Fault

Tolerant Force in Human
and
Robot Cooperation
Hamid Abdi
1
, Member IEEE, Saeid Nahavandi
2
, S
enior
M
ember
IEEE
, Zoran Najdovski
3
, Member IEEE
,
Anthony A. Maciejewski
4
, F
ellow Member
IEEE
1,2,3
Center for Intelligent Systems Research,
Deakin University
, Geelong Waurn Ponds Campus,
V
ictoria
3217, Australia
1,
4
Electrical and Computer Engineering Department
,
Colorado State University
Fort Collins, CO 80523
, USA
Abstract

Fault

tolerant
solutions
greatly
benefi
t
the
dependability of robot
ic systems
. T
h
is
advantage
is
critical for robot
ic
systems
that perform in collaboration
with humans
.
This
work
addresses
the
fault
toleran
ce
of
robotic manipulator
s
for cooperatively manipulating an object
together
with a human.
C
ooperation
occurs for slow lifting or
pushing of the object
.
Reconfiguration
of the manipulator
is
performed to maintain the cooperative force level despite
the occurrence of
robot
joint
failure
s.
We present
several
strategies
that
are
investigat
ed
for
optimally maintain
ing
the
required
force
level for
human

robot
task
co
operation
. For each strategy,
a reconfiguration
control
law
is introduced
that
optimis
es
the fault
tolerance
of the
maintained
force
level
.
T
hree case studies
are introduced
to validate the proposed
reconfiguration laws
,
demons
trating
that
th
is approach
r
esult
s
in an
optimal
fault

tolerant
force
in
human

robot cooperation.
Keywords:
Human

robot
cooperation,
fault

tolerant
robot, safety, reliability
I.
I
NTRODUCTION
Human

robot collaboration has
recently received
increasing interes
t within
the robotic
s
community
[
1
,
2
]
.
Within
this collaboration, for the robotic system to be dependable, a high l
evel of reliability and safety must be achieved
[
3
]
.
R
obotic systems
are
being
specifically design
ed and
developed to
operate
with
in human proximity
. S
uch
examples are
a
w
ork
partner
robot
, which
assist
s
humans
[
4
]
,
astronaut
s
[
5
]
, surgeon
s
[
6
]
,
the
elderly
,
and also
people with disabilities
[
2
,
7

9
]
.
Improving the performance of this collaboration can greatly benefit robot
dependability, and consequently increase human task accuracy and efficiency.
All aspects of
human

robot cooperation
(H
RC) are important
[
10
]
, including
fault tolerance
.
F
ault tolerance
is a
significant factor
due to improving
the
dependability of the robot
ic system
[
10
,
11
]
.
In social robotics,
the level of
dependabilit
y
is a critical component
of the robotic system
for
meet
ing
the specific safety requirements.
The
subject
of safety plays a significant role when it is
crucial
to
complet
e
the require
d
task
even in the event of partial
failure of the robotic
system
[
11

13
]
.
In addition, w
ithout fault toleran
ce
strategies, the dependability of
the robot
is vulnera
ble
,
and
fa
ilure of the robot can result in
non

desired behavior
throughout its process
.
Current research that addresses HRC and human

robot interaction (HRI) can be classified into the three
categories, p
hysical
,
emotional
and
safety
[
14

16
]
.
With presently little focus on the physical category of HRC,
existing work
centres
on the area of manipulation, and does not lend itself to properties such as fault tolerance.
For example,
Kosuge et al.
[
17
]
,
utilise
a double arm robot (
Mr Helper
), to support an object’s weight, where the
human can apply a force to the ob
ject in order to move it.
Such
a
mechanism fails to support the object weight in
the case of joint failure of the robot.
Using
impedance control
methods, a
force
control
HRC
approach
has been
realised
by
Tsumugiwa
[
18
]
and
Takubo
[
19
]
.
By means of
this
method,
other implementations and
applications of force control HRC
have
also
been introduced
[
9
,
20

24
]
.
While this work makes significant contribution to human

robot cooperation, it does
not
address
recovery from
failure of the robotic systems
,
and completing its required process
.
Consequently
, if
the
robot’s joint fails,
the desired cooperation will no longer
be maintained
,
which
can
result in
serious damage or
injury.
Fault

tolerant
HRC
is
advantageous
to increase
the
level of
robot reliability and
ensure that tasks
are completed
despite joint fa
ilure.
The fault

tolerant force
approach for
human

robot cooperation
[
13
]
demonstrates
two fault
tolerance
strategies
based on the reconfiguration of t
he robot joint torques
,
and
the
human’s force. T
he
present
work
extends
on this
by introducing
the
general form of the strategies
.
This
paper is organized as follows: Section II
indicates
the kinematic
s
and dynamic
s
of manipulators
subject to
locked joint
failures. Section III
obtains
the
force

jump
due to the locked joint failures in human and robot
cooperation
.
In
Section I
V
,
six
post failure cooperation strategies
to minimize the
force

jump
are proposed
.
Three
case studies
are demonstrated in section
s
V

VII.
Finally
,
the conclu
ding
remarks are presented
in section VII
.
II.
K
INEMATICS OF REDUNDA
NT MANIPULATORS
A.
Notation hints
1

In all formulas,
bold uppercase
letters are matrices,
bold lowercase
letters are vectors,
and lower case
letters are scalars.
2

There
are three notations for forces. The forces prior to the failure
f
,
at failure time
f
ˆ
, post failure forces
f
~
.
3

The star symbol for parameters indicates the maximum bound
,
f
or example
*
f
is the bound of force.
B.
A
ssumptions
There are three assumptions, including slow moving or stationary force tasks, small operational workspace, and
locked joint failure. The slow moving or stationary assumption is because of the safety of the human
who is in
proximity
to
the robot
and collaborates with
the
robot. The second assumption is because the robot move
s
slowly
or
is
stationary, therefore the task is in a small part of the robot workspace.
One example of this can be surgical
robots as they mo
ve in a small operation workspace with slow velocity.
Another
assumption
is
that the paper addresse
s
the locked

joint failures of the robot
.
Although the presented
method is not applicable for other failures,
it is possible to consider a mechanical brake
in order
to lock the joints.
In this case, the proposed method of this paper will be applicable for other types of
joint
failures.
C.
Kinematics of serial manipulators
Forward kinematics of serial manipulators relates joint variables to the EEF positional var
iables
through
the
forward kinematic equation
)
(
q
k
x
(
1
)
where
n
T
n
R
q
q
q
....
2
1
q
are
joint variables,
m
m
R
x
x
x
'
2
1
...
x
are
positional variables,
and
m
n
R
R
:
(.)
k
The configuration space
(C

space)
or join
t space is defined by
q
and
the workspace
is defined by
x
.
The
dimension of the
C

space
is
n
and the dimension of the workspace is
m
.
For positional manipulators in 3D spac
e
3
m
and in 2D space
2
m
. In
the
planar case
(2D)
, it is possible to consider
3
m
where the z

component
is always fixed.
The fault tolerance is more likely to be achieved in
a
redundant manipulator w
here
m
n
. The
degree of redundancy in non

singular configuration is
m
n
r
.
D.
Velocity and force equations
and
locked joint
fai
lures
The
EFF
translational velocity equation
is
q
J
x
(
2
)
where
n
R
3
J
is
the
analytic
Jacobian
matrix
defined by
q
q
k
J
T
he
EEF
force
f
is related to the
joint

torque
s
by
f
J
τ
T
(
3
)
where
T
n
....
2
1
τ
is torque
vector
.
Fo
r
the
manipulator
in
a
non

singular configuration, the
EEF
force is obtained
by
z
J
J
I
τ
J
f
T
T
T
†
†
(
4
)
where
m
m
R
I
is an identity matrix,
†
T
J
is the pseudo inverse of
T
J
, and
m
R
z
is an arbitrary vector
This arbitrary vector
is
mapped into
the
null space of
T
J
by the null space projection matrix
T
T
J
J
I
†
. The
pseudo inverse of
T
J
at
the
non

singular configuration is define
d
by
the
regular
inverse,
left
inverse,
or
right
inverse
as shown in
Appendix

