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An assembly strategy scheduling
method for human and robot
coordinated cell manufacturing
Fei Chen and Kosuke Sekiyama
Department of Micro-Nano Systems Engineering, Nagoya University,
Nagoya, Japan
Jian Huang
Department of Control Science and Engineering,
Huazhong University of Science and Technology, Wuhan, China
Baiqing Sun
School of Electrical Engineering, Shenyang University of Technology,
Shenyang, China, and
Hironobu Sasaki and Toshio Fukuda
Department of Micro-Nano Systems Engineering, Nagoya University,
Nagoya, Japan
Abstract
Purpose – The purpose of this paper is to propose a model of assembly strategy generation and
selection for human and robot coordinated (HRC) cell assembly. High-Mix, Low-Volume production in
small production manufacturing industry, tends to employ more flexible assembly cells. The authors
propose innovative human and robot coordinated assembly cells to solve the problem of persistent
growing cost for human resources and occasional changes in programs and configurations for robots.
The first issue is to find out an optimal way to allocate the assembly subtasks to both humans and
robots.
Design/methodology/approach – A dual Generalized Stochastic Petri Net (GSPN) model is
theoretically studied and then off line built based on a practical assembly task for human and robot
coordination. Based on GSPN, Monte Carlo method is carried out to study the time cost and payment
cost or possible strategies, and Multiple-Objective Optimization(MOOP)methodrelated
Cost-effectiveness analysis is adopted to select the optimal ones.
Findings – It is discovered that human and robot coordinated assembly can reduce the assembly
time and meanwhile reduce the assembly cost. The authors demonstrate the effectiveness of this
approach by comparing the simulation and experimental results.
Originality/value – The novelty with this work is that the human and robot coordinated flexible
assembly cell, as the authors proved, is the main stream in small production in future due to the higher
human source pressure from society and cost pressure upon the company. Based on this innovative
work, the authors proposed a dual GSPN model to model the assembly task allocation process for
human and robot, the model of which is also effective in modeling the possible robot and human
behaviors.
Keywords Robots, Assembly, Process efficiency, Stochastic Petri-net, Human and robot coordination,
Assembly cell, Monte Carlo, Multiple-objective optimization
Paper type Research paper
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1756-378X.htm
HRC cell
manufacturing
487
Received 6 April 2011
Revised 27 April 2011
3 June 2011
Accepted 9 June 2011
International Journal of Intelligent
Computing and Cybernetics
Vol. 4 No. 4, 2011
pp. 487-510
qEmerald Group Publishing Limited
1756-378X
DOI 10.1108/17563781111186761
1. Introduction
During the past tens of year development in manufacturing industry, this area has
been divided into three main streams: massive production, medium production and
small production. In small production, usually fully with robots, cannot keep step with
the growing social demanding for high-mix, low-volume manufacturing. For the
manufacturing fully with human workers, the labor cost is also increasing, and so that
production system has to face the growing cost pressure in future. When addressing
this problem, it will be more useful and beneficial to make efforts in the cooperation
and coordination between them, consider their trade-off and improve the overall
assembly effectiveness and efficiency. It can also provide the factory with certain
sufficient flexibility in production, guaranteeing the quality and meanwhile reducing
the cost.
From the respect of human workers: the labor-intensive industry forces the human
workers in assembly lines work in a not so human friendly way by repeating some
certain action for long time. If robot can help the human worker doing some repetitive
and boring work, the human worker can concentrate on more creative tasks, produce
more novel productions, and also lower the possibility of work fatigue (Baines et al.,
2004). Meanwhile, the salary for human workers is getting much higher than years ago,
therefore it can also help to increase the profit space for companies.
From the respect of robots: currently in electronic manufacturing industry,
for instance, the connector insertion on circuit board is entirely done by robotic
manipulators. Some simplified models for connector insertion are already studied to
help robotic manipulators recover from insertion error (Huang et al., 2008a, 2010).
However, when confronting complicated shapes of connectors or assembly parts, the
extension of existed connector insertion algorithms worksnot so well. If the robot
wants to detect the error type, it has to try several times by contacting the male
connector with the female connector to look for some predefined models. To solve it,
usually adopted way is to build more intelligent robotic grippers with multiple sensors
and advanced controlling algorithms. But robots equipped with many sensors, such as
vision sensor, laser range finder and force sensor, still cannot cope with all the
assembly cases in industry effectively and efficiently. Moreover, in industry, one does
not want to use too much complicated robots for assembly time consuming. However,
human beings are highly intelligent, and therefore are cognitive of the working
environment. Many researchers currently dedicate into the research of teaching robots
to do assembly (Yuan, 2002) and evaluation the cooperation (Hoc, 2001) according to
human workers’ experience. However, this off-line training teaches robot how to do
without teaching the robot what to do and which is the first needed to be solved for
human and robot coordinated (HRC) assembly work. Furthermore, if human workers
can directly coordinate with robot and help the robot in certain assembly procedure
when it costs much more time for the robot, such as error recovery in connector
insertion, the assembly procedure can be shortened.
However, due to the complication of the sensor system and potential worries of the
safety issue, seldom research has been involved within the HRC cell assembly domain,
even though it is explicit that HRC can bring much advance into current
manufacturing industry, and consequently solve the gradually upcoming various
cost pressure upon industry.
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In small production (high-mix, low-volume), “human in loop” production is the trend.
When addressing the modeling issue for human, there are some issues should be
considered first. The first issue is hardware supporting. A general HRC working cell
or related devices should be built. In Duan et al. (2008), a human and robot hybrid
manufacturing cell is build, and some safety strategy is studied within this framework.
