A UAV trajectory planning method to completely avoid no-fly zones

Abstract

The invention discloses a method for planning a trajectory of a UAV that completely avoids a no-fly zone, belongs to the field of UAV trajectory planning, and includes application scenarios of the method for planning a trajectory of a UAV in a no-fly zone, wherein the application scenarios of the method for planning a trajectory of a UAV in a no-fly zone include communication scenarios between the UAV and a terminal user in a no-fly zone. The invention supports the UAV to absolutely avoid entering any no-fly zone during flight. Multiple straight lines are used to approximate the actual flight trajectory of the UAV, and the distance between the intersection of two adjacent straight lines and the center point of the no-fly zone is calculated to achieve strict monitoring and planning of the flight path of the UAV, thereby improving the accuracy of trajectory planning as well as the flight efficiency and task execution effect of the UAV. The invention increases the constraints on the continuous trajectory between adjacent time slots, and further improves the safety and robustness of the system through multiple straight line approximation and accurate intersection calculation.

Description

Technical Field

[0001] The present invention belongs to the field of unmanned aerial vehicle (UAV) trajectory planning, and in particular relates to a UAV trajectory planning method capable of completely avoiding a no-fly zone. Background Art

[0002] Unmanned Aerial Vehicle (UAV) usually performs flight missions in a wide airspace, and low-altitude airspace is more susceptible to natural terrain obstacles such as mountains and hills than high-altitude airspace, and may also be subject to artificial flight restrictions such as no-fly zones (NFZs). A drone no-fly zone refers to a three-dimensional space defined by a specific geographical location or distance where drones are prohibited from flying routes. In the mission scenario space, no-fly zones are often abstracted as cylinders for easy processing. In the trajectory planning of low-altitude airspace, drones must adopt strategies to bypass no-fly zones.

[0003] Although existing research work has considered obstacle avoidance planning in no-fly zones, it is limited to no-fly zone constraints at discrete points, ignoring the potential risks of flight paths between adjacent points. This discontinuous trajectory planning method may cause the drone to mistakenly enter the no-fly zone, thereby causing serious flight safety issues. Therefore, the present invention proposes an innovative drone trajectory planning method, which aims to completely avoid no-fly zones in low-altitude airspace. Based on time discretization, this method introduces a continuous trajectory processing method, thereby achieving complete obstacle avoidance in drone trajectory planning while ensuring flight safety. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a trajectory planning method to ensure that a UAV completely avoids a no-fly zone; on the one hand, the present invention uses a series of straight line segments to approximate the actual flight trajectory of the UAV, and determines whether the intersection of two adjacent straight line segments is located inside the no-fly zone, so as to determine whether the UAV has entered the no-fly zone, thereby achieving precise control of the flight trajectory and improving the accuracy of trajectory planning; on the other hand, the present invention moderately expands the trajectory of the UAV, so that the UAV can more robustly cope with various challenges when facing a complex flight environment, thereby improving the safety and robustness during the flight process.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for planning a drone trajectory that completely avoids a no-fly zone, including an application scenario of the method for planning a drone trajectory in a no-fly zone, wherein the application scenario of the method for planning a drone trajectory in a no-fly zone includes a communication scenario between the drone and a terminal user in the no-fly zone;

[0007] The communication environment between the drone and the terminal user in the no-fly zone includes a terminal user set, a sparsely distributed and non-overlapping no-fly zone set, and the drone; the terminal user set includes terminal devices such as smart phones, mobile tablets, and unmanned vehicles; the drone serves as an aerial platform to assist the target user in communicating; the drone needs to communicate with each terminal user on the ground while strictly avoiding the no-fly zone;

[0008] The specific steps include:

[0009] Step 1: Construct a communication system model between drones and end users in a no-fly zone. The drone flies over the user and communicates with each user on the ground, while avoiding the no-fly zone to form a flight trajectory. The flight cycle of the drone is evenly divided into several time slots using the time discretization method. The drone coordinates can be represented in the current time slot, and preliminary constraints are set for the no-fly zone.