1.
E.
Model of locked joint failures
To model the
EEF
force
subject to
a
locked joint failure
, we
assume
†
T
J
A
(
5
)
where
n
k
k
k
a
a
a
a
a
A
...
...
1
1
1
and
k
a
is the
k

th
column of
A
Using the abo
ve convention, as the force in E
quation
(
4
) can be written by
z
J
J
I
τ
a
f
T
T
n
i
i
i
†
1
(
6
)
Each column of
A
indicates the contribution of the cor
responding joint to the
EEF
force.
Therefore,
w
hen a
locked joint fa
ilure
occurs
in the
k

th
joint
,
the joint stops
contribut
ing and
the force can be modeled by
eliminating
k
k
τ
a
from
equation
(
6
)
z
J
J
I
τ
a
τ
a
f
T
T
k
k
n
i
i
i
†
1
ˆ
(
7
)
By using t
he
convention of
reduced matri
ces
and vectors (presented in
A
ppendix

2
), the force at
failure time is
z
J
J
I
τ
A
f
T
T
k
k
†
ˆ
(
8
)
where
A
k
is
the
k

th
reduced matrix and
1
n
k
R
τ
is
the
k

th
reduced
vector
F.
Stationary
or slow pushing
or
lifting
force
The dynamic equation of the manipulator when a
n
EEF force
f
m
is required
is
τ
f
J
q
g
q
q
q
V
q
q
M
m
T
)
(
)
,
(
)
(
(
9
)
where
)
(
q
M
is
the
inertia
matrix,
q
q
q
V
)
,
(
is Coriolis

centrifu
gal term and
)
(
q
g
is the gravity term
,
τ
is
the
torque
and
f
J
m
T
in the
left
side is the torque required to apply
EEF force
f
m
.
If an external force is applied to the robot
’s
EEF, th
en
f
J
m
T
is considered in the
right
side. However, in our case,
we don’t apply a force to the EEF
,
therefore the term
f
J
m
T
is not in the
left
side. In this paper, the robot applies
force
f
m
by its EEF
to an external load, therefore the term
f
J
m
T
is considered in the right side of the equation
(9). This is because the required torque
is
for the motion of the robot which is defined by
)
(
)
,
(
)
(
q
g
q
q
q
V
q
q
M
plus for the EEF force
f
m
which is defined by
f
J
m
T
.
I
f
the
manipulator is
stationary or moves
slowly
0
,
q
q
, t
hen
equation (
9
) is simplified to
τ
f
J
q
g
m
T
)
(
.
Therefore, the required torque is the torque
due to the gravity
and the torque to apply the EEF force
.
Hence
)
(
q
g
is
known
, therefore the required torque is obtained by adding
)
(
q
g
to
f
J
m
T
.
G.
Fault

tolerant force for HRC
Assume
a
robot
and
human are providing
a coo
perative
force for lift
ing object
s
as shown in
Figure 1
. The total

force is
f
f
f
h
m
(1
0
)
where
f
m
is the manipulator force and
f
h
is the human force
Figure
1
.
H
uman

robot force coopera
tion
in load lifting application
If
a
locked joint failure occurs in
the
manipulator, then
EEF
force changes
[
25
]
by the
force

jump
f
m
.
Accordingly
,
the
total

force
will
result
to
f
f
f
m
h
m
and
the
total

force

jump
is
f
f
m
.
The present paper aims to
address
the
following questions:
1

How the manipulator and the human can tolerate the fa
ilure or
minimize the
total

force

jump
?
2

What are the strategies for reconfiguring the human
force
and the manipulator
torque
?
3

What are the conditions to provide a zero
force

jump
?
These questions are more challenging when
considering
: (a) the optimality of the post failure cooperation of the
human and the manipulator
,
(b) the physical limitation of the human force, and (c) the physical limitation of the
faulty manipul
ator
[
14
]
.
III.
F
ORCE

JUMP
IN HUMAN AND ROBOT C
OOPERATION
A.
Locked joint failure via perturbation method
When the
k

th
joint of the manipulator fails, then the force equation is perturbed
z
J
J
I
τ
τ
A
A
f
T
T
m
†
ˆ
(11)
where
τ
is
the
torque jump,
A
is matrix perturbation and
f
ˆ
m
is the
force

jump
which is obtaine
d as
A
τ
τ
A
A
f
ˆ
m
(12)
where
T
k
0
...
0
0
...
0
1
τ
and
0
...
0
0
...
0
k
a
A
I
t is easy to
check
that
0
τ
A
A
and
k
k
a
A
τ
.
This results
in
k
k
m
a
f
ˆ
.
Knowing that th
e
force
of
the
human
at failur
e time
is
f
f
h
h
ˆ
. Therefore,
the
total

force
at failure time
is
f
f
f
ˆ
ˆ
ˆ
h
m
and
the
total

force

jump
i
s
k
k
a
f
f
f
ˆ
ˆ
.
B.
Fault

tolerant
force via reconfiguration
The
HRC
aims to
provide
a
total

force
for a task. Th
ese t
w
o
forces
should
not oppose each other and they are
preferred to be
in the
same
or close
direction
s
.
When a fault occurs, then
a
reconfiguration is required
to minimize
the post failure
force

jump
.
This require
s
reconfiguration of the manipulator’s torque and
humans force. After the
reconfiguration,
the post failure
human
force is
f
~
h
and manipulators EEF
force
is
f
~
m
. The reconfiguration of the
manipulator’s force is performed by adding a reconfiguration torque
u
,
to the remaining
healthy joints
z
J
J
I
u
τ
τ
A
A
f
T
T
m
†
~
(13)
Note that
u
should
ha
ve
a zero value in its
k

th
row
because the
k

th
joint is locked
n
T
n
k
k
R
u
u
u
u
...
0
...
1
1
1
u
(14)
Using the convention of reduced matrices
k
k
k
k
m
m
a
u
A
f
f
~
(15)
where
1
1
1
1
...
...
n
T
n
k
k
k
R
u
u
u
u
u
The
total

force

jump
after
reconfigur
ation
i
s
f
f
f
~
~
where
f
f
f
~
~
~
h
m
and force

jump
will be
f
f
a
u
Α
f
~
~
h
h
k
k
k
k
(16)
C.
Optimal fault tolerance
Optimal fault t
olerance is
defined
based on
the
minim
ization of the
post failure
total

force

jump
.
2
~
~
f
f
u,
h
Min
(17)
The constraints associated to
equation
(17)
include: (a) the bounds of the human force and (b) the bounds of the
manipulator join
t
torque.
W
he
n
*
f
h
is
a 3 dimensional vector showing
the maximum human force
in x,y and z
directions in the 3D space
for a particular configuration of the human
,
t
he constraints of the maximum human force
are
:
*
*
~
f
f
f
h
h
h
(18)
Similarly, when
1
*
n
k
R
τ
is the maximum torque
of
the
healthy joints, the
constraints
of the
torques
are
*
*
τ
u
τ
τ
k
k
k
k
(19)
If
the
manipulator
works in
a
3D space
,
then
there are
4
2
n
constrai
nts associated with
equations
(18)