In Bannat et al. (2011), a cognitive factory is introduced. In this factory, multiple sensors
are equipped, and therefore, direct HRC (dHRC) and physical HRC (pHRC) is realized. In
Malosio et al. (2009), a robotic system for small medium enterprises is also built by
removing the fences around the robot to provide this system with sufficient flexibility,
and the effectiveness method is evaluated through simulation. In the past few years,
some representative robotic devices are also developed to assist human with the
cooperation with robots in N.N. (2005) and Schraft et al. (2005). The second issue is the
safety of human. Some theoretical researches about testing and evaluating the potential
safety issue for human worker are already studied in Duan et al. (2009) and Oberer and
Schraft (2007). In Kruger et al. (2005), a PMD named camera is developed to detect the
interested certain position of a multiple objects (human beings and robots) and their
relevant areas. With the help of PMD, the potential collision between human and robot
can be identified and therefore safety of human workers is guaranteed. The third issue is
the control scheme for HRC system. In Mayer et al. (2009), a cell’s numerical control
named CCU is used for the high-level information processing based on the cognitive
architecture named SOAR. Hence to a certain extent the CCU is able to simulate
rule-based behavior of the human operator and improve the manufacturing system with
direct dHRC. The last issue is the task modeling and scheduling. In Duan et al. (2009), the
author describes the task modeling method in context expression. Moreover, safety
strategies and information supporting devices are also developed for HRC cell assembly.
They evaluate HRC work from the respect of safety and riskiness. However, their
method is not described in a uniformly mathematical way, and also is specific task
dependent. Therefore, it is difficult to bring this method to the general use. In Dai et al.
(2011), a game theory-based queueing model is built to study at which situation the robot
should handle the current unsolved issue to human workers by considering various
issues, such as current human worker skills, trade-off of human interaction and
performance time, and so on. In Singer and Akin (2010), the schedules developed meet all
of the mission constraints while minimizing overall task list completion time and
minimizing the wait time between agents. In our study, we also build an intelligent
assembly cell (Chen et al., 2009). Removing the physical barrier devices, and therefore the
human worker and robot can share the both working time and working space to achieve
the real human and robot coordination and collaboration. Human worker and robots
position are monitored by multiple cameras and artificial potential method is used to
ensure the safety for human. In Kruger et al. (2009), the author theoretically studied the
system architecture for human and robot cooperation in assembly lines based on the
recent development in manufacturing. But now, the role that robot plays is still in doubt.
In the examples listed in the paper and mentioned before, robot plays a passive device
role controlled by human to play the assembly together. The robot just memories ever
step during the guidance and paly it afterwards. In other examples listed, the
cooperation is that human or robot holds something for the other, and the other does the
assembly work. The robot is still not so active. In our research, the robot is an
active assistant. It does assembly tasks that are assigned beforehand, and coordinates
HRC cell
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489
with human worker. During the assembly, the robot can monitor the human status and
coordinate with human properly.
Another important issue is that appropriate model should be built for both human
and robot. In manufacturing industry, Petri net is widely used for modeling the
assembly sequence event flow of manufacturing system (Yee and Ventura, 1999)
and also some evolutionary Petri net methods are used to model flexible manufacturing
(Tuysuz and Kahraman, 2010).
When building the model for human workers, one obvious feature of human
beings – work fatigue is considered. Fatigue is a lack of energy and motivation. The
definition of fatigue for human beings varies largely from the exhaustion resulting
from chronic fatigue syndrome to the weariness resulting from working all day long. In
this study, it is supposed that all the human workers participated in the cell assembly
work are within the same physiological level, such as healthy, quality of sleep, and
only fatigue caused by the long time working (work fatigue) is considered. This fatigue
can produce a decline in performance such as slower reaction times, failure to respond
to changes, and the inability to concentrate and make reasonable judgments. Human
workers will make mistakes or be absent minded and take some action unconsciously,
and prolong the whole task finishing time. Generalized stochastic Petri net (GSPN)
model is adopted to describe this human model (Chiola et al., 1993).
This paper is organized as follows. After a brief introduction of Petri net, GSPN, and
also time related parameter definition and calculation, we introduce and discuss the dual
GSPN for modeling HRC assembly task procedure in Section 2. In Section 3, a case study
is carried out. Based on GSPN, Monte Carlo method is carried out to study the time cost
and payment cost for each way of subtasks allocation to human and robot. In Section 4,
we demonstrate the effectiveness of this approach by comparing the simulation and
experimental results. Multiple-objective optimization (MOOP) analysis related methods
are adopted to select the optimal strategies. Conclusions and future works are presented
in Section 5.
2. Dual GSPN model for HRC cell assembly
2.1 Petri net
A Petri net is a five-tuple, PN ¼(P,T,I
2
,I
þ
,M
0
) where:
P¼{p
1
,p
2
,p
n
} is a finite and non-empty set of places.
T¼{t
1
,t
2
,t
m
} is a finite and non-empty set of transitions, P>T¼B.
I
2
,I
þ
:P£T!N
0
are the backward and forward incidence weights,
respectively.
M
0
:P!N
0
is the initial marking.
In the graphical representation of a PN net, I
2
(p,t) weight specifies that a transition
leading from pto tis enabled only when at least as many tokens as given by the arc
weight are located on the place p. Firing will destroy exactly this number of tokens from p.
Similarly I
þ
(p,t) specifies the number of tokens created on place pin case of firing t.
2.2 Generalized stochastic Petri net
GSPN has two different types of transitions: immediate transition (denoted as black
rectangular bar) and timed transition (denoted as white rectangular bar).
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When enabled, immediate transition fires at once, and timed transition fires after a
random exponentially distributed enabling time (Chiola et al., 1993).
A GSPN is a four-tuple, GSPN ¼(PN,T
1
,T
2
,W) where:
PN ¼(P,T,I
2
,I
þ
,M
0
) is a Place-transition net.
T
1
,Tis the set of timed transitions, T
1
–B.
T
2
,Tis the set of immediate transitions, T
1
>T
2
¼B,T¼T
1
<T
2
.
W¼(w
1
,w
2
,...,w
jTj)
is an array whose entry w
i
[R
þ
:
.is a rate of an negative exponential distribution specifying the firing delay,
when transition t
i
is a timed transition, i.e. t
i
[T
1
;or
.is a firing weight, when transition t
i
is an immediate transition, i.e. t
i
[T
2
.
Define I¼I
þ
2I
2
,ifI(p,t),0, the transition twill consume I(p,t) tokens from
place p,andifI(p,t),0, the transition twill generate I(p,t) tokens on place p.
