Wireless charging amr cluster cooperative scheduling method and device considering task sequence constraint, and medium

Abstract

This application discloses a method, device, and medium for collaborative scheduling of wireless charging AMR clusters considering task sequence constraints, relating to the field of AMR job scheduling optimization. The aim of this application is to address the problem that existing AMR cluster job scheduling methods struggle to balance solution efficiency, solution quality, and field executability in medium to large-scale instances. This application selects candidate AMRs for the current task to be assigned. Based on the candidate AMRs, it calculates the maximum amount of electricity that a candidate AMR can obtain through wireless charging during the execution of the current task, as well as the predicted state of charge (SOC) of the candidate AMR after executing the current task. If the predicted SOC is greater than or equal to the minimum SOC safety threshold, the current task to be assigned is allocated to the candidate AMR; otherwise, a charging operation is inserted into the candidate AMR to restore its SOC to full charge, and then the current task to be assigned is allocated to the candidate AMR again.

Description

Technical Field

[0001] This application belongs to the field of AMR job scheduling optimization and wireless charging planning technology. Background Technology

[0002] With the rapid development of digitally driven green and intelligent manufacturing, autonomous mobile robots (AMRs) and automated guided vehicles (AGVs) play an important role in factory material handling and warehousing logistics. They can complete pick-up, put-down and transfer between multiple workstations at high frequency, effectively improving operational efficiency and production line resilience.

[0003] Current engineering practices primarily rely on fixed-site recharging, including wired charging and battery swapping. During operation, the AMR's battery level continuously decreases, requiring it to exit the operation and return to a fixed location for recharging when approaching a threshold, before returning to the production line. This process introduces periods of inactivity, travel time, and energy loss; fixed recharging locations also easily lead to queuing and bottlenecks. Contact charging presents safety hazards such as space occupation, interface wear, and short circuits. Battery swapping typically relies on dedicated facilities and centralized management of backup batteries, resulting in high land occupation and safety requirements, and increased process organization and maintenance costs, making it difficult to meet the demands for efficiency, economy, and green synergy.

[0004] To alleviate the aforementioned issues, Wireless Power Transfer (WPT) provides opportunities for charging during docking phases such as loading or unloading. It can smooth the State of Charge (SOC) trajectory without requiring additional downtime and, to some extent, alleviate congestion at fixed charging sites. However, WPT is inherently a rate-limited resource due to physical constraints such as alignment windows, power limits, and transmission efficiency. If it is not coordinated with mission timing, vehicle docking, and path conflicts, a disconnect between planning and execution may still occur.

[0005] Furthermore, AMR cluster job scheduling faces significant coupling: on the one hand, it needs to satisfy the predefined process's job sequence; on the other hand, it needs to meet the upper limit of battery capacity and the minimum SOC safety threshold throughout the entire process, while also reasonably arranging fixed-duration full charging within the station when opportunistic charging is insufficient to support subsequent tasks. Task allocation, job sequencing, and replenishment strategies influence each other, jointly determining the feasible domain and overall cycle time, and directly impacting system efficiency and operational risks. Existing technologies mostly employ block-based processing, either only replenishing energy at fixed sites or only setting energy threshold checks, lacking a unified scheduling optimization framework that can simultaneously characterize opportunistic charging and full charging within the station, and link job sequence with energy dynamics. This makes it difficult to balance solution efficiency, solution quality, and field executability in medium to large-scale instances. Summary of the Invention

[0006] This application aims to address the problem that existing AMR cluster job scheduling methods struggle to balance solution efficiency, solution quality, and field executability in medium to large-scale instances. It provides a collaborative scheduling modeling and optimization method for AMR clusters in smart manufacturing plants, which integrates wireless opportunistic charging during loading and unloading and full charging at the station, under constraints of battery capacity, minimum SOC safety threshold, and job sequence. The method also includes corresponding solution algorithms, electronic devices, and computer-readable storage media.

[0007] The first aspect of this application provides a wireless charging AMR cluster cooperative scheduling method considering task order constraints, including:

[0008] Candidate AMRs are selected for the current task to be assigned. Based on the current state of charge of the candidate AMRs, wireless charging speed, wireless power transfer efficiency, and loading and unloading time of the current task to be assigned, the maximum amount of electricity that the candidate AMRs can obtain through wireless charging during the execution of the current task to be assigned, and the predicted state of charge of the candidate AMRs after the execution of the current task to be assigned are calculated.

[0009] If the predicted state of charge is greater than or equal to the minimum state of charge safety threshold, the current task to be assigned is assigned to the candidate AMR; otherwise, a charging operation is inserted into the candidate AMR to restore its state of charge to full charge, and then the current task to be assigned is assigned to the candidate AMR.

[0010] In one possible design, the wireless charging AMR cluster cooperative scheduling method is implemented based on the wireless charging AMR cluster cooperative scheduling model;

[0011] The objective of the wireless charging AMR cluster collaborative scheduling model is to minimize the maximum operation completion time of the wireless charging AMR.

[0012] In one possible design, the constraints of the wireless charging AMR cluster cooperative scheduling model include:

[0013] The amount of wireless charging during both the loading and unloading phases is less than the smaller of the theoretical chargeable amount and the remaining usable battery capacity.

[0014] The energy conservation between two adjacent tasks within the same charging cycle of the same AMR;

[0015] The battery level of any AMR after completing any delivery task is greater than or equal to the minimum safe battery level.

[0016] The battery level of any AMR before executing the first task in any charging cycle is equal to the larger of the two values: the remaining battery level after executing the last task in the previous charging cycle, and the full battery level if a fixed charging operation is performed in the current cycle.

[0017] The charge level of any AMR in each task and each charging cycle is greater than the safe charge level corresponding to the minimum state of charge, and does not exceed the upper limit of battery capacity.

