An Optimization Method for the UAV Package Collection Path under the Constraint of No-Fly Zone

Abstract

The present invention relates to a method for optimizing the path of an unmanned aerial vehicle (UAV) to collect packages under the constraint of no-fly zones, comprising the following steps: S1: Establish a package collection scenario model for a single UAV, multiple users, and multiple no-fly zones, as well as a flight path model for the single UAV; S2: Establish a single-UAV package collection model, a UAV-user communication connection model, and a no-fly zone model; S3: Under the constraint conditions, taking the UAV flight path and the package collection strategy as optimization variables, construct a UAV path optimization problem to maximize the total value; S4: Introduce new variables in step S3 to rewrite the problem constraints, and transform the complex optimization problem into an equivalent standard difference-of-convex problem; S5: Solve the problem by using the penalty concave-convex algorithm to obtain a flight path with the maximum total value of the collected packages within a certain flight time. The present invention can provide a method for optimizing the collection path to maximize the total value of the collected packages.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to a method for optimizing the drone parcel collection path under no-fly zone constraints. Background Art

[0002] In the past decade, drones have been widely used in various civilian fields, including aerial photography, logistics, agriculture, infrastructure inspection, etc. With the further development of technology, the cost of drones has been further reduced. Coupled with the fact that drones are not restricted by traditional infrastructure, they can be used for "last-mile" delivery, urban and rural delivery, and internal logistics, etc. to reduce costs. In various applications of drones, optimizing the safe and efficient flight path is a very crucial issue; there are some no-fly zones in cities where drones are prohibited from flying to avoid environmental threats, national security sensitive factors, or policy factors, such as high-voltage power facilities, military facilities, airports, government buildings, etc.

[0003] The problem of optimizing the safe and efficient drone path involves optimizing time, distance, energy consumption, or other objectives while the drone writes a predetermined task, and also considering other restrictions such as parcel weight, no-fly zones, battery or fuel limitations, and nodes to be visited. These latter problems depend on further logistics applications because it will determine the type of drones used and the parameters or additional constraints to be considered, such as time windows, pick-up and delivery constraints, and battery or fuel limitations, etc.

[0004] Current related research generally only considers optimizing time, distance, or energy consumption, which is not very suitable for practical applications because different goods generally have different unit values, and the optimization objective should increase the measurement of the value of goods to improve the benefit of a single flight mission. Moreover, existing research generally does not consider the no-fly zone restrictions in the drone flight mission area, which may not be applicable to the actual drone flight path planning. The drone flight path should be as far away from the no-fly zone as possible, but this will cause an increase in flight time and may lead to the inability to complete the flight mission within the specified time. Summary of the Invention

[0005] Aiming at the deficiencies of the above-mentioned prior art, the technical problem to be solved by this patent application is how to provide a method for optimizing the drone parcel collection path under no-fly zone constraints that can maximize the total value of the collected parcels.

[0006] To solve the above technical problem, the present invention adopts the following technical solutions:

[0007] A method for optimizing the drone parcel collection path under no-fly zone constraints, comprising the following steps:

[0008] S1: Establish a package collection scenario model for a single unmanned aerial vehicle (UAV), multiple users, and multiple no-fly zones, as well as a single-UAV flight path model; S2: Establish a single-UAV package collection model, a UAV-user communication connection model, and a no-fly zone model; S3: Under the constraint conditions, with the UAV flight path and package collection strategy as optimization variables, construct a UAV path optimization problem that maximizes the total value; S4: Introduce new variables in step S3 to rewrite the problem constraints and transform the complex optimization problem into an equivalent standard difference-of-convex problem; S5: Solve the problem by using the penalty concave-convex algorithm to obtain the flight path with the maximum total value of the collected packages within a certain flight time.

[0009] Furthermore, the constraint conditions in step S3 are mission time, start and end points, ground user positions, maximum load, minimum signal-to-noise ratio at package collection points, and no-fly zones.