In the GSPN model for HRC cell assembly, a transition tdenotes a happening event
carried by an agent referring to human or robot, and it is time delayed when tis a timed
transition. In this study, when modeling an event happening, this delayed firing time
can also be treated as the event taken time. Therefore, five transition t-related time
parameters are defined as follows:
.t
a
– the time an event arriving transition t.
.t
b
– the time an event leaving transition t.
.t
v
– the agent response time to this event.
.t
g
– the agent process time for this event. Usually, t
g
is exponentially distributed.
.t
s
– the average time taken within this transition t, usually:
t
a
¼t
v
þt
g
:ð1Þ
Note that ;t
i
[T(0 #i#jTj), if the firing time for t
i
is exponential distributed, the
average time taken for transition t
i
is derived according to: t
i
¼1/w
i
.
2.3 Task finish time calculation on dual GSPN model
Based on the GSPN for HRC cell assembly definition, it is obvious to find out that
t
b
¼t
a
þt
s
for timed transition t, and t
b
¼t
a
,t
s
¼0 for immediate transition t.
In GSPN, because both timed transition and immediate transition exist, the calculation
is depending on which current transition it is.
2.3.1 Task finish time definition. When we use the dual GSPN to model the HRC
assembly process, one of the performance characteristics of GSPN one are interested
with is the time cost for a specific task. If a transition t
i
[Trepresents the last transition
within the dual GSPN model, t
i
b
, referring to event leaving time of transition t
i
,
represents this HRC task finish time (T
f
) as well. If t
i
a
, referring to event leaving time of
transition t
i
, is calculated, t
i
b
can be calculated according to equation (1). coloredSo, the
event leaving time of the last transition within GSPN model is the task finish time. In
order to calculate t
i
b
, some parameters are defined as follows.
(a) pre-transition of t
i
.If;ti[Tð0#i#jTjÞ,;tj[Tð0#j#jTjÞ,
pk[Pð0#k#jPjÞ,s.t.Iþðpk;tjÞ.0andI2ðpk;tiÞ.0, define t
j
as a
pre-transition of t
i
.
HRC cell
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If based on I, pre-transition is defined as follows: ;ti[Tð0#i#jTjÞ,
;tj[Tð0#j#jTjÞ,pk[Pð0#k#jPjÞ,s.t.Iðpk;tjÞ.0, Iðpk;tiÞ,0 and
jIðpk;tjÞj $jIðpk;tiÞj,t
j
is a pre-transition of t
i
.
It implicates that t
j
generates I(p
k
,t
j
) tokens on place p
k
,andt
i
consumes jIðpk;tiÞj
tokens from place p
k
.
(b) pre-transition set U(t
i
). ;ul[UðtiÞð0#l#jUðtiÞjÞ,ifulis a pre-transition of t
i
,
then U(t
i
) is a pre-transition set of t
i
.
In order to calculate the leaving time of a transition, the last transition of a GSPN
model should be found out first. The first step is to find out the pre-transition set of
each transition based on the token consumption and generation matrix I, and then
based on the two situation happened during HRC assembly as follows, calculate the
leaving time for each transition recursively.
2.3.2 Task finish time calculation. Not like a normal GSPN, when a dual GSPN is
modeled for HRC cell assembly process, t
i
a
is calculated based on the following
situations (Figure 1).
Theoretically, ti
a
¼maxðu1
b
;u2
b
;...;ujUðtiÞj
b
ÞðjUðtiÞj denotes the maximum
number of elements in UðtiÞ, and ti
b
¼ti
a
þti
s
for timed transition or ti
b
¼ti
a
for
immediate transition. As shown in Figure 1, based on the definition as described,
t
3
(the last transition of GSPN) is a time-related task end transition, and we can get
Uðt3Þ¼{t1;t2} where jU(t
3
)jis larger than one. If t3
a
is calculated, the task finish time
t
3
b
(T
f
as well) can be calculated according to equation (1). There are two situations
associated with the concurrence and sequential occurrence features of GSPN within HRC
process when calculating the transition arriving time t
3
a
.
(a) Situation a. If both events t
1
and t
2
are carried out by heterogeneous agents, such
as human or robot, t
1
and t
2
can be carried out concurrently. Therefore, the transition t
3
arriving time is calculated based on the following equations:
t3
b
¼maxðt1
b
;t2
b
Þ
subject to:
t1
b
¼t1
a
þt1
s
t2
b
¼t2
a
þt2
s
Figure 1.
A dual GSPN model
demonstration
HUMAN-Event/Robot-Event
p0
p1 p2
p3 p4
t1
t0
t2
t3
HUMAN-Event/Robot-Event
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(b) Situation b. If both events t
1
and t
2
are carried out by homogeneous agents, such as
human and human, or robot and robot. When there are only one human and one robot
in the assembly cell, in this case shown in Figure 1, both of the two events t
1
and t
2
cannot happen concurrently, but one after the other. When there is one token on p
1
and
p
2
, respectively, t
1
and t
2
will be enabled, and they will compete with each other to be
enabled. Based on the time delay distribution defined in t
1
and t
2
, a random number is
generated for each of them. These two random numbers are counted down, and the
one reaches zero is enabled first. If t
1
fires first, and then t
2
continues to compete to
fire. If the former elapsed counted down enabling time of t
2
is forgotten, it is a race
enable rule, otherwise if it is remembered, it is the race age rule. Whatever rule used, if
t
1
fires first, the transition t
3
arriving time t
3
a
is calculated based on the following
equations:
t3
b
¼maxðt1
b
;t2
b
Þ
subject to:
t1
b
¼t1
a
þt1
s
t2
b
¼t1
b
þt2
a
þt2
s
And obviously, t
2
b
.t
1
b
,sot
3
a
¼t
2
b
.
Whichever situation aor bit is, t3
b
¼t3
a
þt3
s
.
2.4 Calculate the human and robot participation time T
h
,T
r
It is also important to know the time human and robot spend, respectively, because the
task finish time is not the sum of human and robot participation time, due to
the concurrent and serial assembly features of the human and robot cooperation
process:
.Th:;ti[Tð0#i#jTjÞ;Th¼sumðti
s
Þiff. t
i
is carried out by human
workers.
