Real-time AGV Action

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European Journal of Scientific Research ISSN 1450-216X Vol.25 No.2 (2009), pp.310-324 © EuroJournals Publishing, Inc. 2009 http://www.eurojournals.com/ejsr.htm

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning
Rizauddin Ramli Department of Mechanical and Materials Engineering, Faculty of Engineering, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia E-mail: [email protected] Tel: +60-3-58917022; Fax: +60-3-89259659 Hidehiko Yamamoto Department of Human and Information Systems Engineering Faculty of Engineering, Gifu University, 501-1193 Gifu-shi, Japan Abu Bakar Sulong Department of Mechanical and Materials Engineering Faculty of Engineering, Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor, Malaysia Dzuraidah Abdul Wahab Department of Mechanical and Materials Engineering Faculty of Engineering, Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor, Malaysia Jaber Abu Qudeiri Department of Mechanical Engineering, Faculty of Engineering Philadelphia University, Amman 19392, Jordan Abstract In this study we present an approach of hypothetical reasoning for action decision of Automated Guided Vehicle (AGV) in Autonomous Decentralized in Flexible Manufacturing Systems (AD-FMS). The AD-FMS is characterized as being online, in realtime mode and of a short-term nature that responds to frequent changing of the production order. The decentralized control in AD-FMS enables to solve dynamically some typical task of production system without using a fixed centralized control system. We adopt a hypothetical reasoning approach that will decide the conceivable next action from the competition hypothesis. Simulation results show that the efficiency of AGV in AD-FMS increased. Keywords: Autonomous Decentralized, Flexible Manufacturing Systems, Automated Guided Vehicle, Hypothetical Reasoning

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning

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1. Introduction
Today, in order to survive in the rapid challenging environment of the modern manufacturing era, manufacturers are forced to adopt new technologies, especially for products that are made in small batch production. Product and process improvements are widely acclaimed to provide economics gains and to increase flexibility, resulting in fast response and rapid adaptability to changing market condition. However, most of the production facilities are made as a complex dynamical environment, which is always plagued by unexpected situations. Equipments may break down and an unexpected urgent job may suddenly be released to the production line, depends to the demands of the clients. Also, the priority of the job may be changed. Consequently, the aspect of flexibility in manufacturing system becomes an essential point in dealing with the unexpected situations. Basically, flexibility is an attribute of contemporary manufacturing systems which is necessitated by the time-based competition underlying current manufacturing strategy. As a result, a Flexible Manufacturing System (FMS) provides an alternative to improve the situation [1-4]. Later, the advancement in numerical control (NC) and computer technology has made lightly manned manufacturing system possible. Conventionally, the FMS are equipped with several CNC machines tools, automated warehouses and Automatic Guided Vehicle (AGV). An AGV based material handling system is designed and implemented to gain production the flexibility and efficiency [5-7]. However, even if the FMS are able to deal with the unexpected situations, most of FMS are still leaning on the centralized control system. A host computer controls and gives instruction to each agents by a predecided rule or route scheduling, i.e. what is the next action they should do after performing the present task. So far, the routing algorithms for AGV are often divided by either a centralized approach or a decentralized approach. For a centralized approach, the route planning of AGV systems is determined by centralized decision making, which handles the entire system [8]. The Petri Net approaches [9-11] are a useful way to analyze the conditions to avoid deadlock in AGV systems. Dispatching algorithms [12-13] and Genetic Algorithms (GA) [14-17] have also been studied to cope with AGV routing problems. In the autonomous decentralized system, the AGV routing is generated by several decision making subsystems. One of the approaches is zone control [18, where the AGV system can be divided to several non-overlapping regions, which restricts the available AGV for a time. Nishi et al. [19] have proposed a distributed routing method for multiple mobile robots using a Lagrangian decomposition and coordination technique. The original problem is decomposed into an individual routing problem for each AGV. Most of the conventional research on autonomous decentralized real time scheduling systems for AGV are based on agent decision selection and object orientation method [20-23]. In the method, the fastest action that can be finished at the existing time is selected as the action that should be taken for the agent. Therefore, in this paper, the concept of Autonomous Decentralized [24-27] in Flexible Manufacturing Systems (AD-FMS) is introduced. It is to realize that each agents in FMS such as machine tools and AGVs run independently from each others. The AD-FMS architecture has the feature that every agent has autonomy to manage itself and coordinates with the other agents. Furthermore, we adopt a concept of hypothetical reasoning to retrieve whether the action taken by the agent is the truth or false and use the hypothesis for the next action decision. Consequently, the proposed coordination between agents is achieved by communication with other agents through a proposed intelligent knowledge (IK), in which the information of the agent circulates or transmits to another agent and after receiving the information; the other agents analyze its content to proceed for the next action decision.