(19) and
there are
2
n
variables associated with
1
n
k
R
u
and
3
~
R
h
f
. However, for 2D planar manipulators, there
are
2
2
n
constraints
and
1
n
variables.
IV.
STRATEGY FOR OPTIMAL
FAULT TOLERANCE
A.
General strategy for optimal fault tolerance
The
constrained
minimization can be solved via
various
iterati
ve
techniques
. This
is
a general
way
for fault
tolerance.
This strategy will be later
demonst
rated in case study
1. For this strategy, i
t is observed that there is no
appropriate
control over the
minimum
force

jump
and the
post failure cooperation
of the human and robot
. The
fact is that
the fault tolerance is very sensitive to the initial guess a
nd the optimization technique.
The lack of
appropriate control on the minimum
force

jump
and
post failure cooperation motivates developing specific
strategies.
T
he
specific
strategies
are expected to provide a
better control o
n
the post failure cooperation
and
specify the minimum
force

jump
.
B.
Specific strategies for optimal fault tolerance and minimum
force

jump
Five
specific
strategies are identified
which
are
introduced and formulated in this section.
We
categoris
e
them into
n
on

cooperative
and c
ooperative
fault tolerance strategies
.
B.1
.
Non

cooperative strategies
Strategy I:
In this strategy, the manipulator is responsible for its fault tolerance and the human would not
contribute
for
tolerating the
fault. Therefore,
the post failure human force remains
a
s
equal to
that
prior
to
failure
f
f
h
h
~
.
A
nd after
the
torque reconfiguration of the
manipulator
k
k
k
k
m
m
a
u
A
f
f
~
.
Then
,
the post failure
total

force

jump
is obtained
by
k
k
k
k
a
u
A
f
~
(2
0
)
The minimum
total

force

jump
is achieved
b
y using
the pseudo inverse
method
[
26
,
27
]
by
k
k
k
opt
k
a
A
u
†
(
2
1
)
By using the optimal
joint

torque
reconfiguration
,
a minimum
total

force

jump
is obtained
by
k
k
k
k
a
A
A
I
f
†
min
~
(
2
2
)
The matrix
†
A
A
I
k
k
is
the
null space projection matrix
that
give
s
the equation (2
2
)
,
a nice physical
interpretation. It says that the minimum
force

jump
is the projection of
k
k
a
into
the
null space
of
A
k
.
Knowing
that
k
k
a
is the lost part of the force due to the failure
,
therefore, i
f this force
does not have
a
ny
projection into
null space of
A
k
or if the null space is
zero
,
then the
post failure
total

force

jump
is
zero.
Strategy II:
In this strategy, the manipulator does not contribute to
the
fault tolerance. Therefore, the whole
responsibility of fault tolerance
is
with
the
human. This can be justified where
the
user aim
s
to
prevent any further
failure to
the manipulator. In this
strategy
u
k
would be a zero vector and the post failure
manipulator
force
is
k
k
m
m
a
f
f
~
(
2
3
)
The
force

jump
of the manipulator
is
k
k
a
. Therefore, the required post fa
ilure human force is
k
k
h
h
a
f
f
~
(
2
4
)
For this strategy,
the
total

force

jump
would be zero if the human force
remains in its bound
*
*
~
f
f
f
h
h
h
.
However, i
f the required post failure human force is
out of
th
is bound
, t
hen
the
force

jump
depends on
the
difference
of
f
~
h
and
the
bound
s
.
B.2.
Cooperative strategies
In this category of the strategies, three cooperative strategies are proposed. These strategies are based on different
ways of distributing the
f
orce

jump
between the faulty manipulator and the human.
Strategy III
: This st
rategy is a cooperative form of
strategy I
,
where
the
main responsibility of the fault tolerance
is with
the manipulator. Therefore, the manipulator maximally compensate
s
the
forc
e

jump
similar to that of
strategy I. The remainder of the
force

jump
which
is
shown by (
2
2
) is assigned to the human.
Therefore, t
he
manipulator optimally compensates the
force

jump
, and
the
reconfiguration joint

torque
is
obtained
by
k
k
k
opt
k
a
A
u
†
(
25
)
T
he remaining
force

jump
k
k
k
k
I
a
A
A
†
need
s
to be
provided
by the human. Therefore the required post
failure human force is
k
k
k
k
h
h
a
A
A
I
f
f
†
~
(
26
)
In
strategy
III
, the
total

force

jump
is
zero
if
the require
d post failure human force is in the bound of
*
*
~
f
f
f
h
h
h
. If
it is not in this
bound
, then t
he
force

jump
depends on
the
difference between
f
~
h
and the
bound.
Strategy IV
: This strategy is a cooperative form
of strategy
II
whe
re
t
he main responsibility of the fault tolerance
is with the human. Therefore, the human maximally covers the
force

jump
. If any force remains which is out
of
the human
’s
capability
, then
it would be assigned to the
faulty manipulator
.
The force of the h
uman is required to be
k
k
h
h
a
f
f
~
that
was introduced
by equation
(2
4
).
If
the
human
is
unable to apply
this
level of
force, then
the difference between
the assigned
human force and the human
’s
force
bound
is assigned to the manipulator.
Note t
hat the force is a vector, therefore
, i
f a
ny
component
of the human force
is in the bound, the
force

jump
associated to the component is zero
,
but if not
,
the
difference is obtained
. For
example
, if the required post failure
human force is
T
N
N
N
h
35
10
25
f
and the maximum human force is
T
N
N
N
h
20
20
20
*
f
then the
human force will be
T
N
N
N
h
20
10
20
~
f
and t
he
remaining
force

jump
is
T
N
N
N
15
0
5
.
T
he
manipulator change
s
its j
oint

torque
to optimally cover th
e
remaining
force

jump
.
If
the
remaining
force

jump
is
depicted
by
f
r
then the required change in the
manipulator
force is
u
A
f
f
f
k
k
r
m
m
~
ˆ
(
27
)
Consequently, the optimal post failure
joint