[0010] Step 2: The flight trajectory of the UAV between two adjacent time slots is evenly divided into several parts according to the same interval; at each segmentation point, the first-order Taylor expansion of the UAV flight trajectory equation is performed to approximate the flight path of the UAV; wherein each segmentation point includes a starting point, an end point, and an intermediate equal division point;

[0011] Step 3: Every two adjacent straight lines generate an intersection point. To ensure that the drone can completely avoid the no-fly zone during actual flight, add a constraint condition. After completing the constraint of one time slot, go to the next time slot, continue the constraint, and repeat the iteration to ensure that the flight trajectory of the drone will not intersect with the no-fly zone at any time, thereby achieving the goal of completely avoiding the no-fly zone.

[0012] Step 4: Construct the UAV trajectory planning objective function, and finally obtain the optimal flight path of the UAV that meets specific constraints by minimizing the objective function.

[0013] As a further preferred embodiment of the method for planning a UAV trajectory that completely avoids a no-fly zone in the present invention, in step 1, the environment of the communication system model adopts a three-dimensional Cartesian coordinate system, and ground terminal users remain stationary and are all located outside the no-fly zone; the UAV flies within a certain altitude range and needs to communicate with each user; the no-fly zone is abstracted as a cylinder with infinite height, sparse distribution, and multiple no-fly zones do not overlap; and a preliminary constraint condition is set: it is required that the coordinates of the UAV corresponding to each discrete time slot are outside the no-fly zone.

[0014] As a further preferred embodiment of the UAV trajectory planning method for completely avoiding no-fly zones of the present invention, in step 1 and in step 2, straight line segments are selected to approximate the flight trajectory in each time slot; the speed and acceleration limits of the UAV are considered at each segmentation point to ensure that these parameters are continuous and conform to physical laws throughout the flight process.

[0015] As a further preferred solution of the UAV trajectory planning method for completely avoiding the no-fly zone of the present invention, in step 3, a new constraint condition is added: all intersection points are located outside the no-fly zone.

[0016] As a further preferred solution of the method for planning the trajectory of a drone that completely avoids a no-fly zone in the present invention, in step 1, a communication system model between the drone and the terminal user in the no-fly zone is constructed, which specifically includes the following:

[0017] 1) System model: The communication system environment between drones and end users in no-fly zones includes a set of end users including smartphones, mobile tablets, and unmanned vehicles, a set of sparsely distributed and non-overlapping no-fly zones, and drones. Drones serve as aerial platforms to assist target users in communication. Drones need to communicate with each end user on the ground while strictly avoiding no-fly zones.

[0018] There is 1 drone in the system model. Users and sparsely distributed non-overlapping cylindrical NFZs; users are not in NFZ; define the user set as , no-fly zone assembly ;set up is a flight cycle, which is divided into time slots and the time slot length is , let the time slot set be ; Based on the three-dimensional Cartesian coordinate system, the user The coordinates can be set to ; The time discrete method is used to express the UAV in the time slot The coordinates below ,in , and are the minimum and maximum altitudes allowed for UAV flight respectively; the central horizontal coordinates and radius of NFZs are respectively expressed as and ; In each time slot The flight speed of the drone is , the acceleration is ,in are the three-axis speeds, They are three-axis accelerations respectively; the coordinates of the drone are expressed as: ;

[0019] 2) Communication model: drone and user The Euclidean distance between them is expressed as: ;

[0020] Since the flying altitude of the UAV is much higher than that of the ground terminal users, the influence of the non-line-of-sight channel formed by ground obstacles and other reasons is ignored, and the wireless channel between the user and the UAV is a line-of-sight channel; the UAV knows the location information of the ground user equipment, so as to obtain the channel status information between them; the UAV and the user The wireless channel between is a free space path loss model, and its channel gain is expressed as follows: ; In the formula, is the channel power gain per unit distance; further, according to Shannon's formula, the distance between the drone and the user The data transmission rate is expressed as: ; In the formula, represents the communication bandwidth, For users The constant transmission power, is the Gaussian noise power.