[0018] If the AMR performs a task within the same charging cycle Then the start time of the next task is equal to the start time of the task. The start time plus its operation duration; if the AMR does not perform the task. Then the start time of the next task is equal to the start time of the task. The start time;

[0019] After completing a task within a certain charging cycle, if the AMR performs a fixed charging operation before entering the next charging cycle, the start time of the first task in the next charging cycle is equal to the start time of the previous task plus its operation time and the fixed charging time; if a fixed charging is not performed, the difference between the two is the task operation time.

[0020] The start time of any task is earlier than or equal to the start time of its successor task.

[0021] For the same AMR, if one task is numbered earlier than another, the charging cycle of the task with the earlier number is earlier than the charging cycle of the task with the later number.

[0022] In one possible design, the constraint condition of the wireless charging AMR cluster cooperative scheduling model is expressed as follows:

[0023] ,

[0024] ,

[0025] ,

[0026] ,

[0027] ,

[0028] ,

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] in, Represents a set of tasks. Represents the AMR set, This represents the set of times the AMR is charged at a charging station. Indicates the total number of delivery tasks; Indicates the first AMR ( ) After completing the first Delivery will commence after the first charging operation. At that time, during the mission The actual amount of electricity obtained through wireless charging during the loading phase; This indicates the charging speed of the wireless charging device at the loading station; Indicates wireless power transmission efficiency; express Execute the task Loading operation time; for In the Should the delivery task be executed after the second charging operation? The decision variable is 1 if it is true, and 0 otherwise; Indicates the upper limit of AMR battery capacity; express In the After the first charging operation, the task begins. Current battery level; express After completing the first Delivery will commence after the first charging operation. At that time, during the mission The actual amount of electricity obtained through wireless charging during the unloading phase; express Execute the task Unloading operation time; Indicates task The amount of electricity consumed during the entire execution process; This represents the minimum SOC (State of Charge) threshold coefficient. for Does the charging station perform the first step? The decision variable for the next fixed charging operation is 1 if it is true and 0 otherwise. express In the The task will be executed after the next charging operation. The start time; Indicates delivery task The duration of the assignment; This indicates the charging time required for each full charge at a charging station. For the task The global start time.

[0034] In one possible design, selecting candidate AMRs for the currently assigned task includes:

[0035] The AMR with the shortest cumulative completion time or the earliest available start time among all AMRs is selected as the candidate AMR.

[0036] In one possible design, the objective function of the wireless charging AMR cluster cooperative scheduling model is... The expression is:

[0037] ,

[0038] in, This is the maximum operation completion time for AMR.

[0039] In one possible design, the maximum job completion time of the AMR The following constraints must be satisfied:

[0040] ,

[0041] in, Represents a set of tasks; This represents the set of times the AMR is charged at a charging station; Indicates delivery task The duration of the assignment; for In the Should the delivery task be executed after the second charging operation? The decision variable is 1 if it is true, and 0 otherwise; This indicates the charging time required for each full charge at a charging station. for Does the charging station perform the first step? The decision variable for the next fixed charging operation is 1 if it is true and 0 otherwise.

[0042] In one possible design, initialization is performed before the coordinated scheduling of the wireless charging AMR cluster, and the initialization includes:

[0043] Based on the aforementioned wireless charging AMR cluster collaborative scheduling model and its constraints, a task set is constructed.

[0044] Set the initial state of charge of all AMRs to full, the start time to 0, and the initial charging cycle number to 1.

[0045] A second aspect of this application provides a wireless charging AMR cluster collaborative scheduling device that considers task order constraints. The wireless charging AMR cluster collaborative scheduling device that considers task order constraints includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the wireless charging AMR cluster collaborative scheduling method that considers task order constraints as described above.

[0046] A third aspect of this application provides a computer storage medium storing at least one instruction, which is loaded and executed by a processor to implement the wireless charging AMR cluster cooperative scheduling method considering task order constraints as described above.

[0047] The beneficial effects of this application are:

[0048] 1. Compared with traditional wired charging or battery swapping methods, wireless charging is integrated with operation scheduling, making full use of the dwell time during loading and unloading for energy replenishment, reducing return to the station and queuing, reducing round-trip losses and land requirements, and mitigating safety hazards caused by contact wear. This shortens the operation cycle, improves system throughput and fleet utilization. By introducing task sequence constraints and energy dynamic constraints into a unified model, this application can fully explore the potential for charging during loading and unloading while ensuring the feasibility of the process sequence.

[0049] 2. Under dynamic circumstances such as order insertion, temporary equipment shutdown, fluctuations in task duration and power consumption, it can continuously meet the battery capacity and SOC safety threshold requirements based on rapid heuristic or rolling optimization strategies, quickly adjust task and power replenishment arrangements and form an executable plan, taking into account both operational efficiency and stability.

[0050] This application can be widely applied to material transportation and warehousing logistics in intelligent manufacturing, which helps to improve production and operation efficiency and energy utilization. Attached Figure Description

[0051] Figure 1 A schematic diagram of collaborative scheduling of wireless charging AMR clusters in a manufacturing plant, taking into account task sequence constraints.

[0052] Figure 2 A Gantt chart for AMR task scheduling (no chance to charge) under the ASPBC model.

[0053] Figure 3 The evolution curve of AMR charge (SOC) under the ASPBC model (no opportunity to recharge);

[0054] Figure 4 A Gantt chart for AMR task scheduling (including opportunistic charging) under the WCASPBC model.

[0055] Figure 5 A diagram showing the AMR charge evolution and opportunistic charging effect under the WCASPBC model (including opportunistic charging).

[0056] Figure 6 A Gantt chart for AMR task scheduling (including task order constraints) under the WCASPBSC model.

[0057] Figure 7 The graph shows the AMR charge evolution curve under the WCASPBSC model (including task sequence constraints).

