CN114527791A - Multi-unmanned aerial vehicle package cooperation delivery path optimization method under constraint of no-fly zone - Google Patents

Multi-unmanned aerial vehicle package cooperation delivery path optimization method under constraint of no-fly zone Download PDF

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CN114527791A
CN114527791A CN202210070393.8A CN202210070393A CN114527791A CN 114527791 A CN114527791 A CN 114527791A CN 202210070393 A CN202210070393 A CN 202210070393A CN 114527791 A CN114527791 A CN 114527791A
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unmanned aerial
formation
aerial vehicle
package
delivery
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刘兰徽
方能炜
侯伯
朱林全
郑屹
龙萍
高信波
温万里
贾云健
关婷
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Chongqing Industrial Big Data Innovation Center Co ltd
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Abstract

The invention relates to a multi-unmanned aerial vehicle package cooperation delivery path optimization method under the constraint of a no-fly zone, which comprises the following steps: s1: establishing an unmanned aerial vehicle formation flight path model, wherein the unmanned aerial vehicle formation flight path model comprises horizontal coordinates and flight heights of unmanned aerial vehicle formation, a starting point and an end point of the unmanned aerial vehicle formation, a minimum distance between unmanned aerial vehicles and a maximum flight speed index and a performance control parameter of the unmanned aerial vehicle; s2: establishing a no-fly zone model and a parcel delivery zone model; s3: establishing an unmanned aerial vehicle formation package delivery task distribution model; s4: constructing a multi-unmanned aerial vehicle package cooperative delivery optimization problem under the constraint of a flight prohibition area; s5: the optimization problem proposed in the construction step S4 is solved. The invention has the advantages of improving the efficiency of parcel delivery and increasing the benefit of parcel delivery.

Description

Multi-unmanned aerial vehicle package cooperation delivery path optimization method under constraint of no-fly zone
Technical Field
The invention relates to the technical field of wireless communication, in particular to a multi-unmanned aerial vehicle package cooperation delivery path optimization method under the constraint of a no-fly area.
Background
In recent years, with the rapid development of the technology in the robot field and the logistics industry, the application of unmanned vehicles and unmanned planes capable of being controlled autonomously to the logistics distribution link has attracted extensive attention in the industrial and academic fields. Compared to unmanned vehicles operating in existing ground traffic networks, unmanned vehicles can enable package delivery in places where ground traffic is congested or inaccessible. Route planning is a significant concern when using drones for package delivery, as logistics enterprises may wish to maximize the economic benefits of drones by shortening routes, reducing package delivery time, and the like.
However, there are many real-world constraints in path planning of the drones, one is environmental threats faced by the drones during flight, for example, safety risks caused by other drones flying at the same time, and as the number of drones increases, the probability of collision also increases. Especially in densely populated areas, such collisions may result in serious casualties. In addition, in urban environments, large buildings and infrastructure are numerous, and when planning the path of the unmanned aerial vehicle, it is necessary to avoid the unmanned aerial vehicle from being too close to the obstacles. In general, the unmanned aerial vehicle path planning stage should be carried out in an effort to avoid collision. Another limitation is that the existence of no-fly zones results in that a part of airspace cannot be used, in urban environments, the no-fly zones include key mechanisms or densely populated places such as government agencies, military bases, airports, railway stations, and the like, and the unmanned aerial vehicle should be far away from the no-fly zones as far as possible during the flight process.
Most current research work on unmanned aerial vehicle path planning does not take into account the influence of wireless communication on unmanned aerial vehicle flight path planning. Although some researches consider the constraint of the no-fly zone on the unmanned aerial vehicle path planning, the methods are not applied to the scene that the unmanned aerial vehicles are grouped to execute package cooperative delivery, and most path planning methods proposed by the researches cannot guarantee the global optimality and effectiveness. Besides, most of the research considers the energy consumption, resource allocation and the like of the unmanned aerial vehicle in the package delivery process, and does not consider the problem of the package delivery cost such as the total package volume delivered in one round.
Disclosure of Invention
Aiming at the defects of the prior art, the technical problem to be solved by the application of the patent is how to provide a multi-unmanned aerial vehicle package cooperation delivery path optimization method under the constraint of a no-fly zone, which can improve the package delivery efficiency and increase the package delivery benefit.
