Proceedings of the 2007 IEEE International Symposium on
Computational Intelligence in Robotics and Automation
Jacksonville, FL, USA, June 20-23, 2007

FrAT3.3

Intelligent Variable Joint Impedance Control and Development of a
New Whole-Sensitive Anthropomorphic Robot Arm
Dzmitry Tsetserukou, Riichiro Tadakuma, Hiroyuki Kajimoto, Naoki Kawakami and Susumu Tachi,
Member, IEEE

Abstract—The paper focuses on design and control of a newanthropomorphic robot arm enabling the torque measurementin each joint to ensure safety while performing tasks of physicalinteraction with human and environment. When the contact of
the arm with an object occurs, local impedance algorithm
provides active compliance of corresponding robot arm joint.
Thus, the whole structure of the manipulator can safely interact
with unstructured environment. A novel variable control
strategy was elaborated to increase the robot functionality andto achieve human-like dynamics of interaction. In the paper, we
detail the design procedure of 4-DOF robot arm and opticaltorque sensors. The experimental results of variable joint
impedance control show that proposed approach not only
provides safe interaction of entire structure of robot arm with aperson, but also improves the effectiveness of contact task
performance, enables thus to contact with environment in a
delicate manner.

N

I. INTRODUCTION

EW technologies and achievements in humanoid
robotics will allow to make a new step in robotics in near
future – to introduce robot as daily activity assistant [1] inhuman domain (such as offices, homes, hospitals). In service
applications of robotics, human-robot interaction represents a
crucial factor for a robot design and imposes strict
requirements on its behavior and control in order to ensure
safe interaction with environment and effectiveness whiletarget task execution.
Conventional straightforward approaches to controllingthe interaction between a manipulator and an environment are
based on compliant control of a robot arm according toapplied force measured at the tip of the end-effectors.
However, collision or expected contact with environment
may occur on the entire surface of the robot arm producing
interactive forces. In the recent years, several effective
methods on enhancement of contact detection ability ofmanipulator were reported. To avoid collisions intime-varying environment, Lumelsky et al. [2] proposed tocover manipulator with a sensitive skin capable of detecting
nearby objects. As this device integrates a huge amount ofManuscript received April 27, 2007.
D. Tsetserukou, R. Tadakuma, N. Kawakami, and S. Tachi are with the
University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo, 113-8656 Japan(e-mail: dima_teterukov@ipc.i.u-tokyo.ac.jp; tadakuma@star.t.u-tokyo.ac.jp,
kawakami@star.t.u-tokyo.ac.jp; tachi@star.t.u-tokyo.ac.jp).
H. Kajimoto was with the University of Tokyo. He is now with the
University of Electro-Communications, 1-5-1, Chofugaoka, Chofu-shi,
Tokyo, 182-8585 Japan (e-mail: kajimoto@hc.uec.ac.jp).

1-4244-0790-7/07/$20.00 ©2007 IEEE.

Fig.1. Developed whole-sensitive robot arm.

small sensors incorporated in tiny rigid platform, and requires
complicated wiring and signal processing hardware, suchdevices have high cost and reliability issues. Besides,
sensitive skin provides only contact pattern information.
Further improvement in human-robot interaction wasachieved by using passively compliant joints and whole-bodytactile sensors for detecting pressure distribution [3].
Whereas the mechanical leaf springs introduced in each joint
allow achieving fast response to external disturbance, they
can also cause vibrations and unstable dynamics.
Another line of research is directed to the development ofcollision detection system without using external sensors [4].
Such system recognizes collisions based on the difference
between the actual torque applied to the joints and thereference torque calculated from manipulator dynamics, andthen generates the compliant motion in response todisturbance. However, inaccuracy in dynamic model
parameters deteriorates sensitivity threshold up to 17.4 N at
the elbow joint. The dexterous robot-human cooperative
work requires continuous precise measurement of force inrange of 0-50 N.
The traditional teleoperated systems also suffer from thebasic safe human-robot interaction issues. A slave robot
controlled by an operator mainly performs the manipulationsin unknown and unstructured human environment. The

