[approximation which relates dT
ci , 1 to dci+1 . The detailsof estimating Rci ,ci+1 are described in III-E.

Algorithm 1 Generate the controller
Input: chain c,
Initialize: control input µ ← ddes − dtarget
1: for i = 1 : P do
2:
Check the relation between ci and ci+1
3:
if Relation is unknown
then
[
]T
4:
µ ← Rci ,ci+1 µT , 1 , (dci+1 = Rci ,ci+1 dci )5:else if Relation is derivative then6:µ ← µ − di7:
end if
8: end for

TABLE IIPARAMETERS OF THE ROBOT ARMl [m]m [kg]
k [N/m]1
1
1

lg [m]
a [N/℃]c [N/m·s]

1
2 l2

1
1

of samples, respectively. d(n) is the n-th sample in d. The
regression coefficient r a,b is estimated as follows:−1 T
r a,b =(D T
D a Db .
a W Da )(22)

W =diag[w1 , · · · , w1 , · · · , wn , · · · , wn ] ∈ R| {z }
|
{z
}

nβ×nβ

Here we give an example with c = [1, 5, 2, 4] and the
known relationship that d2 is the derivative of d5 , as shownin Fig. 4. First, the control input µ is set as µ = ddes −dtarget , thus omitting the feedback gain matrix. Then, we
check the relation between dc1 = d1 and dc2 = d5 , and therelational matrix R1,5 is multiplied to the current control
input µ = R1,5 (ddes − dtarget ) because the relation is
unknown. We then check the next relation between dc2 = d5
and dc3 = d2 , which is relation of derivative, and the control
input becomes µ = R1,2 (ddes −dtarget )−d5 . For the relation
between dc3 = d2 and dc4 = d4 , the controller is built sameas in between d1 and d5 . Finally, the control input becomesµ = R2,4 {R1,2 (ddes − dtarget ) − d5 }.
E. Local estimation of unknown relation
For the online estimation of the unknown relation R
used in the controller, R is locally estimated by the locallyweighted regression (LWR) [15] that weights the data samples on the basis of the Euclidean distance between eachsample and query input because R is generally non-linear,as in the case of the Jacobian in (4). The relation between
the pair of sensor variables da and db is approximated by
the locally linear relation as follows:[]T
db = Ra,b dT, R ∈ Rβ×(α+1) ,(17)a,1
where α and β denote the column size of da and db ,respectively. The element of one under da is added to include
an the offset parameter in the linear approximation.
To apply least squares regression, Eq. (17) is transformed
as follows:D b =D a r a,b , r a,b ∈ R(α+1)β×1
Tnβ × (α+1)βD a = [Φ1 , . . . , Φn ] ∈ R
]T
[
(1)T
(n)T
D b = db , . . . , db
∈ Rnβ × 1
 (1)T
1
...
O 
da


..  β ,..
Φn =  ...

.
. 

1
O
...
d(n)T
a
|
{z
}

(18)
(19)
(20)

(21)

(α+1)βwhere r a,b , D a , D b and n denote the column vector of
the regression coefficient that aligns each line of Ra,b into
one column, the data matrix of da and db , and the number

β

(23)

β

where W denotes the weight matrix. Each weight is defined
as follows:
(
)
1
(24)
wn =exp − h(s(n) − squery )T (s(n) − squery )2Ts =[θ T , θ̇ ]T(25)

where s(n) , squery and h denote the state vector s whensample d(n) was collected, the current state vector, andthe scaling parameter of the weighting range, respectively.
Elements of r ab are reorganized to the original shape ofRa,b for estimation by Eq. (17). h is decided from preparedcandidates by the leave-one-out cross-validation method thatchooses one candidate that associates the minimal squared
error between the current sensor data db and the estimatedvalue by Eq. (17). The total number of samples is fixed to
Nsample , and the oldest sample is discarded whenever a new
sample is collected after reaching the maximum number.
F. Evaluation of the controller
To look for new chain and to quit the current one,the generated controller is evaluated by performing 100 s
simulations and checking whether the robot arm follows
desired position in time or not. All chains that were foundwith Dijkstra’s algorithm are evaluated although some ofthem achieve to follow the target position.
IV. E XPERIMENT
A. Experimental conditions
The control method is verified by using a simulator. The
parameters of the robot arm are listed in Table II. l, lg ,and m denote the length of each link, the length fromthe gravity point to the end of the link, and the mass ofeach link, respectively. The control cycle is 0.05 s. The
maximum number for storing the samples for LSMI and
LWR is Nsample = 300.
B. Result of structure estimation
The relational costs among the sensor variables are shownin TABLE III. All 27 chains obtained with with Dijkstra’salgorithm are shown below. The chains that achieved position
control are shown with ⋄.
(1)• c= [2, 6, 12] (ẋ → ẍ → T )(2)• c= [2, 6, 10, 12] (ẋ → ẍ → L̈ → T )