In order to solve the technical problems, the invention adopts the following technical scheme:
a multi-unmanned aerial vehicle package cooperation delivery path optimization method under the constraint of a no-fly zone comprises the following steps: s1: establishing an unmanned aerial vehicle formation flight path model, wherein the unmanned aerial vehicle formation flight path model comprises horizontal coordinates and flight heights of unmanned aerial vehicle formation, a starting point and an end point of the unmanned aerial vehicle formation, a minimum distance between unmanned aerial vehicles and a maximum flight speed index and a performance control parameter of the unmanned aerial vehicle; s2: establishing a no-fly zone model and a parcel delivery zone model; s3: establishing an unmanned aerial vehicle formation package delivery task distribution model; s4: constructing a multi-unmanned aerial vehicle package cooperative delivery optimization problem under the constraint of a flight prohibition area; s5: the optimization problem proposed in the construction step S4 is solved.
Further, in step S1, the horizontal coordinates of the formation of the drones are used
Figure BDA0003481844950000021
Is shown in which
Figure BDA0003481844950000031
Indicating unmanned plane u executesThe horizontal coordinate set in the package delivery task process is adopted, the flying height of the unmanned aerial vehicle formation in the package delivery process is always kept unchanged, the flying height of the unmanned aerial vehicle formation is represented by a constant h, the unmanned aerial vehicle formation starts from a warehouse, the unmanned aerial vehicle formation flies to an unmanned aerial vehicle formation recovery center after the package delivery task is completed, the starting point of the unmanned aerial vehicle formation is the position of the warehouse, the end point of the unmanned aerial vehicle formation is the position of the unmanned aerial vehicle formation recovery center, and the position is represented as cu[1]＝cstr，cu[T]＝cdstThe unmanned aerial vehicle formation collision is avoided, the minimum distance between unmanned aerial vehicles is specified, namely the horizontal coordinate of the unmanned aerial vehicle in the flight process meets the following constraint conditions:
Figure BDA0003481844950000032
wherein L isminRepresenting the minimum distance between drones.
In order to ensure the safe flight of the formation of the unmanned aerial vehicles, the maximum flight speed of the formation of the unmanned aerial vehicles needs to be limited:
Figure BDA0003481844950000033
wherein
Figure BDA0003481844950000034
Representing the maximum flight distance of the drone in each time slot.
Further, in step S2, when the no-fly zone model is established, the no-fly zone is modeled as a cylinder with a height greater than or equal to the flying height of the formation of the unmanned aerial vehicles, and the horizontal coordinate of the nth no-fly zone is expressed as
Figure BDA0003481844950000035
The radius of which is represented as RnIn order to avoid flying the formation of the unmanned aerial vehicles to the no-fly area, the horizontal coordinates of the formation of the unmanned aerial vehicles need to satisfy the following constraint conditions:
Figure BDA0003481844950000036
further, in step S2, when creating the package delivery area model, the area where the unmanned aerial vehicle can detect the uplink signal of the ground client is used as the division criterion, and the area where the unmanned aerial vehicle can detect the uplink signal of the ground client is used as the package delivery area of the ground client, according to the above criteria, a communication model between the formation of unmanned aerial vehicles and the ground client is first created, and assuming that the channel between the formation of unmanned aerial vehicles and the ground client is determined only by the line-of-sight link, the channel power gain from the ground client k to the unmanned aerial vehicle u in the time slot t can be expressed as:
Figure BDA0003481844950000041
wherein g is0Representing the channel power gain per unit distance (one meter),
Figure BDA0003481844950000042
represents the distance between drone u and ground customer k;
during time slot t, the signal-to-noise ratio of the signal received by drone u from ground client k may be expressed as:
Figure BDA0003481844950000043
wherein p iskRepresents the transmission power of the terrestrial client k; n is a radical of0Representing the noise power;
the package delivery area for the surface customer is defined as the signal-to-noise ratio γk，u[t]Greater than a certain threshold value thetauRegion of (a), thetauIndicating the signal detection capability of drone u.
