A Robust UAV Scheduling Method Considering Jitter Noise and Drift of Monitoring Objects

Abstract

The present invention discloses a robust UAV scheduling method considering jitter noise and monitored object drift. The situation is as follows: there are several monitored objects in a given plane, and they can drift within a certain range; at the same time, some UAVs with determined positions but undetermined monitoring orientations are arranged, and there is jitter noise during their monitoring. The problem is: to give an effective orientation scheduling method for UAVs in the projected two-dimensional plane to maximize the expected monitoring utility. The present invention first gives a probability model of monitoring quality and a monitoring utility model, and proposes a formalized problem; secondly, proposes a method to linearize and discretize the non-linear and continuous monitoring quality through region discretization; thirdly, finitizes the infinite solution space and restricts the change amount of the coverage area by dividing the orientation angle; finally, uses a greedy algorithm to effectively select orientations from the solution space to obtain the final result and restricts the error. The present invention first proposes a robust UAV scheduling method and gives an effective approximation algorithm.

Description

Technical Field

[0001] The present invention relates to the field of robust UAV scheduling, and in particular to a robust UAV scheduling method considering jitter noise and monitored object drift. Background Art

[0002] Video surveillance systems have received increasing attention in recent years due to their ability to provide detailed image and video information of monitored objects. Their application scenarios are diverse, such as monitoring, traffic management, etc. For some temporary monitoring scenarios such as rallies, concerts, sports competitions, etc., building a static monitoring system will consume a large amount of manpower, material resources and financial resources, so it is extremely inconvenient. In recent years, UAV monitoring has gradually emerged, which provides convenience for such temporary monitoring scenarios and has strong flexibility; its relatively lower deployment cost and easy operation and expansion enable the video surveillance system to be dynamically deployed and real-time monitor and transmit back images. Since the monitoring range is usually a directed range for UAVs, when projected onto the monitoring plane, it can be approximately considered that its effective monitoring range is a sector area. Then, for UAV monitoring, there is an important problem. If the monitored object is located within the sector monitoring range of the UAV, it can be monitored; otherwise, it cannot be monitored even if it is nearby. Considering the potential mobility of the monitored object, a monitored object may be monitored with high quality at a specific location, but this situation may not be maintained when the device moves to another location. At the same time, when the UAV transmits the live video back, there may also be channel noise interference, resulting in unstable monitoring quality.

[0003] In recent years, some literature studies on UAV monitoring have emerged. These literatures all assume a deterministic scenario, focusing on optimizing the monitoring quality, without considering the jitter noise generated by the channel during the real-time image transmission process and the random drift of the monitored object within a certain range. For the case of jitter noise, a probability model needs to be proposed to model the monitoring quality; for the case of random drift of the monitored object, the expectation of the monitoring quality within the drift range needs to be maximized. However, the existing research on UAV monitoring is essentially a deterministic problem and cannot be used to solve the probability problem proposed in the present invention. Therefore, the existing work cannot solve the objectives proposed in the present invention.

[0004] Therefore, it is an urgent problem for those skilled in the art to provide a robust UAV scheduling method considering jitter noise and monitored object drift, give a UAV monitoring utility model, conduct a probability analysis on environmental uncertain factors, and then propose a scheduling scheme with an approximation ratio. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a robust UAV scheduling method considering jitter noise and monitored object drift, so as to overcome the shortcoming of not considering environmental uncertain factors in the prior art.

