Proceedings of the 2006 IEEE International Conference on Robotics and Automation
Orlando, Florida - May 2006

Optical Torque Sensors for Implementation of Local
Impedance Control of the Arm of Humanoid Robot
Dzmitry Tsetserukou1, Riichiro Tadakuma2, Hiroyuki Kajimoto1 and Susumu Tachi2
Graduate School of Information Science and Technology
The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan1{dima_teterukov, hiroyuki_kajimoto}@ipc.i.u-tokyo.ac.jp, 2{tadakuma, tachi}@star.t.u-tokyo.ac.jp

Abstract - This paper describes the recent development of
new optical torque sensor in order to replace expensive strain
gauge sensor attached at the tip of the anthropomorphic robot
arm and realize local impedance control in each joint.
Index Terms - Optical torque sensor, Impedance control.

I.

INTRODUCTION

The teleoperated slave robot has been developed to realize
dexterous tasks such as interaction with human in remoteenvironment or manipulation with objects in hazardous
conditions [1]. The slave robot includes anthropomorphic
seven-degree of freedom (7-DOF) arms (Fig. 1) with 8-DOF
hands. To achieve thestability in contact withenvironment and torealize
controlled
dynamic
interaction
between a robot arm
and
human
the
impedance control has
been
successfully
applied. The impedancecontrol of the arm of
the remote slave robot
requires measurementofexternal
force
exertedbyhumanduring interaction. The
force
impartedbyhuman at the tip of theanthropomorphic arm ismeasured by 6-axis
force sensor (MINI
4/20, BL AUTOTEC),
marked by yellow
Fig. 1 Teleoperated slave robot.
rectangles in Fig. 1.
In spite of the fact that developed robotic system ensures
the safety in the interaction at the end-effector, other parts ofthe mechanical structure, such as shoulder and elbow joint,
during operation can hurt people. In these joints there are noforce measurement sensors to limit the motor torque by means
feedback. Direct sensing of the applied torque through thevalue of current in DC motor circuit is unacceptable due tolow backdrivability of the harmonic drives with high gear ratio

0-7803-9505-0/06/$20.00 ©2006 IEEE

1674(=50). Therefore, to realize human friendly interaction of any
part of the anthropomorphic arm we decided to attach torquesensor at each joint to implement local impedance control.
Thus, virtual backdrivability of transmissions can be achievedin each joint of the slave robot.
Besides,commercial
6-axisstrain-gauge-based
force/torque sensors are intended for use at the end-effector ofa robot to monitor assembly or machining forces. In thisapplication very high stiffness is required. However, forhuman-robot interaction high stiffness is not the objective.
Moreover, strain gauges have many disadvantages: difficult to
install, calibrate, easy to break and posses high electrical noise
sensitivity that makes them rather expensive.
The authors introduce the idea of using optical approachto detect torque and discuss the results of realization of thelocal impedance control on the base of developed opticalsensors to provide safety of human-robot interaction.
II.

METHODS of TORQUE MEASUREMENT. ADVANTAGES andDRAWBACKS

Torque transducer is attached to the motor shaft andincludes load cell – structure which supports the load anddeflects a known amount in response to applied torque. To
measure the deformation of the flexure different approaches
can be used. The primary methods are as follows:
1) Electrical methods.
2) Methods based on electromagnetic phenomena.
3) Optical methods.
Within these approaches noncontact transducers
measuring relative displacement by means light radiation
detection, Hall effect, Faraday`s law and contacting ones
measuring strain based on strain gauges, potentiometers,piezoceramics and optical fibre are recognized.
Electrical measuring methods are associated essentiallywith strain gauges, capacitive and piezoelectric sensing. The
operation of strain gauges is based on phenomena of thevariation of their electrical resistance with strain. When force
is applied the strain changes the electrical resistance of thegauges in proportion to the load. In spite of such benefits ofstrain gauges as high accuracy (linearity), about 0.03%-2.5%
of full scale (FS), high resolution of 1-3mV/V, their maximum
allowable strain is close at which they break. To guarantee theoverload protection of transducer the mechanical stops
limiting the deflections of the flexures are necessary. Verystiff sensor may only deflect a few ten-thousandths of1675

dimensional array of radiation detector and two modulating
apertured discs placed between source and detector. As torqueapplied to the shaft the relative position between discs alters
overlapping slots and hence the size of the apertures which
control the pattern of light incident upon the optical detector.
III. DEVELOPMENT OF THE OPTICAL TORQUE SENSOR

