Unmanned aerial vehicle distribution method for auxiliary charging of bus

Abstract

The invention discloses an unmanned aerial vehicle distribution method for bus auxiliary charging so as to improve the distribution efficiency and reduce the cost. The method comprises the following steps: firstly, setting system parameters, acquiring information of a warehouse, a customer and a bus stop, and determining performance parameters of a bus and an unmanned aerial vehicle as well as customer distribution requirements; secondly, an unmanned aerial vehicle distribution mechanism of bus auxiliary charging is analyzed, and a collaborative process and operation limiting conditions between the unmanned aerial vehicle and the bus are determined; then, an optimization model containing a target function and various constraints (such as path, electric quantity, time and resource limitation) is constructed, and the purpose is to minimize the total delivery time; and then, by solving the model, generating an optimal distribution path, determining arrival and departure moments and charging lines of the unmanned aerial vehicle at each node, and ensuring that the task is completed on time and the electric quantity is efficiently utilized. And finally, the unmanned aerial vehicle electric quantity index is analyzed based on a distribution path result, and a basis is provided for further scheme optimization, so that continuous improvement of the unmanned aerial vehicle distribution system is realized, and the overall operation efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of public transportation and drone collaborative transportation technology, specifically relating to a drone delivery method for auxiliary charging of buses. Background Technology

[0002] Last-mile delivery is a crucial link in logistics. Traditional last-mile transportation methods incur high operating costs, leading to the development of drone delivery technology. Drones offer numerous advantages, including high efficiency, low cost, and strong accessibility, significantly improving the user experience and demonstrating broad application prospects in logistics.

[0003] However, current drones suffer from limited flight endurance and payload capacity, restricting their service range and failing to meet the large-scale delivery needs of urban networks. Therefore, some scholars have proposed a new technology: a truck-drone collaborative delivery method. Trucks can not only receive and launch drones but also replenish their cargo and power, thus expanding the drone's service range. While drones are typically unaffected by ground traffic, in urban logistics systems, they are still constrained by truck traffic, preventing them from fully realizing their advantages. Furthermore, restrictions on truck access in some areas limit the service range of drones in urban delivery.

[0004] The collaborative transportation of public transportation and drones can effectively solve the problems brought about by truck-drone collaborative delivery within urban areas. On the one hand, public transportation has a wider coverage network and usually operates on public transport-priority roads, making it less affected by ground traffic congestion. On the other hand, as an existing urban facility, public transportation does not require additional operating costs, is less susceptible to external interference, and is more reliable in terms of operating hours. Therefore, using public transportation to transport and refuel drones better meets the actual needs of urban logistics transportation. In-depth research on the collaborative transportation of public transportation and drones is of great significance to the future development of the drone transportation industry. Summary of the Invention

[0005] To address the technical problems existing in the background art, this invention aims to provide a drone delivery method with auxiliary charging on buses, effectively expanding the service range of drone delivery and improving last-mile delivery efficiency. By utilizing the extensive network of the public transportation system, drones are transferred to locations closer to delivery points, while simultaneously charging on buses. This fully utilizes existing urban public transportation resources, achieving synergy between drones and buses, optimizing urban transportation resource allocation, reducing traffic congestion, and improving delivery range and efficiency.

[0006] To solve the technical problem, the technical solution of the present invention is as follows:

[0007] A method for drone delivery with auxiliary charging for buses, the method comprising:

[0008] S1: Parameter settings, obtain information on warehouses, customers and bus stops, and determine the performance parameters of buses and drones, as well as customer delivery needs;

[0009] S2: The mechanism of drone delivery for auxiliary charging of buses: Analyze the collaborative mechanism between buses and drones, determine the collaborative process and operational constraints between drones and buses, ensure that drones can accurately match the bus timetable and charge, and provide conditions for subsequent route planning.

[0010] S3: Optimization model construction. Based on the data obtained in steps S1 and S2, an optimization model is constructed that includes an objective function and various constraints. The objective is to minimize the total delivery time. The constraints include drone path, drone and bus spatiotemporal matching constraints, drone time constraints, drone power constraints, and drone and bus resource constraints.

[0011] S4: Path solving and analysis: By solving the optimization model, the optimal delivery path, charging nodes and times of the drone are obtained to ensure that the delivery task is completed on time and the power is used efficiently.

[0012] Furthermore, after step S5, the method further includes:

[0013] S5: Results Analysis and Optimization: After solving the optimization model and generating the delivery plan, analyze the delivery time and power utilization indicators, optimize the plan, and further improve the overall efficiency of the delivery system.

[0014] Furthermore, step S1 includes:

[0015] Input the following information: the structure of the delivery system, including warehouse location, customer location, distance between bus stops and nodes; bus operation information, including stop timetables, frequency and routes, and capacity; drone performance parameters, including payload capacity, battery capacity, speed and power consumption; and delivery demand information, including customer demand, latest service time and service duration. Then, perform data processing and standardization, structural modeling and path arc set construction, and output a unified data structure for each node and parameter, the constructed path arc set, the established candidate path graph and attribute matrix, and the determined set of all variables.