[0058] Figure 8 A schematic diagram of the scheduling results of the WCASPBSC model after incorporating effective inequalities;

[0059] Figure 9 The graph shows the AMR charge evolution curve under the effective inequality enhancement model.

[0060] Figure 10 A schematic diagram of the WCASPBSC scheduling results obtained by the heuristic algorithm;

[0061] Figure 11 This is a graph showing the AMR charge evolution under a heuristic algorithm. Detailed Implementation

[0062] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0063] Specific Implementation Method 1: This implementation method provides a task-sequence-constrained collaborative scheduling modeling and optimization method for wireless charging AMR clusters, used to plan the operational efficiency of a scheduling system that includes multiple wireless charging AMRs, multi-stage process tasks, and various types of wireless charging operations. Each step is described in detail below:

[0064] This embodiment provides a collaborative scheduling modeling and optimization method for wireless charging AMR clusters with task sequence constraints, used to plan the operational efficiency of a scheduling system that includes multiple wireless charging AMRs, multi-stage process tasks, and various types of wireless charging operations. This application addresses material handling and work-in-process circulation scenarios in smart manufacturing plants, achieving collaborative optimization of AMR cluster task allocation and charging planning while simultaneously considering task sequence constraints, battery capacity and minimum SOC safety threshold, opportunistic charging during loading and unloading phases, and full-charge operations at fixed charging stations.

[0065] This implementation addresses production tasks with process flow constraints. Each production requirement is decomposed into a series of transportation and processing operations with sequential dependencies. Material handling performed by the AMR (Automatic Mobile Recycler) is considered part of the task execution process. By constraining the service sequence and timing of the AMR between workstations, all tasks are completed as early as possible while satisfying the process sequence. Simultaneously, this application depicts the dynamic process of the AMR's battery level evolving over time and with the operation status within a unified modeling framework, ensuring tight coupling between task scheduling and charging planning at the model level. This application includes planning at three levels:

[0066] 1) Task Allocation and Sequence Planning. Smart manufacturing plants use AMRs (Automatic Mobile Transporters) to transport materials between raw material warehouses, work-in-process buffer zones, and various processing stations. The material transport and intermediate transfer needs that meet the process requirements of different stations are collectively referred to as AMR tasks. Unlike traditional independent tasks, this application explicitly defines the sequential constraints between process tasks with dependencies, ensuring that the same workpiece or batch of materials must complete multiple tasks sequentially according to a predetermined process flow. Since the number of AMRs is usually much smaller than the number of tasks, the same AMR needs to execute multiple tasks with process sequence constraints in series on the timeline, forming a work sequence consisting of alternating loaded and unloaded trips. Each task includes parameters such as travel time, loading / unloading operation time, and corresponding energy consumption. Under the premise of comprehensive process sequence constraints, this application aims to shorten the total system completion time by comprehensively planning the task allocation and work sequence of the AMR cluster.

[0067] 2) Coordinated Planning of Opportunity Charging and Full Charge. Each AMR is equipped with a battery of limited capacity, and its State of Charge (SOC) level gradually decreases with changes in driving distance, loading / unloading operation time, and load conditions. To ensure that the battery does not run out or the SOC falls below the safety threshold during the entire process, this application introduces two types of charging methods during scheduling: one is to use deployed wireless charging devices at loading / unloading stations or intermediate buffer zones to perform short-term opportunity charging during AMR waiting or loading / unloading operations; the other is to perform full charge operations on AMRs at fixed charging stations. By characterizing the opportunity charging duration, charging power, and charging efficiency, as well as the charging constraints of fixed charging stations, in a unified model, this application achieves coordinated planning of AMR operation tasks and the two types of charging operations in the time and energy dimensions. This allows AMRs to replenish energy during fragmented time and perform full charge when necessary without interrupting the key process rhythm.

[0068] 3) Co-modeling of task sequence and energy evolution. Based on the above analysis of task allocation and charging planning, this application establishes a mathematical model for the coordinated scheduling of wireless charging AMR clusters, considering both task sequence constraints and battery capacity constraints. Within a unified time and energy framework, the model aims to minimize the maximum job completion time of the AMR cluster. Decision variables include the task matching relationship of AMRs, the start and end times of each task on the time axis, the start and stop times and durations of opportunity charging at different workstations, the triggering timing and frequency of full-charge operations at fixed charging stations, and the SOC level of AMRs at each time point. Through a set of task allocation constraints, process sequence constraints, time continuity constraints, energy safety constraints, and energy balance constraints between opportunity charging and full charging, the model accurately characterizes the logical relationship and physical constraints of AMRs executing tasks and performing charging operations.

[0069] Based on the above analysis of AMR task allocation and task sequence planning, opportunistic charging and full charging collaborative planning, and unified modeling of task sequence and energy evolution, the task sequence-constrained wireless charging AMR cluster collaborative scheduling modeling and optimization method includes:

[0070] Step 1: Construct a mathematical model for collaborative scheduling of wireless charging AMR clusters with task order constraints.

[0071] The model aims to minimize the maximum operation completion time of wireless charging AMR:

[0072] (1),

[0073] in, This refers to the maximum completion time of AMRs (Automatic Mobile Responders), i.e., the latest completion time after all AMRs have completed their assigned tasks, in order to shorten the overall material delivery cycle and improve production line takt time. It is a continuous variable used to measure the upper bound of the global progress.

[0074] Model constraints include:

[0075] For any AMR, It must be greater than or equal to the sum of the cumulative delivery operation time and the cumulative fixed charging time at the charging station for each AMR, as expressed in equation (2):

[0076] (2),

[0077] in, Represents a set of delivery tasks. This indicates the total number of delivery tasks. ; This represents the set of times the AMR is charged at a charging station. This indicates the maximum number of charging operations. ; Represents the AMR set, This indicates the total number of AMRs. ; Indicates delivery task The duration of the assignment; For 0-1 decision variables, if In its first The delivery task will be carried out after the first charging operation. If the value is 1, then the value is 1; otherwise, the value is 0. This indicates the charging time required for each full charge at a charging station. For 0-1 decision variables, if Performing the first step at the charging station If it is a fixed charging operation, the value is 1; otherwise, it is 0.

