VOLUME 2,

Journal of Automation, Mobile Robotics & Intelligent Systems

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2008

SAFE REACTION OF A ROBOT ARM WITH TORQUE SENSING ABILITY
ON THE EXTERNAL DISTURBANCE AND IMPACT:
IMPLEMENTATION OF A NEW VARIABLE IMPEDANCE CONTROL
Dzmitry Tsetserukou, Hiroyuki Kajimoto, Naoki Kawakami, Susumu Tachi

Abstract:
The paper focuses on control of a new anthropomorphic
robot arm enabling the torque measurement in each joint
to ensure safety while performing tasks of physical interaction with human and environment. A novel variable control strategy was elaborated to increase the robot functionality and to achieve human-like dynamics of interaction.
The algorithm of impact control imparting reflex action
ability to the robot arm was proposed. The experimental
results showed successful recognition and realization of
three different types of interaction: service task, co-operative task, and impact state.
Keywords: human-robot interaction, anthropomorphic
robot arm, variable impedance controller.

1. Introduction
Many operations in specific environments (e.g. nuclear, in-space, underwater) are dangerous for human ordifficult to access (e.g. micromanipulation, surgery).
Recently, teleoperation is gaining increased attention
by researchers interested in studying the possibilities
to overcome the limited functionality of autonomous robots performing specific tasks, and to improve dexterous
operations.
We successfully developed master-slave robot systems (TELESAR I and TELESAR II) based on the telexistence concept and gradually improved performance andstability of teleoperation [1]. The operator cockpit has
two 6-DOF exoskeleton-type structure arms with hands.
The slave robot enables to perform complex interaction
with objects in environment by means of 7-DOF arms and
8-DOF hands. The contact tasks of a tip of the end-effector with environment are provided by impedance control
algorithm. A slave robot controlled by the operator mainly performs the manipulations in unknown and unstructured human environment. The operator has to move theslave robot arm to target position, and to perform manipulations while simultaneously avoiding obstacles. However, operators cannot accomplish these tasks in realtime. Besides, they are not perfect in planning the collision-free motion in dynamic unstructured surroundings.
Recent researches on teleoperation are focusing on automation of collision avoidance and contact task based on
information from sensors, allowing thus operator toconcentrate on the task to be performed. The Robonautteleoperated robot was developed to assist in-space operations and work with humans in space exploration [2].
The developed manipulator hand has very good force
sensing ability due to the 6-axis force sensors attached at

the fingertips and 19 Force Sensing Resistors. Using thisforce/tactile sensing ability, the operator moves therobot arm until the palm contacts an object, and then,grasping algorithm is activated. However, collision or
expected contact with an environment may occur on theentire surface of the robot arm (e.g. forearm, elbow,
upper arm, shoulder) producing interactive forces. Moreover, teleoperated robot in rescue and some other applications has to interact with human being in various cooperative tasks. In these fields, human-robot interaction
represents a crucial factor for a robot design and imposes
strict requirements on its behaviour and control in orderto ensure safe interaction with environment and effectiveness while target task execution.
Several effective methods on enhancement of contact
detection ability of manipulator were reported. To avoid
collisions in time-varying environment, Lumelsky et al.
[3] proposed to cover manipulator with a sensitive skincapable of detecting nearby objects. As this device integrates a huge amount of small sensors incorporated ona tiny rigid platform, and requires complicated wiring andsignal processing hardware, such devices have high costand reliability issues. Besides, sensitive skin provides
only contact pattern information. Finding the technicalsolution for trade-off between safety and performance isthe target of the new manipulation technology. To copewith this issue, the active compliance control implying
fast joint torque controlling based on measuring theapplied external torque in each joint was developed. The
first embodiment of torque measurement is the integration of a torque sensor into each joint of the manipulator.
The impedance control generates compliant trajectory
based on measured external torque information. Suchapproach has two main advantages: (1) sensor detects
not only forces applied to the hand but also those exerted
at other points on the manipulator, (2) and allows toincrease the performance for fast movements by active
vibration dam-ping. Several attempts have been made byresearchers to improve joint torque control. Wu and Paul[4] proposed simple, wide bandwidth, torque servo
system using strain-gauge-based joint torque sensor. The
developed torque-controlled lightweight robot arm withhigh load to weight ratio is described in [5]. Each joint of
the arm is facilitated with strain-gauge-based torquesensor, posi-tion sensor and piezzo-brake. Sakaki andIwakane [6] proposed to use a compact motor drive withembedded magnetostrictive torque sensor for impedancecontrol of the robot arm. The approach of torque measurement through the elasticity of the harmonic drive flexsplines allows keeping the same stiffness and mechanicalstructure of the robot [7]. This method requires the strain
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gauges to be installed on the flexsplines. The crucial
shortcomings of the torque measurement approaches
mentioned above are discussed in the paper [8]. The
alternative method for increasing the safety level ofrobot arms interacting with humans is intentionally introducing compliance at the mechanical design level. The
main idea is decoupling the rotor inertia from the linkinertia through using passive elasticity [9]. However, therobot control is complicated by many unknown parameters (e.g. actuator stiffness and damping). Furthermore,
compliant transmission negatively affects the performance in term of increased oscillations and settling time.
To realize the safe physical contact of entire robot
arm structure with human and to guarantee the collision
avoidance, our primary idea is concentrated on the design of a whole-sensitive robot arm (by using distributed
optical torque sensors in each joint). When contact withenvironment occurs, manipulator automatically adjusts
its dynamic parameters (stiffness and damping) according to the measured external torque and time derivativeof torque. The newly developed anthropomorphic manipulator iSoRA (intelligent Soft Robot Arm) having 4-DOF
arm and 8-DOF hand (Fig. 1) is capable to safely interact
with environment wherever contact occurs on the arm
surface.