[0010] Furthermore, the package collection scenario model for a single UAV, multiple users, and multiple no-fly zones established in step S1 includes the following process; it includes one UAV, assuming that the minimum received signal-to-noise ratio that can be received by the UAV is θ, K users, denoted by , where each user has a device for sending signals, assuming that the users are stationary within T time slots, and are respectively denoted by u k ∈R 2×1 representing the two-dimensional coordinates of user k, N no-fly zones, denoted by , and o n ∈R 2×1 representing the two-dimensional coordinates of the center of the no-fly zone, R n representing the radius of the no-fly zone, and h representing the height of the no-fly zone, where the no-fly zones are high-voltage power facilities, military facilities, airports, and government buildings.

[0011] Furthermore, the single-UAV flight path model established in step S1 includes the following process; use to represent the set of T time slots required for the UAV to perform the package collection task, q[t]∈R 2×1 to represent the horizontal position of the UAV at time slot t∈T, define D max as the maximum flight distance of the UAV within one time slot, and q[t] satisfies ||q[t] - q[t - 1]|| ≤ D max , where t∈T\{1}, use q start = q[1] to represent the starting position, use q end = q[T] to represent the ending position, use to represent the flight path of the UAV, and D(Q) to represent the total flight distance of the UAV within T time slots, where The task of the UAV is to fly from q start to q end within T time slots.Collect the packages of K users in the presence of N no - fly zones.

[0012] Furthermore, establishing the single - UAV package collection model in step S2 includes the following steps:

[0013] A1: Describe the single - UAV package collection strategy; the maximum load of the UAV is W kilograms, and user k has a package with weight and value of w k kilograms and v k respectively. Assume that the UAV cannot collect all the packages at once, i.e., ∑ k∈K w k >> W. Use the indicator function variable c k ∈{0, 1} to represent the collection situation of user k's package, where c k = 1 indicates that user k's package is collected by the UAV, and c k = 0 indicates that user k's package is not collected by the UAV. The total weight of the packages collected by the UAV is ∑ k∈K c k w k ≤W;

[0014] A2: Calculate the total value of the collected packages. Use C to represent the strategy of the packages collected by the UAV, where Use V(C) to represent the total value of the packages collected by the UAV, that is

[0015] Furthermore, in step S2, establishing the UAV - user communication connection model includes the following processes:

[0016] B1: Calculate the physical distance d k [t] between the UAV and the user. Use to calculate the physical distance between the UAV and the user, where h > 0 represents the flight altitude of the UAV;

[0017] B2: Calculate the signal - to - noise ratio γ k [t] of the UAV receiving the signal from user k at the t - th time slot. Use to represent the channel gain of the UAV, where ρ 0 represents the reference channel gain at a distance of one meter. Use to represent the signal - to - noise ratio of the UAV receiving the uplink signal from user k at the t - th time slot, where p k represents the transmission power of user k, and N 0 represents the noise power;

[0018] B3: Determine whether the UAV has reached the user's package collection area. Determine whether γ k [t] is greater than the minimum received signal - to - noise ratio θ of the UAV. γ k[t]Greater than θ means that the UAV in flight can find user k, and the UAV can fly to the package collection area near user k to collect the package, that is, the collection situation c of the package of user k k ≤∑ t∈T I[γ k ≥θ], where k ∈ K and I[·] represents the indicator function.

[0019] Furthermore, the no-fly zone constraint is established in step S2 using the following formula:

[0020]

[0021] where n ∈ N, t ∈ T, o n is the center of the no-fly zone n ∈ N, and R n is the radius of the no-fly zone.

[0022] Furthermore, the UAV path optimization problem of maximizing the total value in step S3 includes calculating the total value of the packages collected by the UAV. Under the constraints of the UAV package collection task time, the UAV flight starting point and target point, the ground user location, the UAV maximum payload, the minimum received signal-to-noise ratio of the UAV at the package collection point, and the no-fly zone, the UAV flight path and the UAV package collection strategy are jointly optimized to construct the UAV path optimization problem P1 of maximizing the total value of a single task.