.T
r
:;t
j
[T(0 #j#jTj,j8i,iþj¼jTj), T
r
¼sum(t
j
s
) iff. tjis carried out by
robots.
2.5 Assembly strategy selection process
Figure 2 shows the procedure to select the best time and payment tradeoff assembly
strategy based on the dual GSPN model.
When there is an assembly task, the first step is to describe the assembly task
process and define the final objective. After decomposing the whole task into subtasks,
the subtask will allocate to human and robot, the way of allocation, of course, is
numerous, according to the exhaustion listing method. Build a dual GSPN model for
each way of allocation, and calculate the time cost and associated payment cost for
accomplishing this assembly task. Monte Carlo method is used when calculating the
task finish time based on the generated dual GSPN model. After we get the task finish
time and payment cost, a MOOP method is carried out to select the best trade-off
assembly strategies.
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493
3. Multiple connector insertion task
3.1 A HRC cell
A HRC assembly is that both of human and robot work within the same room, sharing
the working time and working space, with no physical barriers (Figure 3). The
utilization of their merits will help to achieve the best manufacturing efficiency.
3.2 Task objective and procedure description
A simplified assembly task from an industrial power supply module assembly is
introduced to test the proposed approach. In electronic manufacturing, multiple types of
connectors are assembled totally by robots. However, the unpredictable errors during
the insertion process results in long time gesture search and adjustment and
consequently low successful ratio, and even fatal unrecoverable errors triggering the
stop of the manufacturing system. Therefore, in order to fix the shortcomings for fault
Figure 3.
HRC manufacturing
Figure 2.
Research procedure
architecture
An Assembly Task
(Suitable for H&R Coordinated Assembly)
Task Objective and Procedure Description
and Subtask Decomposition
Criterion: Requirements that Industries
Concerned
Subtasks Allocation to H&R
(List by Exhaustion)
Allocations Optimization
(Multiple Objective Optimization)
Dual GSPN Generation for Each
Allocation
(Automatically or Manually)
Data: Time Cost based on H&R Behavioral
Features Analysis
Monte Carlo Simulation, Calculation
(Task Finish Time, Payment Cost, ...)
Appropriate Assumptions along with
Experts in Industry
Semi-optimal Allocation Generated and
Experiment
Appropriate Assumptions from Researches
of Experts in Psychology
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detection and diagnosis in this area, necessary human involved assembly with robot can
help the robot work effectively, and accomplish the whole assembly task efficiently.
The goal of this assembly task is to assemble all the connectors to the right position
within this power supply module (Figure 4).
3.3 Subtask decompostion and allocation to human and robot
There are three types of connectors within this assembly. C1 denotes the connector
with one head, so as C2andC3. After discussion with the assembly experts, the whole
assembly procedure is decomposed into six subtasks as shown in Table I.
Moreover, two basic assembly rules are conclude due to the limitation of the product
construction, which are the serial assembly rule and parallel assembly rule:
(1) serial assembly rule: C1-C3 connectors should be assembled one after another;
and
(2) parallel assembly rule: within C2 and C3, subtask Nos 2, 3 and Nos 4-6 can be
assembly parallel by human and robot, respectively.
Based on the rules, it is assumed that there is no difference for human or robot to insert
any head of C2orC3 (the position of task Nos 2 and 3 is equal, so as the same with
Figure 4.
Task and HRC scenario
Human
worker
Human and Robot Coordination
Robotic manipulator
Assembly area
Connector fix area
Connectors
Connectors-1
Connectors-3
Connectors-2
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495
task Nos 4-6). After a combinatorial mathematics calculation, there are
21 configurations for the subtasks allocation for human and robot (Table II), and the
aim is to find out the best tradeoff configurations, which bring the best performance
tradeoff for the cost effectiveness in the human and robot cell assembly system.
3.4 Dual GSPN model generation for each allocation (e.g. allocation No. 11)
In this allocation, human does task Nos 1, 2, 4 and robot does task No. 3, 5, 6. The
following dual GSPN model (Figure 5) distributes the subtasks to human and robot.
Only after human inserts connector C1(t
1
), human can assemble C221(t
2
) and robot can
assemble C222(t
4
). Only after C2(t
2
,t
4
) is inserted, human can insert C321(t
3
), and
robot can insert C322(t
5
), and C323(t
6
) sequentially. Therefore, the serial assembly
rule and parallelassembly rule are fully guaranteed.
Task no. Task
1 Pick up connector C121, and insert at P121
2 Pick up connector C221, and insert at P221
3 Pick up connector C222, and insert at P222
4 Pick up connector C321, and insert at P321
5 Pick up connector C322, and insert at P322
6 Pick up connector C323, and insert at P323
Table I.
Task decomposition
Configuration no. Human tasks (task no.) Robot tasks (task no.)
1 1,2,3,4,5,6 –
2 2,3,4,5,6 1
3 1,2,4,5,6 3
4 1,2,3,4,5 6
5 2,4,5,6 1,3
6 2,3,4,5 1,6
7 1,4,5,6 2,3
8 1,2,3,4 5,6
9 4, 5, 6 1, 2, 3
10 1, 4, 5 2, 3, 6
11 1, 2, 4 3, 5, 6
12 1, 2, 3 4, 5, 6
13 4,5 1,2,3,6
14 2,4 1,3,5,6
15 2,3 1,4,5,6
16 1,4 2,3,5,6
17 1,2 3,4,5,6
18 4 1,2,3,5,6
19 2 1,3,4,5,6
20 1 2,3,4,5,6
21 – 1,2,3,4,5,6
Table II.
Task decomposition
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According to the definition of I,I
þ
and I
2
, they are deduced as follows:
I2¼
t0t1t2t3t4t5t6t7
p010000000
p101000000
p200100000
p300010000
p400000001
p500001000
p600000100
p700000010
p800000001
p900001000
p10 00000100
p11 00010000
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
ð2Þ
Figure 5.
A dual GSPN example
HUMAN-PN
Human
is ready
Assembly parts
are ready
Robot
is ready Robot
inserts
C2-2
Robot
inserts
C3-2
Robot
inserts
C3-3
Robot
tasks are
done
Robot
finishes
C2-2
Robot
finishes
C3-2
ROBOT-PN
Human
inserts
C1
t1
t7
T0
p0
t2t3
t1t5t6
p3p2p1 p4
p7p6p5 p8
p9
ρ1 = 1
ρ2 = 1
p10 p11
Human
inserts
C3-1
Human
tasks are
done
Human
finishes
C1
Robot:
Human
finishes
C1
Robot:
Human
finishes
C2-1
Human:
Robot
finishes
C2-2
Human
finishes
C2-1
Human
inserts
C2-1
HRC cell
manufacturing
497
Iþ¼
t0t1t2t3t4t5t6t7
p000000001
p110000000
p201000000
p300100000
p400010000
p510000000
p600001000
p700000100
p800000010
p901000000
p10 00100000
p11 00001000
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
ð3Þ
I¼Iþ2I2¼
t0t1t2t3t4t5t6t7
p0210000000
p1121000000
p2012100000
p3001210000
p4000100021
p5100021000
p600001210 0
p7000001210
p8000000121
p9010021000
p10 00100210 0
p11 000211000
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
ð4Þ
According to the definition of pre-transition set, based on I, we can find out all the
pre-transition sets of t
i
(0 #i#7) as shown in Table III.
Within this table, {t
1
,t
2
,t
3
} are the events carried out by human, while {t
4
,t
5
,t
6
} are
the events carried out by robot, and t
0
,t
7
are immediate transitions. {t
1
,t
2
,t
3
} and
{t
4
,t
5
,t
6
} are heterogeneous, respectively. Therefore, the task finish time T
f
is as well
the event leaving time of t
7
(t
7
b
), which is derived as follows:
IJICC
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498
Tf¼t7
b
¼t7
a
¼maxðt3
b
;t6
b
Þ¼maxðt3
a
þt3
s
;t6
a
þt6
s
Þ
¼maxðmaxðt2
b
;t4
b
Þþt3
s
;t5
b
þt6
s
Þ
¼maxðmaxððt1
b
þt2
s
Þ;t4
b
Þþt3
s
;t4
b
þt5
s
þt6
s
Þ
¼maxðmaxððt0
a
þt1
s
þt2
s
Þ;ðmaxðt0
b
;t1
b
Þþt4
s
ÞÞ þ t3
s
;maxðt0
b
;t1
b
Þ
þt4
s
þt5
s
þt6
s
Þ
¼maxðmaxððt0
a
þt1
s
þt2
s
Þ;ðt1
a
þt1
s
þt4
s
ÞÞ þ t3
s
;t1
a
þt1
s
þt4
s
þt5
s
þt6
s
Þ
Therefore:
Tf¼maxðmaxððt0
a
þt1
s
þt2
s
Þ;ðt0
b
þt1
s
þt4
s
ÞÞ þ t3
s
;t0
b
þt1
s
þt4
s
þt5
s
þt6
s
Þð5Þ
where t
0
a
¼t
0
b
¼0. According to equation (5), to calculate the task finish time is
actually to calculate each transition average time taken t
i
s
(0 #i#jTj).
The objective for modeling HRC assembly is to find out the least time consuming
assembly sequence and also the lowest payment cost for human and robot. With the
cost for human resource keep growing recently in industry, it is also necessary to
consider the payment cost for each assembly configuration based on the working time
of both human and robot, respectively.
3.5 Calculate t
s
In Figure 5, for each time delayed transition of human and robot, it contains another
GSPN, which represents the detailed behavior transition of human or robot, when they
face different situations, such as error detection, and error recovery.
(a) For robot. Figure 6 shows that when robot gets a task, i.e. inserting connectors,
first, it takes the insertion action t
0
. If it succeeds in inserting the connector, it will
directly goes to successful event t
6
, however, it is possible (
r
1
) that the robot fails
inserting the connector with the first try. In that case, the robot has to do error
recovery. Error recovery mainly contains two steps, first the robot has to search for a
better gesture around the connector based on the pre-stored error algorithms, such as
the spiral search (Huang et al., 2008b), probing search, etc. After robot gets a better
gesture, it will take the insertion action t
2
. If the robot fails again, robot will repeat the
error recovery strategy. Based on our former research, the error recovery strategy can
Transition t
i
Direction pre-transition set of t
i
t
0
{B}
t
1
{t
0
}
t
2
{t
1
}
t
3
{t
2
,t
4
}
t
4
{t
0
,t
1
}
t
5
{t
4
}
t
6
{t
5
}
t
7
{t
3
,t
6
}Table III.
Pre-transition set
HRC cell
manufacturing
499
cope with 80-90 percent insertion errors. If the robot has failed once again to insert the
connector, it will alert and stop, waiting for human worker’s help.
Because this process contains the uncertain situation, it is significant to get the
mean time distribution for t
s
. Monte Carlo method is used to study average of t
s
. Monte
Carlo methods (Metropolis, 1987) are useful for modeling phenomena with significant
uncertainty in inputs. Algorithm 1 shows the process to calculate the average time of t
s
for the event shown in Figure 6.
We get the data from the sampling of practical experiments, all the parameters are
shown in the Table IV. M
t0k
denotes the average time for transition t
0
for task No. k
while V
t0k
denotes its variance. According to the practical situation in experiments,
robot failure ratio
r
1
and
r
3
are set as 0.1 percent. From our former research, the search
time for the robot when error occurs is around 5 s.
The robotic manipulator used in the experiment is a Mitsubishi RV 21Aindustrial
manipulator with a mass of 19 kg and repeatability of ^0.02 mm. In order to protect
the safety of human workers, according to ISO (2006) standards (ISO13849), RV-1A
moves with safe reduced speed (less than 250 mm/s) and monitored position:
Algorithm 1. Monte Carlo method for robot transition
Input:
M
t0k
,V
t0k
,M
t2k
, for each subtask k,
r
1
,
r
3
and PI ¼3.14.
1: for n¼1 until n¼N¼10000 do
Figure 6.
