1

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