Performance evaluation method of four-direction shuttle robot system based on path optimization

Abstract

The invention provides a performance evaluation method of a four-way shuttle robot system based on path optimization, which comprises the following steps of: modeling path nodes in a two-dimensional coordinate system, and on the basis of considering the motion characteristics of acceleration, deceleration and the like during operation of a shuttle robot, obtaining a path with shortest operation time of the shuttle robot by improving a Dijkstra algorithm; on the basis, a semi-open-loop queuing network model considering path optimization is constructed, and system performance indexes including a task period, an equipment utilization rate and throughput are solved by adopting an AMVA algorithm. Simulation verification shows that the method is high in calculation precision and excellent in efficiency; sensitivity analysis further reveals an influence rule of structural parameters such as the number of roadways, the number of columns and the number of layers on system performance, and indicates that when the roadways are close to the number of columns and the number of layers is adaptive to the total quantity of goods positions, the throughput capacity of the system is optimal, and a quantitative basis is provided for storage system configuration.

Description

Technical Field

[0001] This invention relates to the field of warehousing and logistics automation technology, and more specifically, to a performance evaluation method for a four-way shuttle robot system based on path optimization. Background Technology

[0002] Traditional shuttle robots typically travel along a fixed aisle direction (X-direction) to complete inbound and outbound operations within a single aisle. However, when inbound / outbound needs involve other aisles, additional equipment such as hoists, transfer vehicles, or shuttle platforms are often required for four-way transport. Such systems have a relatively fixed structure, lack flexibility, and are difficult to implement in high-concurrency task scenarios.

[0003] Existing four-way solutions typically employ a "shuttle robot + hoist + vertical transfer mechanism" model. The process involves shuttle robots operating within their respective lanes; when goods need to cross lanes, the hoist handles the vertical transport, and then shuttle robots in other lanes continue the transport. While this structure achieves four-way operation to some extent, the shuttle robots themselves cannot achieve true lateral movement, still relying on numerous transfer devices. This leads to complex system scheduling, discontinuous paths, and limited overall throughput. Especially during heavy workloads, the hoist often becomes the main bottleneck of the system.

[0004] Furthermore, in traditional path planning research, the shortest path is commonly used as the criterion for determining the robot's travel path. Many studies use Dijkstra's algorithm or other algorithms based on grid graphs or node graphs to solve for the shortest path. However, shuttle robots exhibit dynamic characteristics such as acceleration, constant speed, and deceleration during actual operation, and must completely decelerate and then accelerate at each turn. Therefore, "shortest distance" is not equivalent to "shortest time." Existing research is still lacking in addressing this issue, often neglecting the impact of the number of turns on time, making the path planning results unable to accurately reflect the shuttle robot's travel time, thus affecting the evaluation of system operational efficiency.

[0005] In the performance analysis of logistics systems, existing studies mostly employ open or closed-loop queuing network models to analyze the collaborative operation of multiple devices. However, traditional queuing networks often struggle to accurately describe the "task binding-service-release" interaction between shuttle robots and elevators. Especially in four-way systems, the matching process between shuttle robots and elevators exhibits significant dependence; directly using a general queuing model would make it difficult to accurately predict task cycles, equipment utilization, and external queue lengths. Furthermore, when system structural parameters (such as the number of lanes, columns, and layers) change, existing models fail to reflect the impact of structural adjustments on system throughput.

[0006] In summary, existing technologies have significant shortcomings in the following aspects: shuttle robots lack true lateral movement capabilities, rely on the collaboration of multiple devices in four directions, which increases system complexity and easily leads to new bottlenecks; path planning methods generally aim at the shortest distance, failing to consider the time differences caused by turning losses, and are prone to obtaining non-optimal time paths; existing queuing models cannot accurately describe the task flow process of four-way systems and the correlation between devices, affecting the accuracy of system performance analysis; and there is insufficient research on the impact on system structural parameters, making it difficult to provide quantifiable basis for engineering design, such as the optimal number of layers and the best combination of lane columns.

[0007] The aforementioned shortcomings directly affect the path optimization, operational efficiency prediction, and system configuration design of four-way shuttle robot systems. Therefore, a performance evaluation method for four-way shuttle robot systems based on path optimization is proposed. Summary of the Invention

[0008] Existing systems using transfer shuttle robots to enable four-way operation of tote boxes, while achieving four-way picking in the picking process, still require flexibility because the shuttle robot can only operate within the aisle. Lateral movement of the tote boxes relies on the transfer shuttle robot. This invention selects a four-way shuttle robot system with lateral guide rails as the research object. This system allows the shuttle robot to move straight and laterally along the X-direction aisle and the Y-direction lateral guide rails, thus truly realizing four-way inbound and outbound operations, offering higher flexibility and greater adaptability.

[0009] Shuttle robots exhibit acceleration and deceleration during operation, and the shortest path selected by traditional methods is not necessarily the path with the least time. This invention aims to solve the problems of long running time, excessive inflection points, large acceleration and deceleration losses, and inaccurate system throughput assessment in traditional distance-based path planning for four-way shuttle robots, and to achieve shortest-time path planning for shuttle robots, thereby improving the operating efficiency and throughput capacity of warehousing systems.

