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Robust conflict-free routing of bi-Robust conflict-free routing of bi-
directional Automated Guided directional Automated Guided
Vehicles (AGVs)Vehicles (AGVs)
Robust conflict-free routing of bi-Robust conflict-free routing of bi-
directional Automated Guided directional Automated Guided
Vehicles (AGVs)Vehicles (AGVs)
Institut de Recherche en Communication et Cybernétique de Nantes
Samia MAZA
Pierre Castagna
2
Plan :Plan :
Introduction to the AGV routing problem
Classification of the AGV’s routing methods
The conflict-free shortest time path planning
The robust conflict-free routing (2 algorithms)
Some results & Conclusion
3
DefinitionsDefinitions::
Automated guided vehicles (AGVs) are used to transport materials and goods in
manufacturing systems.
They follow guidance circuits connecting various workstations in the warehouse.
The guidance circuit is a physical track, which can be materialized with different
manners, such as a colored bandage stuck on the ground, or an electrical conductor
buried in the ground.
4
KindsKinds of guidance networks of guidance networks
unidirectional CircuitsA
D
C
B
E(8)
(4)
(5)
(6)
(1)
(3) (2)
(7)
Bi-directional Circuit
5
The advantages of Bi-directionnal CircuitsThe advantages of Bi-directionnal Circuits
Reduction of the total traveled distances
Reduction of flow times
Reduction of the space requirement
Best network reachability
More complex control due to the conflicts between AGVs
Egbelu et al, potentials for bi-directional guide-path for AGV based systems, 1986.
n mV1 V2
collision
6
Classification of the AGV’s routing methodsClassification of the AGV’s routing methods
Not robust.
The Predictive methods *
Find optimal routes for vehicles;
off-line conflicts Prediction;
Planning of the AGV’s path.
Good performances in the theory.
H.Thomas, Optimisation des trajectoires d’une flotte de chariots mobiles, Thèse de Doctorat, Nantes 1994.
N.N.Krishnamurthy et al, Developing conflict-free routes for automated guided vehicles, 1993
Tanchoco et al, Conflict-free-shortest-time bidirectionnal AGV routeing, 1991
Tanchoco et al, Operational control of bidirectional automated guided vehicle system, 1993
*
7
Classification of the AGV’s routing methodsClassification of the AGV’s routing methods
The performances are not optimized a priori.
The reactive methods *
The AGV’s path is not planned;
The decisions are taken in a real time manner
Robust Methods
Ying-Chin Ho, A dynamic zone strategy for vehicle collision prevention and load balancing in an AGV system with a single loop guide path, 2000.
Spyros Reveliotis, Conflict resolution in AGV system, 2000.
Qiu Ling & Hsu Wen –Jing, Conflict free AGV routing in a bidirectionnal path layout, 2001.
*
8
Our objective
Make one predictive control method more reactive to real time changes
9
The conflict-free shortest time AGV path planning
Tanchoco et al, Conflict-free-shortest-time bidirectionnal AGV routeing, 1991
Tanchoco et al, Operational control of bidirectional automated guided vehicle system, 1993
The description of the method
10
21
5
43
6(9) (10)
(2) (3)
(4)
(7) (6) (5)
(8)
(1)
(11)
7
9
8
1
3
2
10
f616
f515
f414
f313
f20 = r2
12
f111
f52
f42 f4
3
f32
r51
r42r4
1
r31
r11 f1
2
V1
V2
V3
0 10 20 30 40 50 60 70Time
Nodes
The nodes reservation table
A free time window
A reserved time window
10
21
5
43
6
7
9
8
11
f616
f515
f414
f313
f20 = r2
12
f111
f52
f42 f4
3
f32
r51
r42r4
1
r31
r11
f12
V1
V2
V3
0 10 20 30 40 50 60 70Time
Nodes
Principle of the method
f12 f3
2
f43
f52
f61
f51
f41
f42
f31
f20
f11
Remark : A mission can appear to be impossible if such a path doesn’t exist
10
21
5
43
6
7
9
8
12
The routing of the AGV V3 by the cfstp cfstp algorithm
f53
f616
f515
f414
f313
r212
f111
f52
f42 f4
3
f32
r51
r43r4
1
r31
r12 f1
3
V1
0 10 20 30 40 50 60 70 Time
The time windows after the routing of V3
Nodes
r11
r42 r4
4
f32
f12
r52
r61
V2
V3
13
The schedule of a new displacementThe schedule of a new displacement
Each AGV has an ordered list of missions
A mission consists in going to visit a node N
The guide path contains garages, their number is at least equal to AGVs fleet size. The garages nodes can not be destination nodes of the AGVs.
