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# 0. introduction

Intelligent factory is the key to realize intelligent manufacturing. In the intelligent factory, intelligent equipment has been widely used. AGV, intelligent manipulator and other intelligent handling equipment constitute the intelligent production material system. The cooperative operation between multi transporters is of great significance to the normal operation of the intelligent factory. In recent years, the research on cooperative operation between multiple carriers has become a hot topic in the field of logistics, and scholars at home and abroad have carried out a lot of research on Cooperative problems.

In the aspect of collaborative research on transport carriers, Chen Min et al. [1] studied the scheduling problem of multiple AGVs in intelligent workshop, proposed seven scheduling operation mechanisms, and verified the rationality of the scheduling scheme by using plant simulation. He Changzheng et al. [2] established a mathematical model of dual resource optimization for the collaborative scheduling problem of AGV and processing equipment in the flexible manufacturing workshop, designed a hybrid algorithm of "time window + Dijkstra + genetic algorithm", and adopted three rules to solve the conflict problem in the optimal path planning. Liu Xu et al [3] established a mathematical optimization model with the shortest travel time in the working process of AGV, improved the crossover mutation operator of genetic algorithm, and solved the best scheme to obtain multi AGV cooperative scheduling. Yuexiaoconvex et al. Studied the cooperative scheduling problem of multi-automatic traction vehicles in FMS. Considering the factors of vehicle endurance, taking the minimum completion time of tasks and the minimum number of vehicles as the scheduling objective, the hybrid genetic particle swarm optimization algorithm was used to solve the problem. The simulation results showed that the model and algorithm were effective. Abdelmaguidtf et al. [5] studied the collaborative optimization between processing equipment and multi AGV dual resources. Taking the maximum task end time as the optimization goal, a new hybrid genetic algorithm coding scheme was proposed to solve the problem. 82 experimental examples were used to verify the performance of the model and the coding scheme.

In the research of intersection collision avoidance, Hu jiejie [6] designed a centralized AGV group control coordination algorithm for the flexible physics of intelligent workshop, gave priority to the task of AGV, and solved the conflict problem at the node. Xiao Meng [7] proposed a collision criterion method and a two-way parallel collision avoidance strategy for the multi AGV collision problem based on the principle of high priority passing, which was verified and implemented by simulation. Xiao Haining et al. [8] studied the AGV system of one-way guidance path, established the AGV system model based on the digraph, proposed the path locking cracking rule based on this, and verified its effectiveness through the piant simulation. Qiaoyan et al. [9] studied in the dynamic environment, aiming at the clearing situation of AGV temporarily changing the route, dynamically adjusted the priority of AGV at the intersection node, and updated the AGV route to improve the time window algorithm for simulation experiments, which proved that the method has better robustness and efficiency.

At present, most of the research focuses on the coordination of single resource and double resource, and there are few researches on the three resource collaborative operation, and there are also few researches on the collision avoidance of the transport vehicle intersection in the collaborative research. In this paper, we consider the cooperation of stacker in warehouse, AGV in work station and manipulator in line loading and unloading. At the same time, we design multi AGV collision avoidance rules which can pass at the same time on the cross road, so as to optimize the logistics efficiency of the whole workshop.

# 1. Optimization model of multi carrier collaborative operation

## 1.1 problem description and assumptions

### 1.1.1 problem description

Aiming at the problem of multi carrier cooperative operation in intelligent factory, this paper studies the stacker, AGV and the manipulator of material loading and unloading at the line side

When the hand three resources cooperate to carry out the transportation task, the collision avoidance problem of multiple AGVs at the intersection is considered. The mathematical programming model with the maximum completion time minimized is established, and the cost penalty function is established as the auxiliary optimization model. As shown in Figure 1, the flow of workshop logistics is as follows: AGV _{ n }. At the material handover point in front of the warehouse, wait for the stacker to transport the materials from the three-dimensional warehouse to AGV _{ m }. AGV. Select the optimal path (red path) to transport the materials to the junction point next to the demand station, and the manipulator will unload them.

src="http://www.agvba.com/wp-content/uploads/2020/04/01-4.png" alt="Optimization of multi-carrier collaborative operation in SmartFactory" alt="Figure 1 Flow chart of multi-carrier carrier collaboration in workshop" width="419" height="368" /> Figure 1 Flow chart of multi-carrier carrier collaboration in workshop[/caption]

### 1.1.2 model assumptions

According to the actual situation of the intelligent workshop, in order to facilitate the solution and analysis of the model and consider the collision situation of the AGV intersection, reasonable assumptions and simplifications are made for the problem:

1) AGV runs at constant speed under no load and load;

2) Acceleration and deceleration of AGV are not considered;

3) The carrier vehicle is in good condition and has rated capacity;

4) The task execution process of AGV is continuous without interruption;

5) AGV can accept multiple tasks at the same time and execute them in turn;

6) Consider the collision and congestion of AGV at the intersection;

7) The operation time and loading and unloading sequence of stacker and manipulator are known;

8) The transporters are independent of each other, and there is no restriction;

9) The trolley can handle multiple materials or workpieces with sufficient capacity;

10) The working capacity index of the same type of carrier is the same.