[0021] As a further preferred solution of the method for completely avoiding a no-fly zone in the present invention, in step 4, a drone trajectory planning objective function is constructed, which specifically includes the following:

[0022] (1) Minimize the length of the UAV’s flight path to reduce flight time and energy consumption;

[0023] (2) Minimize altitude changes during flight to maintain flight stability;

[0024] (3) Maximizing user transmission rate and to improve communication efficiency and quality;

[0025] Among them, the cost function of the UAV flight path length is expressed as: ;

[0026] The flight altitude change cost function is expressed as: ;

[0027] The user transmission rate and function are expressed as: ;

[0028] The objective function of UAV trajectory planning is comprehensively expressed as the weighted sum of the above three cost functions: ; In the formula, The three cost functions mentioned above are The weight coefficient is used to balance the priority and relative importance among the three objectives.

[0029] As a further preferred solution of the method for planning the flight path of a UAV that completely avoids a no-fly zone of the present invention, in step 4, a constraint condition is constructed, which is as follows:

[0030] 1) Existing constraint model: The maximum flight speed and acceleration of the drone are and , the velocity and acceleration need to satisfy the following constraints: ; During the flight, the drone must completely avoid the no-fly zone NFZ; The existing time discretization method can only ensure that the drone is at certain discrete points. and , does not enter the NFZ, and is expressed by the formula: ; and cannot guarantee Transition to When the flight trajectory of each location is always greater than or equal to the radius of the NFZ, the distance from the center of the NFZ is always greater than or equal to the radius of the NFZ. In view of this limitation, it is optimized;

[0031] 2) Add new constraint model: and The actual flight trajectory of the drone is divided into Get points, denoted as ,in Corresponding to the starting point , Corresponding to the end point The flight trajectory of the UAV presents a typical quadratic curve feature of a parabola in each time slot and changes continuously in time. The straight line approximation method is used to approximate its path. Perform a first-order Taylor expansion of the UAV flight trajectory equation at each point: ;

[0032] get The equation of the tangent line is That is, the time slot value, That is, the corresponding time slot value; due to About The parametric equation for It is obtained by chain rule; the tangent equation constitutes a piecewise linear approximation of the actual flight trajectory of the UAV, and each approximation segment closely fits the local form of the original trajectory in the corresponding interval, thereby achieving an effective simulation of the overall trajectory; the tangent equations of two adjacent tangents are combined: ; Solve for intersection point, denoted as ; In order to achieve the goal of completely avoiding the no-fly zone, a new constraint is added, All intersection points are outside the NFZ, which satisfies the condition: ; Through constraints, the drone can completely avoid NFZ in this time slot.

[0033] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0034] The present invention adopts an innovative UAV trajectory planning method to support the UAV to absolutely avoid entering any no-fly zone during flight; multiple straight lines are used to approximate the actual flight trajectory of the UAV, and the distance between the intersection of two adjacent straight lines and the center point of the no-fly zone is calculated to achieve strict monitoring and planning of the UAV flight path, thereby improving the accuracy of trajectory planning as well as the flight efficiency and mission execution effect of the UAV;

[0035] 2. The present invention adds constraints on continuous trajectories between adjacent time slots, and further improves the safety and robustness of the system through multiple straight line approximations and precise intersection calculations. These intersections are actually located on the extension of the UAV flight trajectory, not directly on the trajectory, which provides an additional safety margin for the UAV. Even if there is a slight change in wind speed or a slight deviation of the aircraft during actual flight, the present invention can still maintain a high accuracy in avoiding no-fly zones, which helps to ensure the safe flight of the UAV in various complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 This is an application scenario of the present invention, including 1 drone, Terminal communication users and non-overlapping NFZs;

[0038] Figure 2 Schematic diagram comparing the existing method of the present invention and the method of the present invention;

[0039] Figure 3 It is a schematic diagram of simulation results of the UAV of the present invention avoiding NFZ. DETAILED DESCRIPTION

[0040] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The present invention is described in detail below based on the drawings and preferred embodiments, and the purpose and effect of the present invention will become clearer. It should be understood that the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0042] A method for planning a drone trajectory that completely avoids a no-fly zone. The application scenario of the method for planning a drone trajectory in a no-fly zone includes a communication scenario between the drone and a terminal user in a no-fly zone.