The missions order can not be inverted
A new mission of a vehicle is planned only if this one becomes free
AssumptionsAssumptions
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
14
Drawback of this predictive methodDrawback of this predictive method
This method is effective. It gives an optimal conflict free path by considering the
previously established plans
Open loop control method
not robust:
The disturbances* which can appear in a real system are not taken into account
* ex: an accident, a slowing down in front of obstacles…etc
Introduction of a shift between the predicted time windows and the realized one
15
The routing of the AGV V3 by the cfstp cfstp algorithm
f53
f616
f515
f414
f313
r212
f111
f52
f42 f4
3
f32
r51
r43r4
1
r31
r12 f1
3
V1
0 10 20 30 40 50 60 70 Time
The time windows after the routing of V3
Nodes
r11
r42 r4
4
f32
f12
r52
r61
V2
V3
r42
Conflict
16
Conclusion
This method can not be applied directly on a real system.
17
The conflict free shortest time procedure (CFSTP) Predictive
level
Node’s crossing order controller Real time
control level
Oi= An ordered list of AGVs having to cross the node i
Collision avoidance in Real timeCollision avoidance in Real time
Maza & Castagna, Conflict-free AGV Routing in Bi-directional Network, ETFA 2001
18
Real time collision avoidanceReal time collision avoidance
The conflict free shortestThe conflict free shortesttime procedure (time procedure (cfstpcfstp))
Task for checking the
node’s crossing order of AGV
V1
Task for checking the
node’s crossing order of AGV
Vi
Task for checking the
node’s crossing order of AGV
Vn
The central controller (predictive
level)
Decentrali-zed
controllers (real time
level)
19
4V2
V3
V1
Arrival of the vehicle Vx to the node n
Is the vehicle Vx
the first vehicle in theList On ?
Vx must wait for the crossing of another vehicle
Vx can cross n
Yes
No
End
V2V3V1V3
O4=
20
Consequence Consequence
A robust closed loop control: the system state is taken into account at any
moment, and the conflicts can be avoided in a real time only by respecting the
established crossing order
Forgetting time, the realized system behavior is as predicted in the
planning level
21
Criticism of the methodCriticism of the method
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
NV2
V1V2
V1
If a vehicle undergoes a significant delay, some other vehicles having to cross some
common nodes will be delayed Will undergo a significant delay too
22
The improved robust AGV routingThe improved robust AGV routing
How to improve the robust routing control, by modifying the
node’s crossing order, without causing conflicts ?
23
ExampleExample
V1 V2
V3
{1} {1,3} {1,3,2} {1,3,2} {1,2} {2}
{2} {3}
V1 is the late AGV
Can VCan V22 cross the node i and continue its trip without colliding cross the node i and continue its trip without colliding
with Vwith V11 its predecessor on that node ? its predecessor on that node ?
