Safe Reaction of a Robot Arm with Torque Sensing Ability on theExternal Disturbance and Impact: Implementation of a New
Variable Impedance Control
Dzmitry Tsetserukou* Hiroyuki Kajimoto*† Naoki Kawakami* Susumu Tachi*(*) Department of Information Physics and Computing, The University of Tokyo, Japan(*†) The University of Electro-Communications, Japan
E-mail: dima_teterukov@ipc.i.u-tokyo.ac.jp, kajimoto@hc.uec.ac.jp, kawakami@star.t.u-tokyo.ac.jp,
tachi@star.t.u-tokyo.ac.jp
Abstract - The paper focuses on control of a new anthropomorphic robot arm enabling the torquemeasurement in each joint to ensure safety while performing tasks of physical interaction with humanand 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.
1. Introduction
Many operations in specific environments are dangerous for human (e.g. nuclear, in-space,underwater) or difficult to access (e.g. micromanipulation). 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 thetelexistence concept and gradually improved
performance and stability of teleoperation [1]. The
operator cockpit has two 6-DOF exoskeleton-type
structure arms with hands. The slave robot enables toperform complex interaction with objects inenvironment 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 andunstructured human environment. The operator has tomove the slave robot arm to target position, and to
perform manipulations while simultaneously avoiding
obstacles. However, operators cannot accomplishthese tasks in real time. Besides, they are not perfectin planning the collision-free motion in dynamic
unstructured surroundings.
Fig.1 Whole-sensitive
Recent researches on teleoperation are focusing
teleoperated robot arm
on automation of collision avoidance and contact 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 [2]. The developed manipulator hand has very good force sensing ability due tothe 6-axis force sensors attached at the fingertips and 19 Force Sensing Resistors. Using thisforce/tactile sensing ability, the operator moves the robot arm until the palm contacts an object, andthen, grasping algorithm is activated. However, collision or expected contact with an environment
may occur on the entire 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 behavior 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 werereported. To avoid collisions in time-varying environment, Lumelsky et al. [3] proposed to covermanipulator with a sensitive skin capable of detecting nearby objects. As this device integrates a hugeamount of small sensors incorporated in tiny rigid platform, and requires complicated wiring andsignal processing hardware, such devices have high cost and reliability issues. Besides, sensitive skinprovides only contact pattern information. Finding the technical solution for trade-off between safety
and performance is the target of the new manipulation technology. To cope with this issue, the active
compliance control implying fast joint torque controlling based on measuring applied external torquein each joint was developed. The first embodiment of torque measurement is the integration of atorque sensor into each joint of the manipulator. The impedance control generates compliant
trajectory based on measured external torque information. Such approach 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 to increase the performance for fast movements by active vibration
damping. Several attempts have been made by researchers to improve joint torque control. Wu andPaul [4] proposed simple, wide bandwidth, torque servo system using strain-gauge-based joint torquesensor. The developed torque-controlled lightweight robot arm with high load to weight ratio isdescribed in [5]. Each joint of the arm is facilitated with strain-gauge-based torque sensor, position
sensor and piezzo-brake. Sakaki and Iwakane [6] proposed to use a compact motor drive withembedded magnetostrictive torque sensor for impedance control of the robot arm. The approach of
torque measurement through the elasticity of the harmonic drive flexsplines allows keeping the same
stiffness and mechanical structure of the robot [7]. This method requires the strain gauges to beinstalled 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 of robot arms interacting with humans is
intentionally introducing compliance at the mechanical design level. The main idea is decoupling therotor inertia from the link inertia through using passive elasticity [9]. However, the robot control iscomplicated by many unknown parameters (e.g. actuator stiffness and damping). Furthermore,
compliant transmission negatively affects the performance in term of increased oscillations andsettling time.
To realize the safe physical contact of entire robot arm structure with human and to guarantee thecollision avoidance, our primary idea is concentrated on the design of a whole-sensitive robot arm (byusing distributed torque sensors in each joint). When contact with environment occurs, manipulator
automatically adjusts its dynamic parameters (stiffness and damping) according to the measured
external torque and time derivative of torque. The newly developed anthropomorphic manipulator
having 4-DOF arm and 8-DOF hand (Fig. 1) is capable to safely interact with environment wherevercontact occurs on the arm surface. The distinctive features of our approach are as follows:
1) We use optical approach for torque measurement, which allows avoiding inherent
shortcomings of strain-gauge-based and magnetostrictive force/torque sensors. We developed
new optical torque sensors having high dependability, good accuracy (even in 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, whencollision 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 reflex-action-based impact control were
elaborated to realize safe, smooth and natural human-robot interaction.
The remainder of the paper is structured as follows. Section 2 describes the development of awhole-sensitive robot arm. The elaborated intelligent variable impedance control algorithm allowing
contact state recognition and the experimental results are discussed in Section 3. In Section 4, we
briefly conclude the paper.
2. Design of a New Anthropomorphic Robot Arm
From the safety point of view, to minimize injures in case 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 kinesthetic sensation
during teleoperation.
To remove mechanical subsystems 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 andlightweight component one. The Harmonic Drive offers such advantages as accurate positioning, hightorque capability, torsional stiffness, and high single stage ratios. Developed teleoperated robot arm
has 4-DOF: Roll, Pitch, Yaw joints of a shoulder, and Pitch joint of an elbow. Each joint is equippedwith optical torque sensor directly connected to the output shaft of Harmonic Drive. The sizes andappearance 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 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 andcoordinate systems based on Denavit-Hartenberg convention are represented in Fig. 2.
+