[0006] Technical solution: The robust UAV scheduling method considering jitter noise and monitoring object drift aims at maximizing the monitoring utility expectation under uncertain environmental factors. The UAV is scheduled to move towards the monitoring object, which refers to invasive organisms in security monitoring, buoy status in hydrological monitoring, etc. The method includes the following steps:

[0007] (1) Based on the jitter noise generated during the UAV monitoring process, model the monitoring quality and monitoring utility to obtain a monitoring quality model and a monitoring utility model;

[0008] (2) Based on the drift of the monitoring object within a predetermined range and combined with the monitoring utility model, define a monitoring quality function that continuously changes with distance, formalize the objective problem of maximizing the monitoring utility expectation, and obtain a formalized problem;

[0009] (3) In the formalized problem, divide the projected two-dimensional plane area according to the monitoring quality model to obtain multiple sub-areas with approximately constant monitoring quality. Discretize the monitoring quality function that continuously changes with distance through each sub-area and limit its approximation error, thereby transforming the formalized problem into a discrete summation problem;

[0010] (4) In the discrete summation problem, divide the monitoring angles of the UAVs to obtain a finite number of scheduling directions, thereby transforming the infinite solution space into a finite solution space while ensuring the limitation of the coverage area change caused by the division;

[0011] (5) In the finite solution space, select and schedule each UAV orientation through a greedy algorithm to obtain the final scheduling result, and give the approximation ratio to the optimal solution to obtain the monitoring utility that maximizes the expectation under uncertain environmental factors.

[0012] Further, in step (1), the modeling of the monitoring quality and monitoring utility is specifically as follows:

[0013] Project the UAV and the monitoring object onto the same two-dimensional plane. Model the UAV monitoring range as a sector according to the device monitoring range. Consider the jitter noise and model the UAV monitoring utility. Suppose there is a UAV s i , after its projection onto the two-dimensional plane, the monitoring range is approximately a sector with this point as the center, a central angle of α, a radius of D, and the orientation angle is In the presence of jitter noise, the monitoring quality of any monitoring position p on this plane is defined as:

[0014]

[0015] where a1, b1, a2, b2 are constants determined by the hardware and the environment, indicates a normal distribution with μ as the mean and σ 2 as the variance, d(si , p) represents the drone s i The distance between the projection position and the point p on the plane. When multiple drones monitor the same point, the monitoring quality is:

[0016]

[0017] Among them, N is the number of drones, and Q(p) represents the overall monitoring quality at point p; Since there is a saturation state in the monitoring quality, a monitoring utility model is given, that is, the monitoring utility is defined as when the monitoring quality increases to a certain extent and then reaches the saturation state and no longer increases:

[0018]

[0019] Among them, x is the monitoring quality, and Q thr is the threshold of the monitoring quality saturation state.

[0020] Furthermore, in step (2), the objective problem of maximizing the expected monitoring utility is formalized as follows:

[0021] Based on the drift of the drone within a predetermined range, assuming the monitored object o j can randomly drift within a circle γ j with the center at p o and radius r j , then combined with the monitoring utility model, the formal definition of the problem is:

[0022]

[0023]

[0024] Among them, N represents the number of drones, M represents the number of monitored objects, Ω represents the two-dimensional plane considered, represents the mathematical expectation, and (x, y) represents the coordinates of a point on the plane.

[0025] Furthermore, step (3) is specifically:

[0026] Make the following approximation of the monitoring quality according to the distance:

[0027]

[0028] Among them, Q(d) represents the monitoring quality when the distance between the monitored object and a drone is d, is its approximate value, l(0) = 0, l(K) = D, let represents the monitoring quality generated by the drone s for any point p within the same monitoring quality sub-region i under the above approximation, and set:

[0029]

[0030] Among them, l(k) represents the discretization distance at the k-th level. There are a total of K levels of discretization distances. k = 1,..., K - 1 and l(0) = 0, l(K) = D; ∈1 is a small positive quantity close to 0, and b1, b2 are constants determined by hardware and environment in the monitoring quality model, and

[0031]

[0032] The approximation error of the monitoring utility expectation can be limited to:

[0033]

[0034] Furthermore, step (4) is specifically as follows:

[0035] After discretizing the angle, a finite solution space is obtained to select the orientation angle. The entire 2π angle is divided, and for each orientation taken, discretized orientation angles are obtained. Suppose is a small angle change that can divide 2π evenly. Among them, the maximum change in the area covered by two adjacent discrete orientations is a circle γ j The maximum change in area is