[0043] The communication environment between drones and end users in the no-fly zone includes a set of end users, a set of sparsely distributed and non-overlapping no-fly zones, and drones; the set of end users includes terminal devices such as smart phones, mobile tablets, and unmanned vehicles; drones serve as aerial platforms to assist target users in communicating; drones need to communicate with each end user on the ground while strictly avoiding no-fly zones.

[0044] The method for completely avoiding a no-fly zone in a UAV trajectory planning specifically includes the following steps:

[0045] Step (1) Construct a communication system model between drones and ground terminal users in a no-fly zone. The drone flies above the user and communicates with each user on the ground, while avoiding the no-fly zone, and finally forms a flight trajectory. The flight cycle of the drone is evenly divided into several time slots using the time discretization method. The drone coordinates can be represented in the current time slot, and preliminary constraints are set for the no-fly zone.

[0046] Step (2) divides the flight trajectory of the UAV between two adjacent time slots into several parts at the same interval. At each segmentation point (including the starting point, the end point, and the middle equal division point), the UAV flight trajectory equation is expanded by a first-order Taylor expansion to approximate the flight path of the UAV.

[0047] Step (3) Every two adjacent straight lines generate an intersection point. To ensure that the drone can completely avoid the no-fly zone during actual flight, a key constraint condition is added. After completing the constraint of a time slot, go to the next time slot, continue the constraint, and repeat the iteration to ensure that the flight trajectory of the drone will not intersect with the no-fly zone at any time, thereby achieving the goal of completely avoiding the no-fly zone.

[0048] Step (4) constructs the UAV trajectory planning objective function, and finally obtains the optimal flight path of the UAV that meets specific constraints by minimizing the objective function.

[0049] The communication system environment in step (1) includes the following features: the environment adopts a three-dimensional Cartesian coordinate system, the end users remain stationary and are all located outside the no-fly zone; the drone flies within a certain altitude range and needs to communicate with each user; the no-fly zone is abstracted as a cylinder with infinite height, sparse distribution and multiple no-fly zones do not overlap. In this step, a preliminary constraint condition is set: it is required that the coordinates of the drone corresponding to each discrete time slot are outside the no-fly zone.

[0050] In step (2), in each independent time slot, the flight trajectory of the drone presents parabolic characteristics and changes continuously in time. Therefore, the present invention uses straight line segments to approximate the flight trajectory in each time slot. In order to ensure that this piecewise linear approximation can accurately reflect the actual flight trajectory of the drone, the present invention also considers the speed and acceleration limits of the drone at each segmentation point to ensure that these parameters are continuous and in accordance with physical laws throughout the flight process.

[0051] The newly added constraint in step (3) is that all intersection points are outside the no-fly zone. In fact, these intersection points are located at the virtual intersection points of the extended flight trajectory of the drone, and are not directly located on the actual flight path, achieving the effect of outsourcing the flight path, reserving a safe distance for the drone's flight, and enhancing the drone's fault tolerance and safety factor during flight.

[0052] The objective function of the drone trajectory planning in step (4) can be based on the drone flight trajectory length, flight altitude change and user transmission rate, so that the planned path is optimal while satisfying the constraints.

[0053] The present invention will be described in detail below based on the accompanying drawings and preferred examples, and the purpose and effects of the present invention will become more clearly understood. The preferred examples described herein are only used to explain the present invention and are not used to limit the present invention.

[0054] 1. Model building:

[0055] 1) System model:

[0056] like Figure 1 As shown, the drone and terminal user communication system environment in the no-fly zone includes a set of terminal users such as smart phones, mobile tablets, and unmanned vehicles, a set of sparsely distributed and non-overlapping no-fly zones, and drones; the drone serves as an aerial platform to assist the target user in communicating; the drone needs to communicate with each terminal user on the ground while strictly avoiding the no-fly zone.