[0078] For any delivery task This must be performed once by one of the AMRs in the AMR cluster after a charging operation, as expressed in equation (3):

[0079] (3).

[0080] For any The wireless charging amount during the loading phase cannot exceed the smaller of the theoretical chargeable amount during that phase and the remaining usable battery capacity. That is, the wireless charging amount during loading is constrained by the battery capacity, as expressed in equation (4):

[0081] (4),

[0082] in, express After completing the first Delivery will commence after the first charging operation. At that time, during the mission The actual amount of electricity obtained through wireless charging during the loading phase; This indicates the charging speed of the wireless charging device at the loading station; Indicates wireless power transmission efficiency; express Execute the task Loading operation time; Indicates the upper limit of AMR battery capacity; express In the After the first charging operation, the task begins. Previous battery level.

[0083] The amount of wireless charging during the unloading phase also cannot exceed the smaller of the theoretically rechargeable amount for that phase and the remaining usable battery capacity. In other words, the amount of wireless charging during unloading is also constrained by the battery capacity. Represented as equation (5):

[0084] (5),

[0085] in, express After completing the first Delivery will commence after the first charging operation. At that time, the amount of electricity actually obtained through wireless charging during the task unloading phase; express Execute the task Unloading operation time; Indicates task The amount of electricity consumed during the entire execution process.

[0086] Equation (6) describes the power balance relationship between two adjacent tasks of the same AMR in the same charging cycle. For any Established:

[0087] (6),

[0088] in, Indicates the first During the second charging operation, the task Before starting The amount of electricity.

[0089] Equation (7) links task allocation with fixed charging operations, for any Established:

[0090] (7).

[0091] Equation (7) guarantees that only when The charging station actually performed the first The next fixed charging operation (i.e.) Only if it is 1) can it be assigned to perform a task after the charging period. (at this time You can choose 1); if No first The second charge (i.e.) If the value is 0, then there must be A value of 0 means that no task can be assigned after this charging cycle, thus maintaining consistency between the charging decision and the task assignment decision.

[0092] Equation (8) is used to limit the power safety level of the AMR after completing any delivery task, for any Established:

[0093] (8),

[0094] in, This represents the minimum SOC scale threshold coefficient (a constant between 0 and 1). This refers to the minimum safe charge level allowed by an AMR battery.

[0095] Equations (9)-(10) are used to set the initial charging state and initial power level of the AMR at the start of scheduling.

[0096] Equation (9) applies to any Regulation:

[0097] (9),

[0098] Equation (9) indicates that for each AMR, the charging operation numbered 1 is considered to have been completed before the scheduling begins, and is used to characterize its initial charging state.

[0099] Equation (10) applies to any Regulation:

[0100] (10)

[0101] Equation (10) represents the relationship between the initial task and the current task. and initial charging cycle Under the corresponding conditions, the charge level of each AMR is equal to its battery capacity. That is, all AMRs are fully charged when scheduling begins.

[0102] Equation (11) is used to connect the charge levels between two adjacent charging cycles of the same AMR, for any :

[0103] (11),

[0104] In the formula, This represents each actual charging cycle except for the initial charging state; the last delivery task in the task set is denoted as... Constraints In the The charge level before executing the first task of the next charging cycle. It equals the larger of the two: one is the previous charging cycle. After completing the last task Remaining battery power Secondly, if the first [stage / process] was executed in this cycle... One fixed charging operation ( Full charge at time 1) Equation (11) ensures that if the AMR is charged at a fixed rate in the current cycle, the charge level will be increased to full at the beginning of the current cycle; otherwise, the remaining charge level at the end of the previous cycle will be carried over.

[0105] Equation (12) is used to limit the range of AMR power values ​​under each task and each charging cycle. Established:

[0106] (12),

[0107] This constraint requires that the battery level always be no lower than the safe battery level corresponding to the minimum SOC and not exceed the upper limit of the battery capacity, ensuring that the battery level of the AMR is always within a physically permissible and safe range throughout the entire scheduling process.

[0108] (13)

[0109] (14)

[0110] Equations (13) and (14) provide constraints on the value types of the two types of decision variables. It is clarified that the two types of key decision variables in the model are 0-1 variables, that is, the task allocation variable can only take 0 or 1, and the fixed charging decision variable can also only take 0 or 1.

[0111] Equation (15) is used to describe the relationship between the start times of two adjacent tasks of the same AMR within the same charging cycle. For any Established:

[0112] (15)

[0113] In the formula, express In the The task will be executed after the next charging operation. The start time. Constraints require that it be within the same charging cycle. inside, if The task was executed during this period. ( If the value is 1, then the next task is... The start time is equal to the task The start time plus its duration; if the task Not performed by the AMR during this charging cycle ( If the value is 0, then the start time of both is the same, thus maintaining the continuity and coherence of the task start time within the same charging cycle.

[0114] Equation (16) is used to describe the time connection relationship between two adjacent charging cycles. For any Established:

[0115] (16)

[0116] In the formula, express After completing the first The start time of the first task executed within that charging cycle after the next charging operation. Constraints require that within the charging cycle... Complete the task within the time limit Afterwards, if Entering a charging cycle A fixed charging operation was performed beforehand. If the value is 1, then the start time of the first task in the next charging cycle is equal to the start time of the previous task plus its operation time and a fixed charging time; if a fixed charging is not performed ( If the value is 0, then the only difference between the two is the task duration. This ensures the continuity of task start time and the correct insertion of charging time between different charging cycles.