Yaw

Z0
Y0

X0
Pitch
Roll
+

+

Torque sensor
distribution in Shoulder
Pitch and Roll Joints

Z1
Y2
Z2

J2

Y1

J1

X1

X2

L1
J3

Sensors
in Yaw
and
Elbow
Joints

Z4

Y4

X4

Y3

J4

X3
Z3

Z5

L2

Y5

X5

Fig.2 3D CAD arm model and coordinate systems
The motors are equipped with magnetic encoders having 512 pulses per revolution. To protect
the sensor against influence of bending moment and axial force, the simple supported loaded shaft
configuration was implemented using two sets of bearings. The principal specifications of thedeveloped arm and kinematic parameter values are given in Table 1 and Table 2, respectively.

Table 1. Principal specifications

J1, Pitch

Arm joints
ShoulderJ2, Roll
J3, Yaw

Elbow
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-14GH /100)

7.8,(CSF-14GH /100)

5.0,(CSF-112XH/100)

5.0,(CSF-112XH/100)

Parameters

Table 2. Denavit-Hartenberg
parameters
αi-1

1

[deg]
90

a i-1
[m]
0

di
[m]
0

[deg]
θ1-90

2

-90

0

0

θ2+90

3

90

0

L1

θ3+90

4

-90

0

0

θ4-90

5

0

L2

0

0

i

θi

3. The Impedance Control
3.1 Joint Impedance Control
The dynamic equation of an n DOF manipulator in joint space coordinates (during interaction
with environment) is given by:
M (θ )θ + C (θ , θ)θ + τ f (θ) + g (θ ) = τ + τ EXT ,(1)

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 is the vectorof Coriolis and centrifugal torques; τf( θ )∈ Rn is the vector of actuator joint friction forces; g(θ) ∈ Rn

is the vector of gravitational torques; τ ∈ Rn is the vector of actuator joint torques; τEXT ∈ Rn is thevector of external disturbance joint torques.
People can perform dexterous contact tasks in daily activities while regulating own dynamics
according to time-varying environment. To achieve skillful human-like behavior, the robot has to beable to change its dynamic characteristics depending on time-varying interaction forces. The mostefficient method of controlling the interaction between a manipulator and an environment isimpedance control. This approach enables to regulate response properties of the robot to external
forces through modifying the mechanical impedance parameters. The graphical representation of joint
impedance control is given in Fig. 3.