[0023] Furthermore, step S4 specifically includes introducing new binary variables to replace the indicator function in optimization problem P1 by the big M method, and transforming the original binary variables and the newly introduced binary variables into equivalent continuous constraints to obtain the transformed equivalent optimization problem P2. Optimization problem P2 is a DC problem.

[0024] Furthermore, step S5 includes the following steps. First, optimization problem P2 is relaxed to optimization problem P3. Optimization problem P3 is a penalty DC problem. Then, in the j (j = 1, 2,...) -th iteration, the concave constraint in optimization problem P3 is linearized and a first-order Taylor expansion is performed at a given point to obtain a convex approximation sub-problem, that is, optimization problem P4). Optimization problem P4 is a standard convex problem.

[0025] This solution has the following advantages:

[0026] 1. The present invention comprehensively considers the influence of factors such as the UAV flight time, the ground user location, the flight starting point and target point, the weight and value of the collected packages, the no-fly zone, and the communication signal-to-noise ratio on the UAV flight path optimization, and proposes a method for optimizing the UAV package collection path under the no-fly zone constraint. By solving a challenging non-convex mixed-integer optimization problem, the most suitable UAV flight path is selected, thereby improving the total value of a single UAV flight mission.

[0027] 2. The present invention aims to increase the total value of a single package collection by simultaneously considering the package weight and value when optimizing the package collection strategy.

[0028] 3. The present invention aims to improve the safety of the flight path and avoid national security sensitive factors or policy factors by avoiding no-fly zones when planning the flight path of the unmanned aerial vehicle.

[0029] 4. The present invention aims to determine the package collection point area by calculating the received signal-to-noise ratio of the signal sent by the user received by the unmanned aerial vehicle to determine whether the unmanned aerial vehicle reaches the package collection point area of the user.

[0030] 5. The present invention aims to reduce the computational complexity by transforming a complex non-convex mixed-integer optimization problem into an equivalent DC problem and using the PCCP algorithm to solve the equivalent DC problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flowchart of an optimization method for the unmanned aerial vehicle package collection path under no-fly zone constraints;

[0032] Figure 2 It gives an application scenario diagram of an optimization method for the unmanned aerial vehicle package collection path under no-fly zone constraints;

[0033] Figure 3 It is a flowchart for solving the optimization problem P1;

[0034] Figure 4 It is a flowchart for using the PCCP algorithm to solve the optimization problem P2;

[0035] Figure 5 It is the path diagram of the unmanned aerial vehicle collecting packages and the total value of the collected packages when the starting point is the same and the target points are different in the simulation analysis of the method proposed by the present invention;

[0036] Figure 6 It is the total value of the collected packages (average value of 500 simulations) when the method proposed by the present invention and the comparative method have a fixed starting point, target point and maximum load of the unmanned aerial vehicle at different time slot numbers;

[0037] Figure 7 It is the total value of the collected packages (average value of 500 simulations) when the method proposed by the present invention and the comparative method have a fixed starting point, target point and time slot number at different maximum loads of the unmanned aerial vehicle. DETAILED DESCRIPTION OF THE INVENTION

[0038] The present invention will be further described in detail below with reference to the accompanying drawings. In the description of the present invention, it should be understood that the orientation or positional relationship indicated by orientation words such as "upper, lower" and "top, bottom" is usually based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description. Without contrary description, these orientation words do not indicate and imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation on the protection scope of the present invention; the orientation words "inside, outside" refer to the inside and outside relative to the contour of each component itself.

[0039] As Figure 1-7 shown, an optimization method for the UAV package collection path under no-fly zone constraints includes the following steps: S1: Establish a package collection scenario model for a single UAV, multiple users, and multiple no-fly zones, as well as a single UAV flight path model; S2: Establish a single UAV package collection model, a UAV-user communication connection model, and a no-fly zone model; S3: Under the constraint conditions, with the UAV flight path and the package collection strategy as optimization variables, construct a UAV path optimization problem that maximizes the total value; S4: Introduce new variables in step S3 to rewrite the problem constraints, and transform the complex optimization problem into an equivalent standard convex difference problem; S5: Solve the problem by using the penalty concave-convex algorithm to obtain the flight path with the maximum total value of the collected packages within a certain flight time.

[0040] Specifically, the constraint conditions in step S3 are task time, starting point and target point, ground user location, maximum load, minimum signal-to-noise ratio at the package collection point, and no-fly zone.

[0041] Specifically, the package collection scenario model for a single UAV, multiple users, and multiple no-fly zones established in step S1 includes the following process; it includes a UAV. Assume that the minimum received signal-to-noise ratio that can be accepted by the UAV is θ, K users, denoted by where each user has a device for sending signals. Assume that the users are stationary within T time slots, and are respectively denoted by u k ∈R 2×1 representing the two-dimensional coordinates of user k, N no-fly zones, denoted by using o n ∈R 2×1 to represent the two-dimensional coordinates of the center of the no-fly zone, using R n to represent the radius of the no-fly zone, and using h to represent the height of the no-fly zone, where the no-fly zones are high-voltage power facilities, military facilities, airports, and government buildings.

[0042] Specifically, the single UAV flight path model established in step S1 includes the following process; using to represent the set of T time slots required for the UAV to perform the package collection task, and q[t]∈R 2×1Denote the horizontal position of the UAV at time slot \(t\in T\), and define \(D\) max as the maximum flight distance of the UAV within a time slot. \(q[t]\) satisfies \(\|q[t] - q[t - 1]\|\leq D\) max , where \(t\in T\setminus\{1\}\). Let \(q\) start \(= q[1]\) represent the starting position, and \(q\) end \(= q[T]\) represent the ending position. Denote the flight path of the UAV, and \(D(Q)\) denote the total flight distance of the UAV within \(T\) time slots, where the task of the UAV is to fly from \(q\) start to \(q\) end and collect the packages of \(K\) users in the presence of \(N\) no - fly zones.

[0043] Specifically, establishing the single - UAV package collection model in step S2 includes the following steps:

[0044] A1: Describe the single - UAV package collection strategy; the maximum load of the UAV is \(W\) kilograms. User \(k\) has a package with weight and value \(w\) k kilograms and \(v\) k respectively. Assume that the UAV cannot collect all packages at once, i.e., \(\sum\) k∈K \(w\) k \(\gg W\). Use the indicator function variable \(c\) k \(\in\{0, 1\}\) to represent the collection situation of user \(k\)'s package, where \(c\) k \( = 1\) indicates that user \(k\)'s package is collected by the UAV, and \(c\) k \( = 0\) indicates that user \(k\)'s package is not collected by the UAV. The total weight of the packages collected by the UAV \(\sum\) k∈K \(c\) k \(w\) k \(\leq W\);

[0045] A2: Calculate the total value of the collected packages. Let \(C\) represent the strategy of the packages collected by the UAV, where let \(V(C)\) represent the total value of the packages collected by the UAV, i.e.,

[0046] Specifically, in step S2, establishing the UAV - user communication connection model includes the following processes:

[0047] B1: Calculate the physical distance \(d\) k [t]\) between the UAV and the user. Use to calculate the physical distance between the UAV and the user, where \(h>0\) represents the flight altitude of the UAV;

[0048] B2: Calculate the signal - to - noise ratio \(\gamma\) k [t]\) of the UAV receiving the signal from user \(k\) at the \(t\) - th time slot. Use denotes the channel gain of the UAV, where ρ 0 denotes the reference channel gain at a distance of one meter, and is denoted by denotes the signal-to-noise ratio of the UAV receiving the uplink signal of user k in the t-th time slot, where p k denotes the transmission power of user k, and N 0 denotes the noise power;

[0049] B3: Determine whether the UAV has reached the user's package collection area, and determine whether γ k [t] is greater than the minimum received signal-to-noise ratio θ of the UAV. γ k [t] being greater than θ means that the flying UAV can find user k, and the UAV can fly to the package collection area near user k to collect packages, that is, the collection situation c k ≤∑ t∈T I[γ k ≥θ], where k ∈ K, and I[·] represents the indicator function.

