Development of Distributed Optical Torque Sensors for Realization of Local ImpedanceControl of the Robot Arm
Dzmitry Tsetserukou, Riichiro Tadakuma, Hiroyuki Kajimoto and Susumu Tachi
Graduate School of Information Science and Technology
The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
Email: dima_teterukov@ipc.i.u-tokyo.ac.jp

This paper describes the recent development of 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. Different shapesof mechanical structure of sensor as well as optical measurement approaches are given. The results of calculation ofstress and tangential displacement using Finite Element Method and experimental results of research are presented. The
concept of local impedance control of joints of humanoid robot arm is considered.
1.

INTRODUCTION

The teleoperated slave robot has been developed to realize
dexterous tasks as interaction with human in remoteenvironment or manipulation with objects in hazardous
conditions. The slave robot [1] includes anthropomorphic
seven-degree of freedom (7-DOF) arms with 8-DOF hands(Fig. 1). To achieve the stability in contact withenvironment and torealize
controlled
dynamic interaction
between a robot arm
and
human
the
impedance control has
been
successfullyapplied.
The
impedance control of
the arm of the remoteslave robot requires
measurementof
external force exerted
by human during
interaction [2]. The
force imparted byhuman at the tip of theanthropomorphic arm
is measured by 6-axes
force sensor (MINI
4/20, made by BL
AUTOTEC), marked
Fig. 1 Teleoperated slave robot
by yellow rectangles
in Fig. 1.
In spite of the fact that developed robotic system ensures
the safety in the interaction at the end-effector, other partsof the mechanical structure, such as shoulder and elbow
joint, during operation can hurt people. In these joints
there are no force measurement sensors to limit the motor
torque by means back loop. Direct sensing of applied
torque through the value of current in DC motor circuit isunacceptable due to low backdrivability of harmonic
drives with high gear ratio (=50). Therefore, to realize
human friendly interaction of any part of theanthropomorphic arm we decided to attach torque sensor ateach joint and, thus, to implement local impedance control.
Thus, virtual backdrivability of transmissions can beachieved in each joint of slave robot.
Moreover, commercial force sensors using strain gauges
typically measure all six axes - forces and torques – andintended for use at the end-effector of a robot to monitor
assembly or machining forces. In this application very
high stiffness is required. For human-robot interaction
high stiffness is not the objective. Also strain gauges have
many disadvantages. They are difficult to install, calibrate
and easy to break that makes them expensive.
The authors introduce the idea of using optical approach todetect torque and realization of the local impedancecontrol on the base of optical sensors to provide safety ofinteraction.
2. DEVELOPMENT OF THE OPTICAL TORQUESENSOR
2.1 Optical Approaches of the Torque and Force
Measurement
The idea of optical methods is non-contact measurement ofrelative twist or displacement of the components of thesensor caused by torque or force using photosensors.
Photosensors have the similar drawbacks inherent to thestrain gauges, such as nonlinearity and temperaturesensitivity, but they are considerably more reliable, cheap
and allow simplifying the construction of the design.
A significant contribution to research of the optical force
and moment sensors was made by Shigeo Hirose [3, 4].
The author proposed to use a split type photosensor todetect the displacement of the light source caused byapplied force. In the paper [5] authors used infrared
LED-photodiode pairs to detect force. This optical force
sensor consists of outer mount, inner part and flexureconnected to the inner part. Optical sensors are attached tothe inner part. The force applied to the inner part bend theflexure. Light from LED reflects the output piece and isdetected by a photodiode. Thus, the distance between
flexure and fixed part is measured and, hence, force can becalculated. The idea of the patent [6] is calculating torqueby measuring angle of twist of the torsion shaft throughdetection of difference in the rotation position of discs
attached at the opposite sides of the torsion shaft using
optical encoder. Structure of 6-axes force and torqueconverter using LEDs and photodiodes to detect bending isgiven in [7].
Drawbacks of above-mentioned optically based torquesensors are precise adjustment of the light source anddetector position, complicated calibration procedure due tononlinear output and large overall dimensions. To
overcome main pointed disadvantages of the sensors anddevelop optical torque sensor as light as possible withcompact size and high sensitivity we decided to use
ultra-small size photointerrupters type RPI-131 andRPI-121. The relationship between output and position ofthe shield plate for RPI-121 is presented in Fig. 2 [8].

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000DISTANCE: d (mm)dDdRELATIVE COLLECTOR CURRENT: Ic (%)

521521RELATIVE COLLECTOR CURRENT: Ic (%)

disadvantage is large overall length. Moreover, spring
introduces considerable angle error caused significantcompliance. In “parallel” structure the radial flexures aresubjected by bending forces. The layout of widely used
spoke structure of the hub having three flexures ispresented in Fig. 3. Detector consists of input part, output
part connected by flexure 1, fixedly mounted
photointerrupters 2, shield 3. The operation principle is thefollowing: when torque T is applied to the input shaft theflexures 1 will be deflected. This causes motion of theshield 3. The shield displacement is detected by the degreeof interruption of infrared light falls on the phototransistor.
Thus, magnitude of the output signal of photointerrupter
will correspond to the applied torque.

t

DISTANCE: d (mm)Fig. 2 Relative output vs. distanceFor detecting of relative displacement of torque sensor
components it is possible to use the linear section ofdiagram corresponding approximately 0.3 mm.
2.2 Analysis of Mechanical Structure. Determination of
the Optimal ShapeTo increase the signal-to-noise ratio of the sensor, it isdesirable to design a structure that generates a large angleof twist for a given loading torque and, therefore, provides
a high sensitivity. However, the resulting complianceintroduces a joint angle error that should be minimized.
Thus, one of the primary design trade-offs is between thestiffness and the sensitivity of the sensor.
The other difficulty in design of the torque sensor iseliminating hysteresis. Most metals used as flexures havevery little hysteresis. However, bolted, press fit andwelded joints near the flexure introduce hysteresis.
Therefore, the optimal design requires realization of themechanical structure of the sensor from a single piece ofmetal. It is also important to use differential measurements
to increase the linearity and disturbance rejection of thetorque sensors.
Taking into account above-mentioned, two main types ofthe mechanical structure were investigated: the “serial”
structure – when the input and output section of thedetector are displaced in axial direction by torsion
component. And the “parallel” structure – when input andoutput of the sensor are disposed in one plane and linked
by bending radial flexures.
The “serial” structure permits transmission of large torqueunder small outer diameter of the sensor. The main

Fig. 3 Hub layout

The relationship between the sensed torque TS and theangle of twist θ is following:
TS = kSθ = kS (θ1 − θ 2 )(1)

where kS – torsional stiffness of the cross-shaped spring.
The rigidity of the hub can be increased by introducing
additional evenly distributed spokes [9]. The torsional
stiffness of this sensor is derived from:⎛ 1 3r 3r 2 ⎞kS = 4 NEI ⎜ + 2 + 3 ⎟l ⎠⎝l l(2)

where N – number of spokes, l – the spoke length, E –modulus of elasticity, r – inner radius of the sensor [10].
Moment of inertia of the spoke cross section I can becalculated as:
I=bt 3 .
12(3)Here b – beam width, t – beam thickness. The sensor was
designed to withstand torque of 0.8 Nm. The results ofanalysis using FEM show von Mises stress in MPa (Fig.
4a) and tangential displacement in mm (Fig. 4b) under
torque of 0.8 Nm. The maximum value of von Mises stressequals σvonMises=14.57⋅107 N/m2 <σyield=15.0⋅107 N/m2).
Angle of twist can be calculated from the value oftangential displacement.

a)b)Fig. 4 FEM results

In this sensor the ultra-small photointerruptor RPI-121 isused. The thickness of the sensor body is only 6.5 mm.
The adjustment of shield position is realized by rotation ofscrews. The pitch of the screws is enough for smoothly
movement of slider with shield plate.
In order to improve the reliability of the mechanicalstructure of the transducer and enhance the flexibility thenew topology of the sensor has been developed.
Three-dimensional model and result of stress analysis are
given in Fig. 8.

The test rig for calibration of the optical sensor has beencreated (Fig.5). Force applied to the arm secured by screw
to the rotatable shaft creates the loading torque.
Calibration was realized by means incrementation of angleof twist with small step and measuring output signal fromthe photointerrupter.

Fig. 8 New topology and its stress analysis

Fig. 5 Test rig

The flexible ring is connected with inner and outer part ofthe sensor though beams. The inner and outer beams are
displaced with angle of 90° enabling large compliance ofthe ring-shaped flexure. For calibration of the senor the set
up shown in Fig. 5 was utilized. Obtained relationshipbetween angle of twist θ and the output voltage ofphotointerrupter is shown in Fig. 9.

Obtained relationship between angle of twist and output
voltage is shown in Fig. 6.

Fig. 9 Calibration result
Fig. 6 Calibration result

The sensor was manufactured from one piece of brass byusing wire electrical discharge machining that allowed toreceive very precise dimensions of spokes (Fig.7).

This structure was manufactured from one piece ofaluminum. Components and assembly of the torque sensor
with ring-shaped flexure are presented in Fig. 10.

Fig. 7 Optical torque sensor with spoke topology

Fig. 10 Optical torque sensor with ring-shaped flexure

The thickness of the sensor is 10 mm. The displacement of
the shield is measured by photointerruptor type RPI-131.
Exploded three-dimensional view of the optical sensor isgiven in Fig. 11.

law, τEXT – external torque applied from environment, ) – vector of centrifugal andM(Θ) – mass matrix, V(Θ, ΘCoriolis erms, G(Θ) – vector of gravity terms.
The aim of the impedance control is to establish thedynamic relationship between position error and force
error in interaction similar to Newton`s second low ofmotion. The graphical presentation of concept ofimpedance control is given in Fig. 12.