[0016] Furthermore, step S2 includes:

[0017] Based on the output of step S1, each bus stop is divided into multiple time nodes to form a spatiotemporal network. The impact of the bus operation mechanism on the charging behavior of the drone is analyzed: the boarding time is limited by the departure time, the station hovering time determines the additional power consumption and the charging capacity limit of each bus route. Then, the coordination conditions between the drone and the bus are determined, and the spatiotemporal node mapping table, bus route map and corresponding charging capacity, charging capacity limit matrix and the formula of the hovering and boarding time synchronization mechanism are output.

[0018] Furthermore, step S3 specifically includes:

[0019] The parameters, constraints, and model information obtained in steps S1 and S2 are used, including the performance data of the drone, the operation information of the bus, the delivery demand, and the spatiotemporal matching conditions.

[0020] Then, establish the objective function that minimizes the total travel time;

[0021] This model establishes an objective function that minimizes the total travel time. For the k-th drone in warehouse w, the objective function is measured by calculating the time difference between the drone's departure from the warehouse and its return.

[0022]

[0023] ∑w∈W represents the summation over all warehouses w, K w Refers to the collection of drones dispatched from warehouse w. This indicates the arrival time of drone k in warehouse w. This indicates the takeoff time of drone k in warehouse w;

[0024] And construct constraints in 5 categories:

[0025] Drone path constraints;

[0026] Constraint (2) ensures that each drone performs at most one delivery mission:

[0027]

[0028] x wjk The binary variable is set to 1 when drone k passes through the arc between nodes w∈N and j∈N; otherwise, it is 0. N represents the set of nodes, N=W∪C∪S={0,1,...,n}.

[0029] Constraint (3) stipulates that drones may only depart from their designated warehouses:

[0030]

[0031] x ijkThis indicates that when drone k passes through the arc between nodes i∈N and j∈N, the binary variable equals 1;

[0032] Otherwise, the variable is 0;

[0033] The flow conservation at each node is guaranteed by constraint (4):

[0034]

[0035] The part on the left of the equals sign represents the number of paths that drone k takes from node i to all nodes j; the part on the right of the equals sign represents the number of paths that drone k takes from node j to all nodes i, also using binary transformation.

[0036] Constraint (5) ensures that each customer can be served at most and only once:

[0037]

[0038] Spatiotemporal matching constraints between drones and buses;

[0039] To enable drones to be charged while buses are in motion, it is necessary to ensure spatiotemporal matching between buses and drones. Each bus stop is decomposed into discrete time nodes corresponding to the departure time of each bus trip, thus generating a spatiotemporal network. Each discrete time point corresponds to a bus trip. This spatiotemporal network system not only allows drones to choose from different bus routes, but also allows drones to visit the same bus stop multiple times, thus achieving matching between drones and bus timetables.

[0040] Constraint (6) Ensure that the drone arrives at the station before the bus departs:

[0041]

[0042] T represents the time when drone k arrives at node j. j Let M represent the departure time of the bus at bus stop j, where M is a very large constant.

[0043] Constraints (7) and (8) ensure that the drone arrives at the station earlier than the bus departure time to guarantee that it can board the bus:

[0044]

[0045] T represents the takeoff time of drone k from node j. j The departure time of the bus from bus stop j;

[0046] When the drone arrives at the station before the bus, it must hover at the station until the bus arrives; constraints (9) and (10) record the hovering time of the drone at the station;

[0047]

[0048] h jk This represents the hovering time of drone k at bus stop j;

[0049] In addition, to align with the actual operation mechanism of buses, constraints (11)-(15) specify the timing for drones to board buses, with constraint (11) ensuring that drones must travel a certain distance on the bus after boarding:

[0050]

[0051] x jj″k Let x be a binary decision variable representing whether drone k travels from node j to node j″. In this constraint, j″ typically implies the next node the drone should reach after node j. If the path from j to j″ is chosen, x jj″k =1; otherwise 0;

[0052] Constraint (12) ensures flow conservation at intermediate stations:

[0053]

[0054] x j′jk X is a binary decision variable representing whether the path from node j′ to node j of drone k is selected. If this path is selected, then X... j′jk =1, otherwise 0;

[0055] Constraint (13) requires all drones to leave the bus at the terminal station, where j′ and j represent the predecessor and successor stations of the current station, respectively:

[0056]

[0057] Constraint (14) ensures that buses pass through each bus stop in sequence and are not allowed to run across stops:

[0058]

[0059] Constraint (15) prohibits drones from using buses as transfer points:

[0060]

[0061] Drone time constraints;

[0062] Constraints (16) and (17) record the arrival times of the drone at each node. Here, the arrival times of the drone when taking the bus are not considered because the arrival times of the drone at the station are synchronized with the bus timetable.