i
24
i
j
V
k
m
Oi={U, V}Om={U, V}
Ok={U, V}Oj={U, V} {U}
{V}
{U}
A. A. Approach by delaying the late AGV UApproach by delaying the late AGV U
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
25
i
j
V
k
m
Oi={U, V}Om={U, V}
Ok={U, V}Oj={U, V} {U}
{V}
{U}
A. A. Approach by delaying the late AGV UApproach by delaying the late AGV U
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
26
i
j
V
k
m
Oi={U, V}Om={U, V}
Ok={U, V}Oj={U, V} {U}
{V}
{U}
U
U is outside the blue zone the re-ordering is possible
A. A. Approach by delaying the late AGV UApproach by delaying the late AGV U
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
27
i
j
V
k
m
Oi={V, U}Om={V, U}
Ok={V, U}Oj={V, U} {U}
{V}
{U}
U
Delay-action of the vehicle throughout common way
A. A. Approach by delaying the late AGV UApproach by delaying the late AGV U
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
28
i
j
V
k
m
Oi={U, V}Om={U, V}
Ok={U, V}Oj={U, V} {U}
{V}
{U}U
U is on the common path the vehicle V must wait
A. A. Approach by delaying the late AGV UApproach by delaying the late AGV U
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002
29
B. B. Approach by advancing the AGV VApproach by advancing the AGV V
V2
{1} {1,3} {1,3,2} {1,3,2} {1,2} {2}
{2} {3}
Nj
V2 is the first AGV in the list ?
V2 is the first AGV in the list ?
V2 is the first AGV in the list ?
V2 is the first AGV in the list ?
Li
P={V1}P={V1,V3}P={V1,V3}
The re-ordering is possible update nodes associated lists for each node belonging to the path [Nj, M]
M
MAZA & Castagna, Robust conflict-free routing of bi-directional automated guided vehicles, SMC02
30
B. B. Approach by advancing the AGV VApproach by advancing the AGV V
V2Nj
M
V1
V2
V1
V3
V2
V1
V3
V2
V2V3
V2
V1
V3V1
V2V3
V2
V1 V1
V2
V2
V1
V3
V2
V1
V3V3
V1
MAZA & Castagna, Robust conflict-free routing of bi-directional automated guided vehicles, SMC02
31
SummarySummary
The simulation control scheme
Reading of missions
The CFSTP predictive algorithm
OtherMissions to be
planned?
Is the mission possible ?
The blocked AGV is sent to the garage
yes
No
No
yes
A list of nodes di
to be visited
AGV’s move to node diThe cross of the node di
yes
Call one of the robust routing algorithm No
Nodi =
destinationnode ?
yes
VV kd i
1 ?
32
Improved robust control Robust Control
Gain of optimisation
0
2000
4000
6000
8000
10000
12000
0% 7% 13% 20%
AGVs Failure RateT
ota
l d
ura
tio
n o
f m
issi
on
s re
aliz
atio
n
AGVsFailureRates
Robust AGV
Routing(Time units)
Robust AGV
Routing(Time units)
Gain(Time units)
% ofGain
0,00%
6,66%
13,33%
20,00%
6825
7370
8731
10357
6825
7087
8154
8799
0
283
577
1558
0,00%
3,84%
6,60%
15%
The simulation resultsThe simulation results
A manufacturing system example
17 1 2 3 4 21
18 5 6 7 8 22
19 9 10 11 12 23
20 13 14 15 16 24
G
G
G
G
G
G
Lancement de la simulation informatique Lancement de la simulation informatique Lancement de la simulation informatique Lancement de la simulation informatique
33
Conclusion
Perspectives
- Study other routing algorithms
- Study the sensitivity of these methods to the AGV’s fleet size and other system’s parameters
- Implementation on a real system.
We have proposed a routing method which combines the efficiency of a
predictive method to the robustness of a reactive method.
Our method is generic and can be applied to any network configuration.
34
35
Proof Proof
A
B
B
A
A
B
B
A
nmBefore
B A
After A B
mn B A
Before
AfterA B
Catching-up conflict
Head-on conflict
n
m
36
If the reserved time windows are arranged as follows, there will be no conflicts
n
m
n
m
time time
A shift due to a
contingency
The predited time reserved
windows
The realized time reserved
widows
n
m
n
m