## 1.2 parameter definition

### 1.2.1 parameter setting

H: Represents the set of path nodes, H = 1, 2,..., h; I: represents the set of tasks, I = 1, 2,..., l: represents the set of stacker, I = 1, 2,..., l; m: represents the set of AGV, M = 1, 2,..., m; N: represents the set of manipulator, n = 1, 2,..., N; S: S = 1, 2, ·, s: K: the combination of intersections, k = 1, 2, ·, K: T _{ I }: the completion time of task I; T _{ 1 }: the average time required for the stacker to complete a single task; T _{ n }: the average time required for the manipulator to complete a single task; T _{ Li }: the average time required for the stacker I to start executing a task I E _{ n I }: the time when manipulator n finishes executing task I; T _{ I }: the time when manipulator n starts executing task I: T _{ ILM }: the time when AGV _{ m } starts executing task I executed by stacker 1; Q _{ MS }: the time when AGV starts executing task I executed by stacker 1. Distance travelled; VM: AGV. T _{ 1m n }: the time required for agvm to travel from the stacker to the manipulator n; Q _{ MS } the phase of AGV _{ m } at the intersection; Q _{ QMS }: the set of phases of Ag _{ m } at the intersection.

### 1.2.2 decision variables

T _{ I m }: time I when AGV _{ m } completes the task;

## 1.3 objective function

In order to maximize the efficiency of workshop and minimize the error of material delivery time, this paper proposes two optimization objectives of multi carrier collaborative operation in intelligent workshop, and constructs a multi-objective optimization function with the lowest completion time and penalty cost.

### 1.3.1 minimum completion time

minZ=max{T_{i}} (1)

among

In the formula, T _{ I } represents the completion time of task I, T _{ 1I } represents the time when stacker 1 starts to execute task I, e _{ Ni } represents the time when manipulator n completes task I, and the overall optimization goal is to minimize the maximum completion time.

### 1.3.2 minimum penalty cost

In view of the three possible situations of early delivery, on-time delivery and delayed delivery in the process of material delivery, this paper establishes the corresponding cost penalty function for the three situations, as the second optimization goal, as shown in equation (5).

minC=min{f(t_{im})} (5)

Among them, considering that the delayed delivery of material transportation has a greater impact on the progress of the project than the early delivery of material transportation, the loss of the project progress is more serious. At the same time, in order to enhance the flexibility of the resource allocation process [10,11], the establishment of the figure

The curvilinear soft time window cost penalty function shown in 2.

Assuming that the best time window for arrival is [t _{ a }, t _{ b }], on this basis, the acceptable service time window [t '_{ a can be deviated from }, t '_{ b }], where t' _{ a } = t _{ a } -Δ _{ 1 }, t '_{ b } = t _{ b } + Δ _{ 2 }. If AGV _{ m } delivers the materials to the designated station in [t _{ a }, t _{ b }], the penalty cost is 0; if AGV _{ m } in [t '_{ a }, t' _{ b }] or [t _{ b }, t '_{ b }] to deliver materials to the designated station, only need to bear less penalty costs; if AGV _{ m } is in (0, t '_{ a }) or (t' _{ b }, ∞) to deliver materials to the designated station, you need to bear more punishment costs. The cost penalty function based on the curved soft time window is shown in equation (6).

Equation (6) represents the penalty cost corresponding to the time tim when the AGV

_{ m }finishes the task i under the constraint of the curvilinear soft time window. As shown in Figure 2, if AGV

_{ m }is delivered before time t '

_{ a }, the penalty cost per unit time is cp1, and [t'

_{ a }, t

_{ a }] penalty cost incurred during the time period; if AGV

_{ m }is in [t '

_{ a }, t

_{ a }] is delivered within the time period, the penalty cost per unit time is cp2; if AGV

_{ m }is in [t

_{ a }, t

_{ b }] delivery within the time period, the penalty cost is 0; if AGV

_{ m }is in [t

_{ b }, t '

_{ b }] Delivery within the time period, the penalty cost per unit time is cp3; if AGV

_{ m }is delivered after t '

_{ b }, the corresponding unit time The punishment cost to be borne is cp4, and at the same time, the punishment cost of [t

_{ b }, t '

_{ b }] time period must also be borne.