125

d

100
75
50
25
0

0

0.5

1.0

1.5

2.0 2.5

DISTANCE: d (mm)

RELATIVE COLLECTOR CURRENT: Ic (%)

Above-mentioned sensors have not been adapted toapplication in robot for torque detection. The approach todesign high-performance torque sensor for anthropomorphic
robot arm should follow the guidelines illustrated below.
1. Addition of the torque sensor to a robot joint should
not require redesign of the joint and causes a minimal
modification in kinematics and dynamics. Therefore, sensor
with small width and lightweight is desirable.
2. Noise created by current passing through the DC motor
attached in each joint of the robot arm should not effectconsiderably on sensing element. Hence, usage ofelectromagnetic sensors should be avoided in this application.
3. The angle of twist of the movable part of transducer at
the maximum expected external torque should allow
exploiting as wide range of detector sensitivity as possible toachieve high signal-to-noise ratio.
4. Torsional stiffness of the sensor should notconsiderably reduce the natural frequency of the robot arm.
This introduces the trade-off of stiffness maximization while
maintaining high sensitivity.
5. The other difficulty in design of the torque sensor ishysteresis elimination. Most metals used as flexures have very
little hysteresis. However, bolted, press fit and welded joints
near the flexure introduce hysteresis. Therefore, the optimal
design requires realization of the mechanical structure from asingle piece of metal.
6. Influence from any of the non-torsional components of
the load should be canceled. Behavior of the sensing element
output and mechanical structure should be as close to linear as
possible.
7. Simple to manufacture, low in cost and robust.
We decided to use ultra-small size photointerrupters type
RPI-131 and RPI-121 as sensitive element to measure relative
motion of sensor’s component. The relationship between the
output signal and position of the shield plate for RPI-121 isshown in Fig. 2 [9].
RELATIVE COLLECTOR CURRENT: Ic (%)

millimetre. Manufacturing the limit stops with such small
clearances is very difficult. Besides, strain-gauge-based
torque/force sensors are greatly subjected by radial and otherforce components. Semiconductor as well as foil gages requireelaborate process for attachment which must be done by aspecialist. Another shortcoming of these sensors is their
sensitivity to electrical noise and temperature [2].
Many torque transducers are based on measuring therelative angle between the two ends of the torsion bar. This
principle was realized in differential capacitive sensor formeasuring the relative angle [3]. Developed transducer isnoncontact, robust and compact. Two rotatable electrodes areplaced between two sensor plates. The relative angle between
the two rotors and the absolute position of the rotor blades arecalculated from measurement of capacitive coupling between
different transmitting stator segment and a single receiving
electrode. Its drawback is high sensitivity to a radialdisplacement and high cost. The relationship between value ofcapacitor capacity and permittivity of the dielectric material
between the capacitor plates also was used in patent [4].
In electromagnetic sensors the Faraday`s law (inductive
sensors), magnetostriction and magnetoelastic effect are
employed. As example of electromagnetic sensors – Linear
Variable Differential Transformers (LVDT) have high degreeof robustness, remarkable resolution of about 0.1Pm, good
accuracy (0.01-0.3%), allow easier installation and calibration.
Inductive sensors suffer a reduction in signal at very low
frequencies and affected by electromagnetic noise.
Light source, photosensor and solid object modifying
amount of light incident on optical detector are necessary tomeasure displacement between unmovable and flexible part ofthe optical sensor. The photosensors have such drawbacks asnonlinearity and temperature sensitivity, however, they are
considerably more reliable, cheap and allow simplifying theconstruction of the design. A displacement can be detected byinterrupting light between source and detector, changing theintensity of reflected light or relative movement of source anddetector. S. Hirose and K. Yoneda have made significant
contribution to research of the optical force and moment
sensors [5, 6]. The authors proposed to use a split typephotosensor to detect the displacement of the light source(LED) caused by applied force in two directions. In
cooperation with Minebea Co. OPFT series of 6-axes opticaltorque sensors was manufactured. In comparison withconventional strain-gauge-based transducers they are morecompact, light in weight and low in cost. However, thesesensors suffer from complicated calibration procedure due tononlinear output, require application of DSP for real-time
computation of measured force and have average accuracy of
5% FS. The idea of the patent [7] is calculating torque by
measuring angle of twist of the torsion shaft through detectionof difference in the rotation position of discs attached at the
opposite sides of the torsion shaft using optical encoder.
Encoder type of torque sensor suffers from large overall
dimension and complicated procedure of apertured discs
mounting. To overcome this the author [8] invented torquesensor including a source of optical radiation, a two

125
d
100
75
50
25
0

0

0.5

1.0

1.5

2.0 2.5

DISTANCE: d (mm)Fig. 2 Relative output vs. distance.