Further, in step S3, when building the model for allocating the package delivery tasks in the formation of unmanned aerial vehicles, the package delivery task allocation in the formation of unmanned aerial vehicles needs to consider the package delivery requirements of the ground clients and the carrying capacity of the unmanned aerial vehicles, and first, each ground client is placed in the warehouseAll the packages are packed into one package and are stored on any unmanned aerial vehicle in a centralized manner, so that K packages are stored in the warehouse, each package corresponds to one ground client, the package K is assigned to belong to the ground client K, and w is usedk(kg) and Wu(kilogram) respectively represents the weight of a package k and the maximum bearing capacity of an unmanned aerial vehicle u, the unmanned aerial vehicle formation package delivery task refers to the allocation of a proper delivery package for each unmanned aerial vehicle, and d is definedk，uE {0, 1} represents the package delivery indicator for package k, i.e., when drone u delivers package k, d k，u1, otherwise dk，uWhen a package delivery task is specified, not only is it considered that each customer only needs one drone to deliver, but also it needs to be considered that the total amount of delivered packages specified for the drone cannot exceed the maximum carrying capacity of the drone, so the following constraint conditions need to be satisfied when the package delivery task is specified:
Figure BDA0003481844950000051
Figure BDA0003481844950000052
Figure BDA0003481844950000053
packages can only be delivered when a drone flies to a designated package delivery area, so the package delivery task also needs to meet the following constraints:
Figure BDA0003481844950000054
wherein the content of the first and second substances,
Figure BDA0003481844950000055
the indication function is expressed, that is, when X is True,
Figure BDA0003481844950000056
otherwise
Figure BDA0003481844950000057
Further, define
Figure BDA0003481844950000058
Representing a package delivery task allocation plan for a formation of drones, then the maximum package delivery volume for a formation of drones may be defined as
Figure BDA0003481844950000059
Further, in step S4, a multi-drone package collaborative delivery optimization problem under the constraint of the no-fly zone is constructed, so that a formation of drones can deliver packages along an optimal path in an environment with the no-fly zone by detecting an uplink signal to noise ratio of a ground customer according to a package delivery task requirement, thereby achieving the purpose of maximizing the number of packages delivered by the formation of drones, and the following problem is constructed:
Figure BDA0003481844950000061
Figure BDA0003481844950000062
Figure BDA0003481844950000063
Figure BDA0003481844950000064
Figure BDA0003481844950000065
Figure BDA0003481844950000066
Figure BDA0003481844950000067
Figure BDA0003481844950000068
Figure BDA0003481844950000069
further, in step S5, when deconstruction is performed, the optimization problem is first equivalently converted into an optimization problem that is easier to process, and then the converted optimization problem is solved by using a related optimization method.
This scheme has the advantage:
1. the invention comprehensively considers the influence of a no-fly zone, collision avoidance among unmanned aerial vehicle formations and uplink signal-to-noise ratio received by the unmanned aerial vehicle formations from ground clients on unmanned aerial vehicle formation path planning in a complex environment, and provides a multi-unmanned aerial vehicle package cooperative delivery path optimization method under the restriction of the no-fly zone to maximize the number of packages delivered in one round.
2. The invention models the multi-unmanned aerial vehicle package cooperative delivery into an optimization problem, converts an original problem which is difficult to solve into an equivalent problem which is easier to process by using a proper method, and provides an algorithm with lower complexity.
3. Compared with the existing unmanned aerial vehicle formation path planning, the multi-unmanned aerial vehicle package cooperation delivery path optimization method under the constraint of the no-fly zone provided by the invention is provided.
Drawings
Fig. 1 is a flowchart of a method for optimizing a multi-drone package collaborative delivery path under a no-fly zone constraint according to the present invention;
fig. 2 is a scene diagram of an actual application of the multi-drone package collaborative delivery path optimization method under the constraint of the no-fly zone, according to the present invention;
FIG. 3 is a flow chart for solving an optimization problem;
fig. 4 is a diagram of a path simulation result of a formation of drones performing a package delivery task in an environment with no-fly zones.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings. In the description of the present invention, it is to be understood that the orientation or positional relationship indicated by the orientation words such as "upper, lower" and "top, bottom" etc. are usually based on the orientation or positional relationship shown in the drawings, and are only for convenience of description and simplicity of description, and in the case of not making a reverse 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, and therefore, should not be interpreted as limiting the scope of the present invention; the terms "inner and outer" refer to the inner and outer relative to the profile of the respective component itself.