338

FrAT3.3

operator has to move the slave robot arm to the target position,and to avoid obstacles simultaneously. However, operators
cannot accomplish both tasks in real time, and they are not
perfect in planning of collision-free motion in dynamic
unstructured
surroundings. Recent researches on
teleoperation focus on automation of collision avoidance andcontact task based on information from sensors, allowing thus
operator to concentrate on the task to be performed. The
Robonaut teleoperated robot was developed to assist in-space
operations and work with humans in space exploration [5]. In
the developed system, operator moves the robot arm until thepalm equipped with force sensors contacts the object. The rest
parts (elbow, forearm, and upper arm) of the manipulator
pose the hazard for humans and structure itself.
Our main research is devoted to realization of teleoperated
manipulator and autonomous robot enabling safe interaction
with humans. The line of master-slave robot systems(TELESAR I and TELESAR II) was successfully developedin our laboratory [6]. The performance and stability of
teleoperation were gradually improved. The slave robot
enables to perform dexterous operations by means of 7-DOF
arms and 8-DOF hands. The safety in interaction at the tip ofthe end-effector is provided by impedance control algorithm.
The external force is measured by the 6-axis torque/force
sensor.
To realize safe physical contact of entire robot arm
structure with human and guarantee collision avoidance, ourprimary idea is concentrated on the design of whole-sensitive
robot arm (by using distributed torque sensors in each joint).
When contact with environment occurs, manipulator
automatically adjusts its dynamic parameters (stiffness anddamping) accordingly to the measured external force. The
newly developed anthropomorphic manipulator having 4DOF arm and 8-DOF hand (Fig. 1) is capable to safely
interact with environment wherever contact occurs on the arm
surface.
The first part of the paper is addressed to the description of
the development of whole-sensitive robot arm and new
optical torque sensors. In the second part, we discuss theelaborated intelligent variable impedance control algorithm,
and experimental results.

component one. The Harmonic Drive offers such advantages
as accurate positioning, high torque capability, torsional
stiffness, and high single stage ratios. Developed teleoperated
robot arm has 4-DOF: Roll, Pitch, Yaw joints of the shoulder,
and Pitch joint of elbow. Each joint is equipped with opticaltorque sensor directly connected to the output shaft ofHarmonic Drive. The sizes and appearance of the arm werechosen so that the sense of incongruity during interaction
with human is avoided. We kept the arm proportions the sameas in average height human: upper arm length L1 - 0.308 m;
upper arm circumference - 0.251 m (diameter 0.080 m);
forearm length L2 - 0.241 m; forearm circumference - 0.189 m(diameter 0.06 m). The 3D CAD model of the developed arm
and coordinate systems based on Denavit-Hartenberg
convention are represented in Fig. 2.

Torque sensor
distribution in Shoulder
Pitch and Roll Joints

Sensors
in Yaw
and
Elbow
Joints

Yaw

Z1
Y2
Z2

Y1

Z0

Y0
+
X0 +
Pitch
Roll
J1

X1

X2

L1
J3

II. DESIGN OF THE NEW ANTHROPOMORPHIC ROBOT ARM
From the safety point of view, to minimize injures in caseof collision, most of the robot parts were manufactured fromaluminium alloys to obtain as much lightweight structure as
possible. The robot links were designed in round shape toreduce impact force. The distribution of the arm joints
replicates the human arm structure in order to make it easy tooperate using kinesthetic sensation during teleoperation.
To remove mechanical subsystems without disassembling
the main structure when the failures do occur, we have beenusing a modular approach while designing anthropomorphic
robot arm. Therefore, we selected CSF-series gear head typeof Harmonic Drive instead of compact and lightweight

J2

+

Z4

Y4

X4

Y3

J4

X3
Z3

Z5

L2

Y5

X5
Fig. 2. 3D CAD arm model and coordinate systems.

The principal specifications of the developed arm are given
in Table I.

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FrAT3.3
TABLE I
PRINCIPAL SPECIFICATIONS

IV. JOINT IMPEDANCE CONTROL
A. Joint Impedance Control
The dynamic equation of an n DOF manipulator in joint
space coordinates (during interaction with environment) is
given by:

Arm joints
Parameters

ShoulderElbow

J1, Pitch

J2, Roll

J3, Yaw

J4, Pitch

Mobility
range (Newrobot arm/
Humanarm) [deg]-180 to 180(-60 to 180)

-180 to10(-165 to 0)-180 to 180(-60 to 180)

0 to 112(0 to 130)Motor
power [W],motor type

90,
Maxon
RE 35

60,
Maxon
RE 35

26.6,
Faulhaber
2657

26.6,
Faulhaber
2657

Harmonic
drive rated
torque[Nm], (type/gear ratio)

7.8,(CSF-14-G
H /100)

7.8,(CSF-14-G
H /100)

5.0,(CSF-11-2
XH/100)

5.0,(CSF-11-2
XH/100)M (θ )θ + C (θ , θ)θ + τ f (θ) + g (θ ) = τ + τ EXT ,where θ ,θ,θ are the joint angle, the joint angular velocity,and the joint angle acceleration, respectively; M(θ) ∈ Rn×n is
the symmetric positive definite inertia matrix; C( θ ,θ )∈ Rn isthe vector of Coriolis and centrifugal torques; τf( θ )∈ Rn is theIII. DEVELOPMENT OF THE NEW OPTICAL TORQUE SENSOR
To facilitate torque-controlled joints of the robots, theauthors in [7]-[9] devised magnetostrictive, eddy-current andstrain-gauge-based torque sensors. In our previous work, we
described in detail the crucial shortcomings of suchtechniques of the torque measurement, and pointed out the
motivations behind using an optical approach [10]. We
developed new optical torque sensors having high reliability,
high accuracy (even in electrically noisy environment), easy
mounting procedure, and low price. The novelty of our
method is application of the ultra-small size photointerrupter(PI) RPI-121 as sensitive element to measure relative motionof sensor components. The dimensions of the PI (RPI-121:
3.6 mm × 2.6 mm × 3.3 mm) and its weight of 0.05 g allow
realization of compact design. Furthermore, PI also has small
influence from the electromagnetic field and stray light, good
linearity and high accuracy.

2vector of actuator joint friction forces; g(θ) ∈ Rn is the vectorof gravitational torques; τ ∈ Rn is the vector of actuator joint
torques; τEXT ∈ Rn is the vector of external disturbance joint
torques.
People can perform dexterous contact tasks in daily
activities while regulating own dynamics according totime-varying environment. To achieve skillful human-likebehavior, the robot has to be able to change its dynamic
characteristics depending on time-varying interaction forces.
The most efficient method of controlling the interaction
between a manipulator and an environment is impedancecontrol. This approach enables to regulate response propertiesof the robot to external forces through modifying themechanical impedance parameters. The graphicalrepresentation of joint impedance control is given in Fig. 4.

FEXT
Jdi

R
1

6

Kdi

Z

τ EXT (i+1)

X

τEXTi

D

7
r

Jd(i+1)Kd(i+1)Yl

Dd(i+1)

Ddi

b

5

4

(1)

Fig. 4. Concept of the local impedance control.

T
3

The desired impedance properties of i-th joint ofmanipulator can be expressed as:t
Fig. 3. Hub-spoke structure layout.

J di ∆θi + Ddi ∆θi + K di ∆θ i = τ EXTi ; ∆θi = θ ci − θ di ,The detector (Fig. 3) consists of inner part 1 connected byflexure 3 with outer part 2, shield plate 4, fixed PI 5, andprotrusions 6, 7. The sensors were manufactured from one
piece of high yield-strength AISI 4135 steel using wire
electrical discharge machining (EDM) cutting. To protect thesensor against influence of bending moment, the simple
supported loaded shaft configuration was implemented.

where Jdi, Ddi, Kdi are the desired inertia, damping, andstiffness of i-th joint, respectively; τEXTi is torque applied toi-th joint and caused by external and gravity forces, ∆θi is thedifference between the current compliant angle θci anddesired one θdi. The state-space presentation of the equationof local impedance control is written as follows:

340

(2)

FrAT3.3⎡ ∆θi ⎤ ⎡ 0⎢ ⎥=⎢⎣ vi ⎦ ⎣ − K d J d⎤ ⎡θi ⎤ ⎡ 0 ⎤+τ (t ) , (3)− Dd J d ⎥⎦ ⎢⎣ vi ⎥⎦ ⎢⎣1 J d ⎥⎦ EXTi
1or:⎡ ∆θi ⎤ ⎡θi ⎤⎢ ⎥ =A ⎢ ⎥ + Bτ EXTi (t ) ,⎣ vi ⎦ ⎣ vi ⎦(4)

