Mountainous environment-oriented unmanned aerial vehicle joint resource allocation and trajectory design method

Abstract

The application discloses a mountainous environment-oriented unmanned aerial vehicle joint resource allocation and trajectory design method and belongs to the technical field of unmanned aerial vehicle communication and energy efficiency optimization. The application firstly models a complex mountainous area as a prism and establishes a non-convex shielding constraint, then constructs an optimization problem with a total communication rate / total consumed energy as a target, and incorporates communication quality, power / bandwidth allocation, flight safety and other constraints; the non-convex constraint is transformed through a Big-M method and a Lagrange relaxation technique, the fractional target function is transformed by using a Dinkelbach algorithm, the resource allocation and trajectory design sub-problems are alternately optimized in combination with a block coordinate descent framework, and solving is performed with the aid of a CVX toolbox. The application is suitable for a mountainous area and other multi-obstacle scenes, the communication reliability and energy efficiency are significantly improved, the algorithm converges fast, has strong engineering landing performance, and can be widely applied to the fields of emergency communication, mountainous area survey and the like.

Description

Technical Field

[0001] This invention belongs to the field of UAV communication and energy efficiency optimization technology, specifically relating to a method for joint resource allocation and trajectory design of UAVs for mountainous environments. Background Technology

[0002] With the widespread application of unmanned aerial vehicles (UAVs) in emergency communications, mountain surveying, and signal coverage in remote areas, energy efficiency and communication reliability have become core bottlenecks restricting the implementation of the technology. In complex terrain scenarios such as mountains, users often cannot obtain a stable line-of-sight (LoS) link from ground base stations (BS) due to mountain obstruction, resulting in problems such as reduced communication speed and signal interruption. As an aerial base station, UAVs can flexibly avoid obstructions and fill communication gaps, becoming a key solution to this problem.

[0003] However, existing UAV communication and trajectory optimization technologies still have many limitations and are difficult to adapt to the actual needs of mountainous environments: First, terrain modeling is simplified. Most studies are based on ideal propagation environments or urban planar obstacle models, failing to fully consider the occlusion characteristics of complex mountain geometry and failing to accurately model the mountains into quantifiable constraint forms, resulting in trajectory planning easily getting stuck in occlusion areas and unstable communication links. Second, constraint processing capabilities are insufficient. The non-convex constraints and binary decision variables brought about by mountain occlusion make it difficult to solve the optimization problem directly, and existing technologies lack efficient constraint transformation methods. Third, the objective and optimization logic are separated. Existing solutions mostly focus on single-dimensional optimization (such as only optimizing the trajectory or only allocating resources), failing to jointly consider the strong coupling relationship between resource allocation and trajectory design, and failing to design suitable transformation and solution methods for the fractional energy efficiency target of total system communication rate / total energy consumption, resulting in serious energy waste and low energy efficiency. Fourth, practicality is insufficient. Some solutions ignore actual operational constraints such as UAV flight cycle return and movement speed limits, or the solution process is complex and the convergence speed is slow, making it difficult to meet the real-time application needs of mountainous scenarios.

[0004] Therefore, there is an urgent need for a technical solution that can accurately model the characteristics of mountain occlusion, efficiently handle non-convex constraints and fractional objective functions, and jointly optimize resource allocation and trajectory design, so as to maximize the energy efficiency of UAVs while avoiding mountain occlusion and ensuring the quality of communication services, and promote the reliable application of UAVs in complex terrain scenarios such as mountains. Summary of the Invention

[0005] The purpose of this invention is to provide a method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments, which solves the technical problem of difficulty in accurately modeling the occlusion characteristics of complex mountainous terrain.