[0036]

[0037] Furthermore, step (5) is specifically as follows:

[0038] The problem after region division and angle division is approximated as:

[0039]

[0040]

[0041] Among them, represents the area of the sub-region is the discrete angle, Γ is the entire solution space that contains the discrete angles of all drones, and Γ i represents the set of discrete angle solutions of the i-th drone. The problem is proved to be a submodular maximization problem constrained by a partition matroid. A solution with an approximation ratio of 1 / 2 can be obtained through the greedy algorithm. Considering the overall approximation, by setting and Among them,

[0042]

[0043] ​

[0044] Among them, ∈ is the approximation ratio parameter, and the approximation ratio between the obtained solution and the optimal solution of the original problem is 1 / 2 - ∈.

[0045] The present invention discloses a robust unmanned aerial vehicle (UAV) scheduling method considering jitter noise and monitored object drift. The situation is as follows: there are several monitored objects in a given plane, and they can drift within a certain range; at the same time, some UAVs with determined positions but undetermined monitoring orientations are arranged, and there is jitter noise during their monitoring. The problem is: to give an effective orientation scheduling method for UAVs in the projected two-dimensional plane to maximize the expected monitoring utility.

[0046] In terms of problem modeling and formalization, the objective of this method is to comprehensively consider the jitter noise and monitored object drift in the environment in combination with the actual situation, use a normal random variable to describe the monitoring quality of the UAV and then give the monitoring utility, and consider the situation where the monitored objects drift uniformly and randomly within a certain area. Finally, the problem is formalized as maximizing the expectation of the overall monitoring utility;

[0047] Regarding the non-linear relationship between the monitoring quality and the distance and the need to calculate infinitely many continuous monitoring quality random variables, this method approximates the monitoring quality within each sub-region as the same random variable through region division and limits the approximation error;

[0048] Regarding the infinite solution space of the UAV monitoring angle, this method discretizes the monitoring orientation of the UAV and limits the change in the monitoring coverage area caused by the orientation division;

[0049] Regarding the selection of the final solution, this method first proves that the approximated problem is a submodular function problem maximizing a partition matroid constraint, and then uses a greedy algorithm to solve for the solution with an approximation ratio.

[0050] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The present invention first gives the probability model of the monitoring quality and the monitoring utility model, and proposes a formalized problem; secondly, proposes a method to linearize and discretize the non-linear and continuous monitoring quality through region discretization; thirdly, finitizes the infinite solution space through the division of the orientation angle and limits the change in the coverage area; finally, uses a greedy algorithm to effectively select the orientation from the solution space to obtain the final result and limits the error. The present invention first proposes a robust UAV scheduling method and gives an effective approximation algorithm. Description of the Drawings

[0051] Figure 1 It is a model diagram of a robust UAV scheduling method considering jitter noise and monitored object drift disclosed in an embodiment of the present invention;

[0052] Figure 2 It is a flowchart of a robust UAV scheduling method considering jitter noise and monitored object drift disclosed in an embodiment of the present invention;

[0053] Figure 3 Comparison graph of the expected monitoring energy efficiency of the method of the present invention with the RO, NMJ, and NOO methods under different numbers N of unmanned aerial vehicles

[0054] Figure 4 Comparison graph of the expected monitoring energy efficiency of the method of the present invention with the RO, NMJ, and NOO methods under different numbers M of monitored objects Detailed implementation manner

[0055] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0056] The present invention discloses a robust unmanned aerial vehicle scheduling method considering jitter noise and monitored object drift. The situation is as follows: There are several monitored objects in a given plane, and they can drift within a certain range; at the same time, some unmanned aerial vehicles with determined positions but undetermined monitoring orientations are arranged, and there is jitter noise during their monitoring. The problem is: To give an effective orientation scheduling method for the unmanned aerial vehicles in the projected two-dimensional plane to maximize the expected monitoring utility. The present invention first gives a probability model of monitoring quality and a monitoring utility model, and proposes a formalized problem; secondly, proposes a method for linearizing and discretizing non-linear and continuous monitoring quality through regional discretization; thirdly, finitizes the infinite solution space and restricts the change amount of the coverage area through the division of the orientation angle; finally, uses a greedy algorithm to effectively select the orientation from the solution space to obtain the final result and restricts the error. The present invention first proposes a robust unmanned aerial vehicle scheduling method and gives an effective approximation algorithm.