[0063]

[0064] dis ij This represents the distance between nodes i and j;

[0065] Constraints (18) and (19) record the time it takes for the drone to reach the next node after leaving the bus:

[0066]

[0067] Constraints (20) and (21) ensure that the drone leaves immediately after completing the delivery service at the customer's location:

[0068]

[0069] Constraint (22) ensures that the drone arrives before the latest start time of service at the customer's location:

[0070]

[0071] Constraint (23) clarifies the time relationship between the drone's departure from and return to the warehouse, ensuring that the drone's departure time from the warehouse is no later than its return time:

[0072]

[0073] Drone power constraints;

[0074] Constraints (24) and (25) are used to update the remaining battery power of the drone when it arrives at the next node after departing from the warehouse or customer:

[0075]

[0076] b ik b represents the battery level of drone k at node i. jk γ represents the remaining battery power of drone k at node j; γ represents the power consumption rate of the drone.

[0077] Constraints (26) and (27) determine the remaining battery power of the drone when it arrives at the bus stop to board the bus, and additionally consider the battery power required for the drone to hover while waiting for the bus to arrive:

[0078]

[0079] Constraints (28) and (29) describe the charging process of the drone on the bus and update the remaining battery power of the drone:

[0080]

[0081] b j″k q represents the battery level of drone k when it reaches node j″; jj″ This represents the amount of charge the drone receives along its path from node j to node j″.

[0082] Constraints (30) and (31) calculate the remaining battery power of the drone when it leaves the bus stop and arrives at the next node:

[0083]

[0084] V represents the drone's flight speed;

[0085] Constraint (32) ensures that the drone's remaining battery power is sufficient to support its return to the warehouse:

[0086]

[0087] C represents the set of customer points;

[0088] Resource constraints of drones and buses;

[0089] Constraint (33) ensures that each drone is fully charged when it leaves the warehouse:

[0090]

[0091] E indicates battery capacity;

[0092] Constraint (34) stipulates that the power of the drone must not exceed its maximum battery capacity:

[0093]

[0094] Constraint (35) ensures that the charging amount of the drone does not exceed the maximum allowable charging amount for the bus route:

[0095]

[0096] Constraint (36) ensures that the total weight of packages carried by the drone does not exceed its maximum payload capacity:

[0097]

[0098] Constraint (37) ensures that the number of drones carried on a bus at the same time does not exceed its capacity limit G:

[0099]

[0100] Next, the model is validated and adjusted. After establishing the initial optimized model, feasibility and sensitivity analyses are conducted to ensure the model's effectiveness in practical applications. The model's performance under different parameters and constraints is tested to verify its applicability in various delivery scenarios.

[0101] Finally, the code is compiled to transform the mathematical model into a format that can be processed by the optimized solver, laying the foundation for subsequent path solving and scheduling generation.

[0102] Furthermore, step S4 specifically includes: path solving and schedule generation.

[0103] 1. Input:

[0104] The input optimization model includes the objective function, constraints, and set of variables, which are constructed in step S3.

[0105] Prepare all necessary parameter data, such as drone performance, bus timetables, charging limitations, and customer requirements.

[0106] 2. Solve the optimization model:

[0107] Choose a solution method:

[0108] Use a solver suitable for mixed integer linear programming (MILP) problems (such as CPLEX, Gurobi, or GLPK).

[0109] Alternatively, heuristic algorithms (such as genetic algorithms, ant colony algorithms, etc.) can be used to handle large-scale problems.

[0110] Model solution:

[0111] The input data and model are passed to the solver, the solution process is executed, and the solver's output is compared with the optimization objective.

[0112] The solution process should consider various boundary conditions and constraints to ensure that the obtained solution satisfies all constraints.

[0113] 3. Generate delivery plan:

[0114] Extracting the optimal solution:

[0115] Collect the solver's output, including the drone's optimal delivery route, arrival and departure times at each node, charging time, and charging node.

[0116] The specific generation of paths and schedules:

[0117] Define the specific delivery route for each drone and record its location in warehouses, at customers, and at bus stops.

[0118] Based on the scheduling results, the start and end times, charging node selection, and charging time for each drone are generated.

[0119] 4. Verification of power and capacity:

[0120] Check battery status:

[0121] After the route is generated, the remaining battery power of each drone during the mission is verified to ensure that it is sufficient to complete the delivery and return to the warehouse.

[0122] Ensure that the selection of charging nodes can meet the actual power requirements of drones, and avoid insufficient power during delivery.

[0123] 5. Output results:

[0124] Output the final scheduling scheme:

[0125] This includes the specific delivery route for each drone, the corresponding charging nodes and times, and the arrival and departure times of each node.

[0126] The output should also include records of power changes for subsequent analysis and monitoring.

[0127] Generate a scheduling report:

[0128] Compile scheduling reports that include detailed information on delivery efficiency, charging strategies, and time arrangements, providing a foundation for subsequent results analysis and feedback optimization.

[0129] 6. Next steps:

[0130] The generated scheduling scheme was combined with actual operations and tested to verify the effectiveness and applicability of the model.

[0131] Data is collected based on actual operation to facilitate adjustments and improvements during subsequent execution and optimization.

[0132] Through these specific steps, step S4 clearly describes the complete process from solving the optimization model to generating the actual delivery route and schedule, ensuring that delivery tasks can be completed on time and efficiently.

[0133] Furthermore, step S5 specifically includes:

[0134] Delivery time analysis assesses the delivery path of each drone and the arrival / departure time of each node, analyzes whether the total delivery time has reached the optimization target, and confirms whether there are delivery delays or unnecessary time waste.