[0010] To achieve the above-mentioned objectives, the present invention provides the following technical solution: a performance evaluation method for a four-way shuttle robot system based on path optimization, comprising the following steps: Step 1, Path node modeling: A two-dimensional coordinate system is established for the same-level top-down layout of the four-way shuttle robot system, with the direction of the aisle extension as the X-axis and the direction of the transverse guide rail extension as the Y-axis. All intersections of the aisle and the transverse guide rail are defined as path nodes, and each path node is assigned a unique coordinate; the path inflection point is determined by comparing the coordinate changes of adjacent path nodes. When the node coordinate changes only along the X-axis or only along the Y-axis, it is determined to be a straight line segment. When the node coordinate changes simultaneously along both the X-axis and the Y-axis, it is determined to be an inflection point. Step 2, Shortest Time Path Optimization: Using an improved Dijkstra shortest time path algorithm, firstly, based on the path node model established in Step 1, calculate all shortest distance paths from the starting point elevator position node to the ending point inbound / outbound node, forming a set of shortest distance paths; then, count the number of inflection points for each path in the set, and select the path with the fewest inflection points as the candidate path; then, based on the acceleration, constant speed, and deceleration motion model of the four-way shuttle robot, combined with the total distance of the candidate paths, the number of inflection points, and the robot's motion characteristics, calculate the actual running time of each candidate path, and select the path with the shortest running time as the final optimized path; Step 3, System Operation Time Analysis: Based on the final optimized path determined in Step 2, the time for each of the three operation stages of the four-way shuttle robot is calculated. The three operation stages are the travel time from the elevator position node to the inbound storage location node, the travel time from the inbound storage location node to the outbound storage location node, and the travel time from the outbound storage location node to the elevator position node. During the calculation, the displacement in the X and Y directions of the path and the robot's acceleration and deceleration characteristics are combined to obtain the time of each stage by adding them up in segments. Step 4, Semi-open-loop queuing network modeling: Using the total time of the three operation stages calculated in Step 3 as the service time input, the operation process of the four-way shuttle robot system is abstracted into a semi-open-loop queuing network model; the model contains three core nodes, namely the elevator node responsible for vertical transportation of goods, the task matching node responsible for binding the elevator and shuttle robot tasks, and the target storage location node responsible for goods storage and retrieval; the service rate of each node and the task transfer relationship between nodes are defined. Step 5: Queuing Network Performance Solution: The semi-open-loop queuing network model established in Step 4 is solved using the AMVA approximate average value analysis method. Specifically, this includes: First, removing task matching nodes to construct a closed-loop network CQN1. Inputting the number of elevators, shuttle robots, and external task arrival rate, the system throughput, elevator node queue length, and shuttle robot node queue length of CQN1 are calculated. Second, the task matching nodes are treated as load-dependent nodes to construct a new closed-loop network CQN2. Using the throughput of CQN1 as input, the queue length and utilization rate of the task matching nodes are calculated. Third, combining the results of CQN1 and CQN2, the total system throughput, elevator utilization rate, shuttle robot utilization rate, and target cargo location node utilization rate are calculated. Step 6, System Performance Evaluation and Verification: Based on the calculation results of Step 5, evaluate the core performance indicators of the four-way shuttle robot system. The core performance indicators include task completion cycle, hoist utilization rate, shuttle robot utilization rate, system throughput, and waiting queue length of each node. Verify the evaluation results through system simulation experiments. Compare the performance indicators obtained from the simulation with the calculation results of the AMVA method. When the error is within the acceptable range, the evaluation is deemed valid. Step 7: System structural parameter sensitivity analysis: Adjust the structural parameters of the four-way shuttle robot system, including the number of aisles, columns, layers, and the number of cargo positions between transverse guide rails. Repeat steps 1-6 to calculate the system throughput under different parameter combinations. Determine the optimal parameter configuration through comparative analysis, including the optimal ratio between the number of aisles and columns, and the optimal number of layers corresponding to different total cargo positions. The four-way shuttle robot system consists of high-rise automated racking, shuttle robots that move vertically in the X direction and laterally in the Y direction, high-speed elevators for vertical movement, and transverse guide rails. The automated racking adopts a single-depth storage method, with each storage location holding only one SKU. Storage aisles are set between columns for shuttle robots to move vertically in the X direction, and transverse guide rails are set in the middle of each column for shuttle robots to move laterally in the Y direction at fixed storage locations. Several high-speed elevators are set at the front of the racking. The system allows users to configure the number of elevators and shuttle robots according to the number of storage locations, cost, and throughput requirements.

[0011] As a preferred technical solution of the present invention, the acceleration, constant speed and deceleration motion model of the four-way shuttle robot in step 2 is constructed based on the motion law of the robot in actual operation: first accelerate to the maximum speed, maintain constant speed, and decelerate and stop when approaching the target. The turning time loss generated at the inflection point is included in the total running time.

[0012] As a preferred technical solution of the present invention, the external task arrival rate of the semi-open-loop queuing network model in step 4 is calculated using the moving average method based on the historical operation data of the system. The historical operation data is the number of tasks arriving per hour in the past 24 hours, so that the external task arrival rate can reflect the actual operation load of the system.

[0013] As a preferred technical solution of the present invention, in step 5, when solving the closed-loop network CQN1 using the AMVA method, an iterative calculation method is adopted, setting an initial iteration value and an iteration termination condition. The initial iteration value is determined based on the service capabilities of the hoist and the shuttle robot, and the iteration termination condition is that the difference in throughput between two adjacent calculations is within a very small range.

[0014] As a preferred technical solution of the present invention, the system simulation experiment in step 6 uses discrete event simulation software, sets the simulation duration and data statistics period, the simulation duration includes the warm-up period and the data statistics period, and the simulation is repeated multiple times and the average value is taken as the simulation result.