[0050] Specifically, the no-fly zone constraint is established in step S2 using the following formula:

[0051]

[0052] where n ∈ N, t ∈ T, and o n is the center of the no-fly zone n ∈ N, and R n is the radius of the no-fly zone.

[0053] Specifically, the UAV path optimization problem of maximizing the total value in step S3 includes calculating the total value of the packages collected by the UAV. Under the constraints of the UAV package collection task time, the UAV flight starting point and target point, the ground user location, the UAV maximum payload, the minimum received signal-to-noise ratio of the UAV at the package collection point, and the no-fly zone, jointly optimize the UAV flight path and the UAV package collection strategy to construct the UAV path optimization problem P1 of maximizing the total value of a single task.

[0054] Specifically, the following formula is used:

[0055] P1:

[0056] s.t.C1:

[0057] C2: c k ∈ {0, 1}, k ∈ K

[0058] C3:

[0059] C4: c k ≤∑ t∈T I[γ k≥θ], k ∈ K

[0060] C5:

[0061] Among them, the constraint C1 means that the maximum flight distance of the UAV in each time slot is D max , the starting point is q[1] = q start , the ending point is q[T] = q end , the constraint C2 indicates that c k [t] is a binary variable. The constraint C3 ensures that the total weight of the packages collected by the UAV does not exceed the load limit W. The constraint C4 means that the UAV can find the package collection area of the user only when the received signal-to-noise ratio is greater than the threshold θ. The constraint C5 represents the no-fly zone constraint, and the UAV must avoid flying in the no-fly zone;

[0062] The objective of the optimization problem P1 contains binary variables and the constraints contain indicator functions, integer constraints, and non-convex constraints. It is a complex mixed-integer non-convex problem and an NP (Non-deterministic Polynomial) hard problem, which needs to be transformed before solving to reduce the computational complexity.

[0063] Specifically, step S4 specifically includes introducing new binary variables through the big-M method to replace the indicator function in the optimization problem P1, and transforming the original binary variables and the newly introduced binary variables into equivalent continuous constraints to obtain the transformed equivalent optimization problem P2. The optimization problem P2 is a DC problem.

[0064] Specifically, the detailed steps are as follows:

[0065] 1) Eliminate the indicator function:

[0066] Introduce new binary variables through the big-M method Transform the constraint C4 containing the indicator function into the following several constraints:

[0067] C6: y k [t] ∈ {0, 1}, k ∈ K, t ∈ T

[0068] C7:

[0069] C8:

[0070] Among them, in the constraint C8 M k [t] is a constant much larger than ||q[t] - u k || 2 ;

[0071] 2) Eliminate the binary variables:

[0072] Convert the original binary variable Q (constraint C2) and the newly introduced binary variable Y (constraint C6) into the following equivalent continuous constraints:

[0073] C9: c k ∈ [0, 1], k ∈ K

[0074] C10: y k [t] ∈ [0, 1], k ∈ K, t ∈ T

[0075] C11: c k (1 - c k ) ≤ 0, k ∈ K

[0076] C12: y k [t](1 - y k [t]) ≤ 0, k ∈ K, t ∈ T

[0077] Through sub - steps 1) and 2), the optimization problem P1 is equivalently transformed into the following equivalent optimization problem P2:

[0078] P2:

[0079] s.t. C1, C3, C5, C7 - C12

[0080] Except for C5, C11, and C12, the constraints of the optimization problem P2 are convex. The left - hand sides of the non - convex constraints are concave with respect to the optimization variables (C, Q, Y). Therefore, the optimization problem P2 is a standard DC problem and can be solved using the well - known PCCP algorithm.

[0081] Specifically, step S5 includes the following steps. First, the optimization problem P2 is relaxed to the optimization problem P3, and the optimization problem P3 is a penalty DC problem. Then, in the j - th (j = 1, 2,...) iteration, the concave constraints in the optimization problem P3 are linearized and a first - order Taylor expansion is performed at a given point to obtain a convex approximate sub - problem, that is, the optimization problem P4). The optimization problem P4 is a standard convex problem.