where the state variable is defined as vi = ∆θi ; A, B matrices. After integration of (4), the discrete timepresentation of the impedance equation is expressed as:⎡ ∆θ k +1 ⎤⎡ ∆θ k ⎤⎢ ∆θ ⎥ =Ad ⎢ ∆θ ⎥ + Bd TEXT ( k ) .
⎣ k +1 ⎦⎣ k⎦(5)To achieve the fastest possible non-oscillatory response on
the external force, we assigned the eigenvalues λ1 and λ2 ofmatrix A as real and equal λ1=λ2=λ, λ>0. By using
Cayley-Hamilton
methodformatrixexponential
determination, we have:T⎡ 1 − λ1T⎤
Ad = eλT ⎢⎥,⎣ − Dd T /(4 J d ) 1 − λ1T − Dd T / J d ⎦Bd = ( Ad − I ) A−1 B = −(6)λT
1 ⎡ e (1 − λT ) − 1 ⎤ , (7)⎢⎥K d ⎣⎢ − ( Dd /(2 J d ) )2 TeλT ⎦⎥where T is the sampling time; I is the identity matrix.
There are several conflicting requirements on the choice ofdynamics parameters of impedance model to provide
effectiveness and functionality of robot in tasks of physicalinteractions fulfilled in co-operation with humans, and toensure the collision avoidance. For example, whileaccomplishing service tasks for human in the autonomous
mode, it is required to provide high stiffness (to ensure small
position error during object handling) and high damping (forgood velocity tracking). In the case of collision, the low
stiffness is necessary to reduce the impact forces. Realizationof human following motion – one of the most important
human-robot cooperation functions – also imposes specificrequirements on desired impedance parameter selection.
Basically, there are two types of solution of this problem:
adaptive and functional adjustments of impedance parameters.
In the adaptive control, damping and stiffness of the system
are gradually adjusted according to sensed dynamics andcontact forces [11]. However, due to parametric uncertainties
of the robot dynamics model, it is difficult to obtain thecomplete description of the dynamics. Therefore,
model-based adaptive impedance control must rely on either
repeated motions or time for adaptation to achieve
convergence to the desired system parameters.

In the functional approaches, current impedance
parameters have predetermined relations to the current sensed
variables. Generally, these methods presume determining thecurrent stiffness and damping matrices functionallydependent on sensed variables. The main idea of the paper[12] is that involving contact between slave robot and theenvironment can be classified according to the angle between
commanded velocity and the contact force. It is supposed thatforce and velocity vectors are usually parallel when theimpact occurs or when the object is being pushed. So, thefunctional dependency of stiffness and damping on angle
between sensed force and velocity vectors was proposed. In
real co-operation tasks and, especially, collisions, these
vectors can be not only parallel, but also have independent
arbitrary directions according to external force coming
direction. Another line of variable impedance research is
directed to estimation of human arm stiffness [13]. The
proposed variable impedance controller varies a damping
parameter of target impedance in proportion to an estimatedvalue of the human arm stiffness. Despite the fact that robot
can effectively follow the human arm motion, it cannot
perform task autonomously. Besides, only robot end-effector
impedance parameters can be adjusted. We elaborated a new
methodology for impedance parameter adjustment based on
the interaction mode, and providing dynamic stability of thesystem.
B. Intelligent Variable Joint Impedance Control
The research on impedance characteristics of human arm
shows that, while pushing or pulling the object naturally,
human arm stiffness and damping behavior can beapproximated by exponential curves [14]. The first essential
peculiarity of our control method is that we introduce theexponential functional dependency between sensed force andstiffness to impart the human-like damping and stiffness
behavior to the robot arm interacting with environment. The
second main feature occurred from the fundamental conflictin impedance selection with regard to current working
conditions. We consider the threshold external disturbancetorque value τEXTth to distinct the service task (with highstiffness and damping of joints) from collision avoidance andhuman following motion tasks requiring low stiffness. Thisvalue can be chosen depending on the force necessary toaccomplish service task. We assigned the specific magnitudeof τEXTth to each joint of robot arm.
The procedure of impedance parameters selection (in theexample of elbow joint) is as follows. On the first stage, theparameters of desirable impedance model of robot arecomputed for the case of service task accomplishment andaverage-level-contact-force of human-robot interaction. The
desired stiffness Kd1 (for static equilibrium case) is calculated
from (8) based on the maximum deflection value of joint
angle ∆θmax caused by external torque τEXT while service task
performance.

341

FrAT3.3

τ EXT∆θ maxDd 2 = 2.1 K d 2 J d 1 = 2.1e(8)

Dd 1 = 2ζ K d 1 J d 1(9)To achieve fast response without oscillations on theexternal torque we defined damping coefficient ζ of 1.05. The
value of desired inertia Jd1 of 0.1 (kg⋅m2) was assigned torealize fast response tracking. Thus, the value Dd1 of 2.1(Nm⋅s/rad) was derived from (9). These parameters are valid
till the interaction force does not cause the overload of robot
arm. When sensed value of the torque is larger then thresholdlevel, robot recognizes this condition as collision or humanfollowing motion mode, and adjusts its dynamics parameters(stiffness and damping) in the same way as humans in order toprovide smooth natural interaction. To realize suchcontinuous change of dynamics, we are using exponential
relation between external disturbance torque and desired
stiffness:

K d 2 = K d 1e ( EXTµτ−τ EXTth ),J di ∆θi + 2.1e

∆ θk+1θdTargettrajectory
generator

τ EXT < τ EXTth

0.5 µ (τ EXTi −τ EXTth )K d 1 J d 1 ∆θi + K d 1e ( EXTiµτ−τ EXTth )Comparator

(12)

0.8
0.6

Threshold torque

0.4
0.2
0.0

0

2

4

6

Time (sec.)

