1. Institut de Recherche en Communication et Cybernétique de Nantes
Séminaire Bermudes
Robust conflict-free routing of bi-directional Automated Guided Vehicles (AGVs)
Present my self
I’d like to present you a talk about the robust routing of bi-directional AGVS….
For that, i will follow the following plan OR « the plan of my talk is as follows »
For that, i will start by introduce the problem of agv’s routing
Samia MAZA
Pierre Castagna
Institut de Recherche en Communication et Cybernétique de Nantes

2. 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)
First I’ll introduce the problem of AGV routing, then, I’ll give a classification of the existing methods for the routing of AGVs
After that, I’ll briefly present a method of conflict free routing by time windows, and then I’ll present you our proposed methods for the collision avoidance in real time
I will conclude by some results
 Some results & Conclusion

3. Definitions:
 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.
Automated guided vehicles are advanced material-handling devices used to transport pieces among the workstations of an automated manufacturing system.
They follow guidance circuits materialized with different manners. These circuits are of two types:
« The automated guided vehicles are widly used in the industry to provide the transport function. These vehicles can move by following guidance circuits connecting various workstations in the system.
…………..
These circuits can be classified into two categories: »

4. Kinds of guidance networks
unidirectional Circuits A D C B E
(8)
(4)
(5)
(6)
(1)
(3)
(2)
(7)
Bi-directional Circuit
In the one hand: the unidirectional network, for which the vehicles can move only according to one direction, in the other hand, the bi-directional network where the vehicles are authorized to travel a track into the two directions.
It has been shown that the bidirectional network presents many advantages over the unidirectional one, such as:

5. The 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
La réduction de ….
All these advantages are paid by a more complex control which must face some traffic problems such as the collision prevention and deadlock avoidance.
«  because of the many conflicts situations which exist, as we can see in this picture » n m V1 V2
collision
Egbelu et al, potentials for bi-directional guide-path for AGV based systems, 1986.

6. Classification of the AGV’s routing methods
The Predictive methods *
 Find optimal routes for vehicles;
 off-line conflicts Prediction;
 Planning of the AGV’s path.
 Good performances in the theory.
 Not robust.
Several conflict free routing methods were proposed in the literature and can be classified into two categories :
The predictive methods & the reactive methods
The methods of the first categories aim to find optimal path for the AGVs by predicting the conflicts off line and by planning the AGV’s path to avoid these conflicts
These methods can give good performances but aren’t robust, since they don’t take into account the system’s randomness
However for the reactive methods, the operation…. *
N.N.Krishnamurthy et al, Developing conflict-free routes for automated guided vehicles, 1993
H.Thomas, Optimisation des trajectoires d’une flotte de chariots mobiles, Thèse de Doctorat, Nantes 1994.
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 methods
The reactive methods *
 The AGV’s path is not planned;
 The decisions are taken in a real time manner
 Robust Methods
 The performances are not optimized a priori.
the operation of the AGVs is not planned and the decisions are taken in a real time manner according to the system state
These methods are very robust, but the resulting performances can be poor, because de decisions are taken by considering a very short term horizon, and they are very often proposed for special network configurations (are generally proposed) *
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.
Qiu Ling & Hsu Wen –Jing, Conflict free AGV routing in a bidirectionnal path layout, 2001.
Spyros Reveliotis, Conflict resolution in AGV system, 2000.

8. Make one predictive control method more reactive to real time changes
Our objective
Make one predictive control method more reactive to real time changes
Our objective is to extend one predictive control method to better react to real time changes in order to joint the robustness to the efficiency

9. The conflict-free shortest time AGV path planning
The description of the method 10 2 1 5 4 3 6
(9)
(10)
(2)
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(4)
(7)
(6)
(5)
(8)
(1)
(11) 7 9 8
So we start our work by using the path planning method by the time windows proposed by Kim. To apply this method, the intersections and the characteristic points are modeled by square areas, of dimension at least equal to that of the vehicles. These areas are called nodes. When the AGVs cross these nodes, they reserve them during an interval of time, which will be called the time reserved window
Tanchoco et al, Conflict-free-shortest-time bidirectionnal AGV routeing, 1991
Tanchoco et al, Operational control of bidirectional automated guided vehicle system, 1993