In the formula, α and β are the cost penalty weights for early delivery and delayed delivery, which are 0.1 and 0.8 respectively [12].

## 1.4 Constraints

Where, equation (7) means that one stacker can only be assigned one task at any time; equation (8) means that the same task can only be assigned to one processing station at any time; equation (9) means that two AGVs with conflicting phases cannot pass through the intersection at the same time; equation (10) means that each task can only be executed by one AGV at the same time; equation (1) means that each task can only be assigned at any time It can be assigned to a stacker; formula (12) means that the time when the manipulator starts processing shall not be earlier than the time when AGV delivers the materials to the handover point where the manipulator is located; formula (13) means the time when the task is completed; formula (14) means that the AGV can start executing the task only after the stacker unloads the materials at the handover point; formula (coincidentally) means that the tasks to be executed by each AGV need to be executed in sequence Line: equation (16) indicates the non negative limit of the parameter.

# 2. AGV intersection collision avoidance rules

Intersection collision can be divided into three types: phase conflict, intersection conflict and node occupation conflict [13]. Traditional intersection collision avoidance issues mostly give priority to different levels of AGV, passing by priority level in order, only one AGV can pass at a time [13]. In the research of this paper, in order to make AGV collision avoidance link closer to reality, when AGV passes an intersection, according to the data collected by sensors and RFID, analyze the current traffic situation and AGV driving information of the intersection, judge whether multiple AGVs can pass at the same time by detecting the driving direction of each AGV, and adjust the priority of the conflicting AGV so that the intersection can pass at the same time Passing multiple AGVs can effectively reduce waiting time and collision.

## 2.1 AGV conflict type detection

When AGV driving near the intersection, according to the data collected by sensors and RFID, the control system updates the location and time status of AGV, detects and analyzes whether there will be conflicts and the types of conflicts in the coming intersection.

The parameters in the test are defined as follows:

1) λ _{ b } < sub > m < / sub > is the time when AGV < sub > m < / sub > arrives at node h;

2) ε _{ H } < sub > m < / sub > is the residence time of AGV < sub > m < / sub > at node h;

3) θ is the threshold value of safe time interval for conflict detection;

4) K _{ m } < sub > H is the identification code of node h, and the node is in the planned driving path of AGV < sub > m ;

5) K _{ m } < sub > H-1 < K _{ m } < sub > H < K _{ m } < sub > H + 1 is the node sequence of AGV < sub > m .

The conflict detection model is as follows:

1) Opposite conflict

If the following relation (17), equation (18) and equation (19) are met in the detection process, AGV will have opposite conflict at the intersection.

2) Intersection conflict

If the following relations (20) and (21) are met in the detection process, AGV will encounter intersection conflict in the next road.

3) Node occupancy

If the following relations (22) and (23) are met in the detection process, AGV will encounter node conflict at the next intersection.

## 2.2 The dynamic adjustment of the priority of the intersection conflict AGV

As shown in Figure 3, when AGV _{ m } drives to an intersection, each AGV _{ m } has the possibility of three driving directions of gs, tl, and tr, each representing a straight , Turn left, go straight, set two tolerant and incompatible phases at the intersection. Multiple AGVs in the mutually compatible phase can pass at the same time without collision, and multiple AGVs in the incompatible phase cannot pass the intersection at the same time, (assuming The turning radius of the intersection can accommodate two AGVs with mutually compatible phases passing at the same time). For example, AGV ^{ tr m1 means that AGVm1 turns right at the intersection, and then AGV tl m2 , AGV tr m2 , AGV tr m3 , AGV gs m2 , AGV tr m4 , AGV gs m4 are mutually compatible phases, which can pass through the intersection at the same time, and AGV gs m2 , AGV tl m3 , AGV tl m4 Yes Phases are not tolerated and cannot pass through intersections at the same time. The order of passing through intersections needs to be adjusted according to priority.
}

AGVs that are in phase-tolerant at intersections, in order to ensure that there is a clear priority relationship between AGVs, the priority of the AGVs is assigned to determine the order of the access points, which is based on the theoretical remaining time of the AGV to complete the task being executed. The smaller the value, the greater the AGV priority, and the different priorities are determined by the increment A. If the vehicle is empty, the priority is set to the lowest.

among them:

In the formula, rest (T

_{ i }) represents the remaining completion time of task i; Number (k) represents the number of vehicles that are queued at the current intersection and are not allowed to pass in phase.