ࣂሶ

࢞ሶ

0.5

ࣂ

0.0

0.6

࢞

0.5

0.0

ࣂሷ

Ṃ

1.3

Ṃ

0.6

࢞ሷ

6.3

Ṃ

0.8

Ṃ

1.0

࢞ሶ
0.5

ࣂ

࢞

ࣂሷ

࢞ሷ

࣎

ࡸሶ

ࡸ

ࡸሷ

ࡲ

ࢀ

ĐŽůŽƌďĂƌ
3

Ṃ

0.5

0.0

6.3

1.5

0.4

1.1

0.4

1.3

1.4

0.6

Ṃ

1.3

0.0

0.7

0.5

79.4

0.6

0.7

0.7

0.2

0.0

0.8

0.7

0.4

0.5

0.7

0.8

0.8

0.6

0.0

9.7

0.4

0.4

3.3

3.6

46.6

1.0

1.3

0.5

131

0.4

3.0

1.2

1.4

1.6

466

0.5

0.8

0.8

0.5

9.8

0.5

0.5

1.0

Ṃ

0.0

0.6

0.6

0.0

2196 2236

0.2

࣎

1.5

0.7

0.7

9.7

1.3

1.4

ࡸሶ

0.4

0.5

0.4

0.4

0.5

1.6

0.5

ࡸ

1.1

79.4

0.5

0.4

131

466

9.8

0.0

ࡸሷ

0.4

0.6

0.7

3.3

0.4

0.5

0.5

Ṃ

Ṃ

ࡲ

1.3

0.7

0.8

3.6

3.0

0.8

0.5

0.6

2196

0.5

ࢀ

1.4

0.7

0.8

46.6

1.2

0.8

1.0

0.6

2236

0.5

0.5

2
1.5
1
0.5
0
0

20

40

60

80

0
-1
-2

100

0

20

40

time [s]2Fig. 5.

2:ẋ = d˙target

1

0.5

60

80

x & y trajectory of end-effector controlled by c(16)1:θ̇2:ẋ = d˙target

12:T = µ

3:θ

11:F

1:θ̇

4

12:T = µ

3:θ

11:F

0.2
0.2

100

time [s]

3

0

4:x

10:L̈

9:L

5:θ̈

c = [2, 6, 11, 12] (ẋ → ẍ → F → T )c(4) = [2, 8, 12] (ẋ → L̇ → T )(5)• c= [2, 6, 10, 11, 12] (ẋ → ẍ → L̈ → F → T )(6)• c= [2, 8, 11, 12] (ẋ → L̇ → F → T )(7)• c= [2, 7, 11, 12] (ẋ → τ → F → T )(8)• c= [2, 3, 12] (ẋ → θ → T )(9)• c= [2, 3, 11, 12] (ẋ → θ → F → T )(10)• c= [2, 6, 10, 7, 11, 12] (ẋ → ẍ → L̈ → τ → F → T )⋄ c(11) = [2, 1, 5, 12] (ẋ → θ̇ → θ̈ → T )(12)• c= [2, 1, 12] (ẋ → θ̇ → T )(13)• c= [2, 1, 11, 12] (ẋ → θ̇ → F → T )(14)• c= [2, 3, 7, 11, 12] (ẋ → θ → τ → F → T )(15)• c= [2, 6, 7, 11, 12] (ẋ → ẍ → τ → F → T )(16)⋄ c= [2, 1, 5, 7, 11, 12] (ẋ → θ̇ → θ̈ → τ → F → T )(17)• c= [2, 1, 7, 11, 12] (ẋ → θ̇ → τ → F → T )(18)• c= [2, 11, 12] (ẋ → F → T )(19)• c= [2, 12] (ẋ → T )(20)• c= [2, 8, 7, 11, 12] (ẋ → L̇ → τ → F → T )⋄ c(21) = [2, 1, 5, 11, 12] (ẋ → θ̇ → θ̈ → F → T )(22)• c= [2, 3, 4, 11, 12] (ẋ → θ → x → F → T )(23)• c= [2, 3, 9, 7, 11, 12] (ẋ → θ → L̇ → τ → F → T )(24)• c= [2, 3, 4, 7, 11, 12] (ẋ → θ → x → τ → F → T )(25)• c= [2, 3, 4, 12] (ẋ → θ → x → T )(26)• c= [2, 3, 9, 12] (ẋ → θ → L̇ → T )(27)• c= [2, 3, 9, 11, 12] (ẋ → θ → L̇ → F → T )•ReferenceEnd-effector