Detailed event transition
for robot within a timed
transition
Robot
inserts ρ2
ρ1
ρ3
ρ4
ρ6 = 1
ρ5 = 1
Connector is
inserted
Connector is
inserted
successfully
Connector
insertion is
failed after one
try, asking for
help
Connector
insertion is
failed
Search and
insert again
Connector is
inserted
Failing times
are recorded
t0
t1
t2
t3
t4
t5
t6
p0
p1p2
p3p4
p5
t7
By human (s) Human operation Human buffer Human recover Human action
By human (s) Variance (s) time ratio time (s) repeating ratio
Task no. (k)M
t4k
,M
t6k
V
t4k
,V
t6k
r
2
M
t2k
r
4
1 5 0.67 0.5 percent 0.5 2 percent
2 4.2 0.19
3 4.4 0.49
4 3.8 0.18
5 3.9 0.1
6 5.3 0.23
Notes:
a
r
2
þ
r
3
¼1;
b
r
4
þ
r
5
¼1
Table IV.
Parameters for human
event transition
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500
2: t
temp
¼0
3: Generate a random number Pr
k
between 0 and 1.
4: t
s
nk ¼tempMt0kþð21ÞjPrkjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
22Vt0klog PVt0kffiffiffiffiffiffiffi
2PI
p
q. where
P¼1=Vt0kffiffiffiffiffiffiffi
2PI
p
.
5: if Pr
k
#
r
1
// insert fails then
6: t
s
nk ¼t
s
nk þMt2iþtemp, // insert again.
7: if Pr
k
#
r
3
then
8: Robot alerts. // insert fails again, robot quits.
9: end if
10: end if
11: n¼nþ1
12: end for
13: Calculate average t
r
k
within Nloops.
Output:
t
r
k
// time taken within this transition for subtask k.
(b) For human. Figure 7 shows the possible behavior transition for human worker
during the assembly. When human worker is facing an assembly task, It is possible
(
r
2
) that it takes a short time (t
2
) for him to response. This is human worker’s fatigue
related, the longer the human works, the longer time it will take for him to response.
However, in this model and experiment, it is assumed that human work is under a good
psychological status, and we do not have to concern the performance declining
(possibility
r
i
changes) because of the fatigue with working time growing. After the
short response time, human worker starts to work t
4
. There is a possibility (
r
4
) that
human worker fails to accomplish the task, according to the human nature, he will keep
trying (t
6
) until he succeeds. It is assumed that, human worker usually will succeed
after one try. Monte Carlo method is also used to calculate t
s
for each subtask taken by
human in Algorithm 2:
Algorithm 2. Monte Carlo method for human transition
Input:
M
t4k
,M
t6k
,V
t4k
,V
t6k
,M
t2k
, for each subtask k,
r
1
,
r
4
and PI ¼3.14, where
M
t4k
¼M
t6k
,V
t4k
¼V
t6k
1: for n¼1 until n¼N¼10000 do
2: t
temp
¼0
3: Generate a random number Pr
k
between 0 and 1.
4: if Pr
k
#
r
1
// it takes time for human to response then
Figure 7.
Detailed event transition
for human within a timed
transition
Human
inserts
ρ3
ρ2ρ4
ρ5
ρ6 = 1
Time for human
to work
Connector is
inserted
successfully
Human is mind
unconcentrated
or
environmental
constraints
Human takes
time to recover
or adjust
Human starts
to work
Connector is
inserted
Connector is not
properly
inserted
Human
inserts
again
ρ1 = 1
P0
p1
p2 p3
p4
p5
t0
t1
t2
t3
t4
t5
t7
t8
t6
HRC cell
manufacturing
501
5: t
s
nk
¼t
s
nk
þM
t2k
6: end if
7: t
s
nk ¼t
s
nk þMt4kþð21ÞjPr kjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
22Vt4klog PV t4kffiffiffiffiffiffiffi
2PI
p
q:where
P¼1=ðVt4kffiffiffiffiffiffiffiffiffi
2PIÞ
p.
8: if Prk#
r
2, // insert fails then
9: t
s
nk
¼t
s
nk
þt
temp
// insert fails again, robot quits.
10: end if
11: n¼nþ1
12: end for
13: Calculate average t
r
k
within Nloops.
Output:
t
r
k
// time taken within this transition for subtask k.
We get the data from the sampling of practical experiments, all the parameters are
shown in the Table V.
According to equation (2), the assembly time for configuration 11 could be
calculated. The Gantt diagram chart for this configuration is shown in Figure 8.
By robot (s)
M
t0k
Robot operation variance (s) Robot failure ratio Search time (s)
Task no.
(k) 250 mm/s V
t0k
r
1
,
r
3
M
t2k
1 17 0.1 0.1% 5
2 16 Spiral search
3 16 Probing search
416
516
616
Notes:
a
r
1
þ
r
2
¼1;
b
r
3
þ
r
4
¼1
Table V.
Parameters for robot
event transition
Figure 8.
Gantt diagram chart for
configuration No. 11
IJICC
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502
3.6 Calculate payment P
Beside the task finish time, the payment cost for human and robot based on the time
they spent within this task are also considered as criterions. To calculate the payment
cost for human and robot, the payment cost per unit time for human and robot should
be defined and calculated.
Payment cost per unit time for human: P
h
. According to the data from the World
Bank, we can get the general payment distribution for human worker per hour. The
payment cost per second we choose for human is $0.057.
Payment cost per unit time for robot: P
r.
The depreciation is considered when calculating the cost per hour for robots, including
the cost for equipment, electricity, and maintenances. In the case studied, first, it is
assumed that one human worker is partnered with one small sized industrial robotic
manipulator, which is supposed to be cost US$10,000for hardware. The electricity, second,
the robot consumes also contributes to the basic cost every hour, which is supposed to be
1 kwh/h. Third, because the robot should be carefully instructed, programmed and
calibrated beforehand and maintained afterwards, which are usually done by specialized
experts or programmers. In common sense, we assume that it will cost a human worker six
months of working timeto program and maintain for the robot during its whole useful life.