[0057] There is 1 drone in the system model. Users and Sparsely distributed non-overlapping cylindrical NFZs. All users are not in NFZ. To facilitate expression and analysis, the user set is defined as , no-fly zone assembly .set up is a flight cycle, which is divided into time slots and the time slot length is , let the time slot set be Based on the three-dimensional Cartesian coordinate system, users The coordinates can be set to ; The time discrete method is used to express the UAV in the time slot The coordinates below ,in , and are the minimum and maximum altitudes allowed for UAV flight, respectively. The center horizontal coordinates and radius of NFZs are expressed as and ; In each time slot The flight speed of the drone is , the acceleration is ,in are the three-axis speeds, are the three-axis accelerations respectively;. Therefore, the coordinates of the drone can be expressed as: ;

[0058] 2) Communication model: drone and user The Euclidean distance between them is expressed as: ;

[0059] Since the flying height of drones is much higher than that of ground terminal users, the influence of non-line-of-sight channels caused by ground obstacles and other reasons is ignored, and the wireless channels between users and drones are all line-of-sight channels. The drone knows the location information of the ground user equipment and obtains the channel status information between them. The wireless channel between is a free space path loss model, and its channel gain is expressed as follows: ; In the formula, is the channel power gain per unit distance; further, according to Shannon's formula, the distance between the drone and the user The data transmission rate is expressed as: ; In the formula, represents the communication bandwidth, For users The constant transmission power, is the Gaussian noise power.

[0060] 2. Construct the objective function:

[0061] The objective function of the UAV trajectory planning is the process of optimizing the generated path to achieve the optimal solution while meeting specific constraints. Its goal is to find the shortest path to improve efficiency, select the fastest path to shorten latency, reduce energy consumption and avoid no-fly zones, and ensure the legality and safety of flight. Since the preferred embodiment of the present invention assumes a UAV communication environment in a no-fly zone, the user transmission rate and function are added as key components of the objective function to improve communication efficiency. In view of this, the trajectory planning objective function designed by the present invention, its core is to achieve the following three goals at the same time: minimize the flight path length of the UAV to reduce flight time and energy consumption; minimize altitude changes during flight to maintain flight stability; maximize user transmission rates and to improve communication efficiency and quality.

[0062] The UAV flight path length cost function can be expressed as: ;

[0063] The flight altitude change cost function is expressed as: ;

[0064] The user transmission rate and function are expressed as: ;

[0065] In summary, the objective function of the UAV trajectory planning of the present invention can be comprehensively expressed as the weighted sum of the above three cost functions: ; In the formula, The three cost functions mentioned above are The weight coefficient is used to balance the priority and relative importance among the three objectives.

[0066] 3. Construct constraints:

[0067] like Figure 2 As shown, the left side is the existing mathematical method, and the right side is the new method proposed by the present invention. The specific method of completely avoiding NFZ is as follows:

[0068] 1) Existing constraint model: The maximum flight speed and acceleration of the drone are and , the velocity and acceleration need to satisfy the following constraints: ;

[0069] During the flight, the UAV must completely avoid the NFZ. The existing time discretization method can only ensure that the UAV is at certain discrete points (i.e. Figure 2 In and ), does not enter the NFZ, and is expressed by the formula: ; and cannot guarantee Transition to When the flight trajectory at each location is greater than or equal to the radius of the NFZ, the distance from the center of the NFZ is always greater than or equal to the radius of the NFZ. In view of this limitation, it is optimized.

[0070] 2) Add new constraint model: and The actual flight trajectory of the drone is divided into share,( Figure 2 China-Israel For example), we get points, denoted as ,in Corresponding to the starting point , Corresponding to the end point The flight trajectory of the drone presents a typical quadratic curve feature of a parabola in each time slot and changes continuously in time, so the straight line approximation method can be used to approximate its path. Perform a first-order Taylor expansion of the UAV flight trajectory equation at each point: ;

[0071] get The equation of the tangent line is That is, the time slot value, That is, the corresponding time slot value. About The parametric equation for The tangent equation is a piecewise linear approximation of the actual flight trajectory of the drone. Each approximation segment closely fits the local form of the original trajectory in the corresponding interval, thus achieving an effective simulation of the overall trajectory. The tangent equations of two adjacent tangents are combined: ; Solve for intersection point, denoted as ; In order to achieve the goal of completely avoiding the no-fly zone, a new constraint is added, All intersection points are outside the NFZ, which satisfies the condition: ; Through this strict constraint, it can be achieved that the drone can completely avoid the effect of NFZ during this time slot.

[0072] During the entire flight process, it is unnecessary to further constrain the trajectory between every two adjacent points, which will waste a lot of time. In order to optimize this process, the present invention adopts a more efficient strategy: considering that the radius of the no-fly zone is much larger than the maximum distance that the drone can fly in a time slot, only the flight path between the point whose distance from the center of the no-fly zone is less than or equal to its diameter and its two adjacent points is constrained, which can greatly improve the efficiency of trajectory planning. This method not only ensures that the drone can flexibly adapt to changing environmental conditions, but also ensures that the drone always flies on a safe and efficient path, achieving complete avoidance of the no-fly zone.

[0073] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention should be included in the protection scope of the invention. All technical features in this embodiment can be freely combined according to actual needs.

[0074] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for planning a UAV trajectory that completely avoids a no-fly zone, characterized by: The invention comprises an application scenario of a method for planning a trajectory of a UAV in a no-fly zone, wherein the application scenario of the method for planning a trajectory of a UAV in a no-fly zone comprises a communication scenario between a UAV and a terminal user in a no-fly zone; The communication environment between the drone and the terminal user in the no-fly zone includes a terminal user set, a sparsely distributed and non-overlapping no-fly zone set, and the drone; the terminal user set includes terminal devices such as smart phones, mobile tablets, and unmanned vehicles; the drone serves as an aerial platform to assist the target user in communicating; the drone needs to communicate with each terminal user on the ground while strictly avoiding the no-fly zone; The specific steps include: Step 1: Construct a communication system model between drones and end users in a no-fly zone. The drone flies over the user and communicates with each user on the ground, while avoiding the no-fly zone to form a flight trajectory. The flight cycle of the drone is evenly divided into several time slots using the time discretization method. The drone coordinates can be represented in the current time slot, and preliminary constraints are set for the no-fly zone. Step 2: The flight trajectory of the UAV between two adjacent time slots is evenly divided into several parts according to the same interval; at each segmentation point, the first-order Taylor expansion of the UAV flight trajectory equation is performed to approximate the flight route of the UAV; wherein the segmentation points include the starting point, the end point, and the intermediate equal division point; Step 3: Every two adjacent straight lines generate an intersection point. To ensure that the drone can completely avoid the no-fly zone during actual flight, add a constraint condition. After completing the constraint of one time slot, go to the next time slot, continue the constraint, and repeat the iteration to ensure that the flight trajectory of the drone will not intersect with the no-fly zone at any time, thereby achieving the goal of completely avoiding the no-fly zone. Step 4: construct the UAV trajectory planning objective function, and finally obtain the optimal flight path of the UAV that meets specific constraints by minimizing the objective function; The environment of the communication system model adopts a three-dimensional Cartesian coordinate system. The ground terminal users remain stationary and are all outside the no-fly zone. The drone flies within a certain altitude range and needs to communicate with each user. The no-fly zone is abstracted as a cylinder with infinite height, sparse distribution and multiple no-fly zones do not overlap. A preliminary constraint condition is set: the coordinates of the drone corresponding to each discrete time slot are required to be outside the no-fly zone. Use straight line segments to approximate the flight trajectory within each time slot; consider the speed and acceleration limits of the drone at each segmentation point to ensure that these parameters are continuous and physically consistent throughout the flight; In step 3, an additional constraint is: all intersection points are outside the no-fly zone; In step 1, a communication system model between drones and end users in a no-fly zone is constructed, which specifically includes the following: 1) System model: The communication system environment between drones and end users in no-fly zones includes a collection of end users including smartphones, mobile tablets, and unmanned vehicles, a collection of sparsely distributed and non-overlapping no-fly zones, and drones. As an aerial platform, drones assist target users in communicating. Drones need to communicate with each end user on the ground while strictly avoiding no-fly zones. In the system model, there is 1 UAV, U users and M sparsely distