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The assumptions to formulate the problem are given as follows:

• The lengths of the paths are equal, requiring 0.1 hours of travelling time from one station to another by an AGV. Since modern AGV control systems allow flexible routing of the AGVs, the symmetrical distance is a reasonable assumption [49].

• The AGVs are either in a working or a failed health state. Once an AGV fails, it will stop its movement or action immediately, preventing further damage to the whole vehicle.

• After maintenance has been performed, the recovered AGV will be assumed to be as good as new. It should be noted that this cannot be guaranteed in real applications.

• The weight of each item is the same. In warehouse handling the standard products are often the same, hence this can be seen as a valid assumption creating negligible difference.

• No capacity limits at stations. This factor will be further discussed in Chapter 9. • The operation of an AGV will not stop the operation of other AGVs in the same station. This assumption depends on the application of the AGV. For example, if the operations of the AGVs in the same station are independent, then the assumption is true. However, if a specified machine is required to support an AGV activity, other AGVs needing the same support have to wait. This factor will be further discussed in Chapter 9.

• An AGV failed at a station will not cause a blockage at the station. This is assumed to simplify the modelling and focus on the failure on paths. This factor will be further discussed in Chapter 9.

• The speed of AGVs is assumed to be constant.

7.3 Development of AGV Models

the prescribed system layout consists of eight CPNs. These are described as the following:

• Route Petri Nets (RoPNs) - to describe the optimised routes that the AGV will travel to complete a mission.

• Master Petri Nets (MPNs) - to govern the phase changes in the missions of AGVs.

• Conflict Detection and Avoidance Petri Nets (DAPNs) - to detect and avoid the conflicts in the operation of the AGVs.

• AGV Health State Petri Nets (AHSPNs) – to simulate the change of health state of AGVs.

• Recycle of Failed AGV Petri Nets (RFAPNs) – to recycle the failed AGV in the system back to the base.

• Reroute Petri Nets (RTPNs) – to reroute the AGVs due to the blockage of the path by a failed AGV.

• Corrective Maintenance Petri Nets (CMPNs) – to define the corrective maintenance of the failed AGVs in the system.

• Periodic maintenance Petri Nets (PMPNs) – to definethe periodic maintenance of the failed AGVs in the system.

These PNs connect and share information to simulate all of the operations in the AGV systems. These nets will be described in more detail in Sections 7.4 to 7.9. An overall CPN connection diagram is shown in Figure 7.1. The MPNs, RoPNs and DAPNs link together to simulate the normal operation of the AGVs in the system. Once the AHSPNs diagnose an AGV failure, this information will be fed to the RFAPNs to activate the recycling process. The RTPNs are also activated simultaneously to prevent blockage due to the failure, before the failed AGV is recycled. After the failed AGV has been towed back to the ‘Base’, corrective maintenance to this failed AGV will be simulated by the CMPNs if onsite repair is available. After repair, the health state of the AGV in the AHSPNs will be ‘working’ again and a new mission can be started. It should be noted that the DAPN has been discussed in Section 6.3.4 and not been modified in this chapter.

Figure 7.1 CPN connections

7.4 Master Petri Net (MPN)

The MPN model is developed to govern the change of phases from the beginning of the mission, Phase 1, to the successful completion of the whole mission as described in Section 6.2. Once the travelling route of the AGVs is determined through optimisation, the MPN will be developed to define the phase changes between the RoPNs of different AGVs. This has been developed in Section 6.3.3.

However, due to the increase in the number of multi-load AGVs and the failure factor are included, the MPN has to be extended and modified. To ease understanding, an example of the MPN for 2 two-load AGVs is shown in Figure 7.2, where, one of the two-load AGVs is shown in detail. Firstly, two AGVs are assigned tasks. The AGV, represented by in Phase 1, is assigned a mission consisting of two delivery tasks. The first task of the AGV is to transfer item A from station S2 to station S6, and the second is to transfer item B from station S3 to station S7. After the mission allocation process is completed, the corresponding token will move from Phase 1 to Phase 2. Once the token is transferred to place ‘Phase 2’, the transitions between Phase 2 and the places in respective RoPNs will be enabled.

Figure 7.2 Master Petri Net (MPN) for a two-load AGV

From Figure 7.2, it is seen that the AGV will visit all the pickup stations first. So, the AGV will pass through the paths in the order S1→S2→S3. The AGV will pick up item A in S2 and then travel to S3 to pick up item B. As the arcs connecting the transitions and places representing the pickup stations are double ended, a token will be placed in these places representing S2 and S3 as well as the corresponding ’Pick up item’ and places. By doing this, these pickup actions can be performed and ‘memorised’ while the token representing the AGV can still move in the RoPN. After a token is transferred to the places representing pickup of an item, the inhibitor arc connected back to the transition will inhibit the pickup transition. The transition in the RoPN is then activated so that the AGV can move to the next station. Then, the AGV will travel to the unloading stations S6 and S7. Similar movement of AGVs and their transitions will continue until both items A and B are unloaded. The transition connecting the output place representing unloading an item can only fire if the corresponding tokens exist in both the places representing the unloading station and the corresponding items picked up. Once both items are unloaded, the mission can be considered as being

completed successfully. Finally, the AGVs will be assigned a new mission and they will start from ‘Phase 1’ again. Therefore, the RoPN and MPN of the multi-load AGV are not separable. They can be generated automatically for different missions. On the other hand, once an AGV failure information is received from the AHSPNs, the corresponding token in the MPN will be transferred to ‘Mission abandon’ place. That means the failed AGV will not be able to move or take any further action until its health state is back to working.