According to the standards adopted around the world, the useful life for mechanical
equipment is set to be ten years. The most basic form of depreciation is known as
straight-line depreciation (Kieso et al., 2006). Using this method, the cost of the asset is
spread out equally over the expected life of the asset according to the equation below:
Cdep ¼Cequi þChumNhm NdNh
NrmNdNhþCelec ð6Þ
Where (in Table VI).
According to equation (6), we can get the cost per second for robot is $0.0005. The
overall payment is calculated according to equation (7):
P¼PhThþPrTrð7Þ
4. Experiments and results
4.1 Allocation simulation and experiment results
Table VII shows the experimental results for each way of subtask allocation for human
and robot.
Parameter Description
C
dep
The depreciation cost per hour to be calculated
C
equi
The one-off cost for the equipment (robot)
C
hum
The cost per hour for human to maintain the robot
C
elec
The cost per hour for electricity consumed by the robot, a constant value 0.1 in this case
N
hm
Set to be 6, referring the total month cost to maintain the robot during its useful life
N
rm
Set to be 120, referring the total month during the useful life of the robot
N
d
Set to be 20, referring the total working days within a month
N
h
Set to be 8, referring the total working hours within a day
Table VI.
Parameter description
in equation (6)
HRC cell
manufacturing
503
The simulation and experiment results are shown in Figure 9.
Figure 9 shows the simulation (in dash line) and experimental (in solid line) results.
The simulation results basically agree with the experimental results, proving the
validation and effectiveness of proposed dual GSPN model. In Figure 9, from the respect
Configuration no.
Task execution time T
f
(s)
Human execution time T
h
(s)
Robot execution time T
r
(s)
133330
2341915
3332214
4282215
5421830
6371828
7492029
8441730
9571443
10 49 12 45
11 49 14 44
12 56 12 44
13 60 7 60
14 59 9 59
15 67 8 58
16 63 8 59
17 64 9 58
18 73 5 73
19 75 7 75
20 78 6 72
21 88 0 88
Table VII.
Experiment results
Figure 9.
Simulation and
experiment results
of task finish time and
payment cost
0
50
Configuration No.
Total Assembly Time: s
21 18 19 20 15 13 14 16 17 9 12 10 11 7 5 8 6 2 3 4 1 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Total Money Cost: $
IJICC
4,4
504
of macroscopic view, with the assembly task finish time decrease (in red), due to the
growing participation of human workers, the payment cost increase (in blue), also due
to the higher payment cost for human workers.
From the respect of microscopic view, due to the discrete subtask division, there
occurs that when robot finish one subtask, it cannot immediately start the next
subtask, but wait for the human worker. Consequently, the task finish time line is not
strictly going down, and the payment cost line is not strictly going up. The cross-shape
of these two lines requires that a tradeoff study should be carried out to study the
optimal subtask allocation selection method based on MOOP, which is to shorten the
task finish time, while to reduce the payment cost.
But this two lines are greatly affected by process of human and robot interactivities,
which leads to a result that the results, especially the assembly strategies selected, are
also decided by how accurately this model can present. Here, basically, two issues are
listed as follows.
Human features: human worker performance is not a stable value. Within a working
day, the performance of human worker varies at different segments of working time. In
the modeling for human behavior, the possibility that human tires is set as fixed value.
Long working time-related work fatigue which will cause the estimate results and
construction of dual GSPN changing over time should be taken into consideration.
Consequently, the system can dynamically adjust the construction of dual GSPN when
the human worker performance declines.
Dialogue from human to robot: not only is the robot position monitored by the safety
system, but also the position of human worker is monitored by the robot. In the modeling
and experiment, the robot takes the action just after human finish his subtask. The truth
is that robot has to estimate the state of human worker and do corresponding action.
Better sensor system design can help to reduce the time cost for robot to process the
information, and therefore reduce the overall time cost for HRC cell assembly.
4.2 MOOP method comparison
In this human and robot cooperated cell assembly, the decision maker always prefer
the low time consuming and payment cost assembly strategy, which is a MOOP
problem. In this research, the MOOP is to find out a group of allocation A:
A¼a1;a2;...;ai;i[I¼1;2;...;21
ai¼
0;aiis not one of the optimal selections
1;aiis one of the optimal selections
(
Therefore, the task finish time T
f
is related with a certain way of task allocation A
indicated as T
f
(A), while it is similar with the payment cost Pas P(A). The MOOP is
modeled as follows:
minðTfðAÞ;PðAÞÞ
s. t.
A¼{a1;a2;...;ai};1#i#21 ai¼0;1:
There are two common used MOOP method to choose the optimal alternatives.
HRC cell
manufacturing
505
(a) Weighted method. Because there are two criterions T
f
and Pare used to judge
one way of allocation, different weights are assigned to them to generate an overall
judgment.
First, T
f
and Pare uniformed to [0,100], respectively. Then, assign a weight to both
criterion, denoted as wtand wp, with a constraint that wtþwp¼1. Then, the judgment
parameter Jis calculated according to equation (8):
J¼wtTfþwpPð8Þ
The Junder different setting of w
t
and w
p
are shown in Figure 10.
If the factory demands a shorter manufacturing time, set w
t
.w
p
. If the factory
demands a shorter manufacturing time, set w
t
,w
p
. For a certain setting up of w
t
and
w
p
(as shown in Figure 10 where w
t
¼w
p
¼0.5), a threshold value can be assigned to
filter out the bad allocations based on J. In this case, if this acceptable threshold value is
set as 44, the acceptable allocation group is A¼{a
1
,a
2
,...,a
i
} where:
ai¼
0;i[I2{4;6;10;11;13;14}
1;i[{4;6;10;11;13;14}
(
Figure 10.
The overall judgment of J
21 18 19 20 15 13 14 16 17 9 12 10
(a)
(b)
11 7 5 8 6 2 3 4 1
10
20
30
40
50
60
70
80
Overall Value
Overall Value:wT = 0.2, wC = 0.8
Overall Value:wT = 0.4, wC = 0.6
Overall Value:wT = 0.5, wC = 0.5
Overall Value:wT = 0.6, wC = 0.4
Overall Value:wT = 0.8, wC = 0.2
21 18 19 20 15 13 14 16 17 9 12 10 11 7 5 8 6 2 3 4 1
40
42
44
46
48
50
52
Configuration No.
Overall Value
Overall Value:wT = 0.5, wC = 0.5
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506
(b) skyline method (Morse et al., 2007).Inann-dimensional space, there is a point set
p(jpj¼n). one point Pt¼ðPt1;Pt2;PtnÞðPt[pÞstrongly dominates another point
P:
t¼ðP:
t1;P:
t2;¡;P:
tnÞðP:
t[pÞiff. ;i[{1;2;...;n}, Pti is better (more effective, lower
cost, shorter execution time) than P:
ti. If a point Ptcannot be dominated by any
P:
t[p2Pt.Pis on the skyline. Therefore, the points within a skyline are those cannot
be ruled out by each other, and they are consequently the best choice for one specific
MOOP problem.
In this case, Pt¼ðTf;PÞrepresents an allocation criterion pair, and pis the set of all
the 21 allocations ðPt[p;n¼21Þ.Pt¼ðTf;PÞstrongly dominates another point
P:
t¼ðT:
f;P:Þiff. ;i[{1;2;·s;n}, Tfi ,T:
fi and Pi,P:
i. Figure 11 shows the skyline
of this assembly subtask allocation set p. The skyline for this case is shown in Figure 11.
From Figure 11, it is easy to figure out that the acceptable allocation group within in
the skyline (in red) is A¼{a1;a2;...;ai} where:
ai¼
0;i[I2{1;2;3;7;9;11;15;17;18;21}
1;i[{1;2;3;7;9;11;15;17;18;21}
(
Note that different choose of payment cost per second for human and robot will lead to
different results using above comparison methods. The results are shown in Table VIII.
Figure 11.
Ths Skyline
1.5 21
18
15
9
17
11
7
3
2
1
1
0.5
0
20 30 40 50 60 70 80 90 100
Total Assembly Time: s
Total Money Cost $
Method Selected alternative allocations
Weighted method {4,6,10,11,13,14}
Skyline method {1,2,3,7,9,11,15,17,18,21}
Table VIII.
Result comparison of
different methods
HRC cell
manufacturing
507
Table VIII shows that the configuration No. 11 occurs in the selected allocations of both
the weighted method and skyline method, therefore configuration No. 11 is one of the
preferred selection. According to the practical situation, the decision maker can adjust
the task finish time and payment cost by switch between the selected alternative
allocations.
5. Conclusion
This paper has presented a methodology in selecting the optimal assembly strategy by
building HRC cell assembly model. A dual GSPN model is used to better describe all the
possible situations during HRC assembly, including the possibility that human or robot
makes mistakes. By using Monte Carlo method, a general task finish time and payment
cost of each assembly strategy configuration is obtained, based on which, MOOP
analysis is conducted to study the trade-off of each configuration. Finally, a set of better
configurations is derived. Strategy makers in factory could choose the best solution
among them by considering the practical requirements and environments.
In small production manufacturing, it is difficult to maintain the HRC in an effective
way. This method has provided the decision maker a general and mathematical
method that by analyzing the behavior of robot and, especially human, get the time
distribution for each behavior and then build a dual GSPN. Based on the simulation
results of dual GSPN, one can better estimate time and payment cost for one specific
configuration of the subtasks for human and robot.
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About the authors
Fei Chen received the BS Degreein Computer Science fromXi’an Jiaotong University
(XJTU), China, in 2006, and the MS Degree in Computer Science from Harbin
Institute of Technology (HIT), China, in 2008. He is currently a Doctor candidatein
the Department of Micro-Nano System Engineering and the Department of
Mechano-informatics and Systems, Nagoya University, Japan. His current research
interestsinclude robotic assembly and human and robot cooperation. Fei Chenis the
corresponding author and can be contacted at: chen@robo.mein.nagoya-u.ac.jp
Kosuke Sekiyama received his BE, ME and Dr Eng. Degrees from Nagoya
University in 1992, 1994, and 1997, respectively. Currently, he is an Associate
Professor of Department of Micro-Nano Systems Engineering, Nagoya
University. His main research interests are distributed autonomous systems,
in particular, self-organizing systems in the various system levels and
distributed manufacturing systems.
Jian Huang received PhD Degrees in Control Theory and Control Engineering
from Huazhong University of Science and Technology (HUST), Hubei, China in
2005. Currently, he is an Associate Professor in the Department of Control
Science and Engineering, HUST and his current research interests include
robotic assembly, networked control systems, and bioinformatics.
Baiqing Sun received his PhD Degree from Kochi University of Technology
(KUT), Japan in 2006 and since November 2010 he has been an Associate
Professor at the Electrical Engineering School of SUT. His main research
interests include flexible control of assembly robots, design and control of
intelligent actuators, and artificial intelligent systems.
Hironobu Sasaki received the Doctor of Engineering Degree from Tokyo
Metropolitan University in 2009. He had been a Researcher on GCOE at the
Department of Micro-Nano System Engineering in Nagoya University until June
2009. His main research areas are robotics engineering, intelligent system
engineering, sensor networks and image processing.
Toshio Fukuda received the BS Degree from Waseda University, Tokyo, Japan, in
1971, the MS Degree in 1973, and the PhD Degree with a dissertation entitled
“Malfunction diagnosis and application of stable adaptive schemes for a nuclear
reactor system”, in 1977, both from the University of Tokyo, Japan. From 1977 to
1982, he was with the National Mechanical Engineering Laboratory, Tsukuba, Japan.
From 1982 to 1989, he was with the Science University of Tokyo. Since 1989, he has
been with Nagoya University, Japan, where he is currently a Professor in the
Department of Micro-Nano Systems Engineering. His current research interests include intelligent
robotic systems, cellular robotic systems, mechatronics, and micronanorobotics. Dr Fukuda was the
President of the IEEE Robotics and Automation Society (1998C1999), the Director of the IEEE Division
X, Systems and Control (2001C2001), and the Editor-in-Chief of the IEEE/American Society of
Mechanical Engineers Transactions on Mechatronics (2000-2002), and the President of the IEEE
Nanotechnology Council (2002-2005). He is the AdCom President of the IEEE Nanotech nology Council.
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