[0057] The present invention is tested in a randomly generated monitored object topology and compared with a comparative algorithm, where each obtained data is the average of 100 randomly arranged topology result data. These monitored object topologies are randomly generated in large quantities, so the test results have general explanatory power.

[0058] Please refer to the atta Figure 1 chment, which is a model diagram of a robust unmanned aerial vehicle scheduling method considering jitter noise and monitored object drift disclosed in an embodiment of the present invention. A robust unmanned aerial vehicle scheduling method considering jitter noise and monitored object drift disclosed in an embodiment of the present invention, the specific model is:

[0059] There are M monitored objects O = {o1,..., o M} in the plane Ω, and there are N unmanned aerial vehicles S = {s1,..., s N} in the air for monitoring. Without causing ambiguity, s i(i = 1, ..., N) also represents the position of the i-th unmanned aerial vehicle (UAV) projected onto the plane Ω. The positions of these UAVs have been determined, but their orientations need to be adjusted. Meanwhile, the monitored object can drift within a certain range, which is collectively referred to as DDA (Drifting Disk Area) in the following text, and p j is the center of the DDA of o j ; assume that o j can drift to any position within its DDA and its position follows a uniform distribution. The following will all consider the problem of directly projecting the UAVs onto the two-dimensional plane Ω of the monitored object.

[0060] The present invention establishes a monitoring model based on experience. Among them, the monitoring range of the UAV s i is a sector with s i as the center, radius D, central angle α, and orientation . Here, only the case of α ∈ (0, π / 2] is considered, because generally the monitoring probe of the UAV can only monitor clearly within such an angular range. If the position p = (x, y) where the monitored object o j is located is within the monitoring range of the UAV s i , then o j can obtain a monitoring quality greater than 0 by the UAV s i , otherwise the monitoring quality of o j at the UAV s i is 0. For example, in the appendix Figure 1 , o j can obtain a monitoring quality greater than 0 by the UAV s j,1 when drifting to p i , while it cannot obtain the monitoring quality provided by s j,2 when drifting to the position p i . By combining the directed monitoring and the probability monitoring model considering the jitter noise, the present invention models the monitoring quality as follows:

[0061]

[0062] where a1, b1, a2, b2 are constants determined by the hardware and the environment, represents the normal distribution with μ as the mean and σ 2 as the variance, and d(s i , p) represents the distance between the projection position of the UAV s i and the point p on the plane. This model shows that if the monitored object is within the monitoring sector of the UAV, its monitoring quality follows a normal distribution, and its parameters are related to the distance between the monitored object and the projection position of the UAV.

[0063] When multiple UAVs monitor the same point, it is considered that the monitoring quality is additive, that is:

[0064]

[0065] Among them, N is the number of unmanned aerial vehicles (UAVs), and Q(p) represents the overall monitoring quality at point p.

[0066] Due to the saturation state of the monitoring quality, a monitoring utility model is given. That is, it is considered that the monitoring utility no longer increases when the monitoring quality increases to a certain extent and reaches the saturation state. The specific definition is as follows:

[0067]

[0068] Among them, x is the monitoring quality, and Q thr is the threshold of the saturation state of the monitoring quality.