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Rizauddin Ramli, Hidehiko Yamamoto, Abu Bakar Sulong, Dzuraidah Abdul Wahab and Jaber Abu Qudeiri

2. Architecture of AD-FMS
2.1. Conventional FMS Conventionally, FMS is a computer-controlled configuration of semi-independent work stations and material handling systems designed to efficiently manufacture more than one type of parts at a low to a medium volumes [28]. There are three essential physical components of FMS: • Numerical control (NC) machine tools • Conveyance network or material handling system • FMS control system The NC machine tools do not only consists of NC machining centers but it also may comprise any of the machining units in the FMS such as NC lathe machines, turning machines, etc. On the other hand, the conveyance network or the material handling system such as AGV functions as a device to transfer the work piece between the parts warehouse, product warehouse and machining centers. The FMS control system performs as a centralized host computer that controls the sequence and coordinates all the task flow for every machine tool, parts handling system and the work pieces. Figure 1 depicts the conventional FMS control system giving all instructions to other sub-level control systems, i.e. the machine control system, station control system and transportation control system. Then, these sub-level control systems command the equipment in the FMS to do their task based on the pre-decided sequence or schedule. The disadvantage of this case is once the centralized host fails to communicate with the sub-level control system, the operation of FMS is terminated due failure of coordinating the equipment. In order to overcome this problem, a better control system which does not depends to a centralized oriented structure is needed, i.e., a decentralized control system where every element in the FMS are independently and flexible to decide their own decision through communication, exchanging information and cooperation among them.
Figure 1: Schematic hierarchy of FMS control system

Production Control System Part W-house station

CAD/CAM
Automatic Pallet Stocker Automatic W-house

Station Control System

FMS Control System

Conveyance Control system

AGV 3-D measurement MC

Jig& Tool station MC Control System

MC-2 MC-1

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning 2.2. Concept of AD-FMS

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The AD-FMS is based on the Autonomous Decentralized (AD) that was derived from the analogy of living organisms. Each living thing is composed of cells and each cell is independent in the body. These cells are totally self sufficient for the information for living and multiplication. In our proposed AD-FMS, these cells are analogous to autonomous multi-agents systems. Any communications between these agents are carried between themselves without routing through a centralized system. In Figure 2, a schematic view of information sharing between the autonomous agents of the AD-FMS structure is shown. It shows the agents which are AGVs and machine tools communicate and exchange their information via a wireless communication system. By this way, they are able to estimate the ability of themselves, which machine tools are busy and leisure; so that the AGV can decide which machine tools should the parts to input, or which machine tools are finished processing the parts. Furthermore, through the coordination between AGVs, they can avoid the collision between themselves or to prevent deadlock that can decrease the efficiency of the FMS. Consequently, the AD-FMS can be realized with the multi-flow of information from the any level of computer. For example, once a daily production command is given every control system will automatically schedule their job scheduling based on it. By this way they transmit the information through LAN system to the other computer system and to the station controller. As shown in Figure 3, the station controller is then autonomously give instruction to the agents, which are the AGVs, machine tools and automatic warehouse about the job scheduling and keep coordinating them online.
Figure 2: Information sharing between autonomous agents

Communicate-Exchange-Cooperate

AGV

AGV

MC

MC

With this architecture, it can be realized that in the AD-FMS, there are no specific centralized host controller and no relation of master-slave among the multi-agents. However, few criteria’s of ADFMS should be satisfied in order to gain a full efficiency of AD-FMS that are: • On-Line Expansion As the AD-FMS size increases, a step by step construction is required. Even after completion of construction, the function in the AD-FMS may be are added or removed. • On-Line Maintenance In the AD-FMS, it is possible that frequency of fault occurrence somewhere in the system will be increased. Due to this, it should be ensured that the maintenance and the test procedures can be carried out without suspending the operation of the AD-FMS itself, especially in the case of on-line and real-time systems. • Fault-Tolerance The hardware in the AD-FMS must be reliable to compete with faulty. The hardware in the AD-FMS should be more sufficiently improved in comparison with the software. However,

