Unmanned aerial vehicle task allocation planning method under truck-unmanned aerial vehicle synchronous operation collaborative distribution mode

Abstract

The application discloses a kind of truck unmanned aerial vehicle synchronous operation cooperative distribution mode under unmanned aerial vehicle task allocation planning method, belong to unmanned aerial vehicle task planning technical field, including the truck parking point site selection of unmanned aerial vehicle take-off and landing and the task allocation of unmanned aerial vehicle.Firstly, the truck parking point site selection model of truck and unmanned aerial vehicle synchronous operation cooperative distribution is established, and the influence of the payload carried by unmanned aerial vehicle, the climbing, horizontal flight and landing state of unmanned aerial vehicle on the endurance of unmanned aerial vehicle is considered;In order to improve the utilization rate of unmanned aerial vehicle, one unmanned aerial vehicle can serve multiple customer points, and the task allocation model of unmanned aerial vehicle is established, considering the influence of the weight of the package carried by unmanned aerial vehicle, the take-off, horizontal flight and landing state of unmanned aerial vehicle on the endurance of unmanned aerial vehicle.The practicability and accuracy of truck and unmanned aerial vehicle synchronous cooperative distribution when considering actual operating environment are greatly improved.

Description

Technical fields:

[0001] This invention relates to a drone task allocation and planning method under a truck drone synchronous operation and collaborative delivery mode, which belongs to the field of drone task planning technology. Background technology:

[0002] For the problem of collaborative logistics delivery using trucks and drones, solving the problem by establishing a model that considers payload and drone flight status is increasingly becoming a research hotspot. The purpose of drone mission planning is to fully consider factors such as drone energy consumption and payload while satisfying various constraints, making the drone mission planning more realistic. Drone mission planning mainly includes two aspects: the selection of truck docking points for drone take-off and landing, and the allocation of drone tasks.

[0003] (1) Truck stop selection for truck-drone collaborative delivery

[0004] The asynchronous collaborative delivery model of trucks and drones, such as... Figure 1 As shown, the truck does not have logistics delivery capabilities. After the drone is deployed, the truck will remain stationary, waiting for the drone to complete its delivery to the relevant customer point. The truck will then retrieve the drone and proceed to the next truck stop to repeat the process. The truck and drone operating synchronously for collaborative delivery is as follows: Figure 2 As shown, the truck has logistics delivery capabilities. After the drone is released from the truck, the truck travels to the next customer point to deliver the drone, and simultaneously retrieves the released drone at the next customer point. The same process continues to complete the delivery task. This invention uses trucks carrying multiple drones to perform last-mile logistics delivery to a large number of customer points within a region. Research on truck docking point selection is crucial in the collaborative delivery process using trucks and drones. The main objective is to select suitable truck docking locations after drone release for both release and retrieval. The research findings are summarized into three scenarios: the truck remains stationary while waiting for drone retrieval; the truck moves to a subsequent customer point and waits for drone retrieval; and the truck stops at any point along its subsequent travel path while waiting for drone retrieval.

[0005] Scene 1: The truck is parked in place.

[0006] Ferrandez et al. [1] used the K-means algorithm to cluster customer points within the service range of drones, and selected the location of truck stops at the center of the cluster. They set that the trucks could only stop at the original location and wait for the drones to fly back. Then they studied the impact of the cluster center location of the trucks and the ratio of the speed of the drones to the speed of the trucks on the total delivery time. Boysen [2] proposed two models for selecting the location of truck stops after the drones are launched. The first model assumes that the trucks stop at the original location to retrieve the drones. The second model assumes that the location of the truck stops can be any location afterward. Then, they designed a simulated annealing algorithm to solve the two models. By changing the number of drones, they performed several calculations and analyses on a problem with up to 100 customer points and determined the optimal route for the trucks and drones. Ji Jinhua [3] stipulated that the drones must return to the original truck stop for disinfection after each delivery. With the goal of minimizing the risk of cross-infection among community residents and the delivery cost during the delivery process, a mixed integer programming model was established, and an improved multi-objective particle swarm algorithm was designed to solve the model. Schermer[4] considered that the drone can only serve one customer per trip. When the drone performs a delivery task, the truck is parked in the original position waiting for the drone to be retrieved. He developed two algorithms. The first one uses the nearest neighbor heuristic algorithm to solve the truck route planning and then removes the customer from the truck route to be assigned to the drone route. The second one uses a heuristic method to construct the routes of the truck and the drone at the same time.

[0007] Scenario 2: The truck moves to the next customer's location and stops.

[0008] Murray[5] proposed the FSTSP problem. They assumed that a truck carrying a drone stopped at a customer point and released the drone to deliver the package to the customer. Once the truck released the drone, it had to move to another customer point to stop. The goal of the truck stop location was to minimize the time it took for all customer points to be served, based on the fact that the drone's flight did not exceed its maximum range. Agatz[6] proposed a synchronous truck and drone delivery model that allowed the truck to stop at the launch point or a subsequent customer point on the truck's route to retrieve the launched drone. He also developed a heuristic and exact algorithm based on dynamic programming to solve the problem. Wu Tingying[7] established a mixed integer programming model with the goal of minimizing transportation costs and designed an adaptive large neighborhood search algorithm to solve it. He improved the algorithm performance by designing a variety of efficient destruction and repair operators and introducing a simulated annealing acceptance criterion to avoid getting trapped in local optima. Carlsson[8] used a heuristic method to calculate the coordinated route between the truck and the drone. He found that the efficiency improvement brought by the drone and the truck was related to the square root of the ratio of the truck and the drone's speeds, and proved the correctness of the conclusion through relevant examples. Karak[9] developed a hybrid heuristic algorithm based on the MILP model to minimize the total pickup and delivery costs and solve for the truck parking location and the specific path of the drone. Peng Yong

[10] established a mathematical model of truck and drone delivery with the goal of minimizing the total service time of the vehicle, designed a hybrid neighborhood search algorithm, and verified the effectiveness of the algorithm by the computation time of different scale examples and the volatility of the solutions after multiple computations. Zhu Xiaoning

[11] considered the regional restrictions such as truck traffic restrictions and drone no-fly zones, established a hybrid integer linear programming model, combined the shortest path algorithm and tabu search algorithm to design a solution algorithm, and transformed the drone path optimization subproblem into a shortest path problem for solution.

[0009] Scenario 3: The truck stops at any subsequent location.

[0010] Wang

[12] improved the pairing relationship between trucks and drones. First, a drone can accompany a truck. The drone takes off from the customer point to make a delivery. Then, the truck's stop point must be selected from the pre-set logistics service center. Finally, the drone starts to accompany another truck to make a delivery. The main purpose of this problem is to minimize the total delivery cost. To this end, an arc-based integer scheduling model is proposed to solve the problem. Gonzalez

[13] set two trucks, each carrying a single drone, to serve a set of customer points. The drone is allowed to visit several customers each time it travels between two consecutive meetings with the truck. The meeting point of the truck or drone is not predetermined during the truck stop point selection process. Each location in the area is regarded as a potential truck stop point. To this end, an approximate heuristic method is proposed to solve the problem. Salama

[14] grouped customer points into non-overlapping groups and arranged trucks through the contact points of each group to facilitate simultaneous delivery of drones in the group. At the same time, two decision strategies for truck stop location were developed: one strategy is that trucks can only stop at customer point locations, and the other strategy is that trucks can stop anywhere in the delivery area. Both strategies take the minimization of total cost as the objective function. Then, a machine learning-based heuristic method was introduced to accelerate the solution of the two models.

[0011] (2) Task allocation for UAVs

[0012] In the context of truck drone collaborative delivery of this invention, the research focuses on the two-dimensional path planning problem of drones, mainly determining which customer points the drones serve and the order in which they serve the customer points. Therefore, it involves the task allocation and scheduling problem of multiple drones.

[0013] Yada

[15] proposed a model whose objective function is to minimize the total flight time of the unloaded drone. The drone can collect goods from multiple warehouses to provide services to customers. In most cases, a drone can only serve one customer at a time. Two heuristic methods were designed to solve this problem. Rabta

[16] proposed a drone task allocation model for light relief supplies in disaster relief operations. The drone can serve multiple demand locations and can be charged at charging locations along its path. The goal is to minimize delivery costs. This model is used to solve four different scenarios with different battery size values. Coelho

[17] proposed a two-layer UAV dynamic task allocation model for real-time package retrieval and delivery. It assumes that UAVs can deliver packages between certain designated locations and charge batteries at charging locations. The retrieval and delivery time is optimized by minimizing seven different objectives. For this purpose, a multi-objective mathematical heuristic method is developed to solve several problem instances. Liu

[18] proposed a similar task allocation model for delivering services and random customer demand. The goal is to minimize the total cost of UAV deployment and the cost of operating manpower. Demands accumulate in some pre-specified time intervals and UAVs are dispatched to serve the received orders at the end of each time interval. Several problem instances are solved using the sample average approximation method and genetic algorithm. Guerriero

[19] proposed a UAV system that can solve the distributed dynamic scheduling problem. A multi-objective optimization model is established. The dynamics of events are considered by considering the concept of rolling horizons and heuristic methods are used to solve the problem. Sun

[20] studied an auction algorithm based on Boolean network for the job scheduling problem of multiple UAVs. A cluster-based auction method is adopted to solve the job of multiple UAVs and solve the allocation conflict problem between UAVs.