2. Design of a new anthropomorphic
robot arm
From the safety point of view, to minimize injures incase of collision, most of the robot parts were manufactured from aluminium alloys to obtain as much lightweight structure as possible. The robot links were designed in round shape to reduce impact force. The distribution of the arm joints replicates the human arm structure
in order to make it easy to operate using kinaesthetic
sensation during teleoperation. To remove mechanicalsubsystems without disassembling the main structure
when the failures do occur, we have been using a modular
approach while designing anthropomorphic robot arm.
Therefore, we selected CSF-series gear head type of Harmonic Drive instead of compact and lightweight component one. The Harmonic Drive offers such advantages as
accurate positioning, high torque capability, torsional
stiffness, and high single stage ratios. Developed robot
arm has 4-DOF: Roll, Pitch, Yaw joints of a shoulder, andPitch joint of an elbow. Each joint is equipped with optical torque sensor directly connected to the output shaftof Harmonic Drive. The sizes and appearance of the arm
were chosen so that the sense of incongruity during
interaction with human is avoided. We kept the arm
proportions the same as in average height human: upper arm length L1 of 0.308 m; upper arm circumferenceof 0.251 m (diameter 0.080 m); forearm length L2of 0.241 m; forearm circumference of 0.189 m (diameter
0.06 m). The 3D CAD model of the developed arm andcoordinate systems based on Denavit-Harten-berg 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

J2

Y1

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J1

X2

L1
J3

Z4

Y4

X4

Y3
X3

J4

Z3
Z5

Y5

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

Z0

Y0
+
X0 +
Pitch
Roll

X1

X5

The remainder of the paper is structured as follows.

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Section 2 describes the development of a whole-sensitive
robot arm. The elaborated intelligent variable impedancecontrol algorithm allowing contact state recognition
and the experimental results are discussed in Section 3.
In Section 4, we briefly conclude the paper.

Fig. 1. iSoRA robot arm.
The distinctive features of our approach are as follows:
1) We use optical approach for torque measurement,
which allows avoiding inherent shortcomings ofstrain-gauge-based and magnetostrictive force/torque sensors. We developed new optical torque sensors
having high dependability, good accuracy (evenin electrically noisy environment), low price, compact sizes, and easy manufacturing and calibration
procedure [8].
2) The stiffness of the proposed sensor is much smaller
then previously proposed. So, when collision takes
place, the injuries of human can be considerably reduced through compliant coupling between the motor rotor inertia and the link inertia.
3) The intelligent variable impedance control and reflexaction-based impact control were elaborated to realize safe, smooth and natural human-robot interaction.