torque reconfiguration
is obtained
by
f
A
u
r
k
opt
k
†
(
28
)
Using this
joint

torque
,
the minimum
total

force

jump
will be
f
A
A
I
f
r
k
k
†
min
~
(
29
)
The
minimum
total

force

jump
is
the
projection of
f
r
into the null space of
A
k
.
Strategy V
:
In
this strategy, the fault is
tolerated
using
a decision

making process.
A decision maker
assigns the
force for the
post failure cooperation
for the
human and the robot
.
Optimal decision making for assigning post
failure force to the robot and the human requ
ires further research. For this strategy, we assume that the decision
maker
is known. In this case, the decision maker defines
two arbitrary matrices
W
m
and
W
h
where
I
W
W
h
m
and
W
m
i
s to assign the post failure force for the robot and
W
h
is to assign the post failure force
for the human. T
hen
,
t
he
total

force

jump
is divided in
to
two parts
f
W
f
W
f
W
W
f
ˆ
ˆ
ˆ
)
(
ˆ
h
m
h
m
(
3
0
)
where
f
W
ˆ
m
is the force
assigned to the manipulator, and
f
W
h
is assigned to the human.
Therefore, the require
d
post failure
human force is
k
k
h
h
h
Wa
f
f
~
(
3
1
)
The required
post failure
manipulator
force
is
k
k
m
m
m
Wa
f
f
ˆ
~
(
3
2
)
Knowing that
k
k
k
k
m
m
a
u
A
f
f
~
and
k
k
m
m
a
f
f
ˆ
then
, the reconfiguration is
k
k
m
k
k
Wa
u
A
(
3
3
)
T
he optimal
joint

torque
to
minimis
e
th
e
post failure
force

jump
is
k
k
m
k
opt
k
Wa
A
u
†
(
3
4
)
The optimal po
st failure force
of
the manipulator is
k
k
m
k
k
m
m
a
I
W
A
A
f
f
†
~
(
35
)
Then
,
the optimal
post failure
total

force
is obtained
by
k
k
h
k
k
m
k
k
Wa
a
I
W
A
A
f
f
†
~
(
36
)
Finally,
the minimum
post failure
total

force

jump
is
k
k
m
k
k
Wa
A
A
I
f
†
min
~
(
37
)
In t
his strategy,
if
the human is capable of providing
the assigned force
k
k
h
h
h
Wa
f
f
~
or the assigned human
force is in the bound
then e
quation (
37
)
give
s
the following
condition
s
of a zero
force

jump
.
1

When
0
W
A
A
I
m
k
k
†
(
38
)
2

When
k
k
a
belongs to the null space of
W
A
A
I
m
k
k
†
(
39
)
3

When
0
k
k
a
If the
human is capable of providing
the assigned force
, then the minimum
total

force

jump
only depends
on
the
projection of the
manipula
tor’s
assigned force to the null space of the manipulator.
The conditions of
a
zero
force

jump
is
use
ful
to de
fine values for
W
m
and
W
h
by the decision maker
C.
Consistency between the proposed strategies
To
indicate th
e consistency between the proposed strategies, here we deal with strategy 5. In this strategy, i
f the
whole
force is assigned to the manipulator, then
I
W
m
and
0
W
h
.
T
herefore
f
f
h
h
~
and
k
k
k
opt
k
a
A
u
†
that
are
obtained
by
substitut
i
on
of
I
W
m
and
0
W
h
in equation
(
31
) and
(
34
).
Th
e
s
e
results
are
consistent
with those in strategy I.
On the other hand, if one requires that
the
force is fully compensated by the human the
n
0
W
m
and
I
W
h
simply substituting
0
W
m
into equations (
3
1
)

(
3
2
)
,
results in
k
k
h
a
f
and
f
f
ˆ
~
m
m
. W
hich
are
consistent with
the result
s
of strategy II.
I
nterestingly, the five
propo
sed strategies are consistent with
each other, because they have been built on each
other. This consistency is observed between the
ways
that
the
strategies are
formulated
and between the results of
the assigned force to the human and the manipulator.
For example,
consider
the consistency between equation
(
25
) in strategy III
,
and (
2
1
) in strategy I
,
and
the
s
imilar
observation between
strategy
IV and strategy II.
Despite
the observed consistency, the strategies work differently because
in each strateg
y a key difference
exists
. This
make
s
it independent from the other
strategies
.
This section
proposed one general strategy and five specific strategies. From these six strategies,
strategy
III and
IV h
ave
been already published by the authors in
[
13
]
.
In the following sections, three case studies are presented
to demonstrate the
fault

tolerant
for HRC.
V.
C
ASE STUDY
1

TEST OF THE
GENERALIZED
STRATEGY
A fo
rce is provided
by
a 3
DoF
planar manipulator
and human
. This case study
considers
a stationary
force for
pressing against a surface
.
A.
Case study 1

Parameters
Table 1
presents
the
Denavit Hartenberg (D

H) parameters of a 3
DoF
planar manipulator. Table 2
sho
ws the
configuration parameters of the manipulator at failure time
,
and
includ
es joint
angles and
torque
s. The
manipulator configuration is
depicted
in Figure
2
.
The
robot is
modeled in
Matlab Robotics Toolbox
[
28
]
.
From
the given
joint

torque
s, the
EEF
force prior to the failure is
T
N
N
N
m
0
70
45
f
, a
human and
t
he
manipulator are cooperatively providing
the
total

force
of
T
N
N
N
0
80
50
f
where the
human force prior to
fault is
T
N
N
N
h
0
10
5
f
shown with
an
arrow.
It is
assume
d that
t
he maximum human force
is
T
N
N
N
h
0
20
20
*
f
and t
he maximum torque is
T
m
N
m
N
m
N
.
.
.
*
100
100
100
τ
.
Figure
2
. Manipulator configuration and human force
, the arrow shows the direction of the human force
0.4
0.2
0
0.2
0.4
0.6
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
X(m)
Y(m)
3DOF Arm
x
y
z
x
y
z
x
y
z
Human’s force
TABLE
1
D

H
PARAMETERS OF
TH
E
3
D
O
F
PLANAR MANIPULATOR
Joint No.
i
s
(m)
i
d
(m)
i
(rad)
i
1
0.05
0.50
0
1
2
0.05
0.40
0
2
3
0.05
0.30
0
3
TABLE
2
CONFIGURATION OF THE
MANIPULATOR PRIOR TO
THE
FA
ILURE
TIME
Joint No.
Joint angle
(deg)
Joint

torque
(N.m)
EEF Force
(N)
1
25

22.73
N
N
N
m
0
70
45
f
2
90

44.94
3
80

16.79
At this configuration, the positional Jacobian matrix
of the manipulator is
0.2898

0.4588

0.0057

0.0776
0.2849

0.4962

J
(
40
)
The z

components of the Jacobian matrix, the human force
,
and the manipulator forces are
eliminated because
of
the
2D
application
and
†
T
J
A
1.2255

