Off-Line AGV Routing on the 2D Mesh Topology with Partial Permutation

Off-Line AGV Routing on the 2D Mesh Topology with

Partial Permutation

Zeng Jianyang and Hsu Wen-Jing

Center for Advanced Information Systems

School of Computer Engineering

Nanyang Technological University, Singapore 639798

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IntroductionLiterature ReviewOff-Line Mesh RoutingConclusions and Future Work

Outline

1. Introduction

2. Literature Review

3. Off-Line Mesh Routing

4. Conclusions and Future Work

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Outline

1. Introduction




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Introduction

AGV: Automated Guided Vehicles

Problem of AGV Routing

• Feasible or even optimal path

• Simultaneously, without conflict, deadlock, and congestion

Compared with Shortest Path Problem (SPP)• SPP is simpler than AGV routing problem

Compared with Vehicle Routing Problem (VRP)• Length of vehicle is negligible in VRP

• Collisions can be ignored in VRP

• Topology is fixed and irregular in VRP

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Outline

1. Introduction




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Literature Review

AGV routing for arbitrary topologies Shortest path method

Time-window-based method

Dynamic method

• [Huang et al. 89], [Fujii et al. 89], [Kim et al. 93]• Increased path utilization, expensive in computation, small system

• [Taghaboni et al. 95], [Langevin et al. 96]• Local information required, quick in routes finding, small system

• Dijkstra’s alg, • 0-1 integer programming: [Gaskins et al. 87] [Kaspi et al. 90] [Goetz et al. 90]• Small scale, simple, does not consider congestion, deadlocks

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Literature Review (cont’d)

AGV routing on large scalable systems Linear path layout:

• [Qiu et al 01]

• Conflict-free, but low utilization of land space

Loop topology:• [Banerjee et al. 95] [Bozer et al. 91] [Barad et al. 95], [Sinriech et al.

92]

• Easy to implement, require little computation, low throughput

Mesh path layout: • [Hsu et al. 94], [Qiu et al. 00]

• Conflict-free, extra distance traveled, large time complexity

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Packet routing on mesh topology On-line routing:

• Central-control model [Gramatikakis et al. 98]

• Distributed-control model [Leighton et al. 95] [Sibeyn et al. 97] [Valiant et al 82]

Off-line routing:• [Nassimi et al. 80] [Mou et al. 92] [Krizanc et al. 91] [Kaklamanis et

al. 92]

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Comparisons between AGV and packet routing Similarities:

• Movement patterns: permutation, k-k routing,…

• Static and dynamic routing

• Randomized and deterministic methods

• Other issues: deadlock, live-lock, fault tolerance,…

Differences• Different definitions of link bandwidth at each step

• Different sizes of buffers

• Packets can be discarded, copied, but not AGV’s loads

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New issues• Routing in large scale systems

• Energy-efficient routing algorithms

• Dynamic routing problems

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Outline

1. Introduction




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Off-Line Mesh Routing

# of AGVs= , Movement pattern: partial permutation

Partition of mesh path layout

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Approach Adopted from Valiant’s Algorithm

Use Valiant’s ideas for partial permutation• Distribute AGVs evenly in each group• Shorten the longest distance travelled

Valiant’s routing algorithm • From sources to random intermediate nodes• From intermediate nodes to destinations

Insight of Valiant’s algorithm • Packets are evenly distributed over global network• Packets are routed to their destinations

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Distribute AGVs Evenly in Each Group

Size of group: x=3 rows

of submeshes

1

2

3 4

10

5

6 7

8

9

171

1 12

131

4 15

16

18

19

21

22

23

24

20

1

4

7

10

2

5

8

3

6

191

316

1114

12

22

172023

18

9

15

2124

AGV destinated to submesh_column 2AGV destinated to submesh_column 1

AGV destinated to submesh_column 3

# =3# =3# =2

# =8

# =3# =2# =3

# =8

# =3# =2# =3

# =8

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Off-Line Routing Algorithm

Phase 1: Distribute AGVs evenly in each group Phase 2: Route AGVs to destinations

• Along submesh row

• Along submesh column

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Analysis of Off-Line Routing Algorithm

Theorem 6.1 : Our routing algorithm works successfully in 2n+o(n) steps, provided,

12

k

nn

nx

}1k,3

1max{

)1(21k nnn

where, n: size of mesh; : size of submesh; : number of AGVs; x: size of group;

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Outline

1. Introduction




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Future Work

Fault tolerance Energy evaluation model Movement patterns

• k-to-1• k-to-k

Routing on higher-dimensional mesh• 3D AS/RS(Automated Storage and Retrieval

System)

Thanks!

Q&A

Off-Line AGV Routing on the 2D Mesh Topology with Partial Permutation

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