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The motors are equipped with magnetic encoders having 512 pulses per revolution. To protect the sensor against influence of bending moment and axial force, thesimple supported loaded shaft configuration was implemented using two sets of bearings. The principal specifications of the developed arm and kinematic parametervalues are given in Table 1 and Table 2, respectively.

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ters. The graphical representation of joint impedancecontrol is given in Fig. 3.

Table 1. Principal specifications.

Fig. 3. Concept of the local impedance control.
The desired impedance properties of i-th joint ofmanipulator can be expressed as:(2)
where Jdi , Ddi , Kdi are the desired inertia, damping, andstiffness of i-th joint, respectively;
is torque applied to i-th joint and caused by external and gravity forces,
is the difference between the current positionand desired one . The state-space presentation of theequation of local impedance control is written as follows:

Table 2. Denavit-Hartenberg parameters.

(3)

or:

3. The impedance control(4)3.1. Joint impedance control
The dynamic equation of an n-DOF manipulator injoint space coordinates (during interaction with environment) is given by:where the state variable is defined as; A, B matrices. After integration of (4), the discrete time presentation of the impedance equation is expressed as:

(1)
where
are the joint angle, the joint angular velocity, and the joint angle acceleration, respectively;
is the symmetric positive definite inertia
matrix;is the vector of Coriolis and centrifugal torques;is the vector of actuator joint
friction forces;
is the vector of gravitational
torques;is the vector of actuator joint torques;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 skilful human-likebehaviour, 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 environmentis impedance control. This approach enables to regulate
response properties of the robot to external forces
through modifying the mechanical impedance parame-(5)

To achieve the fastest possible non-oscillatory response to the external force, we assigned the eigenvalues
l1 and l2 of matrix A as real and equal.
By using Cayley-Hamilton method for matrix exponential
determination, we have:

(6)

(7)

where T is the sampling time; I is the identity matrix.
There are several conflicting requirements on the
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choice of dynamics parameters of impedance model toprovide effectiveness and functionality of robot in tasksof physical interactions fulfilled in co-operation with humans, and to ensure the collision avoidance. For example,
while accomplishing service tasks for human in the autonomous mode, it is required to provide high stiffness (toensure small position error during object handling) andhigh damping (for good velocity tracking). Realization ofhuman following motion, mainly used in performing of cooperating tasks, also imposes specific requirements on desired impedance parameter selection. In this approach, byapplying force to the robot arm, it is possible to intuitively
operate the robot along the force and speed direction
without considering any command signals. In the case ofcollision, the very small stiffness is obligatory to reducethe impact forces.
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 tosensed dynamics and contact forces [10]. However, due toparametric uncertainties of the robot dynamics model, it isdifficult to obtain the complete 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. For systems with more then one DOF, such approach
hardly can be applied. In the functional approaches, current impedance parameters have predetermined relations
to the current sensed variables. Generally, these methods
presume determining the current stiffness and damping
matrices functionally dependent on sensed variables. The
main idea of the paper [11] is that the involving contact
between slave robot and the environment can be classified
according to the angle between commanded velocity andthe contact force. It is supposed that force and velocity
vectors are usually parallel when the impact occurs or when
the object is being pushed. So, the functional dependencyof stiffness and damping on angle between sensed force
and velocity vectors was proposed. In real co-operation
tasks and, especially, collisions, these vectors can not only
be parallel, but also have indepenent arbitrary directions
according to external force coming direction.
Another line of variable impedance research is directed to estimation of human arm stiffness [12]. The proposed variable impedance controller varies a damping
parameter of target impedance in proportion to an estimated value of the human arm stiffness. Despite the factthat robot can effectively follow the human arm motion,
it cannot perform task autonomously. Besides, only impedance parameters of the robot end-effector can be adjusted. We elaborated a new methodology for impedance
parameter adjustment based on the interaction mode andproviding the dynamic stability of the system.
3.2.

Intelligent variable joint impedance control

3.2.1. Control of service task and human following
motionThe research on impedance characteristics of humanarm shows that, while pushing or pulling the object naturally, human arm stiffness and damping behaviour can be
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approximated by exponential curves [13]. The first essential peculiarity of new control method is that we introduce the exponential functional dependency between
sensed force and stiffness to impart the human-like damping and stiffness behaviour to the robot arm interactingwith environment. The second main feature originatesfrom the fundamental conflict in impedance selection
with regard to current working conditions. We consider
the threshold of external disturbance torque value
to distinct the service task (with high stiffness and damping of joints) from human following motion tasks requiring low stiffness. This value can be chosen depending on
the force necessary to accomplish the service task. We
assigned the specific magnitude ofto each joint ofrobot arm. The third distinctive contribution is the recognition of the collision based on the time derivative of
joint torque. The procedure of impedance parameters selection is illustrated by the example of elbow joint as follows. On the first stage, the parameters of desirable impedance model of robot are computed for the case of service task accomplishment and average-level-contact-force of human-robot interaction. The desired stiffness Kd1(for static equilibrium case) is calculated from Eq. (8)based on the maximum deflection value of joint angle
caused by external torquewhile service task
performance.
(8)

It was defined that external torque of 1 Nm results inof 0.1 rad giving the Kd1 of 10 (Nm/rad). The
desired damping is expressed as:(9)
To realize fast non-oscillatory response on the external torque, we defined damping coefficient 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 arevalid till the interaction force does not cause the overload of robot arm. When sensed value of the torque is larger then threshold level, robot recognizes this condition
as human following motion mode, and adjusts its dynamics parameters (stiffness and damping) in the same way
as humans in order to provide smooth natural interaction. To realize such continuous change of dynamics, weare using exponential relation between external disturbance torque and desired stiffness:(10)
where Kd2 is the desired stiffness on the second stage ofinteraction; m is the coefficient defining the level of decreasing of arm joint stiffness in response on increasing
difference between external torque and threshold external torque value. The desired damping is adjusted to prevent force responses from being too sluggish while changing stiffness values, and to ensure contact stability:(11)

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Then, variable joint impedance controller is described by:(12)

To verify the theory and to evaluate the feasibility
and performance of the proposed impedance controller,
the experiment with new whole sensitive robot arm wasconducted. To ensure the effectiveness of service task
accomplishment, we decided to implement position-based impedance control (Fig. 4). In this algorithm, compliant trajectory generated by the impedance controller
is tracked by the PD control loop.

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During the experiment, the interaction with arm was
performed to exceed join torque threshold level (of 0.6 Nm was assigned, = -1.155). The experimental
results for the elbow joint – applied torque, impedance
trajectories with constant and variable coefficients, variable stiffness plot, variable damping plot, applied torquewith different magnitudes and corresponding impedance
trajectories with constant and variable coefficients – arepresented in Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, andFig. 10, respectively.
The experimental results show the successful realization of the variable joint impedance control. While contact with human, the robot arm generates compliant soft
motion according to the sensed force. The plot presented
in Fig. 6 shows that the variable impedance control

Fig. 4. Block diagram of position-based impedance control.

Fig. 5. External torque.

Fig. 7. Variable stiffness Kd.

Fig. 9. External torque.

Fig. 6. Impedance trajectories.

Fig. 8. Variable damping Dd.

Fig. 10. Impedance trajectories.

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provides softer trajectory to accomplish human following
motion than the impedance control with constant coefficients. As we assigned the critically damped response ofimpedance model to disturbance force, output angle
has ascending-descending exponential trajectory. As seen from the experimental results shown in Fig.
9 and Fig. 10, the proposed variable impedance control
comprehensively distinguishes and processes the service
tasks (torques under threshold level) and co-operative
human following tasks (torques above threshold level).
As the result of the experiments with variable impedance-controlled arm, tactile sensation of soft friendly
interaction was really achieved.
3.2.2. Impact control
In daily life, a person frequently contacts with an environment. The impact between a limb and environmentis inevitable during interaction. In order to work in human daily environment, robot has to recognize the collision condition, and its control system should be able toquickly and smoothly guide manipulator to avoid excessively large impact force. Different impact control algorithms were proposed. Basically, they are focusing on
preparing for impact in advance [14] and coping with impact during contact transience [15]. However, due to unexpected nature of collision and lack of the robust control strategy of impact effect minimization, the application area of such approaches is highly limited.
We believe that realization of the robust impact control should originate from human reflex system. A reflex
action is an automatic involuntary neuromuscular action
elicited by a defined stimulus, and it can respond to external stimuli with small reaction time retracting thelimbs away from the object. In our control algorithm, impact is processed as follows. When an unexpected colli-