1.4131

0.6196
0.6410
0.3839

1.6947

A
(
41
)
If a
locked joi
nt fault occur
s
in
the second joint
,
t
hen, t
he
2

nd
reduced
matrix of
A
is
1.2255

0.6196
0.6410
1.6947

2
A
(
42
)
The parameters that are use
d
later include
1.4131

0.3839

2
a
,
T
m
N
m
N
.
.
2
00
.
21
03
.
13
τ
,
m
N
.
2
59
.
43
a
nd
T
N
N
h
10
5
f
.
The
force

jump
of
the manipulator is
2
2
a
f
m
that
is
T
N
N
m
63.50

17.25

f
. The force of the
manipulator at fault time
is
T
N
N
m
6.50
27.75
ˆ
f
.
This case study aims to test the general strategy. In this strategy,
the
torq
ue
reconfiguration command is for the
first and third joints
T
u
u
3
1
2
u
, a
nd the post failure human force
is
T
h
h
h
f
f
2
1
~
~
~
f
.
T
he
post failure total

force

jump
is
f
f
a
u
A
f
~
~
2
2
2
2
h
h
the
norm of
the
force

jump
is
f
f
f
~
~
~
2
T
.
We have minimized
2
~
f
by u
sing
“
Optimtool”
of Matlab.
B.
Case study 1

Optimization results
T
he
results
of the
constrained
optimization
of
2
~
f
are
shown in Table 3
for two different executions
.
The
table
includes
the p
ost failure
torque
reconfiguration command
and
the
post failure
human
force
. The
force

jump
for
each run
is
also shown
in the last row of the table
indicating that
the
failure was
tolerated
in
both runs
. The two
runs
are with
different initial guess and tw
o different solver of
“Optimtool”
. The solvers are
active set
and
interior point
.
C.
Discussion
The proposed method for minimum
force

jump
indicated was demonstrated
to be efficient for fault tolerance
. The
minimum
force

jump
was
achieved
in the
both runs.
Fr
om the results, it is observed that there is no
control over
the post failure cooperation
of the human and the robot
. The fact is that the fault tolerance is very sensitive to the
initial guess and the optimization technique.
TABLE
3
T
WO RUNS OF THE OPTIM
IZATION ROUTINE
Variables
Run1
Run 2
1
u

32.87 N.m

38.83 N.m
3
u

67.12 N.m

74.08 N.m
1
~
f
h
9.57 N
3.94 N
2
~
f
h
11.61 N
6.77 N
f
~
2.09e

4 N
4.01
6
e

7 N
VI.
C
ASE STUDY
II

TEST OF THE SPECIFIC
STRATEGIES
A.
Case study parameters
A 3
DoF
planar manipulator
of the
previous case study
is used in this case study with the same parameters
.
The
five proposed specific strategies
presented
in section
I
V are deploye
d
here
for
obtaining the
fault
tolerance force
for
the HRC
illustrated
in Figure 1.
B.
Tests of the
non

cooperati
ve
strategies
Test
of
strategy I:
The manipulator is responsible for the fault tolerance.
Therefore,
from (
2
1
)
and
(2
2
)
2
2
†
2
2
a
A
u
(
4
3
)
2
2
†
2
2
~
a
A
A
I
f
(4
4
)
Using the values
of the parameters
that were indicated in
section V part A
results
in
T
70.43

36.82

2
u
and
the
total

force

jump
is
T
N
N
0
0
~
f
.
The
fault

tolerant
force is achieved bec
ause
the manipulator is a
redundant manipulator
and even the faulty
manipulator
has 2
DoF
that
can
tolerate
the
failure. The post failure
human force would be
T
N
N
h
10
5
~
f
equal to
that of human
prior to
the
failure.
Test
of
strategy II:
The huma
n is responsible for the fault tolerance
, therefore using
(2
4
) the required human force
is
2
2
~
a
f
f
h
h
(
4
5
)
Using the values
of the parameters
that were indicated in
section
V

A
results
in
T
N
N
h
73.50
22.25
~
f
.
However,
the human
force is limited to
T
N
N
20
20
. Therefore, the human would apply
T
N
N
h
20
20
~
f
and the
total

force

jump
would be
T
N
N
53.50
2.25
~
f
.
The post failure force of the manipulator
will
be
T
N
N
m
6.50
27.75
~
f
.
C.
Test
of
the
cooperati
ve
strategies
Test
of
strategy
III:
The manipulator maximally tries to resolve the fault, and if any
force

jump
remains, the
n
the
human contribute
s
.
For th
is strategy
using
equation (
25
)
2
2
†
2
2
a
A
u
(
46
)
The human force is obtained fr
om equation (
26
)
k
k
k
k
h
h
a
A
A
I
f
f
†
~
(
47
)
Using the values
of the parameters
that were indicated in
s
ection
V
part
A
results
in
T
70.43

36.82

2
u
and
T
N
N
h
0
0
~
f
,
t
he r
esults are shown in Table
4.
TABLE
4
HUMAN AND MANIPULATO
R
FORCE COOPERATION

T
HIRD STRATEGY
Joint
No
Joint

torque
Force

jump
at fault time
Manipulator
force
Human
Force
Force

jump
1

59.55
N
N
N
0
50
.
63
25
.
37
N
N
N
0
70
45
N
N
N
0
10
5
N
N
N
0
0
0
2
Locked
3

87.22
Test
of
strategy
IV:
The human maximally tries to
tolerate
t
he fault, if any force remains,
then
it has to be
provided by the manipulator. The result
s
of this strategy
are
indicated in Table 5.
TABLE
5
HUMAN AND MANIPULATO
R FORCE COOPERATION

FORTH ST
RATEGY
Joint
No
Joint

torque
Force

jump
at
fault time
Manipulator
force
Human
Force
Force

jump
1

44.77
N
N
N
0
63.50
17.25
N
N
N
0
60
30
N
N
N
0
20
20
N
N
N
0
0
0
2
Locked
3

71.60
Test 1
of
strategy
V:
The
human and the manipulator cooperatively contribute to the fault tolerance
using
a
decision making process
. Let
’
s
assume that the decision

making
assigns
I
W
W
5
.
0
h
m
where t
he manipulator
is expected to
tolerate
half of the
force

jump
and the hu
man the other half. This test is based on equations (
3
1
)
and (
3
2
) as
2
2
~
Wa
f
f
h
h
h
(
47
)
2
2
ˆ
~
Wa
f
f
m
m
m
(
48
)
This
gives
T
N
N
h
41.75
13.63
~
f
but
the
human force is limited to
T
N
N
h
20
13.63
~
f
.
The result of
this
test is indicated in Table 6.
In this test, because the manipulator is redundant, therefore the first condition of the zero
force

jump
in
equation
(
38
) is satisfied
,
but the human force is out of
the
bound
,
therefore a
total

force

jump
will remain.
T
he
force

jump
is due to the wrong assignment of
I
W
W
5
.
0
h
m
.
TABLE
6
HUMAN AND MANIPULATO
R FORCE COOPERATION

F
IFT
H
STRATEGY WHERE
I
W
W
5
.
0
h
m
Joint
No
Joint

torque
Force

jump
at fault
time
Manipulator
force
Human
Force
Force

ju
mp
1

41.17
N
N
N
0
63.50
17.25
N
N
N
0
38.25
36.37
N
N
N
0
20
63
.
13
N
N
N
0
75
.
21
0
2
Locked
3

52.01
Test 2
of
strategy
V:
If the decision

mak
er
assigns
I
W
m
and
0
0
W
then the
force

ju
mp
is required to be
maximally compensated by the man
ipulator. This should result in
the same
outcome
as that of the
test
in
strategy
I. The result
s
of this case study
are
shown
in Table 7.
TABLE
7
HUMAN AND MANIPULATO
R FORCE COOPERATION