[0014] In summary, most studies on truck stop location selection addressing the issue of truck stopping at the original location rely on simple clustering of customer points, with the central location serving as the truck stop location. The objective function is to minimize the total delivery time, failing to adequately consider the significant impact of truck stop location selection on delivery costs. Furthermore, studies on trucks stopping at any subsequent location often assume an idealized state, implying that any location is acceptable, which does not align with the context of this invention's last-mile logistics delivery. Therefore, this invention adopts a location selection method where trucks can stop at subsequent customer points after delivery via drone release. However, current research on this location selection method requires improvement in the following aspects:

[0015] ①In previous modeling of truck stop location selection for truck and drone collaborative delivery, the truck routes were mostly determined directly, and truck stops were selected from customer locations based on these routes. This invention considers that delivery is mainly carried out by drones, so the location of truck stops should be determined based on the flight endurance of the drones.

[0016] ② Previous truck parking location selection models rarely considered the impact of UAV payload, UAV takeoff, level flight, and landing status on the actual flight range of the UAV, which may cause changes in the location selection results;

[0017] ③ The previous model did not fully consider that trucks also have delivery capabilities. After the drone is released from the truck docking point for delivery, the truck can go to serve other customer points, reducing the overall delivery cost. To address this, the present invention proposes a truck docking point selection model that allows trucks and drones to operate synchronously. The model constraints fully consider the drone's payload and flight status, while also enabling the truck to deliver to customer points, making it more in line with actual last-mile logistics delivery.

[0018] The research on UAV path planning has the following shortcomings:

[0019] ① In the modeling of previous studies, the actual endurance of UAVs was idealized and the impact of UAV payload and UAV climb, level flight and landing states on the actual flight range of UAVs was ignored. This may result in the UAV being unable to fly to the calculated target point in actual flight.

[0020] ② Previous studies on truck and drone collaborative delivery have mostly considered that a drone can only serve one customer point at a time, which will lead to a great waste of drone resources;

[0021] ③ Previous drone path planning models often set the objective function to minimize delivery cost or delivery time, without fully considering the time balance of drones in completing customer point delivery.

[0022] Therefore, it is indeed necessary to improve existing technologies to address their shortcomings.

[0023] References involved:

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[10] Peng Yong, Li Yuanjun. Optimization of truck-drone collaborative delivery routes considering the impact of the epidemic [J]. China Journal of Highway and Transport, 2020, 33(11):73-82.

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[0041]

[18] Liu M, Liu

[0042]

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[0043]

[20] Sun X, Qi N, Yao W.Boolean networks-based auction algorithm fortask assignment of multiple uavs[J].Mathematical Problems in Engineering, 2015, 2015. Summary of the Invention:

[0044] This invention provides a task planning method for drones in collaborative logistics delivery using trucks and drones, aiming to address the problems existing in the prior art. It improves upon the traditional drone path planning model by using the time balance of drones completing delivery tasks as the objective function. The model fully considers the impact of drone payload and drone climb, level flight, and landing states on the actual flight range of the drone, while also taking into account the situation where a single drone launch can serve multiple customer points, ultimately making drone path planning more accurate and efficient.

[0045] The technical solution adopted in this invention is as follows: a method for drone task allocation and planning in a synchronous operation and collaborative delivery mode for truck drones, the specific steps of which are as follows:

[0046] (1) First, obtain drone performance data, population density data of the area under study, and logistics demand index data;

[0047] (2) Based on socio-economic data, the logistics demand levels of each district and county are divided, the number of customer points in each district and county is simulated based on the division results, the specific location of the customer points is simulated based on the population density distribution map, and the specific demand of each customer point is generated using a random generation method.

[0048] (3) Considering the flight status of the UAV and the impact of the UAV's effective payload on the actual flight range of the UAV, with the minimum delivery cost as the objective function, we model the problem of determining the location of the UAV release point at the truck stop, and use the particle swarm algorithm to solve the above model to determine the location of the truck stop.

[0049] (4) Establish a drone task allocation model, taking into account that the actual flight range of the drone under the influence of the drone carrying packages and the drone's flight status shall not exceed its maximum flight range, while also taking into account that the effective payload of the drone shall not exceed the maximum load of the drone, and allowing one drone to serve multiple customer points.

[0050] (5) An improved artificial bee colony algorithm was used to solve the problem. The task allocation results of the UAV were obtained under the scale of multiple customer points to verify its superiority.

[0051] The present invention has the following beneficial effects:

[0052] First, to address the issue that the energy consumption constraints of drones were not fully considered in previous truck and drone collaborative delivery models, the impact of the drone's payload, as well as its climb, level flight, and landing states on energy consumption, will be added to the model's constraints.

[0053] Second: In response to previous studies that adopted a asynchronous operation mode of trucks and drones, this invention improves the previous truck stop location selection model and establishes a truck stop location selection model for synchronous operation and collaborative delivery of trucks and drones. This model takes into account that the truck can go to the next truck stop for drone retrieval while the drone is performing its mission, which improves the utilization rate of the truck, makes the collaborative delivery process of trucks and drones more flexible, and saves delivery costs.

[0054] Third: Addressing the issue of incomplete constraint considerations in the drone path planning model during collaborative delivery involving trucks and drones, this paper incorporates the impact of drone payload, climb, level flight, and landing states on energy consumption into the model's constraints. An improved artificial bee colony algorithm was used to solve the model, achieving a 16% improvement in time balance accuracy for the fifth task group with 100 customer points compared to the standard artificial bee colony algorithm.

[0055] Fourth: Previous studies on truck-drone collaborative delivery often focused on scenarios where a single drone deployment could only serve one customer. This invention considers the possibility of a drone delivering to multiple customers in a single flight, without requiring the drone to return to the truck's drop-off point after completing its delivery mission. This saves on the number of drones needed and improves the economy and efficiency of delivery. Attached image description:

[0056] Figure 1 This is a schematic diagram illustrating asynchronous collaborative delivery between trucks and drones.

[0057] Figure 2 This diagram illustrates the synchronized operation and collaborative delivery of trucks and drones.

[0058] Figure 3 A graph showing the comparison between calculated and experimental flight times.

[0059] Figure 4 This is a graph showing the iteration curves of the particle swarm optimization algorithm.

[0060] Figure 5(a) , 5(b) Figures 5(c) and 5(d) show the comparison of location costs for different numbers of customer points under the two location methods.

[0061] Figure 6 A comparison of the iteration curves of the improved artificial bee colony algorithm and the standard artificial bee colony algorithm.

[0062] Figure 7 This is a schematic diagram of the fifth group of UAV path planning results. Detailed implementation method:

[0063] The invention will now be further described with reference to the accompanying drawings.

[0064] The present invention relates to a task planning method for drones when trucks and drones collaborate in logistics delivery. The specific steps are as follows:

[0065] (1) First, obtain drone performance data, population density data of the area under study, and logistics demand index data;

[0066] (2) Based on socio-economic data, the logistics demand levels of each district and county are divided, the number of customer points in each district and county is simulated based on the division results, the specific location of the customer points is simulated based on the population density distribution map, and the specific demand of each customer point is generated using a random generation method.

[0067] (3) Considering the flight status of the UAV and the impact of the UAV's effective payload on the actual flight range of the UAV, with the minimum delivery cost as the objective function, we model the problem of determining the location of the UAV release point at the truck stop, and use the particle swarm algorithm to solve the above model to determine the location of the truck stop.

[0068] (4) Establish a drone task allocation model, taking into account that the actual flight range of the drone under the influence of the drone carrying packages and the drone's flight status shall not exceed its maximum flight range, while also taking into account that the effective payload of the drone shall not exceed the maximum load of the drone, and allowing one drone to serve multiple customer points.

[0069] (5) An improved artificial bee colony algorithm was used to solve the problem. The task allocation results of the UAV were obtained under the scale of multiple customer points to verify its superiority.

[0070] In step (3), the impact of the effective payload carried by the UAV, the UAV's climb, level flight and landing states on the UAV's endurance is comprehensively considered. The objective function is to minimize the cost of trucks and UAVs to complete the delivery task. The particle swarm algorithm is used to solve the location of the truck stop. The objective function is to achieve the balance of UAV delivery tasks. The improved artificial bee colony algorithm is used to solve the UAV task allocation process.

[0071] I. Truck parking location model considering payload and UAV flight status

[0072] Model assumptions:

[0073] The following assumptions are made regarding the mission planning of drones:

[0074] (1) The coordinates of the customer points where each drone performs its delivery tasks and the truck docking points where the drone is released and retrieved are known.

[0075] (2) The distance of the drone flight is calculated according to the Euclidean distance between each customer point, and the distance of the truck travel is calculated according to the road distance between each customer point.

[0076] (3) The demand for each customer point is known.

[0077] (4) When a truck needs to retrieve a drone at a truck stop, there may be situations where the drone waits for the truck, the truck waits for the drone, or both arrive at the customer's location at the same time.

[0078] (5) Trucks and drones cannot deliver to the same customer point repeatedly; each customer point can only be served once.

[0079] (6) Consider the impact of actual obstacle avoidance by UAVs and set a reserved energy consumption coefficient.

[0080] (7) A truck can assist drones in completing all delivery tasks.

[0081] (8) The climb and landing times of the drone are the same whether it is carrying a package or not.

[0082] (9) The effective payload of the drone is the weight of the package carried by the drone.

[0083] 1) The impact of UAV payload and flight status on UAV endurance

[0084] In collaborative delivery using trucks and drones, the drone is released from the truck and flies to the customer's location along a pre-planned flight path to deliver packages. During the delivery mission, the drone's actual flight range must not exceed its maximum range. Carrying packages increases the drone's payload, affecting its energy consumption. This invention proposes the following drone delivery flight process: the drone climbs with a package from the truck's launch point, flies horizontally with the package, lands at the customer's location with the package, climbs empty, flies horizontally empty, and lands empty at the subsequent truck's launch point. Therefore, in collaborative truck-drone delivery, it's crucial to consider not only the theoretical drone endurance but also the impact of the drone's payload and its climb, horizontal, and landing states on its actual flight range in the model's constraints. Only then can the planned results meet actual delivery requirements and successfully complete the delivery task.

[0085] This invention, based on aerodynamic theory, first uses an approximate power consumption model for rotary-wing unmanned aerial vehicles.

[0086] The power formula for a drone in horizontal flight is expressed by equation (1):

[0087]

[0088] The power formula for the UAV during climb is expressed by equation (2):

[0089]

[0090] The power formula for the drone during landing is expressed by equation (3):

[0091]

[0092] Where ρ represents air density, and W represents the total weight, including the drone's own weight and payload. v represents the rotor area of ​​a drone. c v represents the drone's climb rate. d V represents the descent speed of the drone. horIt is the speed of the drone's horizontal flight, α(V) hor η is the angle of attack during horizontal flight. hor It is the efficiency coefficient during horizontal flight, η c (V c ), η d (V d All of these are empirical coefficients.

[0093] Previous experimental studies have mostly recorded the actual horizontal flight time of UAVs carrying different payloads to explore the relationship between the payload carried by the UAV and the actual flight time. Formula (1) gives the power formula for UAVs during horizontal flight, but parameters such as flight pitch angle are difficult to measure for different types of UAVs. In order to further study the delivery scenarios of different UAV models, this invention selects to use the actual experimental data of the MK8-3500 standard rotary-wing UAV to perform linear regression analysis on the power equation (1) of the rotary-wing UAV during horizontal flight, and obtains the following regression equation:

[0094] p hor (w)=β0+β1w (4)

[0095] In equation (4), w represents the effective payload of the UAV, p hor (w) represents the horizontal flight power when the payload is w, and β0 and β1 are regression coefficients. The average error percentage in regression equation (4) is calculated to be 0.0064%, with a maximum difference of 0.021 kW. Therefore, it can be seen that during the horizontal flight of the UAV, the power demand increases almost linearly with the increase of the payload.

[0096] The formula for the actual flight time of the UAV is shown in Equation (5). Substituting Equation (4) into Equation (5), the flight time of the UAV can be calculated.

[0097]

[0098] In equation (5), T true The actual flight time of the drone is represented by μ, energy transfer efficiency is represented by C, and battery capacity is represented by V. n (V) represents the rated voltage of n batteries, and P(w) represents the power consumed by the drone.

[0099] The comparison between the drone's flight time calculated using the formula and the actual experimental results from the MK8-3500 is shown in the following figure. Figure 3As shown. Equation (4) is obtained from this. The calculated flight time of the UAV is roughly consistent with the experimental flight time of the UAV. Then, a one-sided t-test was used to perform a static evaluation of equation (4). The results show that P and w in equation (4) are related, and the p value is 5%. Therefore, equation (4) can be considered to reflect the relationship between the UAV's payload and the UAV's actual power. In subsequent calculations, this equation is used to solve for the actual power of different rotorcraft UAVs when carrying payloads and flying horizontally.

[0100] Let the power of the drone when it is flying horizontally without carrying any packages be P(w). uav The power during the climb is P' c The power during descent is P' d The drone's own weight is w uav The effective payload carried by the drone is w bag When the UAV is flying with a payload, W in formula (4) is (w uav +w bag Let the horizontal flight power of the drone carrying the package be P(w). uav +w bag The drone's climb power is P. c The power of the drone during landing is P. d .

[0101] Both takeoff and landing of a drone consume energy, which reduces its maximum endurance and maximum flight range. This invention converts the power consumed by an unloaded drone during takeoff and landing within time t into the power consumed by the drone during horizontal flight within time t. Simultaneously, it converts the power consumed by a drone carrying a package during takeoff and landing within time t into the power consumed by the drone during unloaded and horizontal flight, ultimately converting the aforementioned energy consumption into an increase in actual horizontal flight range.

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] In equation (6), σ1 is the ratio of the power of the drone in horizontal flight when carrying a package to the power of the drone in horizontal flight when unloaded; in equation (7), σ2 represents the ratio of the power of the drone in climbing when carrying a package to the power of the drone in horizontal flight when unloaded; in equation (8), σ3 represents the ratio of the power of the drone in landing when carrying a package to the power of the drone in horizontal flight when unloaded; in equation (9), σ4 represents the ratio of the power of the drone in climbing when unloaded to the power of the drone in horizontal flight when unloaded; in equation (10), σ5 represents the ratio of the power of the drone in landing when unloaded to the power of the drone in horizontal flight when unloaded.

[0108] S1=vtσ1 (11)

[0109] S2=vt'σ2 (12)

[0110] S3=vt'σ3 (13)

[0111] S4=vt'σ4 (14)

[0112] S5=vt'σ5 (15)

[0113] Let the drone's horizontal flight time be t, its climb and landing times be t', and its horizontal flight speed be v. Then, under the condition that the drone is carrying a package, the drone's horizontal flight time t corresponds to the standard condition (drone unloaded) drone range S1, as shown in equation (12). The drone's climb time t' when carrying a package corresponds to the standard condition (drone unloaded) drone range S2, as shown in equation (12). The drone's landing time t' when carrying a package corresponds to the standard condition (drone unloaded) drone range S3, as shown in equation (13). The drone's climb time t' when unloaded drone corresponds to the standard condition (drone unloaded) drone range S4, as shown in equation (14). The drone's landing time t' when unloaded drone corresponds to the standard condition (drone unloaded) drone range S5, as shown in equation (15).

[0114] 2) Truck parking location model considering payload and UAV flight status

[0115] Determining the quality of a UAV's planned trajectory requires trajectory evaluation. The key to trajectory evaluation lies in constructing an objective function. The trajectory evaluation function is used to calculate the trajectory's suitability, which is a crucial standard for judging path quality and a key guide for the search algorithm to reach the optimal solution. Evaluating trajectory costs also requires considering various constraints and limitations.

[0116] Model parameters and variables

[0117] The variables for the truck docking location model considering payload and UAV flight status are explained in Table 1:

[0118]

[0119] Consider the minimum delivery cost as the objective function, which is expressed by the following formula:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] L a,b,d =d a,b σ1+d b,d +v uav t uav (σ2+σ3+σ4+σ5) (7)

[0127] L a,b,d ≤L(1-δ) (8)

[0128] x' a,b ≤x a ,a∈M,b∈N2 (9)

[0129] y' b,d ≤y d ,d∈M,b∈N2 (10)

[0130] x' a,b ={0,1},a∈M,b∈N2 (11)

[0131] x' a ={0,1},a∈M (12)

[0132] y' b,d ={0,1},d∈M,b∈N2 (13)

[0133] y' d ={0,1},d∈M (14)

[0134] Equation (17) indicates that each customer point can only be served by one truck stop that releases the drone;

[0135] Equation (18) indicates that each customer point can only be served by one truck stop for recycling drones;

[0136] Equation (19) indicates that a set of truck stops can serve multiple surrounding customer points, and each drone delivery customer point can only be served by a set of truck stops;

[0137] Equation (20) indicates that the number of truck stops selected for releasing the drone is equal to the number of truck stops selected for subsequently recovering the drone;

[0138] Equation (21) indicates that every customer point with demand exceeding the maximum load of the drone will be selected as a truck stop.

[0139] Equation (22) indicates that when a drone is delivering packages, it takes into account the drone's climbing, landing, and level flight states when the drone is carrying packages and when it is empty.

[0140] Equation (23) represents the energy consumption reserve coefficient that the drone needs to meet;

[0141] Equation (24) indicates that customer point b, which requires delivery by drone, can only exist when customer point a is selected as the truck drop-off point released by the drone;

[0142] Equation (25) indicates that a drone that has completed service point b may land only if customer point d is selected as the truck drop-off point for drone recovery.