As shown in fig. 1-4, a method for optimizing a multi-drone package collaborative delivery path under a no-fly zone constraint includes the following steps: s1: establishing an unmanned aerial vehicle formation flight path model, wherein the unmanned aerial vehicle formation flight path model comprises horizontal coordinates and flight heights of unmanned aerial vehicle formation, a starting point and an end point of the unmanned aerial vehicle formation, a minimum distance between unmanned aerial vehicles and a maximum flight speed index and a performance control parameter of the unmanned aerial vehicle; s2: establishing a no-fly zone model and a parcel delivery zone model; s3: establishing an unmanned aerial vehicle formation package delivery task distribution model; s4: constructing a multi-unmanned aerial vehicle package cooperative delivery optimization problem under the constraint of a flight prohibition area; s5: the optimization problem proposed in the construction step S4 is solved.
Further, a warehouse for storing the packages and the unmanned aerial vehicles, and a unmanned aerial vehicle formation recovery center for recovering the unmanned aerial vehicles are included, and the horizontal coordinates of the warehouse are used
Figure BDA0003481844950000081
For horizontal co-ordinates of the centre of recovery
Figure BDA0003481844950000082
Represents; k ground customers who need to deliver packages, using a collection
Figure BDA0003481844950000083
Indicating that the location of the ground client is fixed, indicated as
Figure BDA0003481844950000084
Wherein
Figure BDA0003481844950000085
N no-fly zones including government agencies, gas stations, railway stations and other key agencies and places
Figure BDA0003481844950000086
Showing that the position of the no-fly zone is also fixed, shown as
Figure BDA0003481844950000087
Wherein
Figure BDA0003481844950000088
Formation of drones, consisting of U drones for delivery of packages, with aggregation
Figure BDA0003481844950000089
The unmanned aerial vehicle formation needs to start from the warehouse in T time slots, return to the warehouse after completing the package delivery task, and the total time slot is set
Figure BDA00034818449500000810
And (4) showing.
Further, unmanned aerial vehicle formation flight path model, including the horizontal coordinate and the flying height of unmanned aerial vehicle formation, the starting point and the terminal point of unmanned aerial vehicle formation, indexes such as minimum distance between the unmanned aerial vehicle and unmanned aerial vehicle's maximum flying speed and performance control parameter set up.
Horizontal coordinate for unmanned aerial vehicle formation
Figure BDA00034818449500000811
Is shown in which
Figure BDA00034818449500000812
The method is characterized in that a horizontal coordinate set in the process that the unmanned aerial vehicle u executes a package delivery task is represented, the flight height of a formation of unmanned aerial vehicles in the process of executing package delivery is kept unchanged all the time, and the flight height of the formation of unmanned aerial vehicles is represented by a constant h.
The unmanned aerial vehicle formation starts from the warehouse, and flies to the unmanned aerial vehicle formation recovery center after the package delivery task is completed. Thus the starting point of the formation of drones, i.e. the location of the warehouse, and the end point, i.e. the location of the recovery centre of the formation of drones, i.e. cu[1]＝cstr，cu[T]＝cdst。
In order to avoid collision of the unmanned aerial vehicles during formation flight, the minimum distance between the unmanned aerial vehicles is specified, namely, the horizontal coordinate of the unmanned aerial vehicles during flight meets the following constraint conditions:
Figure BDA0003481844950000091
wherein L isminRepresenting the minimum distance between drones.
Further, in order to ensure safe flight of the formation of the unmanned aerial vehicles, the maximum flight speed of the formation of the unmanned aerial vehicles needs to be limited:
Figure BDA0003481844950000092
wherein
Figure BDA0003481844950000093
Representing the maximum flight distance of the drone in each time slot.
Furthermore, the no-fly zone model is a cylinder with a height greater than or equal to the flying height of the formation of the unmanned aerial vehicles, taking the nth no-fly zone as an example, and the horizontal coordinate of the no-fly zone model is as followsAs hereinbefore described, represented by
Figure BDA0003481844950000094
The radius of which is represented as RnIn order to avoid flying the formation of the unmanned aerial vehicles to the no-fly area, the horizontal coordinates of the formation of the unmanned aerial vehicles need to satisfy the following constraint conditions:
Figure BDA0003481844950000095
further, the package delivery area model takes whether the unmanned aerial vehicle can detect the uplink signal of the ground client as a division standard, and takes the area where the unmanned aerial vehicle can detect the uplink signal of the ground client as the package delivery area of the ground client, a communication model of the formation of the unmanned aerial vehicles and the ground client is firstly established, and assuming that the channel between the formation of the unmanned aerial vehicles and the ground client is determined only by the line-of-sight link, the channel power gain from the ground client k to the unmanned aerial vehicle u in the time slot t can be expressed as:
Figure BDA0003481844950000101
where g0 represents the channel power gain per unit distance (one meter),
Figure BDA0003481844950000102
representing the distance between drone u and ground client k.