FIFTH STRATEGY
I
W
m
,
0
W
h
Joint
No
Joint

torque
Force

jump
at fault time
Manipulator
force
Huma
n
Force
Force

jump
1

59.545
N
N
N
0
63.50
17.25
N
N
N
0
70
45
N
N
N
0
10
5
N
N
N
0
0
0
2
Locked
3

87.22
D.
Discussion
It was
mentioned
earlier
that there is a consistency between the proposed strategies. The consistency is clearly
observed in the test
of
the strategies.
The
manipulator is
a
3
DoF
planar
,
and it is not in
a
singular configurat
ion.
Therefore, if a failure occurs
, the manipulator is capable of
the fault tolerance.
This is observed from the results of
the
tests
of
the strategies
I
and
III and the second test of V
.
If the responsibility of the fault tolerance is
assigned
to the
h
uman
as
was the case
of
strategies II
and
test 1 of
strategy IV, then
the
limit
of
the human force
prevented achieving the
complete
fault tolerance. In strategy II, this
limitation
has resulted in
a
force

jump
.
In
test 1
of
strategy V, a
non

zero
force

jum
p
occurred
because of the
wrong assignment of the force
to
the human.
In both cases, t
he assigned force
to
the human is more than the
maximum human force.
VII.
S
IMULATION
S
TUDY
Work
partner
(Wopa)
robot has been proposed as a service robot
[
4
]
,
or
as an
assistant
to
astronaut
s
[
5
]
. Figure
3
shows
the Wopa robot
in a load lifting task.
Figure
3
. Wopa in a lifting scenario
[
4
]
Th
ese
kind
s
of robot
are
assumed to work in close proximity to humans and even in collaboration with humans.
A.
Simulation scenario
and
parameters
Figure
4
indicates
the force
cooperation scenario
b
etween th
ese
robot
s
and human
s
.
The
human and the arm of
the Wopa robot are
applying a force
to
lift an object. The weight of the object is
N
80
. The object
needs to be
lifted
by
5
.
0
meter
s
in
the
z
direction
with a very slow speed. T
he operator help
s
the robot by applying
N
5
.
A
locked joint failure
is considered for the
first joint.
It is also assumed that
the
arm
is a
3
DoF
planar robot
moving
solely
in the XZ plane. The
D

H para
meters
of the robot are
shown
in
T
able 1.
Figure
4
.
H
uman
and Wopa arm
cooperation
B.
Simulation of the healthy
Wopa arm
The robot is required to move in
the
z direction. It is possible to obtain the
joint profiles
using an iterative inverse
kinematics
pr
ocess
.
Figure
5
.
T
he joint profiles of the healthy
arm (HM
)
and t
he joint profiles
of the
faulty
manipulator (FM
)
Figure
5 shows the
joint profiles
that result in 0.5 meter
s
low speed EEF motion
in
the z direction of the healthy
arm. In order to show th
is,
Figure
6
indicate
s
four snapshots of the configuration of the
arm
.
Where
in
Figure 5, HM indicates the joint profile of the healthy arm and FM indicates the joint profile of the
faulty arm. The method to obtain the joint profiles of the faulty a
rm will
be explained later in
this section.
Figure
6
. four snapshots of
the
heathty
Wopa arm
C.
Simulation of
the
faulty
Wopa arm
A
fai
lure is assumed to
occur
in
the first joint of the
arm
.
T
he
fault

tolerant
HRC requires
fault

tolerant
motion as
well as
fault

tolerant
force.
C.
1
.
Fault

tolerant
motion
of the arm
The fault

toleran
t
m
otion
for the arm can be implemented by using the method in
[
26
,
27
]
that is based on the
reconfiguration of the joint velocities.
Using this
me
thod, the appropriate joint velocities have been obtained
as
s
hown
in Figure
5
.
If the
faulty
arm
joint profiles
are applied to the joints, then
the EEF will move on the
similar
path
as that of the healthy arm
.
Figure
7
indicate
s
four snapshots of the conf
iguration of the faulty
arm where
the
first joint is locked and the same
path as that
of Figure 6 is obtained
.
C
.
2

Fault

tolerant force of HRC
The joint torque profile
s
of the healthy Wopa arm for the EEF force of
T
N
5
7
0
are shown in Figure
8.
The
corresponding
healthy
arm’s
EEF
force
i
s indicated in Figure
9
. The force has two components
of
Fx
and
Fz
;
1
2
3
4
the
y
component of the force
is
always
zero
because the manipulator is planar
.
Wh
en
the
arm’s
first joint fails,
the faulty joint torque will be zero. T
herefore
,
the EEF force
will change
.
The force
at
the EEF after the failure
of
a
joint is indicated in Figure 9.
The difference between
the
corresponding
healthy
and
faulty arm’s force
of Figure 9 determine
the
force

jump.
This force is for the case that no fault tolerance strategy is employed
.
In the following subsection the fault
tolerance strategies are employed to obtain
fault

tolerant
force in HRC.
Figure
7
. four snapshots
of the faulty
Wopa arm
Figure
8
. the
joint

torque
profiles of the health
y arm (HM) and for the faulty arm
(
FM
)
when the first strategy has
been employed
D.
Simulation results
Test of strategy I:
The
manipulator
is responsible for maintaining the force. The
refore, new
joint

torque profile
s
are required to minimize the
force

jump
. Using strategy 1, the optimal
joint

torques
are obtained
and the results
are
shown in Figure
8 by
dashed lines.
The
EEF
force
corresponding t
o
these joint torque profiles of the fau
lty arm
is
indicated in Figure 10
showing that
the faulty arm is capable of maintaining the force. However, the torques required to maintain the force is large
,
which can be seen from Figure 8 and for the torque of the second and third joint.
1
2
3
4
The differen
ce between
the
corresponding
healthy
and
faulty arm’s force determines
the
force

jump. The force

jump when strategy 1 was incorporated is shown in Figure 11 indicating less than
N
3
.
0
force

jump.
Figure 9. EEF force of the healthy
arm
(
H
M
) and the faulty
arm
(
FM
)
,
no
fault tolerance
strateg
y
is
use
d
Figure 10.
EEF
post failure force of the faulty
arm when the
strategy I
is used
Test of strategy II:
If the human is responsible for maintaining the
total

force
, then the required human for
ce is
simply obtained by the difference between
the
forces
prior to
the arm’s
failure
and the post failure
force. One can
simply obtain the required human force by subtracting
corresponding
forces
that we
r
e shown
in
Figure 9.
The
required human force
for
s
trategy II
is shown in Figure 1
2
.
Figure 1
1
.
EEF
post failure
force