[0143] Equation (26) indicates that if the drone is released from the truck parking point at point a and flies to the customer point b to deliver a package, the value is 1; otherwise, the value is 0.

[0144] Equation (27) means that if a is selected as the truck stop point for releasing the drone, it is 1; otherwise, it is 0.

[0145] Equation (28) indicates that if the drone flies from customer point b to truck parking point d for retrieval after delivery, it is 1; otherwise, it is 0.

[0146] Equation (29) indicates that d is 1 if it is selected as the truck docking point for recovering the drone, and 0 otherwise.

[0147] This invention uses a particle swarm optimization algorithm to solve the truck stop location problem. The key objective of solving this problem is to select truck stops from customer locations where both trucks and drones can make deliveries. Each group of truck stops is responsible for the release and retrieval of drones. Each candidate truck stop has only two states: selected and not selected. 1 indicates that the customer location group has been selected as a truck stop, and 0 indicates that the customer location group has not been selected. Each particle represents a location sorting order. The algorithm parameters are shown in Table 2.

[0148] Table 2 Algorithm Parameter Table

[0149]

[0150] 1. Encoding method design and population initialization

[0151] The initial population is formed by selecting several pairs of truck docking points from customer points that can only be delivered by trucks and those that can be delivered by both trucks and drones. One of these pairs serves as the drone release point, and the other as the drone recovery point. This location selection method satisfies the constraint of equation (20) in the model. Truck docking points are selected from the combinations, and α is set as follows: uav Equation (30) is given.

[0152] α uav =t uav v uav (30)

[0153] Then formula (22) can be simplified to formula (31).

[0154] L a,b,d =d a,b σ1+d b,d +α uav (σ2+σ3+σ4+σ5) (31)

[0155] As shown in equation (31), the total cost of selecting truck docking points for coordinated delivery by trucks and drones is related to the location of the truck docking points. Therefore, once the location of the truck docking points is determined, customer locations that meet the drone's flight range limitations (considering the drone's flight status when carrying packages and when empty, and its effective flight payload) can be allocated. If there are 20 alternative truck docking points, then... The group selection combination, where the selected truck stop combination is set to 1 and the remaining unselected combinations are set to 0, can be encoded as [1,1,0,0,1,1......0]. This means that combinations 1, 2, 5, and 6 are selected as truck stops, and the remaining 184 release positions are closed. After the candidate truck stops are determined, they are represented in the form of a matrix. In the matrix, each row represents a customer point, and each column represents a truck stop combination. All columns without selected positions are set to 0. The service of customer points by truck stops adopts the principle of proximity allocation. In the column of selected truck stops, the closure of that row is set to 0, which satisfies equations (17) and (18) in the model. That is, each customer point can only be served by a group of truck stops, and it also satisfies the requirement that a group of truck stops can serve multiple customer points. It is also necessary to determine whether the constraints of equations (21) and (23) in the model are satisfied. Otherwise, the particle stops evolving in that direction until all customer points are allocated.

[0156] 2. Definition of the objective function

[0157] Z1 represents the total cost of selecting the truck parking spot, as shown in equation (32). The lower the cost of the truck parking spot, the better it meets the calculation requirements.

[0158]

[0159] 3. Particle Swarm Optimization Algorithm

[0160] The particle swarm optimization (PSO) algorithm is as follows: First, a solution space is defined. Then, within the solution space, initialization is performed according to the constraints of the model. Each initialized individual becomes a particle, and each particle represents a potential solution to the problem. Each particle moves within the solution space at a certain speed and marks its position. The individual fitness and population fitness of the particles are optimized through several iterative calculations. Each particle is represented as X. i =(x i,1 ,x i,2 ,x i,3 ,...,x i,D The velocity of the particle during the iteration process is V. i =(v i,1 ,v i,2 ,v i,3 ,...,v i,D The optimal position for each individual particle is P. i =(p i,1 ,p i,2 ...,p i,D Also known as P best The best position for all particles in the population is P. h =(p h,1 ,p h,2 ...,p h,D It is also known as G best

[0161] The changes in the position and velocity of the particle during the iteration process are shown in equations (33) and (34):

[0162]

[0163]

[0164] In equation (33): This represents the position of particle i at the d-th dimension after the nth iteration; This represents the particle velocity of particle i at the d-th dimension after the nth iteration; This represents the optimal individual fitness of particle i at the d-th dimension after the nth iteration. ω represents the optimal particle population fitness value at dimension d after the nth iteration; ω represents the inertia weight, which adjusts the search range; c1 and c2 are learning factors. In the binary particle algorithm, the particle's trajectory and velocity are defined probabilistically, with x for each particle... i,d The value of is 0 or 1, where in equation (34) v i,d For x i,d The probability of taking the value 1. The formula for calculation is shown in equation (35):

[0165]

[0166] In expression (35): S(x) = 1 / (1+e x ), where r represents a random number on [0,1].

[0167] The steps for solving the truck parking point location model that considers payload and UAV flight status based on the particle swarm optimization algorithm are as follows:

[0168] (1) Determine the particle swarm size m, the maximum number of iterations n, and the learning factors c1, c2 and inertia weight ω, and generate the distance matrix.

[0169] (2) The truck parking points are generated in pairs, and m feasible solutions X1, X2, X3, ..., X are randomly generated according to the population initialization rules described in the invention above. m The number of rows in the matrix for each solution is the number of combinations of truck stop points. Find the unopened location combination whose corresponding position in the distance matrix is ​​infinity, find the smallest non-zero position in each row, and generate an assignment matrix satisfying equations (19), (20), and (21). If satisfied, calculate X according to the equations. i The fitness and the initial fitness as the initial individual extreme value P best,i Since the objective function in the truck stop location problem is to minimize the cost of truck stop location selection, all P... best,i Assign the minimum value in G best As the initial global extremum, v i The initial value is set to 0.

[0170] (3) Update the position and velocity of the particle swarm according to equations (33) and (34).

[0171] (4) After the update, calculate the truck stop location cost for each individual according to equation (32). If the truck stop location cost of particle i is lower than the previous individual extreme value P, best,i Then set it to P best,i If the optimal P best,i A better global extreme value G than before best Then set it to Gbest .

[0172] (5) If the convergence condition is met or the maximum number of iterations is reached, stop the calculation; otherwise, return to step (3).

[0173] II. Drone Task Allocation Considering Drone Performance in Multi-Customer Location Scenario

[0174] Model assumptions

[0175] (1) The coordinates of the customer points where each drone performs its delivery tasks and the truck docking points where the drone is released and retrieved are known.

[0176] (2) The distance of the drone flight is calculated according to the Euclidean distance between each customer point, and the distance of the truck travel is calculated according to the road distance between each customer point.

[0177] (3) The demand for each customer point is known.

[0178] (4) When a truck needs to retrieve a drone at a truck stop, there may be situations where the drone waits for the truck, the truck waits for the drone, or both arrive at the customer's location at the same time.

[0179] (5) Trucks and drones cannot deliver to the same customer point repeatedly; each customer point can only be served once.

[0180] (6) Consider the impact of actual obstacle avoidance by UAVs and set a reserved energy consumption coefficient.

[0181] (7) A truck can assist drones in completing all delivery tasks.

[0182] (8) The climb and landing times of the drone are the same whether it is carrying a package or not.

[0183] (9) The effective payload of the drone is the weight of the package carried by the drone.

[0184] Model parameters and variables

[0185] Table 3 Parameter Variable Table

[0186]

[0187]

[0188] Model constraints

[0189] In this invention, the task allocation for drones is considered with the objective function of balancing the time required for drones to complete delivery tasks, as expressed by equation (36), where max(T) k' (T) represents the maximum time a drone can perform a delivery task within a set of truck stop locations, min(T)k' This represents the shortest time for a drone to complete a delivery task within a set of truck docking points.

[0190] The objective function is:

[0191]

[0192] The constraints of the model are:

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199] q a' ≤w bag,max (43)

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] u k',a' -u k',b' +1≤(n-1)(1-y a',b' )a',b'∈R'∪{a,d} (50)

[0207] 1≤u k,a' ≤n-1 (51)

[0208]

[0209]

[0210] Equation (37) indicates that the time for each drone to complete the delivery task is the sum of the drone flight delivery time and the take-off and landing time, minus the truck's travel time at the truck parking point;

[0211] Equation (38) represents the time required for the drone to fly from customer point a' to customer point b';

[0212] Equation (39) represents the time required for the truck to travel from truck stop a, where the drone takes off, to truck stop d, where the drone lands, in this group of delivery tasks;

[0213] Equation (40) indicates that if there is a drone flight path from point a' to b' during the drone delivery flight, then a drone must be used to complete the delivery task.

[0214] Equation (41) means that if there is a drone flying to deliver b', then there must also be a drone flying out from b';

[0215] Equation (42) represents the payload of the drone at node a' when customer points a' and b' are in the k' (k'∈K) drone delivery path;

[0216] Equation (43) indicates that the effective payload carried by the UAV during a single trip should be within the maximum load range of the UAV;

[0217] Equation (44) indicates that each customer point can only be delivered by one drone, that is, each customer point has only one delivery route;

[0218] Equations (45) and (46) indicate that the selected truck stop must exist in every drone delivery route.

[0219] Equation (47) indicates that there must be a delivery route between the selected truck drop-off point where the drone takes off and the truck drop-off point where the drone lands. The truck drop-off point must be the starting point and the ending point of the drone delivery route. This route is not considered when calculating the actual flight distance of the drone and the delivery time of the drone.

[0220] Equation (48) indicates that a drone delivery route from point a' to point b' exists only if point a' exists in the path of point k';

[0221] Equation (49) indicates that each delivery route of the drone takes into account the drone's load, and the total flight distance after considering the drone's climb and landing status factors cannot exceed the drone's maximum flight distance; where... Let the drone be on node i' with a load of q. i' The ratio of the drone's climb power to its unloaded horizontal flight power. The drone's load at node i' is q i' The ratio of landing power to the unloaded horizontal flight power of the UAV. The drone flies from the previous node to node i' with a load of q. i'The ratio of the horizontal flight power during flight to the unloaded horizontal flight power of the UAV;

[0222] Equations (50) and (51) represent the elimination of constraints on sub-loops, where n is the number of points contained in the set R'∪{b,l};

[0223] Equation (52) means that if customer point a' is in the k'th path, then the value is 1, otherwise it is 0;

[0224] Equation (53) indicates that if there is a flight path from a' to b' in the k'th drone delivery route, the value is 1, otherwise it is 0.

[0225] Improved artificial bee colony algorithm for solving UAV task allocation

[0226] The Artificial Bee Colony (ABC) algorithm is widely used in solving UAV path planning problems. The basic steps of the standard ABC algorithm implementation are as follows:

[0227] (1) In the initialization phase, all bees are randomly assigned to different nectar source locations. The initial settings are: the number of nectar sources is SN, the maximum number of iterations is set, the maximum number of local optimizations is set, and the number of optimizations is set to limit. In the standard artificial bee colony algorithm, the number of nectar sources SN is equal to the number of hired bees. The formula for calculating the location of each nectar source found by each bee is shown in equation (54).

[0228] x i,j =x minj +rand[0,1](x maxj -x minj (54)

[0229] Where: x i,j Represents the i-th honey source x i The value of the j-th dimension, where i takes values ​​in {1,2,...,SN} and j takes values ​​in {1,2,...,D}; x minj x represents the minimum value of the j-th dimension. maxj This represents the maximum value of the j-th dimension. Initializing a honey source involves assigning a random value within the range to all dimensions of the honey source using the formula above, thereby randomly generating SN initial honey sources.

[0230] (2) The stage of hiring bees: hiring bees search for better new nectar sources near the nectar source according to formula (55).

[0231]

[0232] Where: x ij The nectar source represents the nectar source near the original nectar source, and k takes values ​​in {1,2,...,SN}, and k is not equal to i; It is a random number in the range [-1, 1]. The hired bee decides whether to stay or leave at the new nectar source based on a greedy criterion. If the new location found by the hired bee is better, the bee will move to the new location to continue exploring. If the new location found is worse than the original nectar source, the bee will continue exploring at the original location.

[0233] (3) Follower Bee Phase: After the Hired Bee phase ends, the Follower Bee phase begins. Hired bees search for new locations near their preferred nectar sources and then transmit the information to the Follower Bees. Based on the information about the nectar source location transmitted by the Hired Bees, the Follower Bees use a roulette wheel strategy to select new nectar sources for mining, ensuring a higher probability of mining nectar sources with higher fitness values. The mining process of the Follower Bees is the same as that of the Hired Bees, using equation (55) to find new nectar sources and retaining those with better fitness. A nectar source has a parameter `trail`. When a nectar source update is retained, `trail` is 0; otherwise, `trail` is incremented by 1. Thus, `trail` can count the number of times a nectar source has not been updated.

[0234] (4) In the scout bee stage, if a nectar source is searched by a bee multiple times and the number of searches reaches a certain limit, that is, the trail value of the nectar source is too large and exceeds the pre-set threshold limit, and the nectar source has not been found to be updated under this situation, then the bee will give up this location and search for a new nectar source location. The bee is transformed into a scout bee and searches for a new nectar source location randomly in the nectar source search space through formula (56).

[0235] x ij =x minj +rand[0,1](x maxj -x minj (56)

[0236] Standard artificial bee colony algorithms are prone to getting trapped in local optima and have slow convergence speeds. This invention, based on the selected locations of truck stops and corresponding customer service points, employs an improved artificial bee colony algorithm when solving the drone path planning model for synchronized truck and drone collaborative delivery. It optimizes the process of searching for precise nectar sources by dynamically adjusting the follower bee position update formula. The algorithm introduces the idea of ​​dynamic adjustment by comparing the current solution with the value of the previous iteration. The two added nectar source update methods are as follows:

[0237] ① In order to enhance the overall search capability of the artificial bee colony algorithm, a global guidance mechanism of particle swarm is introduced, which enables the bee colony to search towards the overall optimal nectar source, thereby enhancing the search capability of the nectar source space in the later stage of iteration. The specific nectar source update method is shown in equation (57).

[0238]

[0239] in, It is [-c s ,c s A random number between ] and φ ij It is [0,c f A random number between p and ] gj c represents the value of the j-th dimension of the globally optimal position. s This reflects the algorithm's ability to search for nectar sources. s The larger the value of c, the stronger the algorithm's global search capability. f This reflects the algorithm's ability to perform detailed local searches, c f The larger the value of c, the stronger the algorithm's local fine-grained search capability. The artificial bee colony algorithm's process of finding the optimal solution requires a strong global search capability in the initial stage to find as many excellent nectar source locations as possible, and a strong local fine-grained search capability in the later stages to find the optimal nectar source. Therefore, from the early to the late stages of the search, c... s The value of c decreases linearly. f The value of increases linearly, as shown in equations (58) and (59).

[0240]

[0241]

[0242] Among them, c smax =1,c smin =0.5, c fmax =2,c fmin =1, maxCycle represents the maximum number of iterations, iter represents the current iteration number, and during the iterative calculation, c s From c smax Gradually decrease to c smin c f From c fmin Gradually increase to c fmax Ultimately, a balance is achieved between global search and detailed local search.

[0243] ② To address the problem of weak correlation between the current nectar source location and nearby nectar source locations, leading to decreased search efficiency and slow processing speed for bees, this invention introduces an adaptive dynamic adjustment strategy for the learning factor. This strategy accelerates information sharing between the current nectar source location and surrounding nectar source locations, providing direction for bees' rapid search and speeding up the search for the optimal nectar source. The location update method is shown in equation (60).

[0244]

[0245] Here, t1 represents the memory factor, which is the proportion of historical positions recorded in the artificial bee colony algorithm. A larger value indicates stronger global search capability. Based on the requirements for both global and detailed local search capabilities in the artificial bee colony algorithm's search for the optimal solution mentioned in the invention, the value of t1 should dynamically decrease throughout the search process. t2 represents the degree of information correlation between the current nectar source location and surrounding nectar source locations. This value dynamically changes as the bees search for the optimal nectar source. When the current nectar source is superior to surrounding nectar sources, the current nectar source needs to strengthen its information correlation and sharing with surrounding nectar sources to achieve better search results; therefore, the value of t2 should increase, and vice versa. (Random number) The range of values ​​is shown in equation (61), and the formulas for the changes of t1 and t2 are shown in equations (62) and (63).

[0246]

[0247] t1 = m × (w2 - (iter / maxCycle)) α ×(w2-w1)) (62)

[0248] t2 = m × (w3 - (iter / maxCycle)) β ×(w4-w3)) (63)

[0249] In this context, w1, w2, w3, and w4 are all constants, satisfying w2 > w1 and w4 > w3, with values ​​ranging from [0.1, 1.5]. t1 gradually decreases from w2 to w1, representing a shift from a global search to a more detailed local search. α is generally less than 1, but a value that is too small is detrimental to global convergence; therefore, it is set to [0.6, 1]. t2 gradually increases from w3 to w4, indicating that the current nectar source should gradually strengthen information sharing with surrounding nectar sources, enhancing its search capability within the neighborhood. β is generally set to > 1, but a value that is too large can easily cause follower bees to miss the optimal solution; therefore, β is set to [1, 1.3]. m is a constant obtained by comparing the current nectar source with its surrounding nectar sources. When the location of a surrounding nectar source is better than the current nectar source, the surrounding nectar sources are encouraged to share information, so m = 1.6; otherwise, m = 0.6.

[0250] Therefore, the improved artificial bee colony algorithm has three formulas for updating the location of nectar sources, as shown in equations (55), (57), and (60). The strategies corresponding to the three location update methods are named sy1, sy2, and sy3, respectively. Initially, a strategy is randomly selected for each nectar source. Then, during the subsequent bee search process, the update trends of each nectar source are compared to identify which is better. If the new nectar source is better than the original nectar source, it means that its corresponding search strategy has better search capabilities, and therefore, this strategy should continue to be used for searching. Conversely, if the strategy does not achieve the effect of finding a better nectar source, other strategies need to be randomly used for searching, and the strategy is dynamically adjusted by selecting other strategies.

[0251] The specific steps of the improved artificial bee colony algorithm are as follows:

[0252] (1) Initialize the number of bees NP, the number of bees to collect, the maximum number of iterations maxCycle, and the maximum number of local optimizations limit.

[0253] (2) Set the current UAV path planning node to the truck stop point. This setting satisfies the requirements.

[0254] (3) For each initial nectar source, randomly select an initial strategy from sy1, sy2, sy3, and update the nectar source position according to the position update formula corresponding to the strategy.

[0255] (4) The hired bees begin to search for new nectar sources (customer points) according to formula (54) and determine the initially marked nectar sources. The probability of selecting new nectar sources is determined according to the roulette strategy.

[0256] (5) Follower bees select new nectar sources based on the probability of selection.

[0257] (6) Each follower bee updates the nectar source location according to one of the update formulas (55), (57), and (60) based on the initial strategy it has chosen.

[0258] (7) According to equation (49), determine whether the difference between the current UAV flight path length (considering the UAV's climb, level flight, and landing states, and the UAV's effective payload) and the UAV's total flight distance is greater than the distance the UAV flies from the current customer point back to the truck parking point where the UAV lands. If it does not meet the setting, the current node is the endpoint. If it meets the requirements of equation (49), return to step (2). This setting of the node meets equation (50) to prevent the generation of sub-loop solutions. At the same time, determine whether the UAV's effective payload at this time meets the UAV's maximum payload standard. If it does not meet equation (43), otherwise return to step (2). If it does meet the requirements, calculate the fitness value according to equation (36).

[0259] (8) Compare the fitness value of the current nectar source with the fitness value of the initial nectar source. If the current fitness value is lower than that of the initial nectar source, randomly select a strategy different from the initial setting from sy1, sy2, and sy3. At the same time, determine whether the number of iterations at this time is less than the maximum number of iterations. If it is less, return to step (3). If it is greater, abandon the nectar source. This follower bee becomes a scout bee and searches for a new nectar source according to formula (56). If the current fitness value is higher than that of the initial nectar source, update the marked nectar source. At this time, the update strategy remains unchanged, and the number of iterations trail is set to 0.

[0260] (9) Record the optimal drone path planning scheme found by all bees.

[0261] (10) Determine whether the maximum number of iterations has been reached. If not, continue with step (3).

[0262] (11) When the maximum number of iterations is reached, the optimal solution is output to obtain the UAV path planning scheme.

[0263] III. Numerical Experiments

[0264] Parameter settings

[0265] The relevant data of the Kewetech X6L UAV are shown in Table 4.

[0266] Table 4 Model Parameter Table

[0267]

[0268]

[0269] The particle swarm optimization algorithm is used to solve the truck docking point selection problem in truck-drone collaborative delivery. The algorithm settings are shown in the table.

[0270] Table 5 Particle Swarm Optimization Algorithm Parameter Settings

[0271]

[0272] An improved artificial bee colony algorithm is used to solve the drone task allocation problem in truck-drone collaborative delivery. The algorithm settings are shown in Table 6.

[0273] Table 6 Parameter Setting Table

[0274]

[0275] Results and Analysis of Truck Parking Site Selection

[0276] The iterative curve for solving the truck stop point model of synchronized truck-drone collaborative delivery using the particle swarm optimization algorithm is shown below. Figure 4 As shown.

[0277] In the case study verification, to investigate the effectiveness of truck stop location selection under the truck-drone collaborative delivery mode, four case studies with different scales were selected: 25 customer points, 50 customer points, 75 customer points, and 100 customer points. The solution obtained from solving the truck stop location model consists of several sets of truck stops and the corresponding customer points that the drones can serve. The solution results for the 25 customer point scale are shown in the table below: The table shows that the solution results for the 25 customer point scale selected a total of 5 sets of truck stops.

[0278] Table 7. Site selection results for 25 customer locations using the Keweitai X6L UAV.

[0279]

[0280] To verify the impact of drone delivery's climb, level flight, and landing states on truck stop location selection, the number of locations considering and not considering mileage constraints caused by drone flight states was calculated for customer locations of 25, 50, 75, and 100 locations. The table showing the number of location groups and location costs indicates that when the impact of drone flight states on energy consumption is not considered, the number of locations for each customer location size is less than when drone flight states are considered, and the location cost is also lower. Although the number of locations and cost are lower when drone flight states are not considered, the energy consumption of drones during actual delivery cannot guarantee delivery to all customer locations. Situations may occur where drones fail to reach customer locations or are unable to return to the next truck stop after delivery, leading to drone damage. This is because if the impact of drone flight status on energy consumption is not considered, the calculated drone flight range will be greater than the actual flight range. This results in a larger service area and a greater number of customer points that can be served from the same truck stop, ultimately reducing the number of truck stop locations and lowering the corresponding location costs. Therefore, the truck stop location model that considers drone flight status proposed in this patent is more in line with actual delivery scenarios, more accurately considers the energy consumption of drones delivering packages, and improves the safety and accuracy of delivery solution design.

[0281] Table 8. Comparison of Truck Dock Location Costs with and without Consideration of Drone Flight Status

[0282]

[0283]

[0284] To verify the impact of drone-carried package payload on truck docking point location selection, with a customer point scale of 50, the demand for customer points with a demand greater than 5kg (customer points that must be delivered by truck) was kept unchanged, while the demand for customer points with a demand of less than or equal to 5kg was uniformly set to 1kg, 2kg, 3kg, 4kg, and 5kg respectively. The number of locations and location costs were calculated for each of the five demand scales. Equations (2), (3), and (4) show that the drone's payload and the drone's flight power are positively correlated. As the drone's payload increases, the drone's flight power also increases, leading to a decrease in the drone's maximum endurance. As shown in the table, the location cost also increases as the drone's package payload increases. The number of locations when the demand is 5kg is higher than the number of locations when the demand is 1kg, 2kg, 3kg, and 4kg. This is because as the drone's payload increases, the drone's maximum endurance decreases, causing the existing truck docking points to be unable to meet the delivery needs of all drones, thus increasing the number of locations.

[0285] Table 9 shows the variation of truck stop location results with payload for a customer base of 50.

[0286]

[0287] To compare the advantages and disadvantages of truck stop location selection costs in collaborative delivery under synchronous and asynchronous operation of trucks and drones, we verify this from four aspects in the case study:

[0288] ① Since the solution method uses the particle swarm optimization algorithm, which is an intelligent optimization algorithm, the iterative generation of the optimal solution is random. The cost and location result of each truck stop location solution may not accurately reflect the advantages and disadvantages of the two models. In order to reduce the randomness in the solution, the location solution of the truck-drone synchronous operation collaborative delivery mode and the truck-drone asynchronous operation delivery mode is solved ten times each to eliminate random errors.

[0289] ② When comparing the truck stop location costs in synchronous and asynchronous collaborative delivery using trucks and drones, the number of customer points, i.e., the service scale, may affect the model. To eliminate random errors, this invention selected four different customer point scales: 25 customer points, 50 customer points, 75 customer points, and 100 customer points. By comparing the lowest cost of the truck stop location model for synchronous collaborative delivery using trucks and drones proposed in this invention under these four scales with the lowest cost of the truck stop location model for asynchronous truck and drone operation under these four scales in Karak's paper (Karak A, Abdelghany K. The hybrid vehicle-drone routing problem for pick-up and delivery services[J]. Transportation Research Part C: Emerging Technologies, 2019, 102: 427-449), it is verified that the model proposed in this invention has a better location effect. The comparison of location costs for the two different delivery modes under the four customer point scales is shown in Figure 5.

[0290] As shown in Figure 5, under four customer point scales (25, 50, 75, and 100 customer points), the results of ten calculations consistently show that the site selection cost for the asynchronous truck and drone delivery mode is higher than that for the synchronous truck and drone delivery mode. In summary, the examples considered both the potential errors from the number of calculations and the potential errors from the customer point scale, and the results demonstrate that the model proposed in this invention is superior and has lower site selection costs.

[0291] ③ To explore the advantages and disadvantages of the synchronous truck and drone collaborative delivery mode versus the asynchronous truck and drone collaborative delivery mode, we calculated the number of locations for each mode. Table 10 shows that the number of truck parking locations in the synchronous truck and drone collaborative delivery mode is always less than that in the asynchronous mode. This is because, in the synchronous delivery mode proposed in this invention, truck transportation and drone release and retrieval are more flexible. Trucks can independently travel to the next customer location to perform delivery tasks while the drone is performing its delivery mission, and then retrieve the drone after completing its mission. This improves the utilization rate of both trucks and drones and saves delivery costs.

[0292] Table 10 Number of Locations under Different Location Scales for Two Delivery Modes

[0293]

[0294] ④ To further explore the advantages and disadvantages of the two truck and drone collaborative delivery modes, the average location cost after 10 calculations was calculated, and the cost change rate was calculated. As shown in Table 11, the model proposed in this invention performs better in terms of delivery cost savings. Under different numbers of customer points, the truck and drone synchronous operation delivery mode saves 20.67%, 25.77%, 29.14%, and 19.47% of the cost compared with the truck and drone asynchronous operation delivery mode, respectively.

[0295]

[0296] Table 11. Average site selection costs and cost change rates for different customer location sizes under the two models.

[0297]

[0298] In summary, the truck stop location model proposed in this invention for synchronous operation and collaborative delivery of trucks and drones is verified to be superior in terms of location cost and more in line with actual delivery scenarios by increasing the number of algorithm operations, comparing the location cost under different customer point scales, comparing the number of location locations under different delivery modes, and comparing the rate of change of location cost in actual cases.

[0299] Drone task allocation results

[0300] To verify the performance of the improved artificial bee colony algorithm, the fifth set of tasks with a scale of 100 customer points was solved. Taking the time balance of drone task completion as the objective function, the improved artificial bee colony algorithm was iterated 200 times to solve for the relevant model parameters. The iterative results were obtained by comparing the corresponding drone path planning scheme with the time difference of drone completion of a set of delivery tasks, as shown in the figure below. Figure 6 As shown.

[0301] Depend on Figure 6 It can be seen that the improved artificial bee colony algorithm stabilizes and reaches its optimal solution after about 40 iterations. Compared with the standard artificial bee colony algorithm, it improves the problem of easily getting trapped in local optima, and the improved algorithm has a significant improvement in convergence speed and solution accuracy, with a 16% improvement in the time balance solution accuracy of the fifth task.

[0302] This task requires four drones to complete the delivery mission. The specific task execution order and flight path length of each drone are shown in Table 12. The allocation results are as follows: Figure 7 As shown.

[0303] Table 12 Flight Paths of Each UAV

[0304]

[0305] Based on the aforementioned truck stop location selection results, there are ten sets of tasks for a scale of 100 customer points. In order to eliminate errors, each set of tasks is solved ten times. The final solution results include the time required for each drone to complete each set of delivery tasks, the number of drones required to complete the tasks, and the execution order of each drone delivering to customer points. The remaining nine sets of tasks are then solved, and the final drone path planning results are shown in Table 13.

[0306] Table 13 Solution results for the Kewetech X6L UAV with a scale of 100 customer points.

[0307]

[0308]

[0309] To verify the impact of the drone delivery's climb, level flight, and landing states on the drone path planning results, the first set of tasks at each scale of 25, 50, 75, and 100 customer points were selected for study. The drone path planning considering the mileage constraint formula (49) generated by the drone's flight state and the drone path planning without considering the flight state were calculated respectively. The results are shown in Table 14.

[0310] Table 14 Comparison of Solution Results for the First Set of Tasks at the Customer Point under Four Quantity Scales: Whether or Not the Drone Flight Status Was Considered

[0311]

[0312] As shown in the table, when the drone's flight status is not considered, the number of drones required for each task group decreases, while the maximum flight distance of the drone within that task group increases. This is because if the impact of drone climb, level flight, landing, and drone load on drone energy consumption is not considered, the drone flight range calculated during path planning will be greater than the actual flight range. A drone will serve as many customer points as possible within its maximum load range, resulting in a reduction in the number of drones required for the final path planning and an increase in the drone's flight range. Under customer point scales of 75 and 100, the maximum drone flight range calculated without considering drone flight status is 44786m and 43398m, respectively, both exceeding the maximum flight range of the Keweitai X6L (considering the reserved energy consumption coefficient). Therefore, if this planning scheme is followed during actual drone delivery, it may lead to drones failing to reach the target point, posing a safety hazard. Therefore, the drone path planning model proposed in this invention, which considers drone climb, level flight, landing, and drone payload, calculates the required number of drones and drone flight paths more accurately and realistically.

[0313] This invention focuses on truck-drone collaborative delivery. After selecting truck parking locations, it solves for the drone's path planning. Compared to existing drone path planning models, this invention differs in the following ways: ① The proposed truck-drone collaborative delivery path planning model considers the impact of the drone's climb, level flight, and landing states on its actual endurance, as well as the impact of the drone's payload on its endurance; ② This invention uses the balance of drone delivery task completion as the objective function for modeling. Comparative analysis of calculation results follows.

[0314] Taking the first group of tasks at each scale as an example, the solution considering that a drone can deliver to multiple customers at a time is compared with the solution considering that a drone can only serve one customer at a time. The comparison results are shown in Table 15. Table 15 shows that in the first group of delivery tasks with 25, 50, 75, and 100 customer points, compared to the case where a drone can only serve one customer point at a time, the model of this invention saves 3, 6, 10, and 7 drones respectively. Therefore, the drone path planning model proposed in this invention fully considers the economy of the drone delivery process, significantly reducing the number of drones required for each group of delivery tasks and better completing the delivery tasks.

[0315] Table 15 shows the solution results considering different numbers of customer delivery points when drones fly out.

[0316]

[0317] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for drone task allocation and planning in a truck drone synchronous operation and collaborative delivery mode, characterized in that: The specific steps are as follows: (1) First, obtain drone performance data, population density data of the area under study, and logistics demand index data; (2) Based on socio-economic data, the logistics demand levels of each district and county are divided, the number of customer points in each district and county is simulated based on the division results, the specific location of the customer points is simulated based on the population density distribution map, and the specific demand of each customer point is generated using a random generation method. (3) Considering the flight status of the UAV and the impact of the UAV's effective payload on the actual flight range of the UAV, with the minimum delivery cost as the objective function, model the problem of determining the location of the UAV to be released at the truck stop, and use the particle swarm algorithm to solve the above model to determine the location of the truck stop; (4) Establish a drone task allocation model, taking into account that the actual flight range of the drone under the influence of the drone carrying packages and the drone's flight status shall not exceed its maximum flight range, while also taking into account that the effective payload of the drone shall not exceed the maximum load of the drone, and allowing one drone to serve multiple customer points. (5) An improved artificial bee colony algorithm was used to solve the problem. The task allocation results of the UAV were obtained under the scale of multiple customer points to verify its superiority. The improved artificial bee colony algorithm optimizes the process of searching for precise nectar sources by dynamically adjusting the update formula for the position of following bees. It introduces the idea of ​​dynamic adjustment by comparing the current solution of the algorithm with the value of the previous iteration. The two added nectar source update methods are as follows: The introduction of a global guidance mechanism of particle swarm optimization enables the bee colony to search for the overall optimal nectar source, which enhances the ability to search for nectar sources in the later stages of iteration. The specific nectar source update method is shown in equation (57). （57） in, and Let i represent a nectar source near the original nectar source, where i takes the value {1,2,..., SN}, j takes the value {1,2,..., D}, and k takes the value {1,2,..., SN}, and k is not equal to i. This represents the total value of the i-th honey source in the j-th dimension after the search update; yes Random numbers between yes Random numbers between The first position represents the globally optimal position. Dimension value, This reflects the algorithm's ability to search for nectar sources. This reflects the algorithm's ability to perform detailed local searches, from the early to the later stages of the search. The value of decreases linearly. The value of increases linearly, as shown in equations (58) and (59). （58） （59） in, , , , , Indicates the maximum number of iterations. This indicates the current iteration number. During the iterative calculation process, from Gradually decrease to , from Gradually increase to Ultimately, a balance is achieved between global search and detailed local search; An adaptive dynamic adjustment strategy for the learning factor was introduced, which accelerated the information sharing between the current nectar source location and the surrounding nectar source locations. The location update method is as shown in equation (60). （60） in, The memory factor represents the proportion of historical positions recorded in the artificial bee colony algorithm. This indicates the degree of correlation between the current nectar source location and the locations of surrounding nectar sources; random number. The range of values ​​for is given by equation (61). and The formulas for the changes are shown in equations (62) and (63). （61） （62） （63） in, All are constants and satisfy the following conditions: Its value range is all within , The value is , The range of values ​​is , The value is a constant; when the location of surrounding nectar sources is better than the current location, it is taken as... ,otherwise ; It is a random number, taking the value [0,1].