[0117] Equation (17) is used to define the global start time of each delivery task, for any Established:

[0118] (17)

[0119] in, For the task global start time, Represents the number of AMRs, and the set The cardinality is the same, and the condition is the same. This expression defines a global start time for all tasks after the initial tasks are performed by each AMR. This formula maps the start times scattered across each AMR and each charging cycle to a unified task-level start time, facilitating the subsequent application of process sequence constraints.

[0120] Equation (18) is used to apply global order constraints to delivery tasks, for any Established:

[0121] (18)

[0122] This constraint requires the task The start time is no later than that of its successor task. The start time is determined to ensure that tasks are executed in numerical order at the task level, reflecting the sequential requirements of the process flow.

[0123] Equations (19)-(21) are used to give the initial configuration of the first batch of tasks at the start of scheduling, for any Established:

[0124] (19)

[0125] (20)

[0126] (twenty one),

[0127] Equation (19) indicates that in the initial charging cycle Below, numbered The AMR starts executing from time 0, numbered as The start time of the first task, i.e. the first batch of tasks, is 0.

[0128] Equation (20) represents the task within the initial cycle. It must be composed of the same number Execution is performed to achieve a fixed allocation of the first batch of tasks to AMRs in a one-to-one correspondence.

[0129] Equation (21) indicates that the start time of these first batch of tasks is also 0.

[0130] Equations (19)-(21) clarify the initial task and vehicle matching relationship and its start time at the beginning of scheduling, providing a unified benchmark for the time recursion and sequence constraints of subsequent tasks.

[0131] Equations (22)-(25) are linearized forms of the nonlinear constraint equation (4) for the wireless charging quantity during the loading phase. Established:

[0132] (twenty two),

[0133] (twenty three),

[0134] (twenty four),

[0135] (25),

[0136] Introducing 0-1 auxiliary variables :when During the loading phase, the amount of wireless charging is... From theoretical rechargeable capacity Decide, express linearization; when During the loading phase, the wireless charging amount is determined by the remaining available battery capacity. Decision. Equations (22) and (23) respectively limit the wireless charging amount during the loading phase to no more than the upper limit of the remaining usable capacity of the battery and the theoretical rechargeable amount. Equations (24) and (25) are combined A corresponding lower bound is given so that the wireless charging amount during the loading stage is locked to the smaller of the two values ​​under both conditions. By using equations (22)-(25), while maintaining equivalence with the original nonlinear constraint equation (4), the nonlinear relationship of "taking the minimum value" is transformed into a set of linear inequalities, so that the overall model maintains the mixed integer linear programming form, which is convenient for effective solution using the existing MILP solver.

[0137] (26)

[0138] Equations (26)-(29) are linearized forms of the nonlinear constraint equation (5) on the wireless charging quantity during the unloading phase. For any Established:

[0139] (27)

[0140] (28)

[0141] (29)

[0142] Introducing 0-1 auxiliary variables :when During the unloading phase, the wireless charging capacity is determined by the theoretical rechargeable capacity; when During the unloading phase, the wireless charging amount is determined by the battery's remaining usable capacity after deducting the charging amount during the loading phase and the energy consumption of the task. In the formula, Indicates delivery task The energy consumption parameters. Equations (26) and (27) respectively indicate that the wireless charging amount during the unloading phase cannot exceed the upper limit of the battery's remaining capacity and theoretical rechargeable amount. Equations (28) and (29) combine auxiliary variables. The corresponding lower bound is given so that the wireless charging amount during the unloading stage is locked to the smaller of the two values ​​under different values. Similarly, under the premise of maintaining equivalence with the original nonlinear constraint equation (5), equations (26)-(29) transform the nonlinear relationship of "taking the minimum value" into a set of linear inequalities, thereby ensuring that the overall model is still a mixed integer linear programming problem, which is convenient to solve efficiently using the MILP solver. express Linearization.

[0143] Equations (30)-(32) are for equations (17) containing product terms. The linearized form, for any Established:

[0144] (30)

[0145] (31),

[0146] (32),

[0147] Introducing continuous auxiliary variables and a sufficiently large constant Equation (30) guarantees that when hour Compressed to near 0; Equation (31) gives The upper bound does not exceed the corresponding task start time; Equation (32) is passed exist Forced ,exist Relax the lower bound at that time. Equations (30)-(32) indicate that when the task quilt In the When executed after the second charge ( ),have ;otherwise( )have That's how you use it. Linearly replace the original product term This keeps the model in mixed-integer linear programming form, making it easier to solve using the MILP solver.

[0148] Equation (33) is an effective inequality between task allocation and charging operation. For any Established:

[0149] (33),

[0150] This constraint will apply to equation (7) if "if No first The task-by-task logic that "a subsequent charging operation cannot be assigned any tasks after that charging cycle" is aggregated into a variable for assigning tasks to all tasks. Restrictions on the sum: The left side is In the The sum of all tasks assigned after the next charge, with the right-hand side being a constant. With charging decision variables The product of, where, Take a constant that is not less than the maximum number of tasks that can be allocated to the AMR in a single charging cycle. At that time, the right end is 0, thus forcing all subsequent charging cycles to be zero. All are 0; when When the right-hand side is a sufficiently large number, for This does not constitute an additional constraint. Through this efficient inequality in an aggregate form, the coupling between charging decisions and task allocation decisions can be strengthened and linear relaxation can be tightened without changing the feasible region, thereby improving the solution efficiency of the model.

[0151] Equation (34) is a constraint to break symmetry. This equation is an effective inequality constraint for a fixed charging operation sequence, and it applies to any... Established:

[0152] (34),

[0153] Equation (34) requires: If AMR is numbered During the charging cycle, a fixed charging operation is performed (at this time) In the previous charging cycle, It must also be charged at a fixed time (i.e.) Conversely, if in a certain charging cycle Fixed charging was not performed. If this is the case, then a fixed charging operation cannot occur again in subsequent charging cycles with larger numbers (all). (It can only be 0). This monotonicity constraint can eliminate equivalent permutations between different charging numbers, reduce the symmetry of charging decisions, thereby narrowing the feasible solution space and accelerating model solving.