[0135] The power utilization rate assessment analyzes the drone's power consumption, checks battery efficiency and bus utilization, evaluates whether the drone's service radius can be effectively extended and whether bus utilization can be maximized to improve service efficiency, and ensures that the drone is charged at reasonable bus times and locations each time.

[0136] Performance metrics comparison: Compare key performance metrics under different solutions, and select the optimal solution for further optimization;

[0137] Solution optimization involves adjusting and optimizing the drone's path planning, bus stop selection, and scheduling strategies based on the results analysis, in order to improve system efficiency under different constraints.

[0138] Feedback adjustments are made based on the gap between actual results and expected goals, adjusting parameters or constraints in the model to continuously improve the overall efficiency of the delivery system, reduce costs, and improve service quality.

[0139] Compared with the prior art, the advantages of the present invention are as follows:

[0140] This invention constructs a comprehensive optimization model that systematically considers multiple constraints such as bus operating timetables, bus-assisted drone charging, customer time windows, and drone hovering, to achieve collaborative optimization of multi-dimensional factors.

[0141] This invention optimizes the model design, enabling drones to repeatedly visit the same bus stop, effectively solving the time coordination problem between multiple bus services and multiple drone arrivals, and achieving precise spatiotemporal matching between drones and bus schedules. Attached Figure Description

[0142] Figure 1 A schematic diagram of the solution results for the case. Detailed Implementation

[0143] The specific implementation of the present invention is described below with reference to embodiments:

[0144] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0145] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0146] Example 1:

[0147] This invention addresses the problems of low efficiency and high cost in last-mile delivery, as well as the limited service range of drones due to battery capacity limitations. It proposes a drone-based last-mile delivery method using auxiliary charging on public buses. This method deeply integrates drones with the existing public bus network, fully utilizing the wide coverage and high efficiency of the public bus system to effectively avoid traffic congestion, reduce infrastructure investment costs, and significantly improve delivery efficiency.

[0148] In this invention, to effectively adapt to multiple operating schedules on bus routes, a novel repeated-visit mechanism for bus stops is introduced. This mechanism decomposes each bus stop into multiple discrete time nodes according to the departure times of different bus routes. A time network is constructed based on the bus stop timetable, allowing the same stop to be visited multiple times, thus achieving efficient reuse of the public transportation system by drones. By allowing drones to repeatedly visit bus stops, the system's scheduling flexibility and resource utilization are significantly improved. This mechanism overcomes the limitation of traditional path planning where each node can only be visited once, making it particularly suitable for urban environments with dense public transportation networks but scarce charging facilities.

[0149] This invention proposes a novel research framework for collaborative delivery between public transportation and drones, and constructs an optimization model for drone last-mile delivery based on bus-assisted charging. This model introduces the bus system as a mobile charging platform on the basis of traditional drone path planning, and comprehensively considers multiple dimensions such as public transportation timetable, customer time window, the function of vehicles to charge drones, drone waiting energy consumption, and repeated station visits, so as to achieve efficient collaboration between drones and public transportation systems and significantly improve last-mile delivery efficiency.

[0150] The specific technical solution is as follows:

[0151] S1. Parameter Settings. Obtain information on each node in the delivery system, including multiple warehouses, customers, and bus schedules. Define customer needs, latest service start time, service duration, and bus timetable; record the coordinates of each node to determine the distance between nodes; obtain the drone's payload capacity, battery capacity, flight speed, power consumption rate, and the bus's ability to carry drones.

[0152] S2. Analysis of the Working Characteristics of Bus-Assisted Drone Charging. To address the issues of short drone range and high construction costs of dedicated urban charging facilities, this invention proposes a technology that utilizes buses to assist drone charging. When a drone lands in a bus charging area, the bus replenishes its power. In this process, the coupling mechanism between parameters such as bus schedules, charging efficiency, and the capacity of buses to carry drones was thoroughly investigated to ensure that the proposed bus-assisted charging scheme meets practical requirements.

[0153] S3. Construction of an optimization model for drone last-mile delivery based on bus-assisted charging. Based on the information obtained in S1 and S2, an optimization model for the path planning and charging problem of bus-assisted drones is established:

[0154] (1) Define the specific parameters and decision variables;

[0155] (2) Establish an objective function that minimizes the total travel time, and calculate it by the time difference between the drone's departure from the warehouse and its return.

[0156] (3) Construct five types of constraints: UAV path constraints; UAV and bus spatiotemporal matching constraints; UAV time constraints; UAV power constraints; UAV and bus resource constraints.

[0157] In step S1 parameter settings;

[0158] In the scenario of optimizing the last-mile delivery route for drones used for auxiliary charging of buses, it is necessary to acquire and process diverse information. The spatiotemporal matching between the drone and the bus is the core feature of this scenario. The drone needs to accurately match the arrival time of the bus to complete operations such as landing, takeoff, hovering, and charging, which places strict requirements on the setting of relevant parameters.

[0159] Specific parameters include the drone's payload capacity, battery capacity, flight speed, and power consumption rate. In addition, it involves basic information about the delivery system, covering the geographical locations of warehouses, customer points, and bus stops, as well as bus schedules at each stop.