2. The drone task allocation and planning method in the synchronous operation and collaborative delivery mode of truck drones as described in claim 1, characterized in that: The truck docking site selection model, considering payload and UAV flight status, is as follows: (1) Considering the impact of UAV payload and flight status on UAV endurance The power formula for a drone in horizontal flight is expressed by equation (1): （1） The power formula for the UAV during climb is expressed by equation (2): （2） The power formula for the drone landing is expressed by equation (3): （3） in Indicates air density, The total weight includes the drone's own weight and payload. Indicates the rotor area of ​​the drone. Indicates the drone's climb rate. Indicates the drone's descent speed. It is the speed of the drone's horizontal flight. It is the angle of attack during horizontal flight. It is the efficiency coefficient during horizontal flight. , All are empirical coefficients; Linear regression analysis was performed on the power equation (1) of the rotary-wing UAV during horizontal flight, and the following regression equation was obtained: （4） In equation (4), For drone payload, For the effective payload is Horizontal flight power at time These are the regression coefficients; The formula for the actual flight time of the UAV is shown in Equation (5). Substituting Equation (4) into Equation (5), the flight time of the UAV can be calculated. （5） In equation (5), This indicates the actual flight time of the drone. Indicates energy transfer efficiency. Indicates battery capacity, This represents the rated voltage of n batteries. This indicates the power consumption of the drone; Assume the power of the drone during horizontal flight without carrying any packages is... The power during climbing is The power during landing is The drone's own weight is The effective payload carried by the drone is When the UAV carries a payload and flies, in formula (3) for Let the horizontal flight power of the drone carrying the package be... The drone's climb power is The power of the drone during landing is ; The drone was unloaded. The power consumed during takeoff and landing within a given time is converted into the power of the drone in... The power of horizontal flight within a given time, while simultaneously carrying the package on the drone. The power consumed during takeoff and landing within a given time frame is converted into the power consumed by the UAV during unloaded and level flight, and ultimately, this energy consumption is converted into an increase in actual level flight range. （6） （7） （8） （9） （10） In equation (6) The ratio of the power of the drone in horizontal flight when carrying a package to the power of the drone in horizontal flight when unloaded; Equation (7) This represents the ratio of the power of the drone when climbing while carrying a package to the power of the drone when flying horizontally without a package; Equation (8) This represents the ratio of the power of the drone when landing with a package to the power of the drone when flying horizontally without a load; in equation (9) This represents the ratio of the drone's climb power when unloaded to its power when unloaded and in level flight; in equation (10) This represents the ratio of the drone's landing power when unloaded to its power when flying horizontally while unloaded. （11） （12） （13） （14） （15）； Let the horizontal flight time of the UAV be... The ascent and descent times are both The drone's horizontal flight speed is Then, under the condition that the drone is carrying a package, the horizontal flight time of the drone is... The corresponding standard situation is the unloaded range of the drone. As shown in equation (11), during the climb time is The standard scenario for a drone climbing while carrying a package is the drone's range when unloaded. As shown in equation (12), at the landing time is The standard scenario for a drone landing while carrying a package, i.e., the drone's range when unloaded, is: As shown in equation (13), during the climb time is The standard scenario for a drone climbing unloaded is that the drone's range under unloaded conditions is: As shown in equation (14), at the landing time is The standard scenario for an unloaded drone landing, i.e., the drone's range under unloaded conditions, is: As shown in equation (15); (2) Truck parking location model considering payload and UAV flight status Consider the minimum delivery cost as the objective function, which is expressed by the following formula: （16） Cost of selecting truck parking spot locations (in yuan); Order for customers Truck docking points for alternative drone takeoff The value is 1 if the service is available, and 0 otherwise. Order for customers Alternative drones land at truck parking points The value is 1 if the service is available, and 0 otherwise. To consider the drone's payload and flight status, the drone departs from the truck docking point. Takeoff and delivery The customer point landed at the truck parking point. Total distance required (m); A collection of alternative truck parking spots; For customers whose demand exceeds the maximum payload of the drone; For all customer points; For customers who can only be delivered by truck; For the final customer point of delivery by drone; For truck to customer point Fixed costs incurred in delivery (RMB / delivery); As an alternative point If selected as a truck stop, the value is 1; otherwise, it is 0. If customer point d is selected as a truck stop, the value is 1; otherwise, it is 0. （17） （18） （19） （20） （21） （22） （23） （24） （25） （26） （27） （28） （29） Equation (17) indicates that each customer point can only be served by one truck stop that releases the drone; Equation (18) indicates that each customer point can only be served by one truck stop for recycling drones; Equation (19) indicates that a set of truck stops can serve multiple surrounding customer points, and each drone delivery customer point can only be served by a set of truck stops; Equation (20) indicates that the number of truck stops selected for releasing the drone is equal to the number of truck stops selected for subsequently recovering the drone; Equation (21) indicates that every customer point with demand exceeding the maximum load of the drone will be selected as a truck stop; Equation (22) represents the state of the drone when it is carrying a package and when it is empty, taking into account the climbing, landing and horizontal flight states of the drone when it is delivering packages; Equation (23) represents the energy consumption reserve coefficient that the drone needs to meet; Equation (24) indicates that when Customer points that require drone delivery can only exist if they are selected as truck drop-off points for drone deployment. Delivery is carried out by drones that take off from that point; Equation (25) indicates that if Service completion points are only possible when a customer's location is selected as a truck drop-off point for drone recovery. The drone landed; Equation (26) represents the drone from The truck is released from its parking spot and flies towards the customer's location. The value is 1 if a package is being delivered, otherwise it is 0. Equation (27) represents The truck stop selected for releasing the drone is 1, otherwise it is 0; Equation (28) represents the drone's flight from the customer point. Fly to the truck parking point after delivery is completed The value is 1 if the item is recycled, and 0 otherwise. Equation (29) represents The truck stop selected for drone recovery is designated as 1, otherwise it is designated as 0.

3. The drone task allocation and planning method in the synchronous operation and collaborative delivery mode of truck drones as described in claim 1, characterized in that: The drone task allocation model is as follows: Considering the time balance of drone delivery tasks as the objective function, it is expressed by equation (36), where This indicates the longest time a drone can perform a delivery task across a set of truck docking points. This represents the shortest time for a drone to complete a delivery task within a set of truck docking points; The objective function is: （36） The constraints of the model are: （37） （38） （39） （40） （41） （42） （43） （44） （45） （46） （47） （48） （49） （50） （51） （52） （53） A collection of customer points for drone delivery; Customer point collection A subset of, that is, the set of customer points to which a drone is assigned; A set of drone delivery routes; Let be the difference (in seconds) between the maximum and minimum completion times for delivery tasks corresponding to a set of truck stops; The collection of mission completion times for all drones; To represent the drone delivery route The first in One node; For the first There are points in the path Time The value is 1 if it is 1, otherwise it is 0. If point In the If the path is valid, the value is 1; otherwise, it is 0. Truck drop-off points for drones deployed in this group's delivery mission; A truck docking point for the recovery of drones used in this group's delivery mission; For drones from point arrive Flight time (s); Order for customers The demand (N); For drones at customer points The effective load (N) at that time; The maximum payload (N) of the drone; The truck's speed (m / s); For trucks from truck docking point to truck parking spot The road distance (m); For trucks from truck docking point to truck parking area The travel time (s), The value is 1 if there is a point a' to point b' in the d' (d'∈ K) path, and 0 otherwise; For drones from truck docking points To the customer point The Euclidean distance (m); For drones at nodes The previous node and the load is The ratio of the drone's climb power to its unloaded horizontal flight power. For drones at nodes Load is The ratio of landing power to the unloaded horizontal flight power of the UAV. For drones from nodes Fly from the previous node to the next node Load is The ratio of the horizontal flight power during flight to the unloaded horizontal flight power of the UAV; Equation (37) indicates that the time for each drone to complete the delivery task is the sum of the drone flight delivery time and the take-off and landing time, minus the truck's travel time at the truck parking point; Equation (38) represents the drone's flight from the customer point. Fly to customer point Time required; Equation (39) represents the truck docking point where the trucks take off from the drone in this group of delivery tasks. Drive to the truck parking area where the drone will land. Time required; Equation (40) represents the point during the drone delivery flight if arrive If there is a flight path for the drone, then one drone must be used to complete this delivery task. Equation (41) indicates that if there is drone delivery Therefore, drones must also exist. Fly out; Equation (42) indicates that when the customer points , In the When the drone is on a delivery route, the drone is at the node Effective payload at that time; Equation (43) indicates that the effective payload carried by the UAV during a single trip should be within the maximum load range of the UAV; Equation (44) indicates that each customer point can only be delivered by one drone, that is, each customer point has only one delivery route; Equations (45) and (46) indicate that the selected truck stop must exist in every drone delivery route; Equation (47) indicates that there must be a delivery route between the selected truck stop where the drone takes off and the truck stop where the drone lands, and the truck stop must be the starting point and the end point of the drone delivery route. This route is not considered when calculating the actual flight distance of the drone and the delivery time of the drone. Equation (48) represents only points Existence It only exists in the path. arrive Drone delivery routes; Equation (49) indicates that each delivery route of the UAV takes into account the UAV load, and the total flight distance after the influence of the UAV's climb and landing status factors cannot exceed the UAV's maximum flight distance. Equations (50) and (51) represent the elimination of constraints on sub-loops. For set The number of points contained in it; Equation (52) indicates that if the customer orders In the If a path passes through a given path, the value is 1; otherwise, it is 0. Equation (53) indicates that in the first... If there are any issues along the drone delivery route arrive The flight path is 1 if it is true, otherwise it is 0.

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