10. The nodes reservation table
A reserved time window
A free time window
f61 6
f51 5
f41 4
f31 3
f20 = r21 2
f11 1
f52
f42
f43
f32
r51
r42
r41
r31
r11
f12 V1 V2 V3 10 20 30 40 50 60 70
Time
Nodes 10 2 1 5 4 3 6 7 9 8
Knowing the displacement of each AGV, a table resuming the time reservation nodes can be dressed. In this picture for example, we can see that the vehicle V1 reserves respectively the nodes 5, 4 and 1 during an interval of time.
This method seeks to find through the free time windows the shortest path between a source and a destination node. The free time windows are those interval of time for which the nodes are not reserved (free)
The authors of this method propose an algorithm called the CFSTP, which calculates the shortest path in a graph, where the vertexes are the free time windows, by avoiding conflicts.
(How the search for conflicts is done?)

11. Principle of the method10 2 1 5 4 3 6 7 9 8
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f20 = r21 2
f11 1
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r51
r42
r41
r31
r11
f12 V1 V2 V3 10 20 30 40 50 60 70
Time
Nodes
f12
f32
f43
f52
f61
f51
f41
f42
f31
f20
f11
If we consider the routing of the AGV V3 from the node 2 to the node 6 by considering the precedent table. The CFSTP calculates the shortest path between nodes 2 and 6 in its associated time-window graph, here, each link is the result of different reachability and conflict-free tests done between two different windows
Notice that a mission can be impossible if such path doesn’t exist
Remark : A mission can appear to be impossible if such a path doesn’t exist

12. The time windows after the routing of V3
The routing of the AGV V3 by the cfstp algorithm
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r21 2
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f13 V1 10 20 30 40 50 60 70
Time
The time windows after the routing of V3
Nodes
r11
r42
r44
f12
r52
r61 V2 V3
After planning the path of AGV V3, the table is updated, to take into account this new displacement, so as we can see in this picture, a new time reserved windows are added.

13. The schedule of a new displacement
Assumptions
 Each AGV has an ordered list of missions
 A mission consists in going to visit a node N
 The missions order can not be inverted
 A new mission of a vehicle is planned only if this one becomes free
In order to plan a new displacement at any time, we have proposed a scheme in our paper, and have done some assumptions
….. And we suppose that the guidepath contains as many garages as the AGV fleet size.
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.
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

14. Open loop control method
Drawback 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 
The presented method is very effective since its gives the shortest time path free of conflicts, by considering the current AGV displacements. But it is an open loop control, since it doesn’t take into account the disturbances which can appear in a real system, and which introduce a shift between the realized windows and the predicted ones.
Introduction of a shift between the predicted time windows and the realized one
* ex: an accident, a slowing down in front of obstacles…etc

15. The time windows after the routing of V3
The routing of the AGV V3 by the cfstp algorithm
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f51 5
f41 4
f31 3
r21 2
f11 1
f52
f42
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f13 V1 10 20 30 40 50 60 70
Time
The time windows after the routing of V3
Nodes
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r61 V2 V3
Conflict
r42
We can see that in the following example, we have the predicited windows for each AGV, if the vehicle V3 undergoes a delay between the nodes 1 and 4, the realised window will be different from the predicted one, and as we can see a collision may occur on the node 4

16. This method can not be applied directly on a real system.
Conclusion
This method can not be applied directly on a real system.
It means that the method presented here, can not be applied directly on a real system

17. Collision avoidance in Real time
The conflict free shortest time procedure (CFSTP)
Predictive level
Oi= An ordered list of AGVs having to cross the node i
Node’s crossing order controller
Real time control level
To avoid conflicts when the system is subject to randomness, we have proposed to add a layer of real time ctrl. The CFSTP delivers for each planned AGV a list of nodes to be visited together with their arrival dates. Then we create for each node an ordered list of crossing vehicles. The node’s crossing order is checked in the real time level. This function is realized by decentralized controllers associated to the vehicles.
Maza & Castagna, Conflict-free AGV Routing in Bi-directional Network, ETFA 2001

18. Real time collision avoidance
The central controller (predictive level)
The conflict free shortest
time procedure (cfstp)
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
Decentrali-zed controllers (real time level)
Each decentralized controller executes the following task :

19. 4 O4= Yes No Arrival of the vehicle Vx to the node n V2 V3
Is the vehicle Vx
the first vehicle in the
List On ?
Vx must wait for the crossing of another vehicle
Vx can cross n
Yes No
End V3 V2 V3 V1
O4= 4 V2 V1
When an AGV arrives to the end of a link, before accessing a node, it calls a procedure to check the crossing order of that node. If the actual vehicle is on the head of the node’s list, then it is allowed to cross this node, else, it must waits until it becomes the first vehicle in this list.