jump
of the
faulty
arm when
a
strategy as
strategy I
is
applied
If
the human is able to apply
the
force
of Figure 12
then the fault is tolerated
,
otherwise not.
Figure 1
2
. The requir
ed human force as per strategy II
Test of strategy III:
T
he
arm
is responsible to optimally
tolerate
the failure and human would contribute if
required
.
The
faulty arm
joint

torque
profile
s
and EEF force
are the same as
that of
strategy
I
shown in Figure
8
,
and
the
EEF
force
of
Figure 10.
Accordingly,
the human
’s reconfiguration force needs to be the
force

jump
of
strategy I. This
force

jump
was shown in Figure 11. The required humans force that is shown in F
igure 1
3 is
obtain by adding the
force

jump
of s
trategy I to the
5N initial human force.
Test of
s
trategy IV:
For
strategy IV, the result is very similar to
that of
strategy
II. The results will be exactly
similar if the human can apply the force that was shown in Figure 12.
Test of
s
trategy V:
Impleme
ntation of
strategy V has not been performed because it requires further research to
define the decision maker in order to obtain the weigh
t
matrices.
Figure
1
3
. The required human force
of
strategy III
Test of
the general s
trategy
:
For the general stra
tegy,
we observed that
it does not provi
de a uniform way of
distributing
the force

jump
between
the human and the faulty manipulator. This is because, at any time instance,
the
optimization problem
exists
with multiple global minim
um.
T
hen
,
d
epending
on
th
e initial guess and the
method of solving the optimization, different answers will be obtained. For example
,
for two
sequen
tial
time
instance
s
,
it is possible that the
force

jump
at the first time is a
ssigned
mostly
to
the human and in the second
time
to
t
he faulty
arm
. Therefore, the general strategy
is not suitable for the simulation study.
Limitations:
Every method has some pros and
cons;
this is
also
true for
the
strategies that
are
presented in this
paper. Through
the
three case
studies,
we have shown
that the strategies are us
e
ful for the
fault

tolerance
in
HRC
but there
are
some limitations
indicated
below.
1

I
n this paper
,
t
he manipulators are
positional
and w
e have not considered the orientation of the manipulators.
Therefore, t
he Jacobian matrices
are analytical Jacobian matrices. Further work is required to discuss the
fault
tolerance
for spatial manipulators.
2

T
he strategies are instantaneous. However, via the simulation study, it was shown that the strategies can be
used from the time that failu
re occurs to the end of force task.
Therefore,
at any time instance after failure
up
unti
l
of
the
end
of the
task
,
the strategies
will
be
applicable.
3

T
he pseudo inverse method is suitable for local operation
.
It
was
used in this paper because we assume th
e
robot
’s
effective workspace is small.
4

S
trategy V has
not
been
extensively
discussed
in detail as it
was
relying
heavily
on a decision

making
process
.
The optimal selection of the matrices requires further research.
5

In the present paper, we have discussed
that the stra
tegies are for stationary or
slow moving
cases
.
Fault
toleran
t HRC
for a fast moving manipulator
is not considered because of the safety issues
.
6

Another issue is multiple joint failures. We have developed optimal
fault

tolerant
motion
for
mul
tiple joint
failure
s
of a manipulator in
[
27
]
.
A s
imilar
approach with some modification can be used for
fault
toleran
t
force with multiple actuator failures.
VIII.
C
ONCLUSION
This work has
investigated different strategies for
the application of
optimal
fault

toleran
t
force within
human

robot cooperatio
n
for
the slow
pushing or lifting
of an object.
Six different
strategies were pr
esented
to optimally
maintain a cooperative force despite
manipulator failure through a
locked joint
event.
These strategies determined
the post failure
cooperation
of the faul
ty manipulator and the human.
T
he strategies were validated
using three case studies.
It was indicated that the cooperation strategies not only
result
ed
in
a
fault

tolerant
force when the conditions of full
fault
tolerance
were he
ld, but
they
also provide
d
consistent result
s
in comparison
with
each other.
The third case study simulated the
fault

tolerant
cooperative
force of a Wopa
arm, and a human
.
All three
case
studies indicated the
fault

tolerant
force of the human and the robot. The present strategies
can be
applied
for robots assisting
humans such as
surge
ons
,
astronauts
,
and also the disabled or the elderly
.
The
contribution in this paper
is
complementary to the previous
work
presented
for the study of
fault

tolerant
motion
[
26
,
29
]
,
and fault

tolerant force
for single and multiple manipulators
[
25
,
30
,
31
]
. This is achieved
by
extending the fault

toleran
t
for
ce to
human

robot cooperation
.
IX.
A
PPENDICES
Appendix

1
T
he pseudo inverse
of full rank square matrices is
obtained by regular inverse or
1
†
B
B
when
B
is a
skinny
full rank matrix, then
the
pseudo inverse is
defined by left inverse or
T
T
B
B
B
B
1
†
when
B
is a fat and full rank matrix, then the pseudo inverse is
defined by right
inverse or
1
†
T
T
BB
B
B
Appendix

2
Reduced matrices are defined by eliminating columns
of the
matrices. For example
,
by
eliminating
the
k

th
column
of
A
, the
k

th
reduced matrix
is obtained as
n
k
k
k
a
a
a
a
A
...
...
1
1
1
Reduce
d vectors are defined similar to reduced vertices eliminating the rows. The
k

th
reduced vector of
τ
is
T
n
k
k
k
...
...
1
1
1
τ
.
For single locked joint failures, there are
n
reduced matrices of
A
which
are shown by
A
A
A
n
,...,
,
2
1
.
Acknowledgement
This research was supported by Centre for Intelligent Systems Research

Deakin University in part with U.S.
National Science Foundation under contract IIS

0812437.
References
[1]
S. Lallee, E. Yoshida, A. Mallet, F. Nori, L. Natale, G. Metta, F. Warneken, and P. Dominey, "Human

Robot
Cooperation Based on Interaction Learning
From Motor Learning to Interaction Learning in Robots." vol. 264, O. Sigaud and J. Peters, Eds., ed: S
pringer Berlin /
Heidelberg, 2010, pp. 491

536.
[2]
M. López, R. Barea, L. Bergasa, and M. Escudero, "A human
–
robot cooperative learning system for easy installation of
assistant robots in new working environments,"
Journal of Intelligent and Robotic Syste
ms,
vol. 40, pp. 233

265, 2004.
[3]
T. Wojtara, M. Uchinara, H. Murayama, S. Shimoda, S. Sakai, H. Fujimoto, and H. Kimura, "Human

Robot
Cooperation in Precise Positioning of a Flat Object,"
Automatica
vol. 45, pp. 333

342, 2009.
[4]
J. Suomela and A. Halm
e, "Human robot interaction

case WorkPartner," in
the proceeding of the IEEE/RSJ
International Conference on Intelligent Robots and Systems
, 2004, pp. 3327

3332.
[5]
W. Bluethmann, R. Ambrose, M. Diftler, S. Askew, E. Huber, M. Goza, F. Rehnmark, C. Lovchi
k, and D. Magruder,
"Robonaut: A robot designed to work with humans in space,"
Autonomous Robots,
vol. 14, pp. 179