[0082] By using the PCCP algorithm, obtain the UAV flight path with the maximum total value within a certain flight time;

[0083] Furthermore, the specific content of the PCCP algorithm is as follows:

[0084] 1) Relax the optimization problem P2 to a penalty DC problem, and the specific content is as follows:

[0085] By adding slack variables to the constraints C11, C12, and C13 and penalizing the sum of the corresponding slackness, the optimization problem P2 is relaxed to the following mathematical model P3:

[0086] P3:

[0087] s.t. C1, C3, C7, C8, C9, C10

[0088] C13: c k (1 - c k ) ≤ α k , k ∈ K

[0089] C14: y k [t](1 - y k [t]) ≤ β k [t], k ∈ K, t ∈ T

[0090] C15:

[0091] C16: α k ≥ 0, k ∈ K

[0092] C17: β k [t] ≥ 0, k ∈ K, t ∈ T

[0093] C18: δ n [t] ≥ 0, n ∈ N, t ∈ T

[0094] where η > 0 is the penalty function factor and the total penalty is

[0095]

[0096] where are the slack variables of constraints C5, C11, and C12 respectively;

[0097] The optimization problem P3 is the penalty DC problem;

[0098] 2) Transform the optimization problem P3 into a series of convex approximations as follows:

[0099] Respectively linearize the concave parts of constraints C13, C14, and C15, that is -(y k [t]) 2 and -||q[t] - o n || 2 and perform a first-order Taylor expansion at the given point (C (j) , Q (j) , Y (j) ) in the j-th (j = 1, 2,...) iteration of the PCCP algorithm, where For example, in the j-th iteration, constraints C13, C14, and C15 can be approximated as the following linear constraints:

[0100] C19:

[0101] C20:

[0102] C21:

[0103] Among them, (·) in constraint C21 T represents transpose. By replacing C13, C14, and C15 with constraints C19, C20, and C21, the convex approximate sub-problem P4 of the j-th iteration of the PCCP algorithm can be obtained:

[0104] P4:

[0105] s.t. C1, C3, C7, C8, C9, C10, C16 - C21

[0106] Among them, η (j) is the penalty factor of the j-th iteration;

[0107] The optimization problem P4 is a standard convex problem and can be solved using standard convex optimization techniques or software tools (e.g., CVX);

[0108] 3) Use an iterative algorithm to solve the optimization problem P2:

[0109] The flow of the iterative algorithm A1 for solving the optimization problem P2 is as shown in the appendix Figure 4 as follows:

[0110] F1. Given any starting point (C (0) , Q (0) , Y (0) ), η (0) > 0, η max and v > 1;

[0111] F2. Assign 0 to j;

[0112] F3. Assign the solution of the mathematical model P4 to (C (j+1) , Q (j+1) , Y (j+1) );

[0113] F4. Assign min{vη (j+1) , η j} to η max ;

[0114] F5. Assign j + 1 to j;

[0115] F6. If the algorithm converges, stop the iteration; otherwise, go to F3;

[0116] The algorithm A1 can converge to a fixed point of the optimization problem P3. Since η > ηmax When the optimization problem P3 and the optimization problem P2 are equivalent, it can be inferred that the output of the optimization problem P1 is also a fixed point of the optimization problem P2. Therefore, the computational complexity of the optimization problem P1 is mainly determined by solving the optimization problem P4;

[0117] If CVX is used to solve the optimization problem P4, the computational complexity is O(A 3.5 log(1 / ò)), where A = T(2K + N + 2) + 2K is the total number of variables, and ò > 0 is the accuracy of the given solution;

[0118] Furthermore, the present invention conducts a simulation analysis by using the proposed method for optimizing the UAV parcel collection path under no-fly zone constraints;

[0119] Appendix Figure 5 shows the path map of the UAV collecting parcels and the total value of the collected parcels when the starting point is the same and the target points are different in the simulation analysis of the method proposed in the present invention. From the appendix Figure 5 the following can be seen:

[0120] 1) The flight path of the UAV does not pass through any no-fly zone, which proves that the proposed algorithm A1 of the present invention can effectively avoid flying into the no-fly zone;

[0121] 2) The flight path of the UAV passes through the collection point area because the UAV needs to collect users' parcels in the collection point area;

[0122] 3) The total value of the parcels collected by the UAV on the paths from different target points is different, that is, due to the geographical differences of the destination points, the total value of the parcels collected at different destination points is different.