[0069] The problem is formalized as follows. First, for the monitored object o j at a point p = (x, y) ∈ O j the expected value of the monitoring quality is denotes the mathematical expectation. There are a total of N UAVs for monitoring. Therefore, for the monitored object o j its overall expected monitoring quality within DDAγ j is:

[0070]

[0071] Secondly, there are a total of N monitored objects. The present invention adds up all their monitoring qualities and takes the average to obtain the final goal. That is, the final problem is formalized as:

[0072]

[0073]

[0074] Please refer to the attached Figure 2 , which is a flowchart of a robust UAV scheduling method considering jitter noise and monitored object drift disclosed in an embodiment of the present invention. A robust UAV scheduling method considering jitter noise and monitored object drift disclosed in an embodiment of the present invention, the specific steps are as follows:

[0075] Step 201: Using the method, perform area division according to the monitoring quality model, discretize the monitoring quality that continuously changes with distance, and limit the approximation error to obtain the problem after the first approximation, specifically:

[0076] To solve the continuity and non-linearity problems of the monitoring quality, the present invention first uses a piecewise constant function to approximate the monitoring quality. Let Q(d) represent the monitoring quality provided when the distance between the UAV projection position and the monitored object is d. Then the piecewise constant approximation function is defined as follows:

[0077]

[0078] Among them, is the approximate value of Q(d), l(0) = 0, l(K) = D. Here, is used to simplify the representation of the random variable can only be equal to 0, that is, equivalent to Obviously, if and only if Q(d) = 0.

[0079] After the above approximation, it can be seen that the monitoring quality random variables within a certain range are the same. Let represent the monitoring quality generated by the UAV s at any point p within the same monitoring quality sub-region under the above approximate situation, and set i where ∈1 is a positive small quantity close to 0, k = 1,..., K - 1 and l(0) = 0, l(K) = D, and

[0080]

[0081] wherein, ∈1 is a positive small quantity close to 0, k = 1,..., K - 1 and l(0) = 0, l(K) = D, and

[0082]

[0083] Then, the approximate error of the expected monitoring utility can be limited to:

[0084]

[0085] It should be noted that the approximate error here only discusses the situation when because if and only if Q(d) = 0, then it must be

[0086] After this step of approximation, the original problem is approximated to:

[0087]

[0088]

[0089] Among them, represents the area of the sub-region and

[0090] Step 202: Divide the monitoring angle of the UAV by using the above method, transform the infinite solution space into a finite solution space, and ensure the limitation of the change in the coverage area caused by the division, so as to obtain the problem after the second approximation, specifically:

[0091] Since the monitoring angle of the UAV is still a continuous quantity, the solution space is infinite. In the present invention, by discretizing the orientation angle, dividing the angle at intervals, and limiting the approximation error, this problem is solved. For simplicity, it is assumed here that can be divided evenly by 2π. The present invention proposes that when the monitoring angle α of the UAV ∈ (0, π / 2], for a single UAV to monitor a DDA, the difference between the original coverage area and the coverage area after angle division is within the range.

[0092] After the angle division approximation, the problem is further approximated as:

[0093]

[0094]

[0095] Step 203: Using the said method in the finite solution space, select the orientation of each UAV through the greedy algorithm to obtain the final scheduling result, and give the approximation ratio to the optimal solution, specifically:

[0096] Let Γ denote the discrete angle solution space obtained in Step 202, which can be defined as the union of N non - overlapping different UAV angle solution spaces, that is Define the partition matroid where Based on the above definitions, the problem can be rewritten as maximizing the sub - modular function subject to the partition matroid, that is:

[0097]

[0098]

[0099] Therefore, a solution with an approximation ratio of 1 / 2 for this approximate problem can be obtained by using the greedy algorithm. The specific algorithm is as follows:

[0100] UAV Robust Scheduling Algorithm

[0101] Input: The solution set Γ of the orientation angle of each UAV i (i = 1,..., N), the UAV set S = {s1,..., s N}, the monitoring object set O = {o1,..., o M}, the monitoring quality function Q(.), the monitoring utility function U(.), the approximate sub - modular optimization objective function f(X).

[0102] Output: The selected set of orientation angles Γ S .

[0103] Step 1:

[0104] Step 2:

[0105] Step 3: while |Γ S | < N do

[0106]

[0107] Γ S = Γ S ∪ {e *}

[0108] Γ = Γ \ Γ i where e * ∈ Γ i

[0109] end while

[0110] The present invention can also ensure the overall approximation ratio of the algorithm. Considering the overall approximation, by setting and wherein,

[0111]

[0112]

[0113] the approximation ratio between the obtained solution and the optimal solution of the original problem is 1 / 2 - ∈.

[0114] Please refer to Figure 3 and Figure 4 , which are the experimental comparisons of the method of the present invention, the random orientation selection (RO) method, the method without the influence of monitor drift and jitter noise (NMJ), and the method facing the nearest monitor drift center (NFD) when the number of UAVs N and the number of monitors M change. Among them, the value of each data point is the average of the expected monitoring energy efficiency of 100 random topologies. Among them, the experimental settings are as follows: the monitor drift and the UAV projection plane range are within a square area of 15m × 15m, and the randomly generated UAV projection positions must ensure that there is at least one DDA center near their coverage range. Except for the changing parameters, the remaining default parameter settings are: D = 6m, r o = 2m, M = 8, N = 10, a1 = 100, b1 = 5, a2 = 4, b2 = 3, ∈ = 0.1, α = π / 2, and Q thr = 1.5. From the experimental results, we can see that the robust UAV scheduling method of the present invention considering jitter noise and monitor drift is significantly better than the RO, NMJ, and NFD methods. On average, it is better than the other three comparison methods by 33.88% and 29.64% respectively in two aspects, and shows strong stability, having certain advantages.

[0115] In summary: The present invention discloses a robust UAV scheduling method considering jitter noise and monitored object drift. The situation is as follows: There are several monitored objects in a given plane, and they can drift within a certain range; at the same time, some UAVs with determined positions but undetermined monitoring orientations are deployed, and there is jitter noise during their monitoring. The problem is: to give an effective orientation scheduling method for UAVs in the projected two-dimensional plane to maximize the expected monitoring utility. The present invention first gives a probability model of monitoring quality and a monitoring utility model, and proposes a formalized problem; secondly, proposes a method to linearize and discretize the non-linear and continuous monitoring quality through region discretization; thirdly, finitize the infinite solution space and limit the change in coverage area through the division of orientation angles; finally, use a greedy algorithm to effectively select orientations from the solution space to obtain the final result and limit the error. The present invention first proposes a robust UAV scheduling method and gives an effective approximation algorithm.