## 2.3 Double channel path capacity detection

In order to reduce the congestion of the path between the two intersections, when the AGV is about to reach the two-intersection path, while detecting the conflict at the intersection, the path between the two intersections is detected to assess whether the path can be entered without causing congestion As shown in Figure 4, the evaluation criterion is the number of vehicles remaining in the route:

N(s)=F[(s)-Y(s) (25)

In the formula, N (s) is the number of remaining vehicles that can be accommodated in the path s; F (s) is the rated capacity of the vehicles that can be accommodated in the path, and the value is rounded down; Y (s) is the vehicle that has entered in the path s Number; l

_{ s is the length of the path s; l AGV m is the length of AGV m , and θ is the minimum safety distance during driving. When N (s) <1, the AGV will be prohibited from passing through the intersection and wait until an AGV exits the path. 3 Particle Swarm Optimization PSO is a new swarm intelligence optimization algorithm proposed by Kennedy and Eberhart in 1995 inspired by the group movement of birds [14]. Through information sharing between particles, collaborative optimization tasks are completed, with strong memory and efficiency. It has the characteristics of high and fast search speed, but it is easy to fall into the local optimum, that is, the local optimization ability is strong, and the global optimization ability is weak [15]. In this paper, the particle swarm optimization algorithm is optimized, using dynamic inertial weights and adaptive mutation probability introduced in the genetic algorithm, to avoid the local optimization of the algorithm later, and to improve the algorithm's convergence ability and convergence accuracy. The algorithm flow is shown in Figure 5. Figure 5 Optimized adaptive particle swarm optimization algorithm flow chart 3.1 PSO formula Let the dimension of the solution model be D, with 1 particle, and the particle swarm as L = {p 1 , p 2 ,…, p i ,…, P l } speed expressed as V = {v 1 , v 2 ,…, v i ,…, V D }, the position is expressed as X = {x 1 , x 2 ,…, x i ,…, x D }, pbest i represents the best position for particle i to pass through, and gbest i represents the most experienced by all particles Good location. The P-algorithm particle i's D-dimensional velocity update formula is equation (27), and the particle i's D-dimensional position formula is equation (28): In the formula, v k id represents the D-dimensional component of the velocity vector when particle i performs the kth iteration; v k id represents the D-dimensional component of the position vector when particle i performs the kth iteration; c 1 , c 2 represents the acceleration of the learning factor, and its value is constant; r 1 , r 2 are two random parameters with a value range of [0,1]; w represents the inertia weight, the value is non-negative, used to adjust the solution Search range of space. The inertial weight represents the effect of the previous velocity of particle i on the current velocity. The global optimization ability is directly proportional to its value, and the local optimization ability is inversely proportional to its value; conversely, the particle local optimization ability is strong and the global optimization ability is weak. That is, if the value is too large, it is easy to miss the optimal solution; if the value is too small, the algorithm convergence speed is slow or it is easy to fall into the local optimal solution. When the problem space is large, in order to achieve a balance between search speed and search accuracy, this paper uses dynamic inertia weight formula (29), so that the algorithm has a higher global search ability in the early iterations to obtain a suitable seed, and In the later stage, there is a higher local search capability to improve the convergence accuracy. As the number of iterations increases, w decreases continuously, so that the algorithm has a strong global convergence ability in the early stage, and a strong local convergence ability in the later stage. In the formula, w max represents the maximum inertia weight; w min represents the minimum inertia weight; t represents the current iteration number; t max represents the algorithm maximum iteration frequency. 3.2 Adaptive mutation In the early stage of algorithm iteration, the individual difference of the population is large. In order to avoid bad solutions and at the same time, in order to make the algorithm converge quickly, mutation should be performed with a small probability. In the later stage of the iteration, the individual diversity of the population gradually decreases. In order to avoid the algorithm falling into the local optimum [14], the individual mutation rate should be increased. In the formula, P mmin represents the smallest mutation probability, with a value of 0.01; P mmax represents the largest mutation probability, with a value of 0.1. t represents the current number of iterations; t max represents the maximum number of iterations; D i represents the Euclidean distance from particle i to the current optimal solution; D max represents the maximum Euclidean distance of the particle i in the population farthest from the current optimal solution. 