[0160] In step S2, the analysis of the charging characteristics of the bus-assisted drone:

[0161] Buses have limited capacity to carry drones and follow fixed operating schedules, which means that drones must board or disembark at specific stops and complete charging within a specific time. This places higher demands on drone path planning.

[0162] In traditional models, the collaboration between drones and buses is mostly limited to route matching, failing to fully explore the deeper impact of bus capacity and operating schedules on drone route planning. Therefore, it is necessary to optimize the collaborative scheduling strategy between drones and buses by deeply considering the operational mechanisms and actual limitations of the bus system, adjusting the charging timing of drones to meet actual delivery needs, reduce the number of drones deployed, and lower overall operating costs.

[0163] In step S3, the construction of the drone delivery optimization model based on bus auxiliary charging is as follows:

[0164] To ensure the model's rationality, the following assumptions are made based on actual needs:

[0165] a. Considering multiple warehouses, and that the warehouses can meet the total customer demand, the drone must return to the original departure warehouse after completing the mission;

[0166] b. All drones are of the same type, with identical performance parameters such as shape, capacity, flight speed, power consumption, and charging rate;

[0167] c. The power consumption rate and charging rate are constant and have a linear relationship with time;

[0168] d. Bus routes are one-way, and drones can only get on and off at bus stops.

[0169] (1) Define the set, parameters, and decision variables;

[0170] The symbol definitions required in this application are shown in Table 1.

[0171] Table 1. Symbol Explanation

[0172]

[0173]

[0174] (2) Establish the objective function that minimizes the total travel time;

[0175] This model establishes an objective function that minimizes the total travel time. For the k-th drone in warehouse w, the objective function is measured by calculating the time difference between the drone's departure from the warehouse and its return.

[0176]

[0177] ∑w∈W represents the summation over all warehouses w, K w Refers to the collection of drones dispatched from warehouse w. This indicates the arrival time of drone k in warehouse w. This indicates the takeoff time of drone k in warehouse w;

[0178] And construct constraints in 5 categories:

[0179] Drone path constraints;

[0180] Constraint (2) ensures that each drone performs at most one delivery mission:

[0181]

[0182] x wjk The binary variable is set to 1 when drone k passes through the arc between nodes w∈N and j∈N; otherwise, it is 0. N represents the set of nodes, N=W∪C∪S={0,1,...,n}.

[0183] Constraint (3) stipulates that drones may only depart from their designated warehouses:

[0184]

[0185] x ijk This indicates that when drone k passes through the arc between nodes i∈N and j∈N, the binary variable equals 1;

[0186] Otherwise, the variable is 0;

[0187] The flow conservation at each node is guaranteed by constraint (4):

[0188]

[0189] The part on the left of the equals sign represents the number of paths that drone k takes from node i to all nodes j; the part on the right of the equals sign represents the number of paths that drone k takes from node j to all nodes i, also using binary transformation.

[0190] Constraint (5) ensures that each customer can be served at most and only once:

[0191]

[0192] Spatiotemporal matching constraints between drones and buses;

[0193] To enable drones to be charged while buses are in motion, it is necessary to ensure spatiotemporal matching between buses and drones. Each bus stop is decomposed into discrete time nodes corresponding to the departure time of each bus trip, thus generating a spatiotemporal network. Each discrete time point corresponds to a bus trip. This spatiotemporal network system not only allows drones to choose from different bus routes, but also allows drones to visit the same bus stop multiple times, thus achieving matching between drones and bus timetables.

[0194] Constraint (6) Ensure that the drone arrives at the station before the bus departs:

[0195]

[0196] T represents the time when drone k arrives at node j. j Let M represent the departure time of the bus at bus stop j, where M is a very large constant.

[0197] Constraints (7) and (8) ensure that the drone arrives at the station earlier than the bus departure time to guarantee that it can board the bus:

[0198]

[0199] T represents the takeoff time of drone k from node j. j The departure time of the bus from bus stop j;

[0200] When the drone arrives at the station before the bus, it must hover at the station until the bus arrives; constraints (9) and (10) record the hovering time of the drone at the station;

[0201]

[0202] h jk This represents the hovering time of drone k at bus stop j;

[0203] In addition, to align with the actual operation mechanism of buses, constraints (11)-(15) specify the timing for drones to board buses, with constraint (11) ensuring that drones must travel a certain distance on the bus after boarding:

[0204]

[0205] x jj″k Let x be a binary decision variable representing whether drone k travels from node j to node j″. In this constraint, j″ typically implies the next node the drone should reach after node j. If the path from j to j″ is chosen, x jj″k =1; otherwise 0;

[0206] Constraint (12) ensures flow conservation at intermediate stations:

[0207]

[0208] x j′jk X is a binary decision variable representing whether the path from node j′ to node j of drone k is selected. If this path is selected, then X... j′jk =1, otherwise 0;

[0209] Constraint (13) requires all drones to leave the bus at the terminal station, where j′ and j represent the predecessor and successor stations of the current station, respectively:

[0210]

[0211] Constraint (14) ensures that buses pass through each bus stop in sequence and are not allowed to run across stops:

[0212]

[0213] Constraint (15) prohibits drones from using buses as transfer points:

[0214]

[0215] Drone time constraints;

[0216] Constraints (16) and (17) record the arrival times of the drone at each node. Here, the arrival times of the drone when taking the bus are not considered because the arrival times of the drone at the station are synchronized with the bus timetable.