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even if the software includes some bugs, the system is not required to stop its entire operation to prevent the fault. • Performance In AD-FMS, a high performance of control systems is required. In order to attain the high performance control system, reducing the peak of the computer load and making the load smooth by improving the software processing are required. All this criteria should be met in the construction and operation of new AD-FMS. However, it is difficult to satisfy all these criteria. In this paper, we focused at the forth criteria that is to improve the software processing by introducing the concept of hypothetical reasoning in order to relieve the load of software processing. 2.3. Difficulties of Realizing AD-FMS In AD-FMS, the larger scale of product demands will result to a huge combination of parts varieties, job scheduling, maintenance and control systems of every agent. Due to this, it is necessary to optimize the huge combination efficiently so that the productivity in the AD-FMS will be enhanced. For instance, a manufacturer without AD architecture in their FMS will face difficulties to cope with the customer demands if one of the AGV caused trouble. Most of the Japanese manufacturers practice the concept of Just in Time (JIT) that ensures the needed product with the needed volume in the times could be delivered to the customer without any delay [29]. The failure of it will cause a big problem to the customer and lost the trust for the manufacturer. That is why a robust AD-FMS architecture is needed.
Figure 3: Distribution of task by Controllers

Machine Tool

Computer

Controller

Controller

Automatic Warehouse

Controller

Controller

AGV Controller

Controller

AGV

Computer

Machine Tool

Machine Tool

However, it is not an easy task to develop a robust AD-FMS even now if we have the ability of an efficient computer. This is because it is considerably a difficult task to obtain the optimal solution for all combinations. For instance, if the scheduling job is one of the combinations problems, the computer can enumerate all the solution by its candidates and search for the best solution from among

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning

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them. However, the combination becomes large with the increase in the types of parts, number of machines and AGV. When all these large combinations simultaneously correspond to the control system of the machine tool, the breakdown of the control computer, and the changes in the production plan, etc, it becomes extremely complex to design such an efficient AD-FMS. In other words, it is one of the major problems to construct a real-time AD-FMS. Here, we consider the problems that happen in constructing the AD-FMS as follows: • The method of deciding an autonomous action: Unlike the centralized approach, where all the action decisions are made by a FMS control system, all the agents in the AD-FMS have to decide their own decisions quickly and then execute the action. Therefore, it is important to develop a highly efficient and high-speed algorithm. • The method of achieving cooperated action: In order to perform an autonomous action, each agent should behave as an individual with an intelligent system, so that they can communicate and understand the behaviour of the other agents. However, the control systems of this method are extremely crucial and to structuralize the algorithm is a troublesome task. • The communication cost: To implement a cooperative action between each agent, much information needs to be transferred between agents which require a sophisticated telecommunication system. It required a lot of money to realize a telecommunication system in AD-FMS which not every industry affords to.

3. Model of AD-FMS
3.1. Action Decision in AD-FMS In this paper, the model of the AD-FMS that we study consists of multi-agents inside a factory that is shown in Figure 4. These agents are a Parts Warehouse (PAW) that supplies parts for a factory, a Product Warehouse (PRW) that stores the finished parts from MC, transportation systems for material handling (AGVs) that carry parts and several MCs arranged at some specific positions. Each AGV carries only one parts at one time. The movement of the AGV inside the FMS is restricted on the dashed line grid with uniform speeds. The MCs can machine several types of parts and the machining time and manufacturing process for each type of MC is decided. The set of the same MC is called a group MC and is classified by describing subscript, for example, MC1, MC2,…,MCn. Each MC in the same group is distinguished by attaching a hyphen and figures after the name of the group MC, for example, MC1-1, MC1-2, …,MCn-m.