20. 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
The resulting control is robust since the system state is considered each time, and the conflicts are avoided in a real time manner, only by respecting the node’s crossing order, and by forgetting time the observed system’s behavior is as predicted in the planning level.

21. N Criticism of the method 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
The drawback of that method is that when a vehicle undergoes a significant delay, some other vehicles having to cross some common nodes will be delayed and thus will undergo a significant delay too.
In this picture for example, if the vehicle V2 arrives to the node N before V1, it must wait for it, when it can continue its travel without being affected by the late of V1
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

22. The improved robust AGV routing
How to improve the robust routing control, by modifying the node’s crossing order, without causing conflicts ?
The problem now is how to improve that robust control method of routing by modifying the node’s crossing order, without causing conflicts

23. Example
{1}
{1,3}
{1,3,2}
{1,2}
{2}
{3} V1 V2 i V3
Let us consider the following example of three vehicles, and their associated paths, we associate an ordered lists to each node on these paths. If V1 is the late AGV, the question is: when the V2 arrives to I before V1, can V2 cross I and continue its traveling without colliding with V1 its predecessor on that node?
To answer this question, we have proposed two algorithms in our paper:
V1 is the late AGV
Can V2 cross the node i and continue its trip without colliding with V1 its predecessor on that node ?

24. A. Approach by delaying the late AGV U
Oj={U, V}
Ok={U, V}
{U}
{U} j k
{V} m i V
Om={U, V}
Oi={U, V}
The first approach allow the delay of the late AGV, it was firstly evoked in a paper presented in CIFA, so I’ll explain it very quickly.
When a vehicle V arrives to a node I, where it is not the leader vehicle in its associated list, a procedure will be called. This last will first identify the late AGV U, and calculates the common path between V and U, where U is priority, and then identifies the actual position of the late AGV U. if U is outside this common path then V can cross I and the common path without conflict, but before that, U will be delayed in front of V on each node belonging to this path.
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

25. A. Approach by delaying the late AGV U
Oj={U, V}
Ok={U, V}
{U}
{U} j k
{V} m i V
Om={U, V}
Oi={U, V}
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

26. U is outside the blue zone  the re-ordering is possible
A. Approach by delaying the late AGV U
U is outside the blue zone  the re-ordering is possible U
Oj={U, V}
Ok={U, V}
{U}
{U} j k
{V} m i V
Om={U, V}
Oi={U, V}
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

27. Delay-action of the vehicle throughout common way
A. Approach by delaying the late AGV U
Delay-action of the vehicle throughout common way U
Oj={V, U}
Ok={V, U}
{U}
{U} j k
{V} m i V
Om={V, U}
Oi={V, U}
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

28. U is on the common path  the vehicle V must wait
A. Approach by delaying the late AGV U
Oj={U, V}
Ok={U, V}
{U}
{U} U j k
{V} m i V
Om={U, V}
Oi={U, V}
Otherwise, if the late AGV U is on the common path, then it can not be delayed without causing conflicts. So V must waits for its turn.
U is on the common path  the vehicle V must wait
MAZA & Castagna, Routage robuste sans conflits de chariots autoguidés bidirectionnels, CIFA 2002

29. Li B. Approach by advancing the AGV V
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 ?
P={V1,V3}
P={V1,V3}
P={V1}
{1}
{1,3}
{1,3,2}
{1,2}
{2}
{3} V2 Nj Li
In the second approach proposed in our paper, instead of delaying the late AGV U, we advance the actual AGV V with regard to the late AGV U. I’ll explain the algorithm on an example:
When a vehicle V2 arrives to a node Nj where it isn’t the leader AGV in its associated list, V2 calls our algorithm, which will calculate the set P the vehicles having to cross Nj before V2. Li is the next link to be visited by V2 after crossing Nj, if Li is actually traveled by any AGV in P in the opposite direction, the reordering is impossible and V2 must wait where it, else, this action is repeated for the next node to be visited by V2, and P is recalculated, this operation will be repeated until we arrive at a node M where V2 is the first AGV in its associated list. Then the ordering is possible. Notice if the node M doesn’t exist, the reordering is impossible. M
The re-ordering is possible  update nodes associated lists for each node belonging to the path [Nj, M]
MAZA & Castagna, Robust conflict-free routing of bi-directional automated guided vehicles, SMC02