[0217]

[0218] dis ij This represents the distance between nodes i and j;

[0219] Constraints (18) and (19) record the time it takes for the drone to reach the next node after leaving the bus:

[0220]

[0221] Constraints (20) and (21) ensure that the drone leaves immediately after completing the delivery service at the customer's location:

[0222]

[0223] Constraint (22) ensures that the drone arrives before the latest start time of service at the customer's location:

[0224]

[0225] Constraint (23) clarifies the time relationship between the drone's departure from and return to the warehouse, ensuring that the drone's departure time from the warehouse is no later than its return time:

[0226]

[0227] Drone power constraints;

[0228] Constraints (24) and (25) are used to update the remaining battery power of the drone when it arrives at the next node after departing from the warehouse or customer:

[0229]

[0230]

[0231] b ik b represents the battery level of drone k at node i. jk γ represents the remaining battery power of drone k at node j; γ represents the power consumption rate of the drone.

[0232] Constraints (26) and (27) determine the remaining battery power of the drone when it arrives at the bus stop to board the bus, and additionally consider the battery power required for the drone to hover while waiting for the bus to arrive:

[0233]

[0234] Constraints (28) and (29) describe the charging process of the drone on the bus and update the remaining battery power of the drone:

[0235]

[0236] b j″k q represents the battery level of drone k when it reaches node j″; jj″ This represents the amount of charge the drone receives along its path from node j to node j″.

[0237] Constraints (30) and (31) calculate the remaining battery power of the drone when it leaves the bus stop and arrives at the next node:

[0238]

[0239] V represents the drone's flight speed;

[0240] Constraint (32) ensures that the drone's remaining battery power is sufficient to support its return to the warehouse:

[0241]

[0242] C represents the set of customer points;

[0243] Resource constraints of drones and buses;

[0244] Constraint (33) ensures that each drone is fully charged when it leaves the warehouse:

[0245]

[0246] E indicates battery capacity;

[0247] Constraint (34) stipulates that the power of the drone must not exceed its maximum battery capacity:

[0248]

[0249] Constraint (35) ensures that the charging amount of the drone does not exceed the maximum allowable charging amount for the bus route:

[0250]

[0251] Constraint (36) ensures that the total weight of packages carried by the drone does not exceed its maximum payload capacity:

[0252]

[0253] Constraint (37) ensures that the number of drones carried on a bus at the same time does not exceed its capacity limit G:

[0254]

[0255] Example 2:

[0256] To verify the effectiveness of the model and demonstrate the efficiency of the drone-based last-mile delivery method using bus-assisted charging, a specific case was solved. The coordinates and parameters of each node are set as follows: the coordinates of warehouse W1 are (12,16), and the coordinates of W2 are (28,20); the coordinates of customers C1-C5 are (16,8), (4,8), (28,4), (38,3), and (46,20), respectively; the coordinates of bus stops S1-S17 are (0,24), (0,32), (8,32), (16,32), (24,32), (32,32), (40,32), (40,24), (40,16), (40,8), (40,0), (32,0), (24,0), (16,0), (8,0), (0,0), and (0,8). All customers set the latest service start time to 11:00. The demand quantities for customers C1-C5 are 1kg, 4kg, 3kg, 2kg, and 6kg, respectively.

[0257] Further details regarding the parameters related to drones and buses are shown in Table 2:

[0258] Table 2

[0259]

[0260]

[0261] Solving the optimization model for drone last-mile delivery based on bus auxiliary charging, such as... Figure 1 As shown.

[0262] This study used the C# language on the Visual Studio 2022 platform to call the ILOGCPLEX 12.10 software to solve the problem, setting the GAP to 0.00%, and conducted the experiment on a computer running Windows 11 with a 2.11GHz CPU and 16GB of RAM. The solution results are as follows. Figure 1 As shown: Drone K1 departs from warehouse W2, first serving customer C4, then at 8:00 AM it boards the 7:00 AM bus at bus stop S6, disembarks at bus stop S8, continues serving customer C5, and finally returns to warehouse W2. Similarly, drone K2 departs from warehouse W1, first serving customer C1, then at 9:48 AM it boards the 7:00 AM bus at bus stop S15, disembarks at the bus terminal S17, and successively serves customers C2 and C3, finally returning to warehouse W1. In this experiment, the maximum range of the drones was 27 km. However, the results show that drones K1 and K2 flew distances of 50.44 km and 40.27 km respectively. This demonstrates that by taking advantage of public transportation and utilizing its charging capabilities, drones can effectively expand their service range, serving more and farther-reaching customers. It illustrates that the drone last-mile delivery method based on public transportation-assisted charging can effectively extend the service radius of drones, make fuller use of existing resources, enable drones to efficiently serve more customers, effectively reduce the number of drones required, thereby lowering operating costs and significantly improving last-mile delivery efficiency.