1

4:x

10:L̈

9:L

5:θ̈

2

Edge cost

ƚŽ
ĨƌŽŵ
ࣂሶ

2
ReferenceEnd-effector

2.5

y coordinate [m]R ELATIONAL COSTS AMONG SENSOR VARIABLES

x coordinate [m]3

TABLE III

1

(3)

•

There are enormous pattern of edges that connect d2 andd12 . However, chains are narrowed in 27 patterns because
the edges that has infinity cost is added every time a new
chain is constructed. Although chain 1, 2, 3, 5, 10, 11, 15, 16,
and 21 seem to plausibly associates physical meanings of thevariables, other chains cannot be protested as not plausible
because every variable is related indirectly.
C. Result of Position Control
Position control was achieved when using controllers generated from chain c(11) ,c(16) , and c(21) . However calculation
cycle of LWR exceeds the real time of control cycle. The
trajectory of the end-effector while using the controller
generated from chain c(16) is shown in Fig. 5. The generated

6:ẍ

8:L̇

6:ẍ

7:τ

Fig. 6.

Dependency graph: c(16)

8:L̇
7:τ

Fig. 7.

0

Dependency graph: c(21)controller from c(16) is described as follows:µ = R11,12 R7,11 R5,7 {R2,1 (ddes − dtarget ) − d1 }. (26)
Eq. (26) is interpreted as following equation:µ = A−1 (GT (θ))−1 M (θ){J −1 (θ)(xdes − x) − θ̇}, (27)
Eq. (27) is equivalent to the conventional musculoskeletal
controller [16]: thus the proposed method successfully generated a reasonable controller.
The dependencies of c(16) and c(21) are shown in Fig. 6
and 7, respectively. A chain not including d7 = τ whichis included in c(16) is found in Fig. 7. This result indicatesthat the robot will keep controlling the position of the endeffector by finding alternative chains if sensor malfunctions,e.g., d7 happens and affects the quality of R5,7 and thecontrol.
D. Adaption for change of arm parameters
Adaptivity of the proposed method is verified by changing
parameters of link 2 in TABLE IV in 50 s while the endeffector position is being controlled by chain c(16) . Thechange in the appearance of the robot arm is shown in Fig.
8. This condition considers the case of the robot arm holding
a tool. In addition, we compare the proposed method withthe case of relearning from scratch.
The trajectory of the end-effector is shown in Fig. 9.
The end-effector position eventually converges to the desired
trajectory even though the parameters have changed. The proposed method converges faster than relearning from scratch
because it is not relearning all the approximated relations
but relearning the ones affected by the changes, in this caseR1,2 and R5,7 .

before
1
1
1
2 l2

after
1.5
3
2
3 l2

x coordinate [m]l2 [m]
m2 [kg]l2g [m]2.5

Changed

0.5

2
1.5
1
Reference
Proposed
From scratch

0.5
0
0

50

100

150

200

250

y coordinate [m]TABLE IVC HANGED PARAMETERS OF LINK 2

Reference
Proposed
From scratch

0
-0.5
-1
-1.5
-2

0

time [s]Fig. 9.

Changed

50

100

150

200

250

time [s]Trajectory of end-effector when parameter is changed in 50s

R EFERENCES

Fig. 8. Change of parameters on the robot arm. Blue and pink lines denotelinks and muscles of the robot arm. Green dots on links denote gravity pointsof each movable link. Red circle is the target position.

V. C ONCLUSIONS AND F UTURE W ORK
We presented an approach for estimating the robot structure and building controllers of the dynamic motion ofrobots in order to adapt for changes. The structure wasestimated from observing sensor variables by using MI anda path-finding method. The controller was built based on theestimated structure. We applied the proposed method to a
musculoskeletal arm simulator and verified the behaviour ofthe generated controllers. As a result, Adaptivity of proposed
method for change of structure and parameters was proved.
However, the proposed method is not free of problems
in practice. The calculation cost of LWR must become
shorter than control cycle. The locally weighted projection
regression(LWPR) can deal with this problem because it
keeps local models approximated from a part of whole data
samples in memory [17]. The controller evaluation methodneeds to be automated by the stability analysis method or
the evaluation of the trajectory of the target variable.
In addition, we need to investigate the more efficient use of
the estimated structure. Neuralnetworks and reinforcements
are implemented to learn the motion of robots (e.g., [18],[19]); however these method require large training data andtime-consuming for relearning because of the difficulty inrevising the learned model. The proposed method possibly
have lower relearning costs by revising one part of estimatedstructure where approximation accuracy became worth bychange of structure and reusing other part.
ACKNOWLEDGEMENT
The authors would like to thank Prof. K. Takagi ofNagoya university for useful advice about model of tendondriven manipulator. This work was partly supported by JSPS
KAKENHI (17K00362).

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