The linear section of the diagram corresponding
approximately 0.2 mm can be used for detection of the relative
displacement of the object. The dimensions ofphotointerrupter (RPI-121 3.6 u 2.6 u 3.3 mm) and weight of
0.05 g allow realization of compact sensor design.
Two structures of elastic element were realized: the in-line
structure – when the input and output section of the detector
are displaced in axial direction by the torsion component. And
the “in plane” one – when input and output of the sensor are
disposed in one plane and linked by the bending radial
flexures. The layout of the in-line structure on the basis ofspring with cross-shaped cross section is presented in Fig. 3.
This type of spring allows
3large deflections withoutyielding. Detector consists ofT2
input part 1, output part 2,
2
fixedly
mounted4
photointerrupters 3, shield 4
and spring 5. When torque T
is applied to the input shaft
5
the spring will be deflected.
This causes rotation motion of1
the shield 4. The shield
T T1
displacement is detected by3
the degree of interruption of
infrared light falls on theFig. 3 Construction of thephototransistor.
Thus,
optical torque sensor.
magnitude of the output signalof the photointerrupter willcorrespond to the applied torque. The relationship between thesensed torque TS and the angle of twist T is the following:
TS

k ST

kS T1  T 2 ,(1)

0.98 b  h t 3G 3l .

Mises

stressequals

VvonMises = 2.392108 N/m2
<Vyield = 2.4108 N/m2.

Angle of twist can beb)calculated from the valueof tangential displacement
and for given load it
Fig. 5 Result of analysis using FEM.
equals 0.928q. Since themaximum stress appears in the area of core of the sensor the
improvement of the design can be achieved by realization ofhollow structure with 6 or 8 leaves of spring. The structure of
the test rig for calibration of the optical sensor is given on
three-dimensional model (Fig. 6).
ShieldRotatable shaft

Photointerrupter

Arm

Fixed shaft

Coupling

where kS – torsional stiffness of the cross-shaped spring.
The cross-shaped spring behavior is similar to theequivalent flat plate behavior with some linear factor
differences [10]. The torsional stiffness is defined as:kS

The sensor was designed to withstand torque of 1.75 Nm.
The results of spring analysis using Finite Element Method(FEM) show tangential
displacement in mm (Fig.
5a) and von Mises stressin MPa (Fig. 5b) undera)torque of 1.75 Nm. The
maximum value of vonSpringFig. 6 Structure of the test rig.

Manufactured prototype of the test rig with electricalcircuit is shown in Fig. 7.

(2)

Here l, b, h, t – working length, width, height andthickness of the cross-shaped spring correspondingly, G –shear modulus. As far as angle of twist is very small it can becalculated from the displacement of the shield in tangential
direction 'x, then (1) becomes:
TS

kS 'x RS .

(3)

Where RS – distance from the sensor center to the middleof the shield plate in radial direction. The cross-shaped spring
made from one piece of brass (G=3.71010 N/m2, l = 12 mm, b= 10 mm, h = 10 mm, t = 1.5 mm is shown in Fig. 4.

Fig. 4 Cross-shaped spring.

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Fig. 7 Test rig.

Force applied to the arm, secured by screw to the rotatableshaft, creates the torque. Calibration was realized by meansincrementation of angle of twist with small step and measuring
output signal from the photointerrupter. Obtained relationshipon linear section of transformation of displacement to voltage
is shown in Fig. 8. This diagram can be rebuilt in term of
applied torque, since torsional stiffness is known.

a)b)Fig. 10 Result of analysis of hub-spoke spring using FEM.

The test rig for calibration of the optical sensor has beencreated (Fig.11). The procedure of calibration is the same asprevious sensor.

Fig. 8 Relationship of output voltage vs. angle of twist.

The “in plane” structure of the optical torque sensor
includes the radial flexures subjected by loading bending
forceswhile
loadingstate.
The
layoutofthree-beam-hub-spoke structure is presented in Fig. 9.
b䎃

2

3

䎃

RS
r

Fig. 11 Test rig.

D

l

䎃

Obtained relationship between angle of twist and output
voltage is shown in Fig. 12.

1䎃tFig. 9 Hub-spoke structure layout.