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Rizauddin Ramli, Hidehiko Yamamoto, Abu Bakar Sulong, Dzuraidah Abdul Wahab and Jaber Abu Qudeiri
Figure 4: Model of AD-FMS

P a rts W a reh o u se (P A W ) P ro d u cts W a reh o u se (P R W )

AGV 1

AGV 2

AGV 5

M C 1 -1 AGV 3

M C 2 -1 AGV4

M C 5 -1

M C 1 -2

M C 3 -2

M C 3 -1

M C 4 -1

M C 6 -1

M C 2 -2

M C 1 -3

M C 7 -1

M C 8 -1

M C 7 -2

M C 2 -3

M C 4 -2

M C 3 -3

M C 5 -2

M C 4 -3

M C 8 -2

M C 6 -3

M C 6 -2

M C 5 -3

M C 8 -3

M C 7 -3

The information exchange and cooperation between each agent in this AD-FMS is described as follows. The PAW sends the information on the names of the parts that are stored in the PAW. Meanwhile, the AGV transmits the information of the name of the parts that it brings and the destination of where it is going. The MC gives information of the name of parts that is currently machined and the time remaining to finish the machining process. The PRW sends information to the PAW of what product is kept in it and which product has been sent to customers. By this way, the PAW can understand of the current logistic condition so that it can prepare the next parts that should be input to the FMS. In other words, the information exchange between agents in the AD-FMS is used by the needed agent as a source to decide the next action. In AD-FMS, the full usage of information source among MC, PAW, PRW and AGVs simultaneously will result to the realization of enhancing production efficiency [30]. In the conventional FMS, the action planning of the AGV action is done by a pre-decided scheduling system that does not consider an unexpected problem such as MC troubles or machining delay time. Once this unexpected trouble occurs, the production plan needs to be re-scheduled. Furthermore, in the case of an AD-FMS where many MCs and AGVs are mixed together, it is difficult to schedule an effective instruction for the AGV about where it should go and which parts should be input. In this paper, the processing procedures that we adopt are described as follows; • The usage of information from each agent • The inference of a few steps of AGV action • The forecasting of the AD-FMS operating condition. In order to implement these procedures, we propose an algorithm which is able to forecast the next action decision in the real-time production scheduling of the AGV that is based on hypothetical reasoning. Hypothetical reasoning is the activity of evaluating the effect of the actions that affect a given domain that is now an established subfield of knowledge representation [31-35. The algorithm that we proposed is able to forecast the next action decision in the real-time production scheduling of

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning

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AGV that we called as Future Anticipative Reasoning Algorithm (FARA) which is based on hypothetical reasoning method. The FARA’s real-time production scheduling is performed by 2 types of the hypothetical reasoning; the first hypothesis is the Action Decision Hypothetical Reasoning (ADHR) that decides where the AGV will move to and the second hypothesis is the Parts Input Hypothetical Reasoning (PIHR) that decides the kinds of parts to be input onto the production floor.
Figure 5: Action Planning of AGV
Current Position

Next Action

M C1-1

M C1-2

M C2-1

PAW

PRW

M C3-1

M C1-1

M C1-2

The Follow ing Action
PAW : Part W arehouse PRW : Product W arehouse

The next action decision for AGV is related to many reasons, such as the existence of many MCs with the same machining process, the transportation of product to product warehouse, the input of new parts to the AD-FMS, the existing of other AGV that are doing the same action, etc. Due to these reasons, the action decision necessitates not only a single action decision but could be a multi action decision that is based on the action decision selection branch. Attentively, if the AGV selects one choice from the selection branch and then based on the selected branch, each of the agents inside the AD-FMS is given moving and working instructions. Furthermore, when the AGV meets the condition that is required to do the selection again, then it will re-select one of the choices from the action decision selection branch. In this way, the operating condition in AD-FMS is realized by the continuous process of selecting the AGV next action decision. In other words, as shown in Figure 5, the operating condition of AGV is eternally broadening like a tree structure, where the node is assumed as the next AGV action. Figure 6 shows the outline of the proposed hypothetical reasoning process. The tree structure shows the form of retrieval vertically. In every stage of the tree structure, the retrieval will be done until it finds FALSE results and it will return to one stage back and start the retrieval process again at another selection branch. The peak of the tree structure is set as the last AGV action with the hypothesis depth 0 and the hypothesis depth under this stage represents the action that is taken by the AGV. Similarly, the hypothesis with depth 1 has its own selection branch under it with all of them have their own selection branch respectively. In Figure 6, the selection branch and the arrows connecting the selection branch shows the hypothetical reasoning simulation process of FARA. The hypothetical reasoning simulation runs as if the end of the arrow is TRUTH, then by doing the task following the selection branch, it will display the result of the simulation. The algorithm of the hypothetical reasoning simulation is performed through the following steps: Step1: The existing AGV hypothesis depth is set as 0.