[0006] The technical solution adopted in this invention is a method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments, which specifically includes the following steps: S1: Construct a UAV communication system model including communication rate and energy consumption based on Shannon's formula; S2: Model the complex mountain geometry as a frustum, and establish a mountain occlusion model and the corresponding non-convex constraint expression; S3: Construct an energy efficiency maximization optimization problem with the total system communication rate / total energy consumption as the fractional objective function, and constrain it with non-convex constraints containing binary variables, including communication service quality, power and bandwidth allocation, and trajectory avoidance. S4: Transform the non-convex occlusion constraint of S3 using the Big-M method and Lagrange relaxation technique; S5: The Dinkelbach algorithm is used to transform the fractional objective function. The power / bandwidth allocation and trajectory design sub-problems are alternately optimized through the block coordinate descent framework. The optimal solution is found using the CVX toolbox.

[0007] The invention is further characterized by: The S1 system model includes a mountaintop base station, multiple users whose locations are known but obstructed by the mountain, and a drone responsible for downlink transmission. The drone must satisfy the constraint of returning to its initial position at the end of its flight cycle. The system model includes channel gain. With Gaussian white noise power parameter.

[0008] In S1: The expression for communication rate is: ; The energy consumption expression is: ; In the formula: Bandwidth factor; Total bandwidth; This refers to the transmission power. To increase power; This represents the total number of time slots. This represents the total number of users.

[0009] The non-convex constraint of S2 is expressed as:

[0010] In the formula: For the first n The first obstructed area r The external normal vectors of the plane; This is the offset; This represents the position of the UAV in time slot t.

[0011] The fractional objective function in S3 is: ; Non-convex constraints are specifically: Constraint 1: The sum of the user's communication rates must be greater than a certain threshold. ;Right now:

[0012] Constraint 2: The communication bandwidth factor allocated to users is less than or equal to 1; that is:

[0013] Constraint 3: Ensure that the communication power allocated to users is neither too high nor too low; that is:

[0014] Constraint 4: The drone is in an unobstructed area; that is:

[0015] Constraint 5: The UAV returns to its initial position at the end of the flight cycle; that is:

[0016] Constraint 6: The distance the drone travels in one time slot will not be too large; that is:

[0017] In the formula: D is the bandwidth factor allocated to users; D is the deployable area for drones. It is an obstructed area; η To meet the user's minimum communication rate requirements, The upper limit of drone transmission power, This represents the maximum movable distance for a single time slot.

[0018] The transformation process of S4 is as follows: introduce a positive constant. and binary decision variables ; Transform the non-convex constraint into: Constraint 7:

[0019] Constraint 8:

[0020] Constraint 9:

[0021] Constraint 10:

[0022] In the formula: It is a sufficient positive constant; It is a binary decision variable. For each hyperplane, when When, the constraints are satisfied This means that drones are allowed to operate inside the hyperplane; when When, the constraints are satisfied Furthermore, the drone must be located outside the hyperplane; This represents the position of the UAV in time slot t.

[0023] In S5, the Dinkelbach algorithm transforms the fractional objective function into:

[0024] In the formula: τ is the iteration parameter; η is consistent with the preset threshold of S3.

[0025] The optimization logic of the block coordinate descent framework is as follows: first fix... S3-based constraint solution and The resource allocation sub-problem; then fix and Constraint solution based on S4 transformation The trajectory design subproblem is iterated alternately until convergence.

[0026] The resource allocation subproblem is a convex optimization problem, which can be solved directly using the CVX toolbox; the trajectory design subproblem is solved using Lagrange relaxation. The problem is transformed into a continuous 0-1 variable, and the lower bound of the non-convex constraint is obtained through a first-order Taylor expansion. After transforming it into a convex optimization problem, it is solved using the CVX toolbox.

[0027] The beneficial effects of this invention are: This invention precisely models complex mountain geometry as a frustum and combines the Big-M method with Lagrange relaxation techniques to transform non-convex occlusion constraints, completely solving the problem of trajectories easily getting trapped in occlusion areas due to simplified terrain modeling in traditional solutions. The UAV trajectory always remains in the unobstructed area, effectively ensuring the proportion of line-of-sight (LoS) communication links, improving user communication rate stability, significantly reducing the risk of signal interruption, and perfectly adapting to the communication needs of complex terrains with multiple obstacles, such as mountains. This invention employs a joint optimization framework combining resource allocation and trajectory design, avoiding the limitations of single-dimensional optimization. Simultaneously, the Dinkelbach algorithm transforms the fractional energy efficiency objective function into an easily solvable form, and combined with iterative block coordinate descent, maximizes the transmission rate per unit energy consumption. Compared to traditional solutions such as average resource allocation and isolated trajectory optimization, this invention significantly improves energy efficiency, indirectly extending the drone's endurance and effectively reducing energy replenishment costs in mountainous environments.