Further, during time slot t, the signal-to-noise ratio of the signal received by drone u from ground client k may be expressed as:
Figure BDA0003481844950000103
wherein p iskRepresents the transmission power of the terrestrial client k; n is a radical of0Representing the noise power.
Further, the present invention defines the package delivery area of the surface customer as the signal-to-noise ratio γk，u[t]Greater than a certain thresholdValue thetauRegion of (a), thetauIndicating the signal detection capability of drone u.
Further, the allocation of the package delivery tasks in the formation of the unmanned aerial vehicles takes into consideration the package delivery requirements of the ground customers and the carrying capacity of the unmanned aerial vehicles, and firstly, all packages of each ground customer are packed into one package in a warehouse and stored on any unmanned aerial vehicle in a centralized manner, so that the warehouse has K packages, each package corresponds to one ground customer, and the package K is assigned to belong to the ground customer K, and w is used for allocating the package delivery tasksk(kg) and Wu(kg) represents the weight of package k and the maximum weight bearing capacity of drone u, respectively, that is, the formation of package delivery tasks for each drone, which means that each drone is assigned the appropriate delivery package, and in particular, definition dk，uE {0, 1} represents a package delivery indicator for package k, i.e., when drone u delivers package k, d k，u1, otherwise d k，u0. When a package delivery task is specified, not only is it considered that each customer only needs one drone to deliver, but also it is considered that the total amount of delivered packages assigned to a drone cannot exceed the maximum carrying capacity of that drone. The following constraints therefore need to be satisfied when specifying a package delivery task:
Figure BDA0003481844950000111
Figure BDA0003481844950000112
Figure BDA0003481844950000113
further, a package may be delivered only when the drone is flying to a designated package delivery area, and therefore the package delivery task also needs to satisfy the following constraints:
Figure BDA0003481844950000114
wherein the content of the first and second substances,
Figure BDA0003481844950000115
the indication function is expressed, that is, when X is True,
Figure BDA0003481844950000116
otherwise
Figure BDA0003481844950000117
Further, define
Figure BDA0003481844950000118
Representing a package delivery task allocation plan for a formation of drones, then the maximum package delivery volume for a formation of drones may be defined as
Figure BDA0003481844950000119
Further, a method for jointly optimizing flight path planning and package delivery task allocation of unmanned aerial vehicle formation is designed, so that the unmanned aerial vehicle formation can carry out package delivery along an optimal path in an environment with a no-fly zone by detecting an uplink signal to noise ratio of a ground client according to package delivery task requirements, and the purpose of maximizing the number of packages delivered by the unmanned aerial vehicle formation is achieved.
Further, according to the above object, optimization problem 1 is constructed:
Figure BDA0003481844950000121
Figure BDA0003481844950000122
Figure BDA0003481844950000123
Figure BDA0003481844950000124
Figure BDA0003481844950000125
Figure BDA0003481844950000126
Figure BDA0003481844950000127
Figure BDA0003481844950000128
Figure BDA0003481844950000129
furthermore, because the optimization variable D is a binary variable, all the constraints related to the distribution of the package delivery tasks are constraints containing integer variables; and the constraint conditions related to unmanned aerial vehicle formation collision avoidance and no-fly zone are all non-convex constraints related to the optimization variable C; in addition, an indication function is also included in the constraint condition, so that the optimization problem 1 is a non-convex mixed integer programming problem which is difficult to solve, the optimization problem 1 is equivalently converted into an optimization problem which is easier to process, then the converted optimization problem is solved by adopting a related optimization method, and a multi-unmanned aerial vehicle package cooperation delivery path and a package delivery task allocation method which can maximize the package delivery amount of unmanned aerial vehicles in formation are provided.
Furthermore, the invention utilizes the large M rule and introduces a new optimization variable
Figure BDA0003481844950000131
Will optimize the constraints in problem 1
Figure BDA0003481844950000132
The equivalence translates into the following three new constraints:
Figure BDA0003481844950000133
Figure BDA0003481844950000134
Figure BDA0003481844950000135
wherein M isk，u[t]Is a ratio cu[t]-ak||2Is larger than a constant value.
Further, the integer constraint d in problem 1 will be optimizedk，uE {0, 1} and xk，u[t]E {0, 1} translates equivalently to the following four new constraints:
Figure BDA0003481844950000136
Figure BDA0003481844950000137
Figure BDA0003481844950000138
Figure BDA0003481844950000139
after the transformation, the optimization problem 1 can be equivalently transformed into the optimization problem 2:
Figure BDA00034818449500001310
Figure BDA00034818449500001311
Figure BDA00034818449500001312
Figure BDA0003481844950000141
Figure BDA0003481844950000142
Figure BDA0003481844950000143
Figure BDA0003481844950000144
Figure BDA0003481844950000145
Figure BDA0003481844950000146
Figure BDA0003481844950000147
Figure BDA0003481844950000148
Figure BDA0003481844950000149
Figure BDA00034818449500001410
part of constraint conditions in the optimization problem 2 are non-convex, but the non-convex constraint conditions can be written into a difference form of two convex functions, so that the optimization problem 2 is a standard convex-concave problem and can be solved by using a punishment convex-concave process method.
Further, by using the PCCP method, firstly relaxing the optimization problem 2, then converting the relaxed optimization problem into a series of convex approximation subproblems, and solving by using a convex optimization tool.
Firstly, adding penalty factors to the non-convex constraint conditions and penalizing the sum of corresponding slack to relax the optimization problem 2, so as to obtain the following relaxed optimization problem, which is marked as an optimization problem 3:
Figure BDA0003481844950000151
Figure BDA0003481844950000152
Figure BDA0003481844950000153
Figure BDA0003481844950000154
Figure BDA0003481844950000155
Figure BDA0003481844950000156
Figure BDA0003481844950000157
Figure BDA0003481844950000158
Figure BDA0003481844950000159
Figure BDA00034818449500001510
Figure BDA00034818449500001511
Figure BDA00034818449500001512
Figure BDA00034818449500001513
Figure BDA00034818449500001514
Figure BDA00034818449500001515
Figure BDA00034818449500001516
Figure BDA00034818449500001517
wherein:
Figure BDA0003481844950000161
represents the total penalty;
wherein the content of the first and second substances,
Figure BDA0003481844950000162
and
Figure BDA0003481844950000163
the relaxation variables of the respective non-convex constraints are represented separately. The coefficient xi > 0 in s (d) -xi P (epsilon, sigma, alpha, epsilon 0) represents a penalty factor, with increasing penalty factor the total penalty P (epsilon, sigma, alpha, beta) will be smaller and eventually tend to zero. When P (e, σ, α, β) ═ 0, optimization problem 2 and optimization problem 3 are equivalent.
Further, the concave term in problem 3 is linearized, i.e. at a given point (C), respectively(j)，D(j)，X(j)) To optimize the concave term in problem 3
Figure BDA00034818449500001610
Is subjected to Taylor section expansion, wherein
Figure BDA0003481844950000164
Figure BDA0003481844950000165
Where j ═ 1, 2, … denotes the iteration number of the PCCP method.
Further, in the j-th iteration, the non-convex constraint in optimization problem 3 may be replaced with the following linear constraint:
Figure BDA0003481844950000166
Figure BDA0003481844950000167
Figure BDA0003481844950000168
Figure BDA0003481844950000169
wherein (·)TRepresenting a transpose operation. After the transformation, a ratioless gold problem of the j iteration of the PCCP method is obtained, and is expressed as an optimization problem 4:
Figure BDA0003481844950000171
Figure BDA0003481844950000172
Figure BDA0003481844950000173
Figure BDA0003481844950000174
Figure BDA0003481844950000175
Figure BDA0003481844950000176
Figure BDA0003481844950000177
Figure BDA0003481844950000178
Figure BDA0003481844950000179
Figure BDA00034818449500001710
Figure BDA00034818449500001711
Figure BDA00034818449500001712
Figure BDA00034818449500001713
Figure BDA00034818449500001714
Figure BDA00034818449500001715
Figure BDA0003481844950000181
Figure BDA0003481844950000182
xi therein(j)And (4) representing a penalty factor of the j-th iteration, wherein the optimization problem 4 is a convex optimization problem, and therefore, the optimization problem can be solved by using a standard convex optimization method or a convex optimization tool such as CVX (composite variable X).
Further, the proposed algorithm 1 for solving the optimization problem 3 specifically comprises the following steps:
1) given an arbitrary initial value (C)(0)，D(0)，X(0))，ξ(0)＞0，ξmaxV > 1, and let the iteration number j equal to 0;
2) solving the optimization problem 4 using a convex optimization method or tool, updating the values of the points with the solution of the optimization problem 4, i.e. assigning the solution of the optimization problem to (C)(j+1)，D(j+1)，X(j+1))；
3) Will { u xi(j)，ξmaxAssign the minimum value in xi to xi(j+1)；
4) Updating the iteration sequence number: j is j + 1;
5) repeating steps 2) to 4) until a cycle end condition is reached.
Further, the present invention analyzes the computational complexity of the proposed algorithm. The computational complexity of algorithm 1 is determined by solving optimization problem 4, which is solved using the CVX tool
Figure BDA0003481844950000183
Where a ═ UT (N + U +2K +2) +2KU denote the number of all variables, and e > 0 is a given solution accuracy.
Fig. 4 shows the simulation results of the path of the formation of drones performing the package delivery task in the environment with no-fly zone, wherein the red circles represent the package delivery area and the black circles represent the no-fly zone. First, as can be seen from fig. 4, the formation of the unmanned aerial vehicles does not pass through the no-fly zone in the flight process, which shows that the method provided by the present invention can effectively avoid all the no-fly zones. Second, it has also been found that some drones will pass through the package delivery area of the ground based customer because they need to perform the package delivery task. In addition, all unmanned aerial vehicles finish the task of flying to the unmanned aerial vehicle formation recovery center after package delivery from the starting point, and the method provided by the invention can ensure that the unmanned aerial vehicle formation can smoothly finish the package cooperative delivery task within a limited time.
Finally, it should be noted that: various modifications and alterations of this invention may be made by those skilled in the art without departing from the spirit and scope of this invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

Claims (7)

1. A multi-unmanned aerial vehicle package cooperation delivery path optimization method under the constraint of a no-fly zone is characterized by comprising the following steps:
s1: establishing an unmanned aerial vehicle formation flight path model, wherein the unmanned aerial vehicle formation flight path model comprises horizontal coordinates and flight heights of unmanned aerial vehicle formation, a starting point and an end point of the unmanned aerial vehicle formation, a minimum distance between unmanned aerial vehicles and a maximum flight speed index and a performance control parameter of the unmanned aerial vehicle;
s2: establishing a no-fly zone model and a parcel delivery zone model;
s3: establishing an unmanned aerial vehicle formation package delivery task distribution model;
s4: constructing a multi-unmanned aerial vehicle package cooperative delivery optimization problem under the constraint of a flight prohibition area;
s5: the optimization problem proposed in the construction step S4 is solved.
2. The method for optimizing the package collaborative delivery path of multiple drones under the constraint of no-fly zone of claim 1, wherein in step S1, the horizontal coordinates of the formation of drones are used as the horizontal coordinates
Figure FDA0003481844940000011
Is shown in which
Figure FDA0003481844940000012
The horizontal coordinate set in the process that the unmanned aerial vehicle u executes the package delivery task is represented, the flying height of a formation of the unmanned aerial vehicles in the process of executing the package delivery is always kept unchanged, the flying height of the formation of the unmanned aerial vehicles is represented by a constant h, the formation of the unmanned aerial vehicles starts from a warehouse, the unmanned aerial vehicles fly to a recovery center of the formation of the unmanned aerial vehicles after completing the package delivery task, the starting point of the formation of the unmanned aerial vehicles is the position of the warehouse, the end point of the formation of the unmanned aerial vehicles is the position of the recovery center of the formation of the unmanned aerial vehicles, and the horizontal coordinate set is represented as cu[1]＝cstr，cu[T]＝cdstThe unmanned aerial vehicle formation collision is avoided, the minimum distance between unmanned aerial vehicles is specified, namely the horizontal coordinate of the unmanned aerial vehicle in the flight process meets the following constraint conditions:
Figure FDA0003481844940000013
wherein L isminRepresenting the minimum distance between drones.
In order to ensure the safe flight of the formation of the unmanned aerial vehicles, the maximum flight speed of the formation of the unmanned aerial vehicles needs to be limited:
Figure FDA0003481844940000021
wherein
Figure FDA0003481844940000022
Representing the maximum flight distance of the drone in each time slot.