FEXT
Jdi

Dd(i+1)Jd(i+1)
τ EXT (i+1)

Ddi
Kd(i+1)Kdi

τEXTi
Fig. 3 Concept of the local impedance control

The desired impedance properties of i-th joint of manipulator can be expressed as:

J di ∆θi + Ddi ∆θi + K di ∆θ i = τ EXTi ; ∆θ i = θ ci − θ di ,(2)

where Jdi, Ddi, Kdi are the desired inertia, damping, and stiffness of i-th joint, respectively; τEXTi is
torque applied to i-th joint and caused by external and gravity forces, ∆θi is the difference between
the current position θci and desired one θdi. The state-space presentation of the equation of local
impedance control is written as follows:⎡ ∆θi ⎤ ⎡ 0⎢⎥=⎢⎣ vi ⎦ ⎣ − K d J d⎤ ⎡θi ⎤ ⎡ 0 ⎤τ (t ) ,+− Dd J d ⎥⎦ ⎢⎣ vi ⎥⎦ ⎢⎣1 J d ⎥⎦ EXTi
1

(3)

or:

⎡ ∆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
time presentation of the impedance equation is expressed as:⎡ ∆θ k +1 ⎤⎡ ∆θ k ⎤=Ad⎢ ∆θ ⎥⎢ ∆θ ⎥ + Bd TEXT ( k ) .
⎣ k +1 ⎦⎣ k⎦(5)To achieve the fastest possible non-oscillatory response to the external force, we assigned theeigenvalues λ1 and λ2 of matrix A as real and equal λ1=λ2=λ, λ>0. By using Cayley-Hamilton method
for matrix exponential determination, we have:T⎡ 1 − λ1T⎤
Ad = eλT ⎢⎥,⎣ − Dd T /(4 J d ) 1 − λ1T − Dd T / J d ⎦λT
1 ⎡ e (1 − λT ) − 1 ⎤ ,Bd = ( Ad − I ) A B = −⎢⎥K d ⎣⎢ − ( Dd /(2 J d ) )2 TeλT ⎦⎥
−1

(6)

(7)

where T is the sampling time; I is the identity matrix.
There are several conflicting requirements on the choice of dynamics parameters of impedancemodel to provide effectiveness and functionality of robot in tasks of 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 (to ensuresmall position error during object handling) and high damping (for good velocity tracking).
Realization of human following motion, mainly used in performing of co-operating 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 of collision, the very small stiffness
is obligatory to reduce the impact forces. Basically, there are two types of solution of this problem:
adaptive and functional adjustments of impedance parameters. In the adaptive control, damping andstiffness of the system are gradually adjusted according to sensed dynamics and contact forces [10].
However, due to parametric uncertainties of the robot dynamics model, it is difficult to obtain thecomplete description of the dynamics. Therefore, model-based adaptive impedance control must relyon either repeated motions or time for adaptation to achieve convergence to the desired systemparameters. For systems with more then one DOF, such approach hardly can be applied.
In the functional approaches, current impedance parameters have predetermined relations to thecurrent sensed variables. Generally, these methods presume determining the current stiffness anddamping matrices functionally dependent on sensed variables. The main idea of the paper [11] is thatthe involving contact between slave robot and the environment can be classified according to theangle between commanded velocity and the 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, 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 not only beparallel, 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 [12].
The proposed variable impedance controller varies a damping parameter of target impedance inproportion to an estimated value of the human arm stiffness. Despite the fact that robot caneffectively 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 and providing the dynamic
stability of the system.
3.2 Intelligent Variable Joint Impedance Control
The research on impedance characteristics of human arm shows that, while pushing or pullingthe object naturally, human arm stiffness and damping behavior can be approximated by exponential
curves [13]. The first essential peculiarity of new control method is that we introduce the exponentialfunctional dependency between sensed force and stiffness to impart the human-like damping andstiffness behavior to the robot arm interacting with 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 τEXTth to distinct the service task (withhigh stiffness and damping of joints) from human following motion tasks requiring low stiffness. Thisvalue can be chosen depending on the force necessary to accomplish the service task. We assigned
the specific magnitude of τEXTth to each joint of robot arm. The third distinctive contribution is therecognition of the collision avoidance based on the time derivative of the joint torque.
The procedure of impedance parameters selection (in the example of elbow joint) is as follows.
On the first stage, the parameters of desirable impedance model of robot are computed for the case ofservice 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 ∆θmax caused by external torque τEXT while service task performance.
K d1 =