197, 2003.
[6]
R. Kumar, P. Berkelman, P. Gupta, A. Barnes, P. Jensen, L. Whitcomb, and R. Taylor, "Preliminary experiments in
cooperative hu
man/robot force control for robot assisted microsurgical manipulation," in
the proceeding of the IEEE
International Conference on Robotics and Automation
, San Francisco, CA , USA 2000, pp. 610

617.
[7]
A. Kargov, T. Asfour, C. Pylatiuk, R. Oberle, H. Klose
k, S. Schulz, K. Regenstein, G. Bretthauer, and R. Dillmann,
"Development of an anthropomorphic hand for a mobile assistive robot," in
the proceeding of the IEEE International
Conference on Rehabilitation Robotics
, Chicago, IL, USA, 2005, pp. 182

186.
[8]
R. Koeppe, D. Engelhardt, A. Hagenauer, P. Heiligensetzer, B. Kneifel, A. Knipfer, and K. Stoddard, "Robot

robot and
human

robot cooperation in commercial robotics applications,"
Robotics Research,
pp. 202

216, 2005.
[9]
Y. Yong, W. Lan, T. Jie, and Z. Li
xun, "Arm Rehabilitation Robot Impedance Control and Experimentation," in
the
proceeding of the IEEE International Conference on Robotics and Biomimetics
, 2006, pp. 914

918.
[10]
T. Fong, I. Nourbakhsh, and K. Dautenhahn, "A survey of socially interactive
robots,"
Robotics and Autonomous
Systems,
vol. 42, pp. 143

166, 2003.
[11]
H. Abdi and S. Nahavandi, "Well

conditioned configurations of fault

tolerant manipulators,"
Robotics and
Autonomous Systems,
vol. 60, pp. 242

251, 2012.
[12]
S. Haddadin, A. Albu

S
chäffer, and G. Hirzinger, "Safe Physical Human

Robot Interaction: Measurements, Analysis
and New Insights,"
Springer Tracts in Advanced Robotics,
vol. 66, pp. 395

407, 2011.
[13]
H. Abdi, S. Nahavandi, and M. T. Masouleh, "Minimal force jump within human
and assistive robot cooperation," in
the proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, Taiwan, 2010, pp. 2651

2656.
[14]
R. Alami, A. Albu

Schaeffer, A. Bicchi, R. Bischoff, R. Chatila, A. De Luca, A. De Santis, G.
Giralt, J. Guiochet, and
G. Hirzinger, "Safe and dependable physical human

robot interaction in anthropic domains: State of the art and
challenges," in
the proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 'Workshop
on
pHRI

Physical Human

Robot Interaction in Anthropic Domains'
, 2006, pp. 1

15.
[15]
J. Goetz, S. Kiesler, and A. Powers, "Matching robot appearance and behavior to tasks to improve human

robot
cooperation," in
the proceeding of trhe 12th IEEE Internationa
l Workshop on Robot and Human Interactive
Communication
, 2003, pp. 55

60.
[16]
Y. Yamada, T. Yamamoto, T. Morizono, and Y. Umetani, "FTA

based issues on securing human safety in a
human/robot coexistence system," in
the proceeding of the IEEE Internationa
l Conference on Systems, Man, and
Cybernetics
, 1999, pp. 1058

1063.
[17]
K. Kosuge, H. Kakuya, and Y. Hirata, "Control algorithm of dual arms mobile robot for cooperative works with
human," in
the proceeding of the IEEE International Conference on System
s, Man, and Cybernetics
, 2001, pp. 3223

3228.
[18]
T. Tsumugiwa, R. Yokogawa, and K. Hara, "Variable impedance control based on estimation of human arm stiffness
for human

robot cooperative calligraphic task," in
the proceeding of the IEEE International Co
nference on Robotics and
Automation
, San Diego, CA , USA 2002, pp. 644

650.
[19]
T. Takubo, H. Arai, Y. Hayashibara, and K. Tanie, "Human

robot cooperative manipulation using a virtual
nonholonomic constraint,"
International Journal of Robotics Research,
v
ol. 21, p. 541, 2002.
[20]
W. S. Harwin, "Impedance mismatch: Some differences between the way humans and robots control interaction
forces," in
the proceeding of the IEEE International Conference on Rehabilitation Robotics
, 2009, pp. 19

19.
[21]
J. Hyowo
n and J. Seul, "Hardware design on an FPGA chip of impedance force control for interaction between a
human operator and a robot arm," in
the proceeding of the 7th Asian Control Conference (ACC)
, 2009, pp. 1480

1485.
[22]
L. Kye

Young, L. Seung

Yeol, C. Jo
ng

Ho, L. Sang

Heon, and H. Chang

Soo, "The application of the human

robot
cooperative system for construction robot manipulating and installing heavy materials," in
the proceeding of the
International Joint Conference SICE

ICASE
, 2006, pp. 4798

4802.
[23]
X. Lamy, F. Colledani, and P. O. Gutman, "Identification and experimentation of an industrial robot operating in
varying

impedance environments," in
the proceeding of the IEEE/RSJ International Conference on Intelligent Robots and
Systems (IROS),
, 2010,
pp. 3138

3143.
[24]
P. Minyong, K. Mouri, H. Kitagawa, T. Miyoshi, and K. Terashima, "Hybrid impedance and force control for
massage system by using humanoid multi

fingered robot hand," in
the proceeding of the IEEE International Conference
on Systems, Man
and Cybernetics
, 2007, pp. 3021

3026.
[25]
H. Abdi and S. Nahavandi, "Fault tolerance force for redundant manipulators," in
the proceeding of the IEEE
International Conference on Advanced Computer Control
, 2010, pp. 612

617.
[26]
H. Abdi and S. Nahavandi,
"Joint velocity redistribution for fault tolerant manipulators," in
the proceeding of the
IEEE Conference on Robotics Automation and Mechatronics
, 2010, pp. 492

497.
[27]
H. Abdi, S. Nahavandi, Y. Frayman, and A. A. Maciejewski, "Optimal Mapping of Joint
Faults into Healthy Joint
Velocity Space for Fault Tolerant Redundant Manipulators,"
Robotica,
pp. 1

14, DOI 10.1017/S0263574711000671,
August 2011.
[28]
P. I. Corke, "A robotics toolbox for MATLAB,"
IEEE Robotics and Automation Magazine,
vol. 3, pp. 24

32
, 1996.
[29]
H. Abdi and S. Nahavandi, "Optimal actuator fault tolerance for static nonlinear systems based on minimum output
velocity jump," in
the proceeding of the IEEE International Conference on Information and Automation
, 2010, pp. 1165

1170.
[30]
H
. Abdi, S. Nahavandi, and Z. Najdovski, "On the effort of task completion for partially

failed manipulators," in
the
proceeding of the IEEE International Conference on Industrial Informatics
, 2010, pp. 201

206.
[31]
H. Abdi, S. Nahavandi, and Z. Najdovski
, "Fault tolerance operation of cooperative manipulators," in
the proceeding
of the IEEE International Symposium on Artificial Intelligence, Robotics and Automation in Space
, Japan, 2010, pp. 144

151.
Σχόλια 0
Συνδεθείτε για να κοινοποιήσετε σχόλιο