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sion is detected, the impact control algorithm provides
the pre-programmed reflex action of the robot arm. Afteraccomplishment of a safe and smooth collision, the control system is returned to the original mode aimed at distinguishing the service and co-operating tasks.
While analysing the results of collision experiments,
we came to conclusion that the large contact forces,
mainly used as criterion of collision, do not indicate theimpact, while the time derivative of force value does.
In the developed impact control system, the value of thetime derivative of torqueexceeding the assigned
threshold is inter-preted as collision state. To realize
reflexive human-like behaviour, the stiffness of the impedance model of the robot arm on the first stage of contact transient has to be reduced drastically. Hence, exponential relation between time derivative of external
torque and desired stiffness coefficient Kd3 was definedwith large coefficient of 0.7:
(13)
To attenuate the oscillations of the robot arm, which
are inherent to collision, the larger constant damping
coefficient of 1.25 was assigned. The value of desired
damping coefficient is calculated from Eq. (9). In thesecond stage of contact transient, while time derivativeof torque is negative, the high damping value reducing
arm inertia effect is desired. For this case, the following
relation between desired damping Dd3 and time derivative of torque was specified:
(14)
where
1.2).

is the weighting factor for damping (equals to

Fig. 11. Torque derivation.

Fig. 13. Variable damping Dd.

Fig. 15. Torque derivation.

Fig. 12. Variable stiffness.

Fig. 14. Impedance trajectories.

Fig. 16. Impedance trajectories.

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The threshold value of the time derivative of torque
was assigned to 2.6 Nm/s. The experimental results
for the elbow joint – time derivative of applied torque,desired collision stiffness Kd3, desired collision damping
Dd3 plot, impedance trajectories with constant and collision variable coefficients, time derivative of torque fortwo different contact states and corresponding impedance trajectories – are presented in Fig. 11, Fig. 12, Fig. 13,
Fig. 14, Fig. 15, and Fig. 16, respectively.
From the plots of experimental results, it is apparent
that, when impact is recognized (time derivative of torque becomes larger than threshold value), the stiffnessand damping are decreasing drastically (Fig. 12, Fig. 13),
allowing avoidance of large impact forces. On the second
stage of interaction, when the impact force is decreasing,the damping coefficient of impedance model (Fig. 13) isincreased to suppress the dynamic oscillations. The Fig.
15 indicates that nature of co-operation tasks (time derivative of torque has small and stretched in time scale value) completely differs from impact state (time derivativeof torque has large spike and is shortened in time scalevalue). The developed control takes advantage of thisfeature to generate reflex-action-based motion.

AUTHORS
Dzmitry Tsetserukou, Naoki Kawakami and Susumu
Tachi - Department of Information Physics and Computing, The University of Tokyo, Japan. E-mails:
dima_teterukov@ipc.i.u-tokyo.ac.jp,
kawakami@star.t.u-tokyo.ac.jp,
tachi@star.t.u-tokyo.ac.jp.
Hiroyuki Kajimoto - Professor at Department of Human
Communication, The Universityof Electro-Communications, Japan. E-mail: kajimoto@hc.uec.ac.jp.

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[2]

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[4]

[5]

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4. Conclusion
New whole-sensitive robot arm iSoRA was developed
to provide human-like capabilities of contact task performing in a broad variety of environments. Each joint was
facilitated with high-performance optical torque sensor.
The intelligent variable impedance control and reflexaction-based impact control were elaborated to realize
safe, smooth, and natural human-robot interaction. We
introduced the exponential functional dependency between sensed force and stiffness to impart human-like
damping and stiffness behavior to the robot arm. Experimental results of impact revealed that large contact forces, mainly used as criterion of collision, do not indicate
the impact state, while the time derivative of force value
does. The magnitude of time derivative of torque wasused as an indicator of collision state. To realize reflexive
human-like behavior, stiffness of the impedance modelof robot arm was reduced drastically during collisiontransient. This was achieved by means of reciprocal functional dependency of stiffness on the value of time derivative of torque.
The conventionally impedance-controlled robot can
provide contacting task only at the tip of the end-effector with predetermined dynamics. By contrast, approaches developed by us provide delicate continuous safeinteraction of all surface of the arm with environment.

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[10]

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