[0263] This is understandable. This invention proposes a drone-based last-mile delivery method using bus-assisted charging by introducing a repeated visit mechanism to bus stops. It also constructs an optimization model for drone-based last-mile delivery using bus-assisted charging, effectively addressing the drone endurance problem in urban last-mile delivery scenarios. This technical solution not only significantly expands the service radius of drones but also improves the flexibility of system scheduling and resource utilization efficiency. By integrating the public transportation system as both a mobile and charging platform, it solves the problem of limited delivery capabilities of traditional drones in complex urban environments, providing theoretical support and technical pathways for intelligent logistics systems based on multimodal transport, and contributing to the promotion of low-carbon, efficient, and sustainable urban logistics development.

[0264] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0265] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A method for drone delivery with auxiliary charging for buses, characterized in that, The method includes: S1: Parameter settings, obtain information on warehouses, customers and bus stops, and determine the performance parameters of buses and drones; as well as customer delivery needs; S2: The mechanism of drone delivery for bus auxiliary charging: Analyze the collaborative mechanism between buses and drones, determine the collaborative process and operational constraints between drones and buses, ensure that drones can accurately match the bus timetable and charge, and provide conditions for subsequent route planning. S3: Optimization model construction. Based on the data obtained in steps S1 and S2, an optimization model is constructed that includes an objective function and various constraints. The objective is to minimize the total delivery time. The constraints include drone path, drone-bus spatiotemporal matching constraints, drone time constraints, drone battery constraints, and drone-bus resource constraints. S4: Path solving and analysis: By solving the optimization model, the optimal delivery path, charging nodes and times of the drone are obtained to ensure that the delivery task is completed on time and the power is used efficiently.

2. The method for drone delivery with auxiliary charging for buses according to claim 1, characterized in that, After step S5, the method further includes: S5: Results Analysis and Optimization: After solving the optimization model and generating the delivery plan, analyze the delivery time and power utilization indicators, optimize the plan, and further improve the overall efficiency of the delivery system.

3. The method for drone delivery with auxiliary charging for buses according to claim 1, characterized in that, Step S1 includes: Input the following information: the structure of the delivery system, including warehouse location, customer location, distance between bus stops and nodes; bus operation information, including stop timetables, frequency and routes, and capacity; drone performance parameters, including payload capacity, battery capacity, speed and power consumption; and delivery demand information, including customer demand, latest service time and service duration. Then, perform data processing and standardization, structural modeling and path arc set construction, and output a unified data structure for each node and parameter, the constructed path arc set, the established candidate path graph and attribute matrix, and the determined set of all variables.

4. The method for drone delivery with auxiliary charging for buses according to claim 1, characterized in that, Step S2 includes: Based on the output of step S1, each bus stop is divided into multiple time nodes to form a spatiotemporal network. The impact of the bus operation mechanism on the charging behavior of the drone is analyzed: the boarding time is limited by the departure time, the station hovering time determines the additional power consumption and the charging capacity limit of each bus route. Then, the coordination conditions between the drone and the bus are determined, and the spatiotemporal node mapping table, bus route map and corresponding charging capacity, charging capacity limit matrix and the formula of the hovering and boarding time synchronization mechanism are output.