τ EXT∆θ max(8)

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:
Dd 1 = 2ζ K d 1 J d 1(9)To realize fast non-oscillatory response on the external torque, we defined damping coefficient ζof 1.05. The value of desired inertia Jd1 of 0.1 (kg⋅m2) was assigned to realize 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 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 smoothnatural interaction. To realize such continuous change of dynamics, we are using exponential relation
between external disturbance torque and desired stiffness:
K d 2 = K d 1e ( EXTµτ−τ EXTth )

,

(10)

where Kd2 is the desired stiffness on the second stage of interaction; µ is the coefficient defining thelevel of decreasing of arm joint stiffness in response on increasing difference between external torqueand threshold external torque value.
The desired damping is adjusted to prevent force responses from being too sluggish whilechanging stiffness values, and to ensure contact stability:
Dd 2 = 2.1 K d 2 J d 1 = 2.1e

0.5 µ (τ EXT −τ EXTth )Kd1J d1(11)Then, variable joint impedance controller is described by:
0.5 µ τ−τµτ−τJ di ∆θi + 2.1e ( EXTi EXTth ) K d 1 J d 1 ∆θi + K d 1e ( EXTi EXTth ) ∆θ i = τ EXTi ; ∆θ i = θ ci − θ di(12)

To verify the theory and to evaluate the feasibility and performance of the proposed impedancecontroller, the experiment with new whole sensitive robot arm was conducted. To ensure theeffectiveness of service task accomplishment, we decided to implement position-based impedancecontrol (Fig. 4). In this algorithm, compliant trajectory generated by the impedance controller istracked by the PD control loop.
Constant impedance
trajectory generator

τ EXT < τ EXTth
Comparator

Variable impedance
trajectory generator

τ EXT > τ EXTth τEXT

∆ θk+1 ∆ θk+1

∆θk+1
θd
Targettrajectory
generator

θd

θc

θc
θd

ε
+-

Kv

+-

θ

s

Kp

T

- G

TZ

τ EXT > τ EXTthCollision avoidance
trajectory generator

Gravitycompensation

1
Ki KT

Optical torquesensor

A/D

D/A

θ

Driver

im

Link

θc
θ

EncoderFig. 4 Block diagram of position-based impedance control
During the experiment, the interaction with arm was performed to exceed join torque thresholdlevel (τEXTth of 0.6 Nm was assigned, µ = -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 torque with different magnitudes and corresponding impedancetrajectories with constant and variable coefficients – are presented in Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig.
9, and Fig. 10, respectively.

τEXTth

0.4
0.2
0.0
0.0

1.5

3.0

4.5

6.0

Time t, (sec.)

7.5

9.0

External Torque τEXT , (Nm)Threshold torque

0.6

Joint Stiffness Kd , (Nm/rad)

0.8

0.8

8

0.4

4

0.2

2
0
0.0

1.5

3.0

4.5

6.0

Time t, (sec.)

7.5

2.4

Damping Dd , (Nm s/rad)

-2

1.8

-4

-8
Varible coefficients
Constant coefficients

3.0

4.5

6.0

Time t, (sec.)

7.5

0

9.

0.0
0.0

2

4

6

Time t, (sec.)

8

10

Fig. 9 External torque
0

-4
-6

0.6

1.5

0.0

-2

1.2

-6

-12
0.0

9.0

Fig. 7 Variable stiffness Kd

0-10

Threshold torqueτEXTth0.6

6

Fig. 5 External torque
Impedance Trajectory, ∆θk+1 (deg.)

1.0

10

1.0

Impedance Trajectory, ∆θk+1 (deg.)

External Torque τEXT , (Nm)

1.2

Varible coefficients
Constant coefficients

-8

1.5

3.0

4.5

6.0

Time t, (sec.)

7.5

9.0

0

2

4

6

Time t, (sec.)