[0015] As a preferred technical solution of the present invention, the value of the number of goods at the horizontal guide rail interval in step 7 needs to balance the efficiency of the shuttle robot moving across the aisle and the utilization rate of the shelf space. The number of goods at the horizontal guide rail interval that minimizes the average time of the shuttle robot moving across the aisle is determined through sensitivity analysis.

[0016] As a preferred technical solution of the present invention, the coordinate accuracy of the path nodes in step 1 needs to match the actual layout error of the system to ensure that the positional deviation of the intersection of the roadway and the transverse guide rail does not affect the accuracy of the path inflection point judgment.

[0017] As a preferred technical solution of the present invention, the selection criteria for the shortest distance path set in step 2 are: the difference between the total path distance and the shortest distance is within a very small range, and the path does not contain invalid nodes without actual guide rail connections.

[0018] As a preferred technical solution of the present invention, the calculation of the vertical running time of the hoist in step 4 is based on the acceleration, uniform speed and deceleration motion characteristics of the hoist and the height of each layer of the shelf, and together with the operation time of the shuttle robot, constitutes the total service time of the system.

[0019] As a preferred technical solution of the present invention, the sensitivity analysis of system structural parameters in step 7 adopts the control variable method, adjusting only one structural parameter each time while keeping other parameters unchanged. The analysis results can accurately reflect the influence of a single parameter on system performance.

[0020] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention, through an improved Dijkstra algorithm, enables the shuttle robot to prioritize paths with fewer inflection points while satisfying the shortest distance requirement, thereby reducing time loss due to turns and achieving a "short distance and short time" travel path selection. Based on the semi-open-loop queuing network model established after path optimization and solved using AMVA, the system performance (including task completion cycle, hoist / shuttle robot utilization, external queue, and throughput) under the matching of the hoist and shuttle robot can be effectively evaluated. Simulation verification shows that the calculation results of the model and algorithm are within an acceptable range of error compared to the simulation results, indicating that the method has practical value in both accuracy and efficiency. Sensitivity analysis reveals the influence of system structural parameters (number of lanes, number of columns, number of layers, number of transverse guide rails, etc.) on system throughput and operational efficiency, providing a quantitative basis for system configuration (such as selecting the optimal number of layers or lane / column ratio). Attached Figure Description

[0021] Figure 1 The front and side views of the four-way shuttle robot system provided by the present invention; Figure 2 The system operation flowchart under dual instructions provided by this invention; Figure 3 The system dual-command order shuttle robot movement diagram provided by this invention; Figure 4 This is a layout diagram of the shuttle robot route nodes provided by the present invention; Figure 5 This is a layout diagram of the shuttle robot route nodes provided by the present invention; Figure 6 The motion characteristic diagram of the shuttle robot provided by this invention; Figure 7 This is a schematic diagram of the coordinates of the top view provided by the present invention; Figure 8 Example diagram of the improved Dijkstra algorithm provided by this invention; Figure 9 This is a diagram of a semi-open-loop queuing network model provided by the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention.

[0023] Therefore, the following detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely illustrates some embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments and features and technical solutions in the embodiments of the present invention can be combined with each other. It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0024] Example 1: A performance evaluation method for a four-way shuttle robot system based on path optimization, system layout and process: as follows Figure 1 As shown, the four-way shuttle robot system mainly consists of high-rise automated racking, shuttle robots capable of both straight and lateral movement, high-speed elevators capable of vertical movement, and transverse guide rails. The automated racking uses a single-depth storage method, with each storage location holding only one SKU. Between each column of racking, a storage aisle allows the shuttle robots to move straight along the X-axis. Transverse guide rails, allowing the shuttle robots to move laterally along the Y-axis, are installed at fixed intervals between storage locations in each column, enabling four-way movement of the shuttle robots. At the front of the racking, several high-speed elevators facilitate vertical movement of the goods. Users can flexibly configure the number of elevators and shuttle robots according to their current requirements for the number of storage locations, cost, and throughput.

[0025] The system's workflow under dual-instruction operation is as follows: Figure 2 As shown: Step 1: Once the inbound and outbound tasks at the same level are completed and bound simultaneously, an idle elevator service is requested. If an elevator is available, it is bound to the inbound / outbound task. If no idle elevator is available, the task order enters the waiting queue to wait for an idle elevator to match it.

[0026] Step 2: The hoist picks up the storage turnover box and moves it to the target storage layer.

[0027] Step 3: The elevator requests a matching idle shuttle robot service. If there is an idle shuttle robot, the shuttle robot will run to the elevator. If there is no idle shuttle robot, the elevator will enter the waiting queue and wait for an idle shuttle robot to match it.

[0028] Step 4: The shuttle robot travels to the elevator position, picks up the turnover box, runs to the target storage location, and unloads the turnover box.

[0029] Step 5: The shuttle robot travels to the target outbound location and picks up the turnover box to be shipped out.

[0030] Step 6: The shuttle robot requests a matching elevator for service. If the elevator is available at this time, the shuttle robot travels to the target elevator, and the elevator moves to the target layer of the goods to be shipped out.

[0031] Step 7: The shuttle robot unloads and releases the turnover box.

[0032] Step 8: The hoist picks up the turnover box and moves it to the first floor. After unloading the turnover box, the hoist releases it to enter a new operation phase, and the task ends.

[0033] 1.1 System Assumptions and Operational Analysis Based on the actual operation of the system, it is assumed that the operation of the four-way shuttle robot system conforms to the following assumptions: (1) Follow the POSC (Point-Of-Service-Completion) principle, that is, after the shuttle robot and the hoist complete the task, they stop at the position where the previous task was completed.

[0034] (2) Follow the FCFS (First-Come First-Served) principle, that is, the shuttle robot, the elevator and the picking station all serve the received requests according to the principle of first-come, first-served.