Case

B

ShieldPhotointerrupter

KSensor
Case
Gear box
Fig. 11 Exploded view

The shortcomings of this design are complicated procedureof adjusting the position of the shield relatively
photosensor and lack of the housing to prevent fromdamage of the optical transducer. Mechanical properties ofthe realized topologies of load cell are listed in Table 1.
Table 1 Mechanical properties

Type

Spoke- shaped
flexureMaterial

Brass C2801

Ring-shaped
flexureAluminium
A5052
9.2

Mass, g
18.52
Thickness/
35Length, mm
Outer diameter, mm
4242
Max. torque, Nm
0.8
0.8
Factor of safety
1.03
1.0
Torsional stiffness,
219.8
121.91
Nm/radConsidering obtained characteristics we can define
advantages and shortcomings of the developed structures.
Spoke-hub topology allows realization compact in axial
direction sensor, however, big torsional stiffness
diminishes the resolution of the photointerrupter. The
ring-shaped flexure provides wide range of the torsional
stiffness with high mechanical strength. To enlarge theallowable transmitted torque such material as spring steel
or brass can be used.
2.

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

τ iEXT = M dθi + Bd (θi − θ0 ) + K d (θi − θ 0 )Dynamics of the manipulator during interaction withenvironment is described by the equation:(4)

Where τ – required torque from actuator to realize control(5)Here Md – desired inertia, Bd – desired viscousness, Kd –desired stiffness, θ0 – desired joint angle, θ0 – desired
angular velocity of the joint, τiEXT – external torque applied
to the joint i. The concept of local impedance control ispresented in Fig. 13.

BB

τ

iK
K

i+1

τ

i+1EXTi+1iEXTiFig. 13 Concept of local impedance control

In order to verify the dynamic behaviour of the opticaltorque sensor the torque control of three links of simple
SCARA type manipulator has been developed. The control
law of a PD controller is as follows [11]:iτ m = τ d − K P (τ S − τ d ) − K Dτ SLOCAL IMPEDANCE CONTROL

 + V (Θ, Θ ) + G (Θ )
τ + τ EXT = M (Θ)Θ

Fig. 12 Concept of the impedance control(6)

where i – gear ratio, τm – motor torque, KP and KD –proportional and derivative feedback gains respectively, τd– desirable torque, τS – sensed torque. Block diagram ofPD torque control is presented in Fig. 14, the three links
with driving motors and control circuits are shown in Fig.
15.τd+τError

KP++−iτ m1iKtimMotor

τSKD ddt
Fig. 14 Block diagram of PD torque control

Fig. 15 Torque controlled links

4. CONCLUSION
New optical torque sensor has been developed using
photointerrupter to measure the relative rotation. This
invention allows realization of compact and light sensor.
Besides, photointerrupter is easy to mount and replace, hasa good linearity, enough resolution and does not affectedby electromagnetic noise. New stage of research isrealization of the local impedance control on the base ofdeveloped sensors.
5. REFERENCES[1] Tadakuma, R., Kawabuchi, I., Kajimoto, H.,
Kawakami, N. and Tachi, S., “Mechanism of an
Anthropomorphic
7-DOF
SlaveArmforTelexistence,” Proceedings of 13th International
Symposium on Measurement & Control in Robotics(ISMCR’03), Madrid, Spain, pp. 79-82, 2003.
[2] Tadakuma, R., Sogen, K., Kajimoto, H., Kawakami,N. and Tachi, S., “Development of Multi-D.O.F.
Master-Slave Arm with Bilateral Impedance Controlfor Telexistence,” Proceedings of 14th International
Symposium on Measurement & Control in Robotics(ISMCR’04), Houston, Texas, D21, 2004.
[3] S. Hirose and K. Yoneda, “Robotic sensors withphotodetectingtechnology,”Proc.
of20thInternational Symposium on Industrial Robotics, pp.
271-278, 1989.
[4] 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.
[5] W. A. Lorenz, M. A. Peshkin, and J. E. Colgate,“New sensors for new applications: Force sensors forhuman/robot interaction,” Proc. of the 1999 IEEE
International Conference on Robotics & Automation,
Detroit, Michigan, pp. 2855-2860, May 1999.
[6] N. Okutani and K. Nakazawa, “Torsion Angle
Detection Apparatus and Torque Sensor,” U. S.

Patent 5 247 839, 1993.
[7] A. J. Hilton, “Force and Torque Converter,” U. S.
Patent 4 811 608, 1989.
[8] Photointerrupter Design Guide. Product catalog ofROHM, pp. 6-7, 2005.
[9] C. Nicot, “Torque Sensor for a Turning Shaft,” U. S.
Patent 6 694 828 B1, 2004.
[10] D. Vischer and O. Khatib, “Design and developmentof high-performance torque controlled joints,” IEEE
Transactions on Robotic and Automation, vol. 11, no.
4, pp. 537-544, August 1995.
[11] D. Vischer, O. Khatib, and J. Hake, “Joint torquesensory feedback in the control of PUMA
manipulator,” IEEE Transactions on Robotic andAutomation, vol. 5, no. 4, pp. 418-425, August 1989.