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Rizauddin Ramli, Hidehiko Yamamoto, Abu Bakar Sulong, Dzuraidah Abdul Wahab and Jaber Abu Qudeiri

Step2: For the next hypothesis depth, if the selected branch is FALSE, then the farthest left side branch is selected and assumed as the TRUTH. Step3: Run simulation to the selected branch. Step4: Based on the simulation result, the selection branch is judged whether it is TRUTH or not. Step5: If the simulation result is FALSE, then go to STEP 6. If it is TRUTH, then go to STEP 8. Step6: In the depth of the same hypothesis that has been judged to be FALSE, if the left side of the selection branch that has not yet judged as TRUTH or FALSE is then selected to be assumed as TRUTH and go to STEP 3.
Figure 6: Hypothetical reasoning processes

Hypothesis Depth 0

Hypothesis Depth 1

Hypothesis Depth 2

FALSE decision branch TRUTH decison Order of reasoning hypothetical reasoning finished

Hypothesis Depth 3

Step7: Go up to another depth of hypothesis and go to STEP 6. Step8: If the hypothesis is above a value then go to STEP 9, if not go to STEP 2. Step9: Selection branch becomes TRUTH, then the hypothetical reasoning is finished. 3.2. Action Decision in AD-FMS Two types of hypothetical reasoning, the ADHR and PIHR can be used by recalling each others respectively. For instance, when one AGV is moving from one place to the parts warehouse under the ADHR, if the hypothesis is judged as TRUTH, then after it arrives at the parts warehouse; it will become the next hypothesis. Then, when the AGV takes parts from the parts warehouse under the decision of PIHR, next it will execute the ADHR for the next action. Furthermore, when the hypothetical reasoning is being performed, only one AGV will carry out the hypothesis. In other words, when the hypothetical reasoning is performed by one AGV, the other AGV will only start the hypothesis after the AGV finishes its hypothesis. In the hypothetical reasoning simulation process, in the case where there is a selection branch with same level of efficiency, the higher ranking of selection branch will be selected, i.e., the possibility of the higher ranking of selection branch to be selected arises. For examples, when there are two selection branches with the same efficiency in existence, the selection branch that is precedent judged to be TRUTH will be automatically carried out. In this way, we use the characteristic of hypothetical reasoning to bring the products production rates to be closer to its target by using the selection order function which depends to the production situation.

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning

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3.3. AGV with Intelligent Knowledge In this paper, we consider the AGVs as intelligent agents that are able to adopt knowledge, transmit their information to each other and understand AGVs behaviour. If one AGV can understand the behaviour of another AGV, it is possible to avoid their collision, and to cooperate in their task together. Here, we define each AGV as having 6 types of intelligent knowledge, i.e., Routing knowledge, Self knowledge, Sending knowledge, Others knowledge, Answer knowledge and finally Avoidance knowledge. These 6 types of knowledge are divided into 2 types of memories: long term memory and short term memory. Sending, Answer and Avoidance knowledge are kept in the short term memory, while Routing knowledge, Self and Others knowledge are kept inside the long term memory. Figure 7 shows the Self knowledge. The first parameter and second parameter indicates the name and emergency command of the specified AGV respectively. The third, fourth and fifth parameter indicates the position of the location that the AGV has just passed, the next position that the AGV will go to and the next position after that. The Others knowledge has the same characteristic with the Self knowledge. The Answer knowledge has 4 parameters, i.e., the AGV’s name, emergency command, the name of AGV opponent and the next position that the AGV will go. All of the information are transmitted to other AGV, so that they can share and exchange their information to avoid collision between them. By this way, all the AGV can reduce their collision and as well as can avoid deadlocks that will decrease the production efficiency.
Figure 7: Self knowledge