[0035] (4) When the elevator and the shuttle robot are in the same picking task, only one cargo turnover box can be transported.

[0036] (5) The arrival rate of the task follows the parameter: The Poisson distribution is used, and the service time of each service device follows an exponential distribution.

[0037] (6) Each service equipment shall carry no more than one turnover box.

[0038] In the system, each hoist is paired with a fixed number of shuttle robots for operation, and each shuttle robot is paired with only one hoist for operation. For example... Figure 3 As shown, the cargo hoist requests a matching idle shuttle robot service. After the shuttle robot picks up the to-be-stored turnover box, it first performs the storage operation. The shuttle robot first reaches the storage target location along route 1 according to the pre-planned route. After unloading the storage turnover box, the shuttle robot reaches the outbound target location along route 2. The shuttle robot picks up the outbound turnover box, and then reaches the matching hoist along route 3 to unload the turnover box, completing the outbound operation.

[0039] 2. Shuttle Robot Path Optimization Table 1: Definitions of all parameters 2.1 Dijkstra's Algorithm Dijkstra's algorithm can be used to solve specified... and The shortest path problem between two points, given a weighted directed graph. ,use , Representing points respectively v of P Labels and T Label, Indicates the first i When walking, it has P The set of labeled points. In order to find the... While calculating the distances to each point, we also calculate the distances from... The shortest path to each point, given each point v With one The value of , when the algorithm terminates, if , indicating from arrive v On the shortest path, v The previous point is ;if , then it means D Not including from arrive v The shortest path; express .

[0040] The specific steps of Dijkstra's algorithm are as follows: Step 1, Begin make , , For each ,make , ,make .

[0041] Step 2, if The algorithm terminates at this point, for each , Otherwise, proceed to step 3. .

[0042] Step 3, examine each user and point .if Then Modified to ,Bundle Modified to k Otherwise, proceed to step 4.

[0043] Step 4, let .

[0044] if Then of T The label becomes P label ,make , ,Bundle i Change to i+ 1. Proceed to step 2; otherwise, the algorithm terminates. At this point, for each... , And for each , .

[0045] In the system, the layout of each layer is the same, and the number of shuttle robots in each layer is the same. Since the nodes where the shuttle robots choose their direction during movement only exist at the intersection of the X and Y directions, each intersection of the X and Y directions is labeled. ,like Figure 4 As shown. The length, width, and height of each storage location, the width of each aisle, and the width of each transverse guide rail are all the same. Assume the starting point of the shuttle robot is... The target point is Furthermore, the shuttle robot is adjacent to only two nodes at any starting and ending point in the storage location. Therefore, once the nodes traversed by the shuttle robot during its journey are determined, its path can be accurately predicted. For example... Figure 4 As shown, the number of nodes in this layout Now looking for from arrive The shortest path, assuming the length of the storage location. Meters, width Meters, the width of the storage aisles and transverse guides rice.

[0046] The steps are as follows: (1) i =1, Step 1, , , , ; as well as ; Step 2, because Then proceed to step 3; Step 3, because , , Therefore, Modified to , Similarly, with There are 3 adjacent points, then , ; Step 4, in all T In the labeled point Minimum, therefore let ,make , .

[0047] (2) i =2, Proceed to Step 3. , , , Proceed to Step 4. Therefore, , , .

[0048] (2) i =3, Proceed to Step 3. , , , Proceed to Step 4. Therefore, , , .

[0049] Repeat steps 3 and 4 above until all points, including the target node, have been traversed, completing the solution and obtaining the shortest path. 3, 8 The shortest path is .

[0050] like Figure 5 As shown, the Dijkstra algorithm mentioned in Section 4.2.1 is used to solve the problem from... arrive There are three shortest paths, which gives us: (1) 2 3 8 13 (2) 2 7 12 13 (3) 2 7 8 13 according to Figure 6 As shown, the shuttle robot accelerates and decelerates during its movement. It needs to slow down and stop at each turning point before resuming its operation. Assume the shuttle robot's speed... acceleration .

[0051] (1) In the formula This indicates the number of storage locations visited. This represents the number of intersections traversed. The travel time for each path is calculated using formula (1). Figure 5 The results of the example can be simplified based on the turning nodes as follows: (1) 3 13 (2) 2 12 (3) 2 7 8 13 It can be seen that the first and second routes have two inflection points, and the walking time is 8.6 seconds each; the third route has four inflection points and the walking time is 10.2 seconds. For the same path length, it takes 1.6 seconds longer than the other two routes.

[0052] 2.2 Improved Dijkstra's Algorithm First, establish a two-dimensional coordinate system from the top view of the system layer, as follows: Figure 7 As shown, the X-axis represents the aisle direction, and the Y-axis represents the transverse guide rail direction. The storage locations, aisles, and transverse guide rails are arranged according to... Figure 7 Each small area shown is assigned coordinates. , x Indicates which alleyway, y This represents the nth horizontal sliding rail. Each coordinate region contains a path node, and each node exists in only one coordinate region. Therefore, the nodes traversed by the path can be represented in coordinate form.

[0053] Assume the coordinates on the path are nodes The previous node of this node Coordinates are The coordinates of the next node Coordinates are If the shuttle robot travels straight within the alleyway, the node coordinates... x The value remains unchanged. y If the value changes and a turning point occurs, then... x Value change, y The value remains unchanged; if the shuttle robot moves on the transverse guide rail, then y The value remains unchanged. x If the value changes and a turning point occurs, then... x The value remains unchanged. yThe value changes. Therefore, to determine whether the shuttle robot has turned on the path, we only need to determine the relationship between the nodes before and after each node. The situation where a turn occurs is as follows: (2) The first formula determines the inflection point in the path, and the second formula determines whether the nodes in the region where the initial point and the end point are located are inflection points.

[0054] Due to the initial point The coordinates are End point The coordinates are Then the number of inflection points is: (3) The number of nodes in the path can be determined by checking whether the left side of each node before and after it satisfies formula (2). The steps of Dijkstra's algorithm are improved as follows: In a given weighted directed graph ,use , Representing points respectively v of P Labels and T Label, Indicates the first i When walking, it has P The set of labeled points. In order to find the... While calculating the distances to each point, we also calculate the distances from... The shortest path to each point, given each point With one The value of , when the algorithm terminates, if , indicating from arrive v On the shortest path, v The previous point is The coordinates of the area are ;if , then it means D Not including from arrive v The shortest path; express .

[0055] The specific steps for improving Dijkstra's algorithm are as follows: Step 1, Begin make , , For each ,make , ,make .

[0056] Step 2, if The algorithm terminates at this point, for each , Otherwise, proceed to step 3.

[0057] Step 3, examine each user and point .if Then Modified to ,Bundle Modified to Otherwise, proceed to step 4.

[0058] Step 4, let .

[0059] if Then of T The label becomes P label ,make , ,Bundle i Change to i+ 1. Proceed to step 2; otherwise, the algorithm terminates. At this point, for each... , And for each , .

[0060] Step 5, through Determine the nodes in the node path The preceding and following nodes and Is it an inflection point, and through... Determine whether the starting and ending points are inflection points, and select the path containing the node with the smaller number of nodes that meet the conditions.

[0061] 2.3 Numerical Example Verification like Figure 8 As shown, the number of nodes in this layout Now looking for from arrive The shortest path. Assume the length of the storage location. Meters, width Meters, the width of the storage aisles and transverse guides rice.

[0062] The steps are as follows: (1) i =1, Step 1, , , , ; as well as ; Step 2, because Then proceed to step 3; Step 3, because , , Therefore, Modified to , Similarly, with There are 12 adjacent points, then , ; Step 4, in all T In the labeled point Minimum, therefore let ,make , ; (2) i =2, Proceed to Step 3. , , , ; Proceed to Step 4. Therefore, , , ; (3) i =3, Proceed to Step 3. , , ,Revise , Proceed to Step 4. Therefore, , , ; Repeat steps 3 and 4 above to obtain... The shortest path is: (1) 12,(2,3) 13,(3,3) 14,(4,3) 9,(4,2) 4,(4,1) (2) 12,(2,3)7,(2,2)8,(3,2)9,(4,2)4,(4,1) (3) 12,(2,3)7,(2,2)8,(3,2)3,(3,1)4,(4,1) (4) 12,(2,3) 13,(3,3) 8,(3,2) 9,(4,2) 4,(4,1) (5) 12,(2,3)13,(3,3)8,(3,2)3,(3,1)4,(4,1) (6) 12,(2,3)7,(2,2)2,(2,1)3,(3,1)4,(4,1) Proceed to Step 5, determine if a node is an inflection point, and obtain the number of inflection points for each path as follows: 2, 4, 4, 4, 2, 2 Therefore, there are three shortest paths, namely (1), (5), and (6). When the shuttle robot selects a path, any one of these three paths satisfies the conditions of the shortest distance and the minimum time.

[0063] 3. Model Establishment and Solution This section analyzes the performance of a four-way shuttle robot system, considering both the shortest travel path and the shortest travel time. Based on... Figure 2 The system's workflow involves the following steps: Inbound tote boxes are transported to the target layer via elevators, then carried by shuttle robots to their designated inbound storage locations. From there, they reach their outbound storage locations and are transported back to the elevators, which then carry them to the first floor. Since the structure of the four-way shuttle robot system is identical across all layers, and considering a random storage strategy, the probability of the elevator reaching each layer is the same. Therefore, the service rate of the elevator is the same on each layer. Thus, we can consider the first layer of the system as the focus of our study. Assuming that one elevator corresponds to one or more fixed shuttle robots, and each shuttle robot responds to only one elevator, we can assume the service rate from the elevator to the target inbound storage location is... The service rates of the shuttle robot for transporting inbound and outbound turnover boxes are respectively and .like Figure 9 Establish a semi-open-loop queuing network model for this system.

[0064] 3.1 Solving the semi-open-loop queuing network model based on AMVA For the performance evaluation model of the half-open queuing network, this invention designs a solution method based on the Approximate Mean Value Analysis (AMVA) algorithm. The specific solution steps are as follows.

[0065] Step 1: Remove the arriving task and shuttle robot matching node from the semi-open-loop queuing network to obtain a new closed-loop queuing network CQN1. In this CQN1, the service rate of the elevator entering the target storage location is: The service rate from the inbound target location to the outbound target location is The service rate from the target outbound location to the elevator location is The AMVA method is used to solve the network model of the closed-loop CQN1. The specific parameters used are shown in Table 2. The specific solution steps are as follows.

[0066] Table 2. Main parameters used in the AMVA algorithm Regarding the number of elevators ,exist: (4) Regarding the number of elevators Number of shuttle robots ,exist: (5) Regarding the number of shuttle robots ,exist (6) Regarding the number of elevators Number of shuttle robots , ,exist: (7) Regarding the number of elevators Number of shuttle robots ,if ,So ,otherwise: (8) Regarding the number of elevators Number of shuttle robots ,exist: (9) Regarding the number of elevators Number of shuttle robots ,if , ,otherwise: (10) Regarding the number of elevators Number of shuttle robots ,exist: (11) Step 2: Treat the shuttle robot and task matching node as a separate load-dependent service node, and establish a new closed-loop queuing network CQN2. When there are... r When the shuttle robot was in Taiwan, and So, what is the reach rate of this newly created node? Similarly, by using the AMVA method from step 1 to solve for CQN2, we can obtain the throughput of CQN2. Similarly, the queue length of the elevator can be calculated when r shuttle robots are at the elevator. .

[0067] Step 3: Analyze the matching nodes between the shuttle robot and the task separately to obtain the average length of the external queue. Assuming the utilization rate of the shuttle robot is... The average time to complete an order is The utilization rate of the hoist is The expected captain of the shuttle robot and the matching node of the task is obtained in Step 2 as follows. So when the number of cars in the system is At that time, the utilization rate of the shuttle robot was .make Let's say it's the expected queue size of other nodes. Therefore, the average time to complete an order is: (12) The utilization rate of the hoist can then be expressed as: (13) In the formula, This indicates the rate of achievement at the hoist. This indicates the service time of the hoist.

[0068] 3.2 Task Time Analysis according to Figure 3 The shuttle robot's route can be divided into three parts: the first part is from the elevator position to the target storage location; the second part is from the target storage location to the target outbound storage location; and the third part is from the target outbound storage location to the elevator.

[0069] Assuming the size is In the system, the coordinates of the hoist are The coordinates of the target storage location are The coordinates of the target outbound storage location are The width of each coordinate unit in the Y-axis direction is: The length along the X-axis is: , This indicates the number of columns of the shelf in each coordinate unit.

[0070] First, the shuttle robot starts from the elevator position. Transport the inbound turnover boxes to the designated inbound storage locations. This process can be divided into two parts: one part along the X-axis and the other part along the Y-axis.

[0071] So, in the Y-axis direction, the shuttle robot travels for... for: (14) (15) In the formula This represents the minimum number of coordinate units required for a shuttle robot to accelerate to its maximum speed in the Y-axis direction and then immediately decelerate to 0.

[0072] In the Y-axis direction, the average service time of the shuttle robot is... for: (16) In the X-axis direction, the time it takes for the shuttle robot to travel... for: (17) (18) In the formula This indicates the minimum number of coordinate units required for a shuttle robot to accelerate to its maximum speed in the X-axis direction and then immediately decelerate to 0.

[0073] In the X-axis direction, the average service time of the shuttle robot's travel. for: (19) Then, the shuttle robot moves from the target storage location. After unloading the turnover box, it runs to the target outbound storage location. The process of retrieving turnover boxes to be shipped out can be divided into two parts: one part along the X-axis and the other part along the Y-axis.

[0074] The time taken by the shuttle robot in the Y-axis direction and The expression is the same, representing the average travel time of the shuttle robot in the Y-axis direction. .

[0075] In the X-axis direction, the time it takes for the shuttle robot to travel... for: (20) In the X-axis direction, the average service time of the shuttle robot's travel. for: (twenty one) Finally, the shuttle robot departs from the target storage location. Run to the hoist position The location of the shuttle robot unloading the turnover box can be divided into two parts: one part along the X-axis and the other part along the Y-axis.

[0076] The time taken by the shuttle robot in the Y-axis direction and The expression is the same, representing the average travel time of the shuttle robot in the Y-axis direction. Average travel time of the shuttle robot in the Y-axis direction .

[0077] In the X-axis direction, the time it takes for the shuttle robot to travel... and The expression is the same, representing the average travel time of the shuttle robot in the Y-axis direction. The average travel time of the shuttle robot in the X-axis direction .

[0078] Inside the coordinate unit, the shuttle robot moves only along the X-axis. Assume the target location is located after the [number]th node. If there are [number] cells, then the distance the shuttle robot travels within the coordinate unit is: Therefore, the travel time of the shuttle robot within the coordinate unit for (twenty two) (twenty three) In the formula, This indicates the number of shelves the shuttle robot passes through as it moves along the X-axis within the coordinate unit, first accelerating to its maximum speed and then immediately decelerating to 0.

[0079] So, the average time for the shuttle robot to travel within the coordinate unit... for: (twenty four) Since the shuttle robot chooses the shortest path with the fewest turning points when selecting its route, let's assume that the time lost by the shuttle robot when turning is... Therefore, the average time lost by the shuttle robot when turning is: (25) For a hoist, there are two operational stages. The first stage is to transport the inbound tote boxes from the first floor to the target inbound floor. The second stage is to transport the outbound tote boxes from the floor where the tote boxes are located back to the first floor. Assume the system has 12 floors. So, the hoist from the first floor to the second floor... i Layer runtime for: (26) (27) In the formula, The number of floors the hoist passes through in the vertical direction, accelerating from 0 to its maximum speed and then immediately decelerating back to 0. The height of one layer of the system.

[0080] The hoist from the first floor to the second floor i Average time of layer for: (28) The second stage of the hoisting process takes the same amount of time as the first stage. , .

[0081] In summary, the average service time for the hoist to complete one task is: (29) The average service time for the shuttle robot from the elevator position to the target storage location is: (30) The average service time for the shuttle robot from the target inbound storage location to the target outbound storage location is: (31) The average service time for the shuttle robot from the target outbound location to the elevator is: (32) 4. Experimental Results and Analysis This experiment investigates the following three aspects: First, we verify the effectiveness of the algorithm. Assuming fixed system parameters, we study the system order completion cycle, elevator utilization rate, four-way shuttle robot utilization rate, and external queue simulation results and solution results under different arrival rates to verify the effectiveness and accuracy of the performance evaluation model and solution established in this chapter.

[0082] Then, with a fixed number of cargo bays in the system, sensitivity analysis was used to study the impact of different configurations of the number of lanes and columns on the system's task completion cycle, hoist utilization, shuttle robot utilization, external queues, and throughput. Furthermore, the influence of the number of lanes and columns on system performance was summarized.

[0083] Finally, the impact of the number of system layers on the total system throughput capacity is studied under different total number of storage locations.

[0084] All experiments in this invention were conducted on a computer with an Intel(R) Core(TM) i5-3210M CPU@2.50GHz dual-core processor and 8.00G of memory, and the simulation was performed on MATLAB 2019b.

[0085] First, the effectiveness and accuracy of the performance evaluation model are verified in the first experiment. Based on the characteristics and parameters of the system's mechanical structure in the actual project, the specific structural parameters of the four-way shuttle robot system are shown in Table 3. Assuming other system parameters are as shown in Table 4, 100 experiments are conducted under different achievement rates, and the average value is taken as the simulation result, which is then compared with the result obtained from the solution in Section 2.2.

[0086] Table 3 Main parameters of the system Table 4 Other assumptions about the system A comparison of the simulation output and calculation results in Table 5 reveals that, under different arrival rates, the errors between the calculated and simulation results for the system order completion cycle, elevator utilization rate, shuttle robot utilization rate, and external queue are all within a certain range. Within this period, the effectiveness and accuracy of this performance evaluation model and solution were verified.

[0087] Table 5 Comparison of Simulation Results and Calculation Results Table 5 Comparison of Simulation Results and Calculation Results (Continued) The second experiment investigated the impact of the number of aisles and columns on system performance. With the number of elevators and shuttle robots remaining constant, and assuming a single-depth shelf, a total demand of 10,000 storage locations, and 5 columns per coordinate unit, the experiment studied the system's task cycle for completing a task, the utilization rate of elevators and four-way shuttle robots, external queue conditions, and system throughput under different arrival rates when the number of shelves was 5 and 10. This allowed for the summarization of the influencing factors.

[0088] Table 6 Performance Indicators of Different System Parameters (1) Table 7 Performance Indicators of Different System Parameters (2) Table 7 Performance Indicators of Different System Parameters (2) Continued Table 8 Performance Indicators of Different System Parameters (3) Table 9 Performance Indicators of Different System Parameters (4) Table 10 Performance Indicators of Different System Parameters (5) Table 11 Performance Indicators of Different System Parameters (6) The experimental results obtained by changing the system parameters are shown in Tables 6, 7, 8, 9, 10, and 11.

[0089] Firstly, comparing Tables 6, 7, and 8, and Tables 9, 10, and 11, we can see that, with the same number of layers, when the completion rate is low, the configuration parameters of different numbers of lanes and columns have little impact on the task completion cycle. However, when the completion rate is high, the configuration parameters of different numbers of lanes and columns have a significant impact on the task completion cycle. When the difference between the number of lanes and columns in the system is small, the system's throughput capacity is greater than when the difference is large.

[0090] Secondly, comparing Tables 6 and 10, Tables 8 and 9, and Tables 7 and 11, under the condition of similar roadway number and column number ratio, when the completion rate is small, different layers have little impact on the task completion cycle; when the completion rate is large, different layers have a greater impact on the task completion cycle.

[0091] To further investigate the impact of different numbers of layers on the system's total throughput, a third experiment was conducted. This experiment investigated the effect of different numbers of layers on the system's total throughput when the total number of storage locations was 6000, 10000, and 16000, and the difference between the number of aisles and columns was minimized. The total number of shuttle robots in the system remained constant. As shown in Tables 12, 13, and 14, when the total number of storage locations was 6000 and 10000, the system had the strongest throughput with 5 layers; when the total number of storage locations was 16000, the system had the strongest throughput with 10 layers. The results indicate that the number of layers also affects the system's total throughput, and there exists an optimal number of layers that maximizes the system's total throughput.

[0092] Table 12 Impact of different number of layers on total system throughput (1) Table 13 Impact of different number of layers on total system throughput (2) Table 14 Impact of different number of layers on total system throughput (3) The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described herein. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, as well as all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.

Claims

1. A method for performance evaluation of a path-optimized four-way shuttle robot system, characterized by, Comprising the following steps: Step 1, path node modeling: a two-dimensional coordinate system is established for the same layer overhead layout of the four-way shuttle robot system, taking the roadway extension direction as the X axis and the transverse guide rail extension direction as the Y axis, all intersection points of the roadway and the transverse guide rail are defined as path nodes, and each path node is assigned a unique coordinate; the path inflection point is judged by comparing the coordinate changes of adjacent path nodes, when the node coordinates change only along the X axis or only along the Y axis, it is determined as a straight line segment, and when the node coordinates change along the X axis and the Y axis at the same time, it is determined as an inflection point; Step 2, shortest time path optimization: an improved Dijkstra shortest time path algorithm is used, first, based on the path node model established in step 1, calculate all the shortest distance paths from the starting point of the hoist position node to the end point of the warehouse entry and exit point node, form a shortest distance path set; then count the number of inflection points of each path in the set, and screen out the path with the least number of inflection points as the candidate path; then based on the acceleration, uniform speed and deceleration motion model of the four-way shuttle robot, combined with the total distance, the number of inflection points of the candidate path and the motion characteristics of the robot, calculate the actual running time of each candidate path, and select the path with the shortest running time as the final optimized path; Step 3, system operation time analysis: based on the final optimized path determined in step 2, the time of three operation stages of the four-way shuttle robot is calculated respectively, the three operation stages are the driving time from the hoist position node to the warehouse entry node, the driving time from the warehouse entry node to the warehouse exit node, and the driving time from the warehouse exit node to the hoist position node; When calculating, combine the displacement amount of X direction and Y direction in the path and the acceleration and deceleration characteristics of the robot to obtain the time of each stage by piecewise accumulation; Step 4, semi-open loop queuing network modeling: taking the total time of the three operation stages calculated in step 3 as the service time input, the operation process of the four-way shuttle robot system is abstracted into a semi-open loop queuing network model; the model includes three core nodes, respectively, the hoist node responsible for vertical transportation of goods, the task matching node responsible for binding the hoist and the shuttle robot task, and the target storage node responsible for storage and retrieval of goods; define the service rate of each node and the task transfer relationship between nodes; Step 5, queuing network performance solution: the AMVA approximate mean value analysis method is used to solve the semi-open loop queuing network model established in step 4, which specifically includes: first, remove the task matching node to build a closed loop network CQN1, input the number of hoists, the number of shuttle robots and the external task arrival rate, solve the system throughput, the queue length of the hoist node and the queue length of the shuttle robot node of CQN1; second, the task matching node is constructed as a load-dependent node to build a new closed loop network CQN2, taking the throughput of CQN1 as the input, solving the queue length and utilization rate of the task matching node; third, combining the results of CQN1 and CQN2, the total throughput of the system, the utilization rate of the hoist, the utilization rate of the shuttle robot and the utilization rate of the target storage node are calculated; Step 6, system performance evaluation and verification: based on the calculation results of step 5, the core performance indicators of the four-way shuttle robot system are evaluated, including task completion cycle, elevator utilization rate, shuttle robot utilization rate, system throughput and node waiting queue length; the evaluation results are verified by system simulation experiment, and the performance indicators obtained by simulation are compared with the calculation results of AMVA method. When the error is within the acceptable range, it is determined that the evaluation is effective. Step 7, system structure parameter sensitivity analysis: adjust the structure parameters of the four-way shuttle robot system, including the number of lanes, the number of columns, the number of layers, and the number of interval storage spaces in the transverse guide rail. Repeat steps 1-6 to calculate the system throughput under different parameter combinations. Through comparative analysis, determine the optimal parameter configuration, including the optimal proportional relationship between the number of lanes and the number of columns, and the optimal number of layers corresponding to different total storage spaces. The four-way shuttle robot system is composed of high-level storage shelves, shuttle robots moving straight along the X direction and transversely along the Y direction, vertical high-speed elevators, and transverse guide rails. The storage shelves use single deep storage mode, each storage space only stores one SKU, and storage lanes for shuttle robots to move straight along the X direction are set between columns. The transverse guide rails for shuttle robots to move transversely along the Y direction are set in the middle of each column of shelves according to fixed storage space number, and several high-speed elevators are set at the front end of the shelves. The system supports users to configure the number of elevators and shuttle robots according to the number of storage spaces, cost and throughput requirements.

2. The method of claim 1, wherein, The acceleration, constant speed and deceleration motion models of the four-way shuttle robot in step 2 are constructed according to the motion law of the robot in actual operation, which first accelerates to the maximum speed, maintains constant speed, and decelerates to stop near the target. The turning time loss at the inflection point is included in the total running time.

3. The method of claim 1, wherein, In step 4, the external task arrival rate of the semi-open loop queuing network model is calculated based on the system historical operation data using the moving average method. The historical operation data is the number of tasks arriving per hour in the past 24 hours, so that the external task arrival rate can reflect the actual operation load of the system.

4. The method of claim 1, wherein, In step 5, the AMVA method uses iterative calculation to solve the closed loop network CQN1. The initial iteration value is determined based on the service capacity of the elevator and the shuttle robot, and the iteration termination condition is that the difference between the throughputs calculated in the adjacent two times is within a small range.

5. The method of claim 1, wherein, In step 6, the discrete event simulation software is used for system simulation experiment, and the simulation time and data statistics period are set. The simulation time includes the warm-up period and the data statistics period, and the simulation results are obtained by repeating the simulation multiple times and taking the average value.

6. The method of claim 1, wherein, In step 7, the value of the interval storage space in the transverse guide rail needs to balance the efficiency of the shuttle robot moving across the lane and the space utilization rate of the shelf. Through sensitivity analysis, the interval storage space in the transverse guide rail that makes the average time of the shuttle robot moving across the lane shortest is determined.

7. The method of claim 1, wherein, In step 1, the coordinate accuracy of the path node needs to match the actual layout error of the system to ensure that the position deviation of the intersection of the lane and the transverse guide rail does not affect the accuracy of the path inflection point judgment.

8. The method of claim 1, wherein, The screening criteria of the shortest distance path set in step 2 is that the difference between the total distance of the path and the shortest distance is in a minimum range, and the path does not contain invalid nodes without actual rail connection.

9. The method of claim 1, wherein, The calculation of the vertical running time of the lifting machine in step 4 is based on the acceleration, uniform speed and deceleration motion characteristics of the lifting machine and the height of each layer of the shelf, and the total service time of the system is composed of the working stage time of the shuttle robot.

10. The method of claim 1, wherein, The sensitivity analysis of the system structure parameters in step 7 uses the control variable method, and only one structure parameter is adjusted each time, and other parameters remain unchanged. The analysis result can accurately reflect the influence law of a single parameter on the system performance.

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