30. B. Approach by advancing the AGV VNj
So we advance the vehicle V2 over all other vehicles on the lists associated to the nodes belonging to this calculated path as we can see in this picture. M
MAZA & Castagna, Robust conflict-free routing of bi-directional automated guided vehicles, SMC02

31. The simulation control scheme
Summary
The simulation control scheme
Reading of missions
The CFSTP predictive algorithm
Other
Missions to be
planned? Is
the mission
possible ?
The blocked AGV is sent to the garage
yes No
A list of nodes di
to be visited
AGV’s move to node di
The cross of the node di
Call one of the robust routing algorithm
di =
destination
node ? ?
This flow chart resumes our control scheme. After reading the mission to be realized, the CFSTP algorithm will calculates the path to the destination node. if this mission is possible we’ll have a set of nodes to be visited, at the entry of each node, one robust algorithm will be called. If the mission is impossible, we try to plan other missions if they exist of other vehicles, and we try again to plan the precedent one. If there is no mission for other vehicles, we send the blocked AGV to the garage to avoid deadlocks

32. Lancement de la simulation informatique
The 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
Improved robust control
Robust Control
Gain of optimisation
2000
4000
6000
8000
10000
12000 0% 7%
13%
20%
AGVs Failure Rate
Total duration of missions realization
AGVs
Failure
Rates
Robust
AGV
Routing
(Time units)
Gain
% of
0,00%
6,66%
13,33%
20,00%
6825
7370
8731
10357
7087
8154
8799
283
577
1558
3,84%
6,60%
15%
Here, we have reported some simulation results realized with ARENA package; for a manufacturing system which consists of 24 nodes and 32 lanes. The size of the AGV’s fleet is 6. Two models have been constructed to model a perfect system, and a real system where the AGVs are subject to failures. The simulation has been realized with different AGVs failure rates. As we can see in this picture, the gain in the makesspan is as important as the failure rates. Wich prove the efficiency of our method over the “classical robust control method” where the node’s crossing order is strictly respected.
Lancement de la simulation informatique

33. Conclusion Perspectives
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.
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.
D’etudier la sensibilité de ces mehodes aux nombre de chariots, le régime de pannes et des différenent parametres du sys

34. Thanks for your attention

35. Proof n m Catching-up conflict Before After Before After n m B A m n
Head-on conflict A B n n m
Before B A
After m A B
Catching-up conflict m n
B A
Before
After
A B
Cette tâche est résumé ici, on a donc pour un chariot Vi, à chaque arrivée à l’entrée d’un nœud, on regarde s’il est le premier chariot dans la liste associée, si c’est le cas, il traverse le nœud normalement, sinon, il doit attendre que les chariots prioritaires passent, et cela même s’il arrive à la date prévue à ce nœud là.
La démonstration est simple, i s’agit de montrer que le respect de l’ordre de passage même si les dates d’arrivée prévues ne sont pas respectées conserve la propriété de non conflits. Je rappelles que les conflits sont détectés en comparant l’ordre de réservation des nœud, s’il est inversé, c’est qu’il y a conflits

36. A shift due to a contingency
 If the reserved time windows are arranged as follows, there will be no conflicts n m
time m
A shift due to a contingency
The predited time reserved windows n
Cela revient à dire que les fenêtres temps doivent êtres disposées comme indiquée ici.
Ici par exemple si on considère que les fen^tres prédites sont diposées ainsi, et que le chariot vert doit traverser [m, n] en permier, si celui ci subit un retard, il y aura un décalage entre les fen^tres rédites réalisées. Si par contre le chariot rouge arrive à la date prévue, le respect de cette date va engendrer un conflits, ouisque on aura un croisement des fenêtres, si par contre on respecte l’ordre, il sera retardé, jusqu’à ce que le chariot vert passe, et on aura la configuration de non conflit de départ m
The realized time reserved widows n