[0028] By employing a hierarchical transformation strategy (non-convex constraint transformation + fractional objective transformation), complex non-convex mixed integer problems are transformed into convex optimization problems, which are then solved quickly using the CVX toolbox. The algorithm converges rapidly and requires fewer iterations, meeting the timeliness requirements of scenarios such as mountain emergency communication and real-time surveying; moreover, the solution process does not require complex hardware support, making it easy to implement and deploy in engineering. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the system model in the UAV joint resource allocation and trajectory design method for mountainous environments of this invention; Figure 2 This is a schematic diagram of the occlusion model in the UAV joint resource allocation and trajectory design method for mountainous environments of the present invention; Figure 3 This is a schematic diagram of the UAV trajectory in the UAV joint resource allocation and trajectory design method for mountainous environments of the present invention; Figure 4 This is a schematic diagram illustrating the energy efficiency of the UAV joint resource allocation and trajectory design method for mountainous environments under different numbers of users in this invention. Detailed Implementation

[0030] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] Example 1 The UAV joint resource allocation and trajectory design method for mountainous environments disclosed in this embodiment specifically includes the following steps: S1: Construct a UAV communication system model including communication rate and energy consumption based on Shannon's formula; S2: Model the complex mountain geometry as a frustum, and establish a mountain occlusion model and the corresponding non-convex constraint expression; S3: Construct an energy efficiency maximization optimization problem with the total system communication rate / total energy consumption as the fractional objective function, and constrain it with non-convex constraints containing binary variables, including communication service quality, power and bandwidth allocation, and trajectory avoidance. S4: Transform the non-convex occlusion constraint of S3 using the Big-M method and Lagrange relaxation technique; S5: The Dinkelbach algorithm is used to transform the fractional objective function. The power / bandwidth allocation and trajectory design sub-problems are alternately optimized through the block coordinate descent framework. The optimal solution is found using the CVX toolbox.

[0032] Example 2 Based on Example 1, the system model of S1 includes a mountaintop base station, multiple users whose locations are known and obstructed by the mountain (users are randomly distributed in this area), and a drone responsible for downlink transmission. The drone must satisfy the constraint of returning to its initial position at the end of its flight cycle. The system model includes channel gain. With Gaussian white noise power parameter.

[0033] Furthermore, the signals transmitted by the drone to the user are Then, the obtained signal is used to solve for the communication signal-to-noise ratio. Then, substituting into Shannon's formula, we obtain the target's communication rate. Based on the transmitted signal power and propulsion power, we calculate the UAV's energy consumption. Therefore, in S1: The expression for communication rate is: ; The energy consumption expression is: ; In the formula: Bandwidth factor; Total bandwidth; This refers to the transmission power. To increase power; This represents the total number of time slots. Total number of users; It is channel gain; It is Gaussian white noise.

[0034] Example 3 Based on Example 1, the non-convex constraint of S2 is expressed as follows:

[0035] In the formula: For the first n The first obstructed area r The external normal vectors of the plane; This is the offset; This represents the position of the UAV in time slot t.

[0036] Example 4 Based on Example 1, the fractional objective function in S3 is: ; Non-convex constraints are specifically: Constraint 1: The sum of the user's communication rates must be greater than a certain threshold. ;Right now:

[0037] Constraint 2: The communication bandwidth factor allocated to users is less than or equal to 1; that is:

[0038] Constraint 3: Ensure that the communication power allocated to users is neither too high nor too low; that is:

[0039] Constraint 4: The drone is in an unobstructed area; that is:

[0040] Constraint 5: The UAV returns to its initial position at the end of the flight cycle; that is:

[0041] Constraint 6: The distance the drone travels in one time slot will not be too large; that is:

[0042] In the formula: D is the bandwidth factor allocated to users; D is the deployable area for drones. It is an obstructed area; η To meet the user's minimum communication rate requirements, The upper limit of drone transmission power, This represents the maximum movable distance for a single time slot.

[0043] Example 5 Based on Example 1, the transformation process of S4 is as follows: introducing a positive constant. and binary decision variables The non-convex constraint condition 4 is transformed into: Constraint 7:

[0044] Constraint 8:

[0045] Constraint 9:

[0046] Constraint 10:

[0047] In the formula: It is a sufficient positive constant; It is a binary decision variable. For each hyperplane, when When, the constraints are satisfied That is, the drone in the time slot It is allowed to be located inside the hyperplane; when When, the constraints are satisfied Furthermore, the drone must be located outside the hyperplane; This represents the position of the UAV in time slot t.

[0048] Furthermore, the Dinkelbach algorithm in S5 transforms it into:

[0049] In the formula: τ is the iteration parameter; η is consistent with the preset threshold of S3.

[0050] The strong coupling between variables can be addressed by using an alternating optimization algorithm to decompose the original optimization problem into two sub-problems: a resource allocation problem and a trajectory design problem.

[0051] Furthermore, the optimization logic for the block coordinate descent framework is as follows: first fix... S3-based constraint solution and The resource allocation subproblem is as follows: its objective function and constraints are as follows: Objective function:

[0052] Constraint 1:

[0053] Constraint 2: ; Constraint 3: ; Constraint 1 is an achievable rate constraint, which must be greater than or equal to the minimum rate. Constraint 2 is the bandwidth allocation factor, and constraint 3 is the transmission power of the UAV. The transmission power must be positive and not exceed a threshold. The resource allocation subproblem is clearly a convex optimization problem, which can be solved using CVX.

[0054] Re-fix and Constraint solution based on S4 transformation The trajectory design subproblem is iterated alternately until convergence, specifically as follows: its objective function and constraints are as follows: Objective function:

[0055] Constraint 1:

[0056] Constraint 5: ; Constraint 6: ; Constraint 7:

[0057] Constraint 8:

[0058] Constraint 9:

[0059] Constraint 10:

[0060] Constraint 5 ensures the drone returns to its starting position at the end of its flight cycle, and constraint 6 ensures the drone does not travel excessive distances within a time slot. Constraints 7, 8, 9, and 10 ensure the drone remains in an unobstructed region. This problem is clearly a non-convex mixed integer problem, solvable using Lagrange relaxation and SCA techniques. For the transformed convex optimization problem, CVX can be used.

[0061] The resource allocation subproblem is a convex optimization problem, which can be solved directly using the CVX toolbox; the trajectory design subproblem is solved using Lagrange relaxation. The problem is transformed into a continuous 0-1 variable, and the lower bound of the non-convex constraint is obtained through a first-order Taylor expansion. After transforming it into a convex optimization problem, it is solved using the CVX toolbox.

[0062] Example 6 like Figure 1 As shown, this is a drone-assisted communication system consisting of a BS, a UAV, and M users. As can be seen from the figure, there is a mountain blocking the connection between the BS and the users, resulting in an NLoS connection between the BS and the users, which leads to a decrease in signal communication speed.

[0063] set up The user set is: M = {1, 2, ..., m, ..., M}; The location of the drone is:

[0064] The location of the drone is recorded as:

[0065] Unmanned aerial vehicles (UAVs) are used as aerial base stations to improve communication rates. Downlink transmission from the UAV to the user is considered in the system. To provide continuous periodic service, the UAV will return to its initial position at the end of the period. The periodic constraint can be expressed as...

[0066]

[0067] The signal transmitted by the drone to the user is Calculate the signal-to-noise ratio of the communication. for:

[0068] In the formula: It is channel gain; It is Gaussian white noise; Define the bandwidth factor of time slot t for user m as follows:

[0069] Substituting this into Shannon's formula, we obtain the target's communication rate and speed.

[0070] In the formula: B represents the total system bandwidth. The energy consumption of the UAV is calculated based on the transmitted signal power and propulsion power as follows:

[0071] like Figure 2 As shown, a mountain obstacle model is constructed, with the complex mountain geometry modeled as a frustum, and the set of mountain occlusion areas as... Its definition is:

[0072] In the formula: It is the outward normal vector of the r-th plane in the n-th occlusion region; This is the offset. Therefore, the deployable area for the drone is:

[0073] Since the occlusion constraint is non-convex, the Big-M method is used to transform it into a mixed-integer linear constraint. This will result in:

[0074] Rewritten as:

[0075] In the formula: It is a sufficient positive constant; It is a binary decision variable For each hyperplane, when When, the constraints are satisfied This means that drones are allowed to operate inside the hyperplane; when When, the constraint is Furthermore, the drone must be located outside the hyperplane.

[0076] Therefore, the occlusion constraint can be rewritten as:

[0077] According to the blocking model, the drone's location Need to be in a blocked area In addition.

[0078] Therefore, at least one is needed. For the 0th For a congested region, the constraint can be represented as:

[0079] Based on the above analysis, each congested area The constraints can be rewritten as:

[0080]

[0081]

[0082]

[0083] In this invention, an optimization problem is designed with the goal of maximizing the overall energy efficiency of the system. The strong coupling between variables can be decomposed into two sub-problems, namely, a resource allocation problem and a trajectory design problem, by using an alternating optimization algorithm.

[0084] Objective function:

[0085] Constraint 1:

[0086] Constraint 2:

[0087] Constraint 3:

[0088] Among them, constraint 1 is an achievable rate constraint, which is greater than or equal to the minimum rate. Constraint 2 is the bandwidth allocation factor, and constraint 3 is the transmission power of the UAV. The transmission power must be positive and not exceed a threshold. The resource allocation subproblem is clearly a convex optimization problem, which can be solved using CVX.

[0089] For the trajectory design subproblem, the objective function and constraints are as follows: Objective function:

[0090] Constraint 1:

[0091] Constraint 5:

[0092] Constraint 6:

[0093] Constraint 7:

[0094] Constraint 8:

[0095] Constraint 9:

[0096] Constraint 10:

[0097] Constraint 5 ensures the drone returns to its starting position at the end of its flight cycle, and constraint 6 ensures the drone's distance traveled within a time slot is not excessive. Constraints 7, 8, 9, and 10 ensure the drone remains in an unobstructed region. Due to the non-convexity of constraints 7 and 8, the trajectory design subproblem is a non-convex mixed integer problem. To address this, the Lagrange relaxation method is applied. (Binary variables...) It can be transformed into a continuous variable from 0 to 1. Constraints. It can be equivalently expressed as:

[0098] Then, according to the Lagrange method, the constraints can be... This is incorporated into the objective function as a penalty term. In this way, a Lagrange problem can be constructed. For a non-concave objective function, local points are given. In the alternating iterative framework, the first The next iteration. Then, we can obtain... The lower bound of . It can be represented as:

[0099] For nonconvex constraints The lower bound of dm is obtained by using a first-order Taylor expansion.

[0100] Specifically, given the current local point The left-hand side of the constraint can be approximated using a Taylor expansion. Then, its lower bound can be obtained. Here, we define... As the lower bound. Therefore, The constraint can be restated as:

[0101] In the formula: For reference distance Channel gain at that location, It is the path loss exponent, where:

[0102]

[0103]

[0104]

[0105] Since the objective function is concave and all constraints are linear or convex, this optimization problem is transformed into a convex optimization problem, which can be solved using a standard convex optimization solver. Figure 3 As shown, the optimized drone trajectory moves towards the ideal position and satisfies the constraints. Figure 4 As shown, it can be observed that the EE of the proposed method gradually increases with the increase of the number of iterations, eventually reaching a stable value. The EE value is the largest when the number of users is 4.

[0106] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0107] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0108] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments, characterized in that, Specifically, the following steps are included: S1: Construct a UAV communication system model including communication rate and energy consumption based on Shannon's formula; S2: Model the complex mountain geometry as a frustum, and establish a mountain occlusion model and the corresponding non-convex constraint expression; S3: Construct an energy efficiency maximization optimization problem with the total system communication rate / total energy consumption as the fractional objective function, and constrain it with non-convex constraints containing binary variables, including communication service quality, power and bandwidth allocation, and trajectory avoidance. S4: Transform the non-convex occlusion constraint of S3 using the Big-M method and Lagrange relaxation technique; S5: The Dinkelbach algorithm is used to transform the fractional objective function. The power / bandwidth allocation and trajectory design sub-problems are alternately optimized through the block coordinate descent framework. The optimal solution is found using the CVX toolbox.

2. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 1, characterized in that, The system model of S1 includes a mountaintop base station, multiple users whose locations are known but obstructed by the mountain, and a drone responsible for downlink transmission. The drone must satisfy the constraint of returning to its initial position at the end of its flight cycle. The system model includes channel gain. With Gaussian white noise power parameter.

3. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 2, characterized in that, In S1: The expression for communication rate is: ; The energy consumption expression is: ; In the formula: Bandwidth factor; Total bandwidth; This refers to the transmission power. To increase power; This represents the total number of time slots. This represents the total number of users.

4. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 1, characterized in that, The non-convex constraint of S2 is expressed as: In the formula: For the first n The first obstructed area r The external normal vectors of the plane; This is the offset; This represents the position of the UAV in time slot t.

5. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 1, characterized in that, The fractional objective function in S3 is: ; Non-convex constraints are specifically: Constraint 1: The sum of the user's communication rates must be greater than a certain threshold. ;Right now: Constraint 2: The communication bandwidth factor allocated to users is less than or equal to 1; that is: Constraint 3: Ensure that the communication power allocated to users is neither too high nor too low; that is: Constraint 4: The drone is in an unobstructed area; that is: Constraint 5: The UAV returns to its initial position at the end of the flight cycle; that is: Constraint 6: The distance the drone travels in one time slot will not be too large; that is: In the formula: It is the bandwidth factor allocated to users; D is the area where drones can be deployed. It is an obstructed area; η To meet the user's minimum communication rate requirements, The upper limit of drone transmission power, This represents the maximum movable distance for a single time slot.

6. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 1, characterized in that, The transformation process of S4 is as follows: introduce a positive constant. and binary decision variables ; Transform the non-convex constraint into: Constraint 7: Constraint 8: Constraint 9: Constraint 10: In the formula: It is a sufficient positive constant; It is a binary decision variable. For each hyperplane, when When, the constraints are satisfied This means that drones are allowed to operate inside the hyperplane; when When, the constraints are satisfied Furthermore, the drone must be located outside the hyperplane; This represents the position of the UAV in time slot t.

7. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 1, characterized in that, In S5, the Dinkelbach algorithm transforms the fractional objective function into: In the formula: τ is the iteration parameter; η is consistent with the preset threshold of S3.

8. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 7, characterized in that, The optimization logic of the block coordinate descent framework is as follows: first fix... S3-based constraint solution and The resource allocation sub-problem; then fix and Constraint solution based on S4 transformation The trajectory design subproblem is iterated alternately until convergence.

9. The method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in mountainous environments according to claim 8, characterized in that, The resource allocation subproblem is a convex optimization problem, which can be solved directly using the CVX toolbox; the trajectory design subproblem is solved using Lagrange relaxation. The problem is transformed into a continuous 0-1 variable, and the lower bound of the non-convex constraint is obtained through a first-order Taylor expansion. After transforming it into a convex optimization problem, it is solved using the CVX toolbox.

Images