3. The method for optimizing the parcel cooperative delivery path of multiple drones under the restriction of no-fly zone of claim 2, wherein in step S2, when the no-fly zone model is established, the no-fly zone is modeled as a cylinder with a height greater than or equal to the formation flight height of drones, and the horizontal coordinate of the nth no-fly zone is expressed as the horizontal coordinate of the nth no-fly zone
Figure FDA0003481844940000023
The radius of which is represented as RnIn order to avoid flying the formation of the unmanned aerial vehicles to the no-fly area, the horizontal coordinates of the formation of the unmanned aerial vehicles need to satisfy the following constraint conditions:
Figure FDA0003481844940000024
4. the method of claim 3, wherein in step S2, when creating the package delivery area model, the area where the unmanned aerial vehicle can detect the uplink signal of the ground client is used as the partition criteria, and the package delivery area of the ground client is the area where the unmanned aerial vehicle can detect the uplink signal of the ground client, according to the above criteria, a communication model between the formation of unmanned aerial vehicles and the ground client is first created, and assuming that the channel between the formation of unmanned aerial vehicles and the ground client is determined only by the line-of-sight link, the power gain of the channel from the ground client k to the unmanned aerial vehicle u in the time slot t can be expressed as:
Figure FDA0003481844940000025
wherein g is0Representing the channel power gain per unit distance (one meter),
Figure FDA0003481844940000026
represents the distance between drone u and ground client k;
during time slot t, the signal-to-noise ratio of the signal received by drone u from ground client k may be expressed as:
Figure FDA0003481844940000031
wherein p iskRepresents the transmission power of the terrestrial client k; n is a radical of0Representing work of noiseRate;
the package delivery area for the surface customer is defined as the signal-to-noise ratio γk，u[t]Greater than a certain threshold value thetauRegion of (a), thetauIndicating the signal detection capability of drone u.
5. The method of claim 4, wherein in step S3, when building the model for allocating the package delivery tasks in formation of UAVs, the distribution of the package delivery tasks in formation of UAVs needs to take into account the package delivery requirements of ground clients and the carrying capacity of the UAVs, first, all the packages of each ground client are packaged into one package in the warehouse and stored on any one UAV in a centralized manner, so that there are K packages in the warehouse, each package corresponds to one ground client, and package K is assigned to ground client K, and w is used for w clientsk(kg) and Wu(kilogram) respectively represents the weight of a package k and the maximum bearing capacity of an unmanned aerial vehicle u, the unmanned aerial vehicle formation package delivery task refers to the allocation of a proper delivery package for each unmanned aerial vehicle, and d is definedk，uE {0, 1} represents a package delivery indicator for package k, i.e., when drone u delivers package k, dk，u1, otherwise dk，uWhen a package delivery task is specified, not only is it considered that each customer only needs one drone to deliver, but also it needs to be considered that the total amount of delivered packages specified for the drone cannot exceed the maximum carrying capacity of the drone, so the following constraint conditions need to be satisfied when the package delivery task is specified:
Figure FDA0003481844940000041
Figure FDA0003481844940000042
Figure FDA0003481844940000043
packages can only be delivered when a drone flies to a designated package delivery area, so the package delivery task also needs to meet the following constraints:
Figure FDA0003481844940000044
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003481844940000045
the indication function is expressed, that is, when X is True,
Figure FDA0003481844940000046
otherwise
Figure FDA0003481844940000047
Further, define
Figure FDA0003481844940000048
Representing a package delivery task allocation plan for a formation of drones, then the maximum package delivery volume for a formation of drones may be defined as
Figure FDA0003481844940000049
6. The method according to claim 5, wherein in step S4, a coordinated delivery optimization problem of packages with multiple drones under the constraint of no-fly zone is constructed, so that a formation of drones can deliver packages along an optimal path in an environment with no-fly zone according to package delivery task requirements by detecting the uplink signal-to-noise ratio of ground customers, thereby maximizing the number of packages delivered by the formation of drones, and the following problem is constructed:
Figure FDA00034818449400000410
Figure FDA00034818449400000411
Figure FDA00034818449400000412
Figure FDA00034818449400000413
Figure FDA00034818449400000414
Figure FDA0003481844940000051
Figure FDA0003481844940000052
Figure FDA0003481844940000053
Figure FDA0003481844940000054
7. the method for optimizing the package cooperative delivery path of the multiple drones under the no-fly zone constraint according to claim 6, wherein in step S5, when deconstruction is performed, the optimization problem is first equivalently converted into a more manageable optimization problem, and then the converted optimization problem is solved by using a related optimization method.
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