8

Fig. 6. External torque.

Gravitycompensation

TG
TZ

θ

Optical torquesensorA/D∆ θk+1 ∆ θk+1

θd

θc
θd

ε
+-

Kv

+-

θ

∆θ i =

1.0

τEXT > τ EXTth τ EXT

θc

(11)

To verify the theory and to evaluate the feasibility andperformance of the proposed impedance controller, theexperiment with new whole sensitive robot arm wasconducted. To ensure the effectiveness of service task
accomplishment we decided to implement position-based
impedance control (Fig. 5). In this algorithm, compliant
trajectory generated by the impedance controller is tracked by
the PD control loop. During the experiment, the interaction
with arm was performed to exceed join torque threshold level(τEXTth of 0.6 Nm was assigned, µ = -1.155). The experimental
results for the elbow joint – applied torque, stiffness anddamping plot, impedance trajectory with constant andvariable coefficients, and measured joint angle – arepresented in Fig. 6, Fig. 7, Fig. 8, and Fig. 9, correspondingly.

(10)

Variable impedance
trajectory generator

K d1J d1

= τ EXTi ; ∆θi = θ ci − θ diwhere Kd2 is the variable desired stiffness aimed at softcompliant interaction; µ is the coefficient defining the level ofdecreasing of arm joint stiffness in response on increasing
external torque value.
The desired damping is adjusted to prevent force responses
from being too sluggish while changing stiffness values, andto ensure contact stability:

Constant impedance
trajectory generator

0.5 µ (τ EXT −τ EXTth )Then, variable joint impedance controller is described by:

It was defined that external torque of 1 Nm results in ∆θimax
of 0.1 rad giving the Kd1 of 10 (Nm/rad). The desired damping
is expressed as:External Torque, τEXT (Nm)

Kd1 =

Kp

1
Ki KT

D/A

DriverθcθsFig. 5. Block diagram of the position-based impedance control.

342

Encoderim

Link

FrAT3.3

V. CONCLUSION AND FUTURE WORK

10

New whole-sensitive teleoperated robot arm wasdeveloped to provide human-like capabilities of contact task
performing in a broad variety of environments. To facilitate
this arm with joint torque measuring ability, the new opticaltorque sensors having good accuracy, high signal-to-noise
ratio and compact sizes were designed and manufactured. The
effectiveness of the position-based variable impedancecontrol for providing safe human-robot interaction was
experimentally illustrated on a new whole-sensitive robot
arm. Our future research will be devoted to elaboration of theapproach to precise estimation of external force vector andcontact area recognition.

8
6

Stiffness, Kd (Nm/rad)Dampind, Dd (Nm s/rad)

4
2
0

2

4

Time (sec.)

6

8

Impedance Trajectory, ∆θk+1 (deg.)

Fig. 7. Variable stiffness and damping parameters.
0

REFERENCES

-2

[1]
-4
-6
Variable coefficiens
Constant coefficiens

-8

-10

0

2

4

Time (sec.)

6

8

Fig. 8. Measured joint angle.

Joint Angle, θ (deg.)

10
8
6
4
2
0

0

2

4

Time (sec.)

6

8

Fig. 9. Trajectories generated by impedance model withconstant and variable coefficients.

The experimental results show the successful realization of
the variable joint impedance control. While contacting withhuman, the robot arm generates compliant soft motion
according to the sensed force. The plot represented in Fig. 8
shows that the variable impedance control provides better
trajectory to avoid impact and to accomplish humanfollowing motion than the impedance control with constantcoefficients. As we assigned critically damped response ofimpedance model to disturbance force, output angle (∆θk+1)
has ascending-descending exponential trajectory. The
conventionally impedance-controlled robot can provide
contacting task only at the tip of the end-effector withpredetermined dynamics. By contrast, our approach provides
delicate continuous safe interaction of all surface of the armwith environment. As the result of the experiments withvariable impedance-controlled arm, tactile sensation of soft
friendly interaction was really achieved.

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