[0116] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A robust UAV scheduling method considering jitter noise and monitored object drift, characterized in that, Regarding the monitoring of target objects within a target area by an unmanned aerial vehicle (UAV), aiming at the problem of maximizing the expected monitoring utility under uncertain environmental factors, the steps for scheduling the UAV's orientation are as follows: (1) Based on the jitter noise generated during the UAV's monitoring process, model the monitoring quality and monitoring utility, and establish a monitoring quality model and a monitoring utility model; In step (1), the monitoring quality model and the monitoring utility model are modeled as follows: Project the drone and the monitored object onto the same two-dimensional plane. Model the monitoring range of the drone as a sector according to the device monitoring range. Model the monitoring utility of the drone considering jitter noise. Let the drone be s i , after it is projected onto the two-dimensional plane, the monitoring range of the drone is approximately a sector with the point where the drone s i is located as the center, the central angle of α, and the radius of D. The discrete angle of the drone is In the presence of jitter noise, its monitoring quality function for any monitoring position p on this two-dimensional plane is defined as: where a1, b1, a2, b2 are constants determined by hardware and environment, indicating a normal distribution with mean μ and variance σ 2 , and d(s i , p) represents the distance between the projection position of the UAV s i and the point p on the plane. When multiple UAVs monitor the same point p on the plane, the monitoring quality model is: Among them, N is the number of UAVs, and Q(p) represents the overall monitoring quality at point p; since there is a saturation state in the monitoring quality, a monitoring utility model is given, that is, the monitoring utility stops increasing when the monitoring quality reaches a certain level and reaches the saturation state. The monitoring utility model is defined as: where x is the monitoring quality, and Q thr is the threshold for the saturation state of the monitoring quality; (2) Based on the drift of the target object within a predetermined range, combined with the monitoring utility model, define the UAV monitoring quality function, formalize the problem of maximizing the expected monitoring utility, and obtain the formalized problem of maximizing the expected monitoring utility in the scenario of the UAV monitoring the target object; (3) In the formalized problem of maximizing the expected monitoring utility, project the three-dimensional space where the UAV is located onto a two-dimensional plane area, divide the projected two-dimensional plane area according to the monitoring quality model, obtain multiple sub-areas with approximately constant monitoring quality, discretize the UAV monitoring quality function through each sub-area, and combine the preset limit of its approximation error, thereby transforming the formalized problem of maximizing the expected monitoring utility into a discrete summation problem of maximizing the expected monitoring utility; (4) Divide the UAV monitoring angles in the discrete summation problem of maximizing the expected monitoring utility, obtain a finite number of scheduling orientations for the UAV, thereby transforming the infinite solution space into a finite solution space, and at the same time ensuring the coverage area change limit brought by the division; (5) In the finite solution space, select and schedule the finite number of scheduling orientations of the UAV through the greedy algorithm to obtain the final scheduling result, and give the approximation ratio to the optimal solution, and obtain the monitoring utility that maximizes the expectation under uncertain environmental factors; Step (5) is specifically as follows: The problem after area division and angle division is approximated as: Among them, represents the area of the sub-region , is the discrete angle of the UAV, Γ is the entire solution space containing the discrete angles of all UAVs, Γ i represents the solution set of the discrete angles of the i-th UAV. The problem is proven to be a submodular maximization problem constrained by a partition matroid. A solution with an approximation ratio of 1 / 2 can be obtained through the greedy algorithm. Considering the overall approximation, by setting and Among them, Among them, ∈ is the approximation ratio parameter, and the approximation ratio of the solution to the optimal solution of the original problem is obtained.

2. The robust UAV scheduling method considering jitter noise and monitored object drift according to claim 1, wherein In step (2), the problem of maximizing the expected monitoring utility is formalized as follows: Based on the drift of the monitored object within a predetermined range, assume the monitored object o j randomly drifts within a circle γ j with center p o and radius r j Then, combined with the monitoring utility model, the formal definition of the objective problem of maximizing the expected monitoring utility is as follows: where \(N\) represents the number of UAVs, \(M\) represents the number of monitored objects, \(\Omega\) represents the two-dimensional plane under consideration, denotes the mathematical expectation, and \((x, y)\) represents the coordinates of a point on the plane, is the discrete angle of the UAV.

3. The robust UAV scheduling method considering jitter noise and monitoring object drift according to claim 1, wherein Step (3) is specifically as follows: Make the following approximation of the monitoring quality according to the distance: Among them, Q(d) represents the monitoring quality when the distance between the monitored object and a drone is d, is its approximate value, l(0) = 0, l(K) = D, where D is the farthest monitoring range of the drone in the monitoring quality model; let represent the same monitoring quality sub-region according to the above approximate situation at any point p within, the monitoring quality generated by the drone s i is set as: Among them, l(k) represents the discretized distance at the k-th level. There are a total of K levels of discretized distances, k = 1,..., K - 1 and l(0) = 0, l(K) = D; ∈1 is a positive small quantity close to 0, and b1, b2 are constants determined by the hardware and environment in the monitoring quality model, and The approximation error of the expected monitoring utility is limited to:

4. The robust UAV scheduling method considering jitter noise and monitored object drift according to claim 1, wherein Step (4) is specifically as follows: After discretizing the angle, a finite solution space is obtained to select the orientation angle. The entire 2π angle is divided, and each orientation is taken to obtain discretized orientation angles. Suppose is a small angular change that is divisible by 2π. Among them, the maximum change in the area covered by two adjacent discrete orientations is a circle γ j and is

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