8

10

Fig. 6 Impedance trajectories
Fig. 8 Variable damping Dd
Fig. 10 Impedance trajectories
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 provides softer
trajectory to accomplish human following motion than the impedance control with constantcoefficients. As we assigned the critically damped response of impedance model to disturbance force,
output angle (∆θk+1) 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 humanfollowing 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.
In daily life, a person frequently contacts with an environment. The impact between the limb andenvironment is 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 to quickly 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 therobust control strategy of impact effect minimization, the application area of such approaches ishighly 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 the limbs awayfrom the object. In our control algorithm, impact is processed as follows. When an unexpectedcollision is detected, the impact control algorithm provides the pre-programmed reflex action of therobot arm. After accomplishment of a safe and smooth collision, the control system is returned to theoriginal mode aimed at distinguishing the service and co-operating tasks. While analyzing the resultsof collision experiments, we came to conclusion that the large contact forces, mainly used as criterionof collision, do not indicate the impact, while the time derivative of force value does. In thedeveloped impact control system, the value of the time derivative of torque τEXTth exceeding theassigned threshold is interpreted as collision state. To realize reflexive human-like behavior, thestiffness 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 anddesired stiffness coefficient Kd3 was defined with large coefficient µ of 0.7:
K d 3 = K d 1e − µτEXTth(13)

To attenuate the oscillations of the robot arm, which are inherent to collision, the larger constantdamping coefficient ζ of 1.25 was assigned. The value of desired damping coefficient is calculated
from Eq. (9). In the second stage of contact transient, while time derivative of torque is negative, thehigh 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:Dd 3 = 2.5 K d 1 J d 1 − α dτ ,

(14)

2.6
1.3
0.0
-1.3
0.00

0.25

0.50

0.75

1.00

Time t, (sec.)

4
3
2
1

Impedance Trajectory, ∆θk+1 (deg.)

Joint Stiffness Kd , (Nm/rad)

8

0.25

0.50

0.75

1.00

Time t, (sec.)

1.25

0

2

Collision coefficients
Constant coefficients

-6

0
0.00

0.25

0.50

0.75

1.00

Time t, (sec.)

1.25

Fig. 12 Variable stiffness Kd

Service task
1.3
0.0

0

1

2

3

Time t, (sec.)

4

5

Fig. 15 Torque derivation
0

-4

-4

4

Threshold value

2.6

-2

-2

6

Impact3.9

Fig. 13 Variable damping Dd

Fig. 11 Torque derivation
10

5.2

-1.3

0
0.00

1.25

Time derivative of torque, (Nm/s)

Threshold value

5

Impedance Trajectory, ∆θk+1 (deg.)

3.9

Damping Dd , (Nm s/rad)Time derivative of torque, (Nm/s)

where αd is the weighting factor for damping (equals to1.2).
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 collisionvariable coefficients, time derivative of torque for two different contact states and corresponding
impedance trajectories – are presented in Fig. 11, Fig. 12, Fig. 13, Fig. 14, Fig. 15, and Fig. 16,
respectively. The threshold value of the time derivative of torque τEXTth was assigned to 2.6 Nm/s.

-6-8
Collision coefficients
Constant coefficients

-10

-8
0.00

0.25

0.50

0.75

1.00

Time t, (sec.)

1.25

Fig. 14 Impedance trajectories

0

1

2

3

Time t, (sec.)

4

5

Fig. 16 Impedance trajectories

From the plots of experimental results, it is apparent that, when impact is recognized (timederivative of torque becomes larger then threshold value), the stiffness and damping are decreasing
drastically (Fig. 12, Fig. 13), allowing avoidance of large impact forces. On the second stage ofinteraction, when the impact force is decreasing, the damping coefficient of impedance model (Fig.
13) is increased 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 derivative of torque has large spike and is shortened in time scale value). The
developed control takes advantage of this feature to generate reflex-action-based motion.
4. Conclusion

The conventionally impedance-controlled robot can provide contacting task only at the tip of theend-effector with predetermined dynamics. By contrast, approaches developed by us provide delicate
continuous safe interaction of all surface of the arm with environment.

[1]

[2]

[3]

[4]
[5]

[6]

[7]

[8]

[9]

[10]
[11]
[12]

[13]

[14]

[15]

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