4 Example analysis Take the electrical parts manufacturing workshop as an example to verify the examples in this paper. The electrical parts manufacturing process in this workshop includes riveting, crimping, spot welding, tapping, spray printing, pad printing, pre-assembly, general assembly, etc. The plant's assembly workshop has a raw material warehouse, including 4 three-dimensional warehouses, 3 stackers, 15 workshops, numbered 1-15, the workshop is S-shaped distribution, the distribution step is 5 meters, each There is one line-side manipulator and six laser-guided AGVs in front of the processing station. AGV is responsible for the distribution of raw materials and work-in-progress. The parameters of the transportation equipment in the workshop are shown in Table 1. The vehicle travel time between the work stations is shown in Table 2. 0 indicates the raw material warehouse, and the distance between the processing stations is shown in Table 2. In this paper, the experiment is carried out with a fixed number of handling tasks and a fixed number of AGVs used, and the two cases of collision avoidance at the intersection and no collision avoidance are considered for comparison. In Example 1, the handling task is 40, the number of stackers is 3, and the number of AGVs is 3; in Example 2 the handling task is 40, the number of stackers is 3, and the number of AGVs is 6; in Example 3, the handling task is 70, the number of stackers 3. The number of AGVs is 3; in Example 4, the handling task is 70, the number of stackers is 3, and the number of AGVs is 6. Table 1 Actual parameter table of door handling equipment Table 2 Distance table between working stations The experimental results are shown in Table 3. When the number of transport tasks is the same, the time taken by the AGV at the intersection is proportional to the number of AGVs, and the total completion time is inversely proportional to the number of AGVs. When the number of AGVs is the same, the time and total completion time of the AGV at the intersection are directly proportional to the number of handling tasks, that is, the number of AGVs used, the more the handling tasks, the greater the time and total completion time of the AGV at the intersection. increase. 1) Consider collision avoidance at intersections The experimental results are shown in Table 4. Considering the collision avoidance situation of the AGV at the intersection, the waiting time of the AGV at the intersection has been reduced to varying degrees in each calculation example. As the number of AGVs or the number of handling tasks increases, Table 3 Experimental results without collision avoidance at intersections The possibility of AGV collision at the intersection increases, which makes the effect of reducing the waiting time of the AGV at the intersection more obvious. At the intersection, we will compare the two cases without considering collision avoidance rules and considering collision avoidance rules. As shown in Figure 6 and Figure 7, in the calculation example 1-4, considering the collision avoidance rules, the intersection waiting time and the total completion time are both A certain degree of reduction, that is, when considering collision avoidance at intersections, the total completion time of multi-device cooperative operations, intersection waiting time, and operation efficiency have all been improved. able 4 Experimental results of collision avoidance at intersections 2) Comparison of results Figure 6 Waiting time at the intersection of two situations Figure 7 The total completion time chart of the two cases 3) Algorithm performance comparison Comparing the optimized adaptive PSO of this paper with the traditional PSO through Example 2, we can see from Figure 8 and Table 5 that in the early iterations, the algorithm tends to converge quickly, and the sub-optimal solution is found around 25 generations. In the late iteration, based on the adaptive mutation probability, its probability value increases, the search space of the algorithm is increased, and the global optimal solution is found around 35 generations. The change of the solution of the optimized adaptive PSO and the change of the population mean are more stable and the convergence speed is faster. Table 5 Comparison of algorithm operation results Figure 8 Change graph of objective function 5 Conclusion In this paper, aiming at the cooperative operation of multiple carriers in a smart factory, a collaborative operation optimization model with the minimum total task completion time as the main decision goal and the minimum penalty cost as the auxiliary decision goal is established. Considering the collision avoidance rules of AGVs at intersections, the AGV detects two phases of mutual tolerance and incompatibility to determine whether multiple AGVs can pass through the intersection at the same time. For AGVs that are not in phase, dynamically adjust the driving priority rules to maximize To a certain extent ensure the punctuality of task execution. The collaborative operation model is solved by the optimized PSO algorithm. In order to avoid falling into the local optimum at the later stage of the iteration, the adaptive mutation in the genetic algorithm is introduced to enhance the dimensional space of the algorithm search solution. Taking the electrical parts manufacturing and assembly workshop as an example, the control variable method is used to compare the collision avoidance rules at the intersection with the collision avoidance rules. Do not consider the situation of collision avoidance. Comparing the optimized PSO algorithm and the traditional PSO with the model and the example, the results show that the optimized PSO algorithm has obvious advantages in the optimal solution, the mean value of the population optimal solution, and the number of convergences. 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