5. A method for drone delivery with auxiliary charging for buses according to claim 1, characterized in that, Step S3 specifically includes: The parameters, constraints, and model information obtained in steps S1 and S2 are used, including the performance data of the drone, the operation information of the bus, the delivery demand, and the spatiotemporal matching conditions. Then, establish the objective function that minimizes the total travel time; This model establishes an objective function that minimizes the total travel time. For the k-th drone in warehouse w, the objective function is measured by calculating the time difference between the drone's departure from the warehouse and its return. ∑w∈W represents the summation over all warehouses w, K w Refers to the collection of drones dispatched from warehouse w. This indicates the arrival time of drone k in warehouse w. This indicates the takeoff time of drone k in warehouse w; And construct constraints in 5 categories: Drone path constraints; Constraint (2) ensures that each drone performs at most one delivery mission: x wjk The binary variable is set to 1 when drone k passes through the arc between nodes w∈N and j∈N; otherwise, it is 0. N represents the set of nodes, N=W∪C∪S={0,1,...,n}. Constraint (3) stipulates that drones may only depart from their designated warehouses: x ijk This indicates that when drone k passes through the arc between nodes i∈N and j∈N, the binary variable equals 1; Otherwise, the variable is 0; The flow conservation at each node is guaranteed by constraint (4): The part on the left of the equals sign represents the number of paths that drone k takes from node i to all nodes j; the part on the right of the equals sign represents the number of paths that drone k takes from node j to all nodes i, also using binary transformation. Constraint (5) ensures that each customer can be served at most and only once: Spatiotemporal matching constraints between drones and buses; To enable drones to be charged while buses are in motion, it is necessary to ensure spatiotemporal matching between buses and drones. Each bus stop is decomposed into discrete time nodes corresponding to the departure time of each bus trip, thus generating a spatiotemporal network. Each discrete time point corresponds to a bus trip. This spatiotemporal network system not only allows drones to choose from different bus routes, but also allows drones to visit the same bus stop multiple times, thus achieving matching between drones and bus timetables. Constraint (6) Ensure that the drone arrives at the station before the bus departs: T represents the time when drone k arrives at node j. j Let M represent the departure time of the bus at bus stop j, where M is a very large constant. Constraints (7) and (8) ensure that the drone arrives at the station earlier than the bus departure time to guarantee that it can board the bus: T represents the takeoff time of drone k from node j. j The departure time of the bus from bus stop j; When the drone arrives at the station before the bus, it must hover at the station until the bus arrives; constraints (9) and (10) record the hovering time of the drone at the station; h jk This represents the hovering time of drone k at bus stop j; In addition, to align with the actual operation mechanism of buses, constraints (11)-(15) specify the timing for drones to board buses, with constraint (11) ensuring that drones must travel a certain distance on the bus after boarding: x jj″k Let x be a binary decision variable representing whether drone k travels from node j to node j″. In this constraint, j″ typically implies the next node the drone should reach after node j. If the path from j to j″ is chosen, x jj″k =1; otherwise 0; Constraint (12) ensures flow conservation at intermediate stations: x j′jk X is a binary decision variable representing whether the path from node j′ to node j of drone k is selected. If this path is selected, then X... j′jk =1, otherwise 0; Constraint (13) requires all drones to leave the bus at the terminal station, where j′ and j represent the predecessor and successor stations of the current station, respectively: Constraint (14) ensures that buses pass through each bus stop in sequence and are not allowed to run across stops: Constraint (15) prohibits drones from using buses as transfer points: Drone time constraints; Constraints (16) and (17) record the arrival times of the drone at each node. Here, the arrival times of the drone when taking the bus are not considered because the arrival times of the drone at the station are synchronized with the bus timetable. dis ij This represents the distance between nodes i and j; Constraints (18) and (19) record the time it takes for the drone to reach the next node after leaving the bus: Constraints (20) and (21) ensure that the drone leaves immediately after completing the delivery service at the customer's location: Constraint (22) ensures that the drone arrives before the latest start time of service at the customer's location: Constraint (23) clarifies the time relationship between the drone's departure from and return to the warehouse, ensuring that the drone's departure time from the warehouse is no later than its return time: Drone power constraints; Constraints (24) and (25) are used to update the remaining battery power of the drone when it arrives at the next node after departing from the warehouse or customer: b ik b represents the battery level of drone k at node i. jk γ represents the remaining battery power of drone k at node j; γ represents the power consumption rate of the drone. Constraints (26) and (27) determine the remaining battery power of the drone when it arrives at the bus stop to board the bus, and additionally consider the battery power required for the drone to hover while waiting for the bus to arrive: Constraints (28) and (29) describe the charging process of the drone on the bus and update the remaining battery power of the drone: b j″k q represents the battery level of drone k when it reaches node j″; jj″ This represents the amount of charge the drone receives along its path from node j to node j″. Constraints (30) and (31) calculate the remaining battery power of the drone when it leaves the bus stop and arrives at the next node: V represents the drone's flight speed; Constraint (32) ensures that the drone's remaining battery power is sufficient to support its return to the warehouse: C represents the set of customer points; Resource constraints of drones and buses; Constraint (33) ensures that each drone is fully charged when it leaves the warehouse: E indicates battery capacity; Constraint (34) stipulates that the power of the drone must not exceed its maximum battery capacity: Constraint (35) ensures that the charging amount of the drone does not exceed the maximum allowable charging amount for the bus route: Constraint (36) ensures that the total weight of packages carried by the drone does not exceed its maximum payload capacity: Constraint (37) ensures that the number of drones carried on a bus at the same time does not exceed its capacity limit G: Next, the model is validated and adjusted. After establishing the initial optimized model, feasibility and sensitivity analyses are conducted to ensure the model's effectiveness in practical applications. The model's performance under different parameters and constraints is tested to verify its applicability in various delivery scenarios. Finally, the code is compiled to transform the mathematical model into a format that can be processed by the optimized solver, laying the foundation for subsequent path solving and scheduling generation.

6. The method for drone delivery with auxiliary charging for buses according to claim 1, characterized in that, Step S5 specifically includes: Delivery time analysis assesses the delivery path of each drone and the arrival / departure time of each node, analyzes whether the total delivery time has reached the optimization target, and confirms whether there are delivery delays or unnecessary time waste. Power utilization assessment analyzes the drone's power consumption, checks battery efficiency and charging station utilization, and evaluates whether the drone can minimize power consumption to ensure that each charge is performed at a reasonable time and place. Performance metrics comparison: Compare key performance metrics under different solutions, and select the optimal solution for further optimization; Solution optimization involves adjusting and optimizing the drone's path planning, charging node selection, and scheduling strategies based on the results analysis, in order to improve system efficiency under different constraints. Model optimization involves adjusting parameters or constraints in the model based on the gap between actual results and expected goals, in order to continuously improve the overall efficiency of the delivery system, reduce costs, and improve service quality.

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