1st para 2nd para

3rd para

4th para

5th para

AGV
para: parameter

4. Simulations
The production floor is a 60m × 60m square. (The parts warehouse and the product warehouse are located outside of the floors). The distance that AGV are able to move is 5 m from the inside floor wall. It is assumed that the entrance to the parts warehouse and the product warehouse use the shortest route from the grid. Furthermore, the positions of MCs are located at the edge of the grid of the AGV route. In this research, in order to facilitate the dynamic AD-FMS simulation, the following assumptions are made. • The maximum number of AGV is 5. The AGV moves on the grid of the floor, and the travelling speed of AGV is constant, but it depends on the type of carried parts and products. • The maximum types of MCs are 8 types and the maximum numbers of same type of MC are 3 types. The position is assumed as entrance of parts handling position. • The maximum numbers of parts types are 9 types with each types can only be processed maximum 8 times. In this paper, 3 kinds of simulation conditions were performed to ascertain the effectiveness of our proposed algorithm with AGV-wIK. The position of parts warehouse, product warehouse, and the MCs on the production floor are configured as Figure 8, Figure 9 and Figure 10, respectively. The

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position of MCs (represents by ■) and numbers of AGVs are changed in each different simulation conditions. Each simulation time is 8 hours and the numbers of AGV used in each simulation condition are 3:4:5. In order to verify the effectiveness of AGV-wIK, we ran simulations with the same condition without intelligent knowledge (i.e. Conventional Method) where the moving destination is decided and fixed. (a). Simulation 1: AD-FMS with 9 Machine Tools In Simulation 1, we ran 3 types of simulations (S1-1, S1-2 and S1-3) with different numbers of AGV are performed with the following conditions: 3 types of products with the rates of each product and production ratios as P1:P2:P3=5:6:3.
Figure 8: MCs position in Simulation 1

PAW

PRW

(b). Simulation 2: AD-FMS with 18 Machine Tools In Simulation 2, we ran 3 types of simulations (S2-1, S2-2 and S2-3) with 6 types of products with the following conditions: The rates of each product and production ratios as P1:P2:P3:P4:P5: P6=5:6:3:3:2:1.
Figure 9: MCs position in Simulation 2

PAW

PRW

Real-time AGV Action Decision in AD-FMS by Hypothetical Reasoning (c). Simulation 3: AD-FMS with 24 Machine Tools
Figure 10: MCs position in Simulation 3

321

PAW

PRW

In Simulation 3, we ran 3 types of simulations (S3-1, S3-2 and S3-3) with different numbers of AGV under the following condition: 9 types of products with the rates of each product and production ratios as P1: P2: P3: P4: P5: P5: P6: P7: P8: P9 = 5: 6: 3: 3: 2:1: 4: 5: 2. In Figure 11(a), each Simulation 1, Simulation 2 and Simulation 3 indicates that the efficiency of AGV becomes better with AGV-wIK than using the Conventional Method. Similar results obtained where the number of AGV collisions are reduced as shown in Figure 11(b). This proved that our proposed technique works effectively.

5. Conclusions
In this paper, we proposed a technique of forecasting the next action of AGV that includes the advance prediction of action in few steps, which will enable to enhance the efficiency condition of the autonomous decentralized flexible manufacturing systems. The technique, Future Anticipative Reasoning Algorithm or FARA is used to forecast the next action decision of AGV. By using FARA, we adopt a hypothetical reasoning technique that will decide the conceivable next action from the competition hypothesis. Simulation results show that the efficiency of AGV in AD-FMS increased. The numbers of collisions are also decreased, which means we can obtain a proper navigation for the AGV. It confirmed that our technique is useful in collision avoidance.
Figure 11: Results in each simulation conditions
70

AGV efficiencies(%)

60 50 40 30 20 10 0

Conventional Method AGV-wIK

S1-1

S1-2

S1-3

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S2-2

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Simulation Conditions

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Rizauddin Ramli, Hidehiko Yamamoto, Abu Bakar Sulong, Dzuraidah Abdul Wahab and Jaber Abu Qudeiri
(b) Comparison of number of collisions between AGVs
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Number of collisions

1200 1000 800 600 400 200 0

Conventional M ethod AGV-wIK

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Simulation Conditions

References
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