[0154] Equation (35) is an effective inequality constraint for ensuring consistency between the task sequence and the charging cycle sequence. For any Established:

[0155] (35),

[0156] Equation (35) requires: For the same AMR, if the task The number predates the mission. (That is, the process should precede the task) If executed, no task will occur. Allocated to a later charging cycle Up, and the task However, it was assigned to an earlier charging cycle. Above, that is By using this pairwise constraint, charging cycle allocation schemes that clearly violate the task order can be eliminated in advance, strengthening the consistency between task order constraints and charging cycle numbering, thereby tightening the feasible region and improving the model solution efficiency.

[0157] Finally, with Equation (1) as the objective function and Equations (2)-(35) as constraints, a mixed integer linear programming model for collaborative scheduling of wireless charging AMR clusters considering task order constraints is constructed.

[0158] In practical manufacturing systems, when the number of delivery tasks and AMRs is large, directly solving the aforementioned mixed-integer linear programming model is computationally expensive. Therefore, this implementation proposes a fast heuristic scheduling optimization method based on the mathematical model described above.

[0159] Step 2: Design a fast heuristic-based wireless charging AMR cluster scheduling optimization algorithm based on task order constraints.

[0160] 1) Initialize the AMR status and complete the balanced allocation of the first batch of delivery tasks.

[0161] This step, based on the mathematical model established in step 1, performs a unified initialization of the wireless charging AMR cluster and constructs a feasible initial task allocation scheme. Specifically, it initializes the battery power of all AMRs to the upper limit of AMR battery capacity. This means setting the State of Charge (SOC) to full; uniformly setting the available start time of all AMRs to 0, and initializing the charging cycle counter of each AMR to the first charging cycle. Subsequently, while satisfying process sequence constraints, the numbers preceding... Each delivery task was assigned to Each AMR is assigned a delivery task during its initial charging cycle, thereby obtaining a balanced initial task vehicle matching relationship.

[0162] After task allocation, the key states of each AMR after completing its first delivery task are calculated sequentially using the energy balance constraints and start time constraints in step 1. These include the current charging cycle number of the AMR, the earliest start time of the next task, the current SOC level, the cumulative working time, and the amount of electricity obtained through wireless charging during the loading and unloading phases. This forms a set of initial system states that satisfy the power and time constraints, providing a unified starting point for subsequent heuristic iterative allocation of the remaining tasks.

[0163] 2) Task feasibility testing and charging decision-making sub-process based on forward-looking inspection.

[0164] This step determines whether a given delivery task can be directly executed by a designated AMR within the current charging cycle, or requires a pre-emptive full charge operation, taking into account battery capacity and the minimum SOC safety threshold. Specifically, after selecting a task and its candidate AMRs, the maximum amount of electricity that can be obtained through wireless charging during the entire task execution process is predicted based on the AMR's current SOC level, wireless charging speed, wireless power transfer efficiency, and the task's loading and unloading operation time. Combined with the task's energy consumption parameters, the predicted SOC after the task execution is completed is calculated.

[0165] SOC is not lower than the minimum SOC threshold (i.e., not lower than) If the task is deemed feasible within the current charging cycle, it is officially assigned to the AMR: the corresponding task assignment variable is set to 1, and if necessary, a fixed charging operation is recorded during the cycle, and the AMR's SOC, the start time of the next task, the cumulative working time, and the wireless charging amount during the loading and unloading phases are updated accordingly.

[0166] If the State of Charge (SOC) is below the minimum SOC threshold, it is determined that directly executing the task within the current charging cycle is not feasible. A fixed full charge operation needs to be scheduled for the AMR first. In this step, the charging cycle counter of the AMR is incremented by 1, and a fixed-length segment is inserted between two charging cycles. The charging time will restore the AMR's SOC to [value missing]. The system updates the available start time and cumulative working time accordingly; then, in the new charging cycle, it re-examines the feasibility of the task and completes the allocation. Through the above-mentioned forward-looking feasibility check and charging decision mechanism, it is ensured that the allocation of each task will not cause the AMR's SOC to fall below the safety threshold, realizing dynamic linkage between task allocation, wireless opportunistic charging, and fixed full charging.

[0167] 3) Master-heuristic scheduling process based on greedy allocation strategy.

[0168] This step, based on the initialization state and task feasibility detection sub-processes, uses a greedy approach to construct a high-quality, feasible scheduling scheme for all delivery tasks. First, the unscheduled delivery tasks are sorted according to the process sequence, and the tasks to be assigned are selected sequentially. Then, the "most idle" AMR is selected from all AMRs as a candidate executor, for example, the AMR with the shortest cumulative completion time or the earliest available start time, in order to shorten the overall maximum completion time.

[0169] After selecting a candidate AMR, the maximum wireless charging amount it can obtain during the loading and unloading phases of the task is calculated based on its current SOC level and available time, and a candidate state for the "task-AMR-charging cycle" combination is generated. Subsequently, this candidate state, along with the task information, is input into the aforementioned task feasibility detection and charging decision sub-process: if the sub-process determines that it can be executed directly within the current charging cycle, the task is ultimately assigned to the AMR, and its SOC, task start time, charging cycle number, and cumulative operation time are updated; if it determines that fixed charging needs to be inserted, a fixed charging operation is first inserted into the AMR's scheduling sequence, and then the task allocation and state update are completed within the new charging cycle.

[0170] The above method is used to iteratively allocate all unscheduled delivery tasks until all tasks are successfully scheduled. Finally, this step outputs the latest completion time of the last task among all AMRs as the total completion time of the entire delivery process.