In Fig. 9 the following designations are given: 1 – beam, 2– photointerrupter, 3 – shield. The rigidity of the hub can beincreased by introducing additional evenly distributed spokes[11]. The torsional stiffness of hub-spoke structure is derived
from:
kS

§ 1 3r 3r 2 ·4 NEI ¨  2  3 ¸ ,
l ¹
©l l

(4)

where N – number of spokes, l – the spoke length, E –modulus of elasticity, r – inner radius of the sensor [12].
Moment of inertia of the spoke cross section I can becalculated as:Ibt 3 ,
12

Fig. 12 Calibration result.

The sensor was manufactured from one piece of brass byusing wire electrical discharge machining (EDM) cutting toeliminate hysteresis and guarantee high strength (Fig.13).

(5)

here b – beam width, t – beam thickness. The sensor was
designed to support of 0.8 Nm torque which arises in theelbow joint of the robot arm. The results of analysis using
FEM show von Mises stress in MPa (Fig. 10a) and thetangential displacement in mm (Fig. 10b) under torque of 0.8
Nm. The maximum value of von Mises stress equals VvonMises =14.57107 N/m2 < Vyield = 15.0107 N/m2.

1677

Fig. 13 Optical torque sensor with hub-spoke-shaped flexure.

In this sensor the photointerrupter type RPI-121 was used.
The thickness of the sensor body is only 6.5 mm. The
adjustment of the shield position is realized by rotation of
oppositely located screws. The pitch of the screws is enoughfor smooth movement of the slider with shield plate.
In order to extend exploiting range of photodetector
sensitivity keeping same strength the ring-shaped spring was
designed. Components and assembly of the developed opticaltorque sensor are presented in Fig. 14. The flexible ring isconnected with inner and outer part of the sensor thoughbeams. The inner and outer beams are displaced with angle of
90q that enables large compliance of the ring-shaped flexure.

Type of sensor
Spring material
Load capacity,
Nm
Torsional
stiffness,
Nm/radFactor of safety
Photointerrupter
type
Outer diameter,mm
Thickness, mm
Sensor mass, g

Fig. 14 Optical torque sensor with ring-shaped flexure.

The results of analysis using FEM under torque of 0.8 Nm
are given in Fig. 14 (a – von Mises stress in MPa; b –tangential displacement in mm). The maximum value of stressequals VvonMises = 8.62107 N/m2 < Vyield = 8.96107 N/m2.

a)

The thickness of the sensor is 10 mm. Displacement of theshield is measured by photointerrupter type RPI-131. The
shortcomings of this design are complicated procedure ofadjusting the position of the shield relatively photosensor anddeficiency of the housing to prevent from damage of the
optical transducer. Technical specification of the realized
optical torque sensors is listed in Table I.

b)

TABLE ITECHNICAL SPECIFICATION
Cross-shaped
Hub-spoke-shaped
springspringRing-shaped
springAluminium
A5052

Brass C2801

Brass C2801

1.75

0.8

0.8

90.02

219.8

115.9

1.0

1.0

1.0

RPI-131

RPI-121

RPI-131

30

42

42

30
36

6.5
34.7

10
28.7

Cross-shaped spring provides transmission of large torqueand small outer diameter of the sensor. However, this spring
introduces considerable angle error caused significant
compliance. Spoke-hub topology allows realization ofcompact in axial direction sensor. However, big torsional
stiffness diminishes resolution of photointerrupter. Probably,
the optimal solution is the ring-shaped flexure providing wide
range of torsional stiffness with high mechanical strength. The
main shortcoming of this topology is high sensitivity to thebending moment. Nevertheless, this obstacle can be overcome
trough realization of simple supported loading shaft of therobot joint. In the most loaded joints, e.g. shoulder joint, suchmaterial as hardened stainless steel can be used for elastic
element to keep the sensor dimension.
IV. LOCAL IMPEDANCE CONTROL

Fig. 15 Result of analysis of the ring-shaped spring using FEM.

The aim of the impedance control is to establish the
dynamic relationship between position error and force error ininteraction similar to Newton`s second low of motion. The
graphical presentation of concept of the local impedancecontrol is given in Fig. 17.

Obtained relationship between angle of twist T and theoutput voltage of photointerrupter is shown in Fig. 16.

FEXT
Jdi

Dd(i+1)

Ddi

Jd(i+1)W EXT (i+1)

Kd(i+1)Kdi

WEXTi

Fig. 16 Calibration result.
Fig. 17 Concept of the local impedance control.