[0123] Appendix Figure 6 and Appendix Figure 7 show the relationship diagrams of the maximum flight time slot and the maximum load of the UAV and the total value of the collected parcels when the method proposed in the present invention and three other comparison methods are used for UAV parcel collection. The values therein are the averages of 500 simulations. The contents of the comparison methods are as follows:

[0124] 1) The comparison method 1 adopts a parcel collection scheme with value priority, and preferentially collects parcels with higher value under the constraint of the maximum load;

[0125] 2) The comparison method 2 adopts a parcel collection scheme with weight priority, and preferentially collects lighter parcels under the constraint of the maximum load;

[0126] 3) The comparison method 3 adopts a parcel collection scheme with distance priority, and preferentially collects parcels closer to the target point under the constraint of the maximum load.

[0127] For each package collection method, after determining the package collection plan, the UAV path can be obtained by Algorithm A1 that fixes C, as shown in the appendix Figure 6 As can be seen, when the number of time slots is less than or equal to 13, the total value of the packages collected by the UAV is 0 because there is no feasible solution to the optimization problem P2 at this time, that is, the UAV does not have enough time to collect the user packages, as shown in the appendix Figure 6 and the appendix Figure 7 As can be seen, the total value of the packages collected increases with the increase of the maximum flight time slots and the maximum load of the UAV. The total value of the packages collected by the method proposed in the present invention is higher than that of the comparative method, which proves the advantage of the method proposed in the present invention in efficiently collecting packages.

[0128] Based on the comprehensive analysis of the appendix Figure 5 , the appendix Figure 6 and the appendix Figure 7 It can be seen that the method proposed in the present invention can effectively jointly optimize the UAV path and the package collection strategy, and avoid the no-fly zone to maximize the total value of the collected packages.

[0129] Finally, it should be noted that those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these changes and modifications.

Claims

1. A method for optimizing the drone package collection path under no-fly zone constraints, characterized in that, it includes the following steps: S1: Establish a package collection scenario model for a single drone, multiple users, and multiple no-fly zones, as well as a single drone flight path model; S2: Establish a single drone package collection model, a drone-user communication connection model, and a no-fly zone model; S3: Under the constraint conditions, with the drone flight path and the package collection strategy as optimization variables, construct a drone path optimization problem that maximizes the total value; S4: Introduce new variables in step S3 to rewrite the problem constraints, and transform the complex optimization problem into an equivalent standard difference of convex problem; S5: Solve the problem by using the penalty concave-convex algorithm to obtain the flight path with the maximum total value of the collected packages within a certain flight time; The constraint conditions in step S3 are the task time, the starting point, the target point, the ground user location, the maximum load, the minimum signal-to-noise ratio at the package collection point, and the no-fly zone.

2. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 1, characterized in that, the package collection scenario model for a single drone, multiple users, and multiple no-fly zones established in step S1 includes the following processes; It includes a drone. Assume that the minimum received signal-to-noise ratio for the drone to receive the signal is θ, and there are K users, denoted by , where each user has a device for sending signals. Assume that the users are stationary within T time slots, and the two-dimensional coordinates of user k are denoted by u k ∈R 2×1 . There are N no-fly zones, denoted by . The two-dimensional coordinates of the center of the no-fly zone are denoted by o n ∈R 2×1 , and the radius of the no-fly zone is denoted by R n . The height of the no-fly zone is denoted by h. The no-fly zones are high-voltage power facilities, military facilities, airports, and government buildings.

3. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 2, characterized in that, In step S1, a single UAV flight path model is established, including the following processes: Use to represent the set of T time slots required for the UAV to perform the package collection task, and use q[t] ∈ R 2×1 to represent the horizontal position of the UAV at time slot t ∈ T. Define D max as the maximum flight distance of the UAV within one time slot. q[t] satisfies ||q[t] - q[t - 1]|| ≤ D max , where t ∈ T\{1}. Use q start = q[1] to represent the starting position, and use q end = q[T] to represent the ending position. Use to represent the flight path of the UAV, and use D(Q) to represent the total flight distance of the UAV within T time slots, where the task of the UAV is to fly from q start to q end and collect packages from K users in the presence of N no-fly zones.

4. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 3, characterized in that, the steps for establishing the single drone package collection model in step S2 include the following steps: A1: Describe the single UAV package collection strategy: The maximum load of the UAV is W kilograms. User k has a package with a weight and value of w k kilograms and v k respectively. Assume that the UAV cannot collect all the packages at once, i.e., ∑ k∈K w k >> W. Use the indicator function variable c k ∈ {0, 1} to represent the collection status of user k's package, where c k = 1 means that user k's package is collected by the UAV, and c k = 0 means that user k's package is not collected by the UAV. The total weight of the packages collected by the UAV ∑ k∈K c k w k ≤ W; A2: Calculate the total value of the collected packages. Let \(C\) represent the strategy of the drone for collecting packages, where let \(V(C)\) represent the total value of the packages collected by the drone, that is 5. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 4, characterized in that, in step S2, the process of establishing the drone-user communication connection model includes the following: B1: Calculate the physical distance d between the drone and the user k [t], and use to calculate the physical distance between the drone and the user, where h > 0 represents the flight altitude of the drone; B2: Calculate the signal-to-noise ratio γ of the UAV receiving the signal from user k in the t-th time slot k [t], where represents the channel gain of the UAV, where ρ 0 represents the reference channel gain at a distance of one meter, and represents the signal-to-noise ratio of the UAV receiving the uplink signal from user k in the t-th time slot, where p k represents the transmission power of user k, and N 0 represents the noise power; B3: Determine whether the drone has reached the user's package collection area and determine if γ k [t] is greater than the minimum received signal-to-noise ratio θ of the drone. If γ k [t] is greater than θ, it means that the drone in flight can find user k, and the drone can fly to the package collection area near user k to collect the package. That is, the collection situation c of the package of user k k ≤∑ t∈T I[γ k [t]≥θ], where k ∈ K and I[·] represents the indicator function.

6. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 5, characterized in that, the no-fly zone constraint established in step S2 adopts the following formula: where \(n\in N\), \(t\in T\), \(o\) n is the center of the no - fly zone \(n\in N\), \(R\) n is the radius of the no - fly zone.

7. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 6, characterized in that, the process of constructing the drone path optimization problem that maximizes the total value in step S3 includes calculating the total value of the packages collected by the drone. Under the constraints of the drone package collection task time, the drone flight starting point and target point, the ground user location, the maximum effective load of the drone, the minimum received signal-to-noise ratio of the drone at the package collection point, and the no-fly zone, jointly optimize the drone flight path and the drone package collection strategy to construct a drone path optimization problem P1 that maximizes the total value of a single task.

8. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 7, characterized in that, step S4 specifically includes introducing new binary variables through the big M method to replace the indicator function in the optimization problem P1, and transforming the original binary variables and the newly introduced binary variables into equivalent continuous constraints to obtain the transformed equivalent optimization problem P2, and the optimization problem P2 is a DC problem.

9. A method for optimizing the drone package collection path under no-fly zone constraints according to claim 8, characterized in that, step S5 It includes the following steps. First, the optimization problem P2 is relaxed into the optimization problem P3, and the optimization problem P3 is a penalized DC problem. Then, in the j-th (j = 1, 2,...) iteration, the concave constraints in the optimization problem P3 are linearized and a first-order Taylor expansion is performed at a given point to obtain a convex approximate sub-problem, that is, the optimization problem P4, and the optimization problem P4 is a standard convex problem.

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