[0171] This implementation uses a smart manufacturing workshop as an application scenario to verify and illustrate the proposed wireless charging AMR cluster collaborative scheduling method considering battery capacity constraints. The system sets up three homogeneous AMRs to participate in job scheduling, with each AMR having a battery capacity... Set to 10, minimum safe power ratio The minimum charge level is 0.15, meaning the battery level must not be lower than 1.5. The system includes 30 tasks, with the time and energy consumption of each task randomly generated from a normal distribution. The average task duration is approximately 8 seconds, and the average energy consumption is approximately 1.5. Loading and unloading times are also generated according to a random distribution. Wireless charging efficiency and charging power are set according to system parameters.

[0172] Under this example condition, the basic model, the model with added opportunity charging, the model with added task order constraints, the model with introduced effective inequality reinforcement, and the heuristic algorithm are solved respectively, yielding the following results. Figures 2 to 11 The results are shown.

[0173] Figure 2 This is a Gantt chart for task scheduling under the ASPBC model. Figure 3 To correspond to the SOC change curve, the horizontal axis "Time" in the graph represents time, "CS" represents the charging state, and "MBC" represents the minimum safe charge threshold. This model does not consider charging opportunities during loading and unloading; it only performs fixed full-charge operations when necessary. Figure 2 It can be seen that each AMR must enter a fixed charging phase after its battery level drops to near the threshold, significantly interrupting the operation process. The SOC curve is shown below. Figure 3 The diagram shows a cyclical fluctuation pattern of "decline - concentrated charging - further decline".

[0174] Figure 4 This is a Gantt chart for task scheduling under the WCASPBC model. Figure 5 This corresponds to the SOC change curve. The model allows for opportunistic charging during loading and unloading phases, but it doesn't fully consider the coupling between task sequence and energy evolution. Compared to... Figure 2 The number of fixed charging cycles has decreased, and the SOC curve fluctuations are smoother, but the overall scheduling structure still exhibits some concentrated charging phenomena.

[0175] Figure 6 This is a Gantt chart for task scheduling under the WCASPBSC model. Figure 7 This corresponds to the SOC variation curve. The model, while considering task sequence constraints, allows opportunistic charging to participate in energy balance. It can be observed that the task arrangement is more compact, the number of fixed charging cycles is further reduced, and the overall SOC curve is higher than [previous curve]. Figure 3 and Figure 5 The minimum power level remained above the safety threshold, indicating that the combination of task sequence constraints and opportunistic charging can effectively improve energy utilization efficiency.

[0176] Figure 8 The results of MILP are obtained by adding effective inequalities to the WCASPBSC model. Figure 9 This corresponds to the SOC change curve. (From...) Figure 8 It can be seen that its scheduling structure is similar to... Figure 6 They are basically the same, with the same final completion time or only minor numerical differences. Figure 9 The evolution trend of SOC in China is also related to Figure 7 This demonstrates that the effective inequality does not alter the feasible region and optimal solution structure of the original model. Instead, it significantly improves solution efficiency by tightening linear relaxation and eliminating symmetry. In practical tests, the MILP solution time is significantly shortened after introducing the effective inequality, verifying its role in improving the computational efficiency of the accurate model.

[0177] Figure 10 The scheduling Gantt chart obtained by the heuristic algorithm. Figure 11 This corresponds to the SOC change curve. Figure 8 In comparison, the scheduling structure obtained by the heuristic algorithm differs slightly, with some tasks assigned in a different order. Therefore, the final Makespan solution differs slightly from the optimal solution of MILP. However, the overall structure shows that its job arrangement and charging logic remain reasonable, and the SOC always meets the power safety constraint, without falling below the threshold. At the same time, the computation time of the heuristic algorithm is much shorter than that of the MILP model, especially for medium-to-large-scale problems, where it can obtain high-quality feasible solutions in a very short time.

[0178] comprehensive Figures 2 to 11 visible:

[0179] By introducing the opportunistic charging mechanism, AMR can utilize loading and unloading dwell time to replenish energy during task execution, significantly reducing the number of fixed full charging cycles and improving job continuity. Adding an effective inequality to the MILP model does not change the optimal solution, but effectively compresses the search space, significantly improving solution efficiency and making it suitable for accurate solutions of small to medium-sized instances.

[0180] Heuristic algorithms can quickly obtain scheduling schemes that are close to the optimal solution of MILP while maintaining the feasibility of power constraints and task order constraints. Although there are differences in the ordering of individual tasks, the final completion time deviation is small, and the computation speed advantage is significant. It is suitable for medium-to-large-scale or rolling scheduling scenarios.

[0181] Therefore, this implementation method achieves a balance between optimality and high efficiency under different scale problems through the dual mechanisms of "exact model with effective inequality reinforcement" and "fast heuristic algorithm". It ensures the availability of the theoretical optimal solution of the model and meets the real-time requirements of practical engineering applications.

[0182] In summary, this implementation method addresses efficient material scheduling in green and intelligent manufacturing plants, proposing a collaborative scheduling modeling and optimization method for wireless charging AMR clusters under the constraints of battery capacity, minimum SOC safety threshold, and task sequence. By implementing WPT opportunistic charging during the loading and unloading dwell phases and linking it with fixed-duration full charging within the station, task assignment, task sequencing, and charging timing are uniformly optimized to minimize the total completion time while satisfying energy dynamics and sequential feasibility. To this end, a computable Mixed Integer Linear Program (MILP) model is established to equivalently linearize the nonlinear processes of energy balance and charging, supplemented by effective inequalities. A rapid heuristic is also provided to support large-scale and rolling engineering applications, achieving efficient collaboration between AMR operations and charging planning.

[0183] Specific Implementation Method Two: The wireless charging AMR cluster collaborative scheduling device considering task order constraints described in this implementation method includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the wireless charging AMR cluster collaborative scheduling method considering task order constraints as described in Specific Implementation Method One.