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In joint space system desired dynamics of robot joint i is:

J di 'Ti  Ddi 'Ti  K di 'Ti ; 'Ti

W EXTiT ci  T di ,The second-order low-pass filter was implemented toeliminate noise component with cutoff frequency of 80 Hz.

(6)

V. CONCLUSION

here WEXTi – torque applied to joint i caused by external force
FEXT, Jdi – desired inertia, Ddi – desired damping, Kdi – desired
stiffness, Tci – output joint angle of the impedance model, Tdi –desired joint angle. The state-space presentation of theequation of local impedance control can be written:ª 'Ti º ª 0« »=«¬ vi ¼ ¬  K d J dNew optical torque sensors in order to replace thestrain-gage-based 6-axis force/torque sensor and realize virtual
backdrivability of joint transmissions have been developed.
These sensors are compact, light in weight, easy to
manufacture, moreover, they have good linearity, enoughresolution and electromagnetic noise immunity. Position based
local impedance control of SCARA type manipulator has beensuccessfully implemented. The new anthropomorphic armwith ability build in developed torque sensors has been
designed. New stage of research is realization of the local
impedance control of each joint of the robot arm.

1º ªTi º ª 0 ºW (t ) . (7) Dd J d »¼ «¬ vi »¼ «¬1 J d »¼ EXTi

'Ti .
After integration of (7) the discrete time presentation ofimpedance equation can be expressed as:
Where state variable is defined as viª 'T k +1 º
ª 'T k º« 'T » =Ad « 'T »  Bd TEXT ( k ) .
¬ k +1 ¼¬ k¼

REFERENCES[1] R. Tadakuma, Y. Asahara, H. Kajimoto, N. Kawakami, and S. Tachi:
̌Development of anthropomorphic multi-D.O.F. master-slave arm for
mutual telexistence,̍ IEEE Transactions on Visualization and Computer
Graphics, vol. 11, no. 6, pp. 626-636, November 2005[2] J. D. Turner and M. H. Westbrook, Automotive Sensors. Bristol, U.K.:IOP,
1993.
[3] P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak,“Capacitive sensor for relative angle measurement, ” IEEE Transactions
on Instrumentation and Measurement, vol. 51, no. 6, pp. 1145-1149,
December 2002.
[4] A. M. Madni, R. K. Hansen, and J. B. Vuong, “Differential capacitive
torque sensor,” U.S. Patent No. 6 772 646, 2004.
[5] S. Hirose and K. Yoneda, “Robotic sensors with photodetecting
technology,” Proc. of 20th International Symposium on Industrial
Robotics, pp. 271-278, 1989.
[6] S. Hirose and K. Yoneda, “Development of optical 6-axial force sensor
and its non-linear calibration,” J. of RSJ, vol. 8-25, pp. 19-28, 1990.
[7] N. Okutani and K. Nakazawa, “Torsion angle detection apparatus andtorque sensor,” U. S. Patent No. 5 247 839, 1993.
[8] S. J. Horton, “Displacement and torque sensor,” U. S. Patent No. 6 800
843 B2, 2004.
[9] Photointerrupter Design Guide. Product catalog of ROHM, pp. 6-7,
2005.
[10] M. M. Williamson, “Robot arm control exploiting natural dynamics,”
PhD thesis, Massachusetts Institute of Technology, 1999.
[11] C. Nicot, “Torque sensor for a turning shaft,” U. S. Patent No. 6 694 828
B1, 2004.
[12] D. Vischer and O. Khatib, “Design and development ofhigh-performance torque controlled joints,” IEEE Transactions on
Robotic and Automation, vol. 11, no. 4, pp. 537-544, August 1995.

(8)

Where Ad and Bd – matrixes mapped by discretization. In
order to verify the dynamic behavior of the optical torquesensor the local impedance control of links of simple SCARA
type manipulator was implemented (Fig.18, torque sensors aremarked by ovals, gear ratio of speed reducers equals 2548).

Fig. 18 SCARA manipulator and response plot.

Block diagram of realized position based local impedancecontrol system is presented in Fig. 19 (KP and KD –proportional and derivative feedback gains respectively).

Impedance
trajectory
generator' T k+1

A/D' T k+1 ' T k+1

Td
Targettrajectory
generator

Tc

Td

Optical torquesensorDigital low䎐pass filter

Tc

Kv

Td
T

Kp

1
Ki KT

D/A

DriverTc
T

sFig. 19 Block diagram of the position based impedance control.

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Encoderim

Link