[0184] Specific Implementation Method 3: A computer storage medium as described in this embodiment stores at least one instruction, which is loaded and executed by a processor to implement the wireless charging AMR cluster cooperative scheduling method considering task order constraints as described in Specific Implementation Method 1.

[0185] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A wireless charging AMR cluster cooperative scheduling method considering task order constraints, characterized in that, include: Candidate AMRs are selected for the current task to be assigned. Based on the current state of charge of the candidate AMRs, wireless charging speed, wireless power transfer efficiency, and loading and unloading time of the current task to be assigned, the maximum amount of electricity that the candidate AMRs can obtain through wireless charging during the execution of the current task to be assigned, and the predicted state of charge of the candidate AMRs after the execution of the current task to be assigned are calculated. If the predicted state of charge is greater than or equal to the minimum state of charge safety threshold, the current task to be assigned is assigned to the candidate AMR; otherwise, a charging operation is inserted into the candidate AMR to restore its state of charge to full charge, and then the current task to be assigned is assigned to the candidate AMR.

2. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 1, characterized in that, The wireless charging AMR cluster collaborative scheduling method is implemented based on the wireless charging AMR cluster collaborative scheduling model. The objective of the wireless charging AMR cluster collaborative scheduling model is to minimize the maximum operation completion time of the wireless charging AMR.

3. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 2, characterized in that, The constraints of the wireless charging AMR cluster cooperative scheduling model include: The amount of wireless charging during both the loading and unloading phases is less than the smaller of the theoretical chargeable amount and the remaining usable battery capacity. The energy conservation between two adjacent tasks within the same charging cycle of the same AMR; The battery level of any AMR after completing any delivery task is greater than or equal to the minimum safe battery level. The battery level of any AMR before executing the first task in any charging cycle is equal to the larger of the two values: the remaining battery level after executing the last task in the previous charging cycle, and the full battery level if a fixed charging operation is performed in the current cycle. The charge level of any AMR in each task and each charging cycle is greater than the safe charge level corresponding to the minimum state of charge, and does not exceed the upper limit of battery capacity. If the AMR performs a task within the same charging cycle Then the start time of the next task is equal to the start time of the task. The start time plus its operation duration; if the AMR does not perform the task. Then the start time of the next task is equal to the start time of the task. The start time; After completing a task within a certain charging cycle, if the AMR performs a fixed charging operation before entering the next charging cycle, the start time of the first task in the next charging cycle is equal to the start time of the previous task plus its operation time and the fixed charging time; if a fixed charging is not performed, the difference between the two is the task operation time. The start time of any task is earlier than or equal to the start time of its successor task. For the same AMR, if one task is numbered earlier than another, the charging cycle of the task with the earlier number is earlier than the charging cycle of the task with the later number.

4. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 3, characterized in that, The constraint conditions of the wireless charging AMR cluster cooperative scheduling model are expressed as follows: ， ， ， ， ， ， ， ， ， ， in, Represents a set of tasks. Represents the AMR set, This represents the set of times the AMR is charged at a charging station. Indicates the total number of delivery tasks; Indicates the first AMR After completing the first Delivery will commence after the first charging operation. At that time, during the mission The actual amount of electricity obtained through wireless charging during the loading phase; This indicates the charging speed of the wireless charging device at the loading station; Indicates wireless power transmission efficiency; express Execute the task Loading operation time; for In the Should the delivery task be executed after the second charging operation? The decision variable is 1 if it is true, and 0 otherwise; Indicates the upper limit of AMR battery capacity; express In the After the first charging operation, the task begins. Current battery level; express After completing the first Delivery will commence after the first charging operation. At that time, during the mission The actual amount of electricity obtained through wireless charging during the unloading phase; express Execute the task Unloading operation time; Indicates task The amount of electricity consumed during the entire execution process; This represents the minimum SOC (State of Charge) threshold coefficient. for Does the charging station perform the first step? The decision variable for the next fixed charging operation is 1 if it is true and 0 otherwise. express In the The task will be executed after the next charging operation. The start time; Indicates delivery task The duration of the assignment; This indicates the charging time required for each full charge at a charging station. For the task The global start time.

5. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 1, 2, 3 or 4, characterized in that, The step of selecting candidate AMRs for the currently assigned task includes: The AMR with the shortest cumulative completion time or the earliest available start time among all AMRs is selected as the candidate AMR.

6. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 2, 3, or 4, characterized in that, The objective function of the wireless charging AMR cluster cooperative scheduling model The expression is: ， in, This is the maximum operation completion time for AMR.

7. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 6, characterized in that, The maximum operation completion time of the AMR The following constraints must be satisfied: ， in, Represents a set of tasks; This represents the set of times the AMR is charged at the charging station; Indicates delivery task The duration of the assignment; for In the Should the delivery task be executed after the second charging operation? The decision variable is 1 if it is true, and 0 otherwise; This indicates the charging time required for each full charge at a charging station. for Does the charging station perform the first step? The decision variable for the next fixed charging operation is 1 if it is true and 0 otherwise.

8. The wireless charging AMR cluster cooperative scheduling method considering task order constraints according to claim 1, 2, 3 or 4, characterized in that, Initialization is performed before the coordinated scheduling of the wireless charging AMR cluster, and the initialization includes: Based on the aforementioned wireless charging AMR cluster collaborative scheduling model and its constraints, a task set is constructed. Set the initial state of charge of all AMRs to full, the start time to 0, and the initial charging cycle number to 1.

9. A wireless charging AMR cluster collaborative scheduling device considering task sequence constraints, characterized in that, The wireless charging AMR cluster collaborative scheduling device considering task order constraints includes a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the wireless charging AMR cluster collaborative scheduling method considering task order constraints as described in any one of claims 1 to 8.

10. A computer storage medium, characterized in that, The computer storage medium stores at least one instruction, which is loaded and executed by a processor to implement the wireless charging AMR cluster cooperative scheduling method considering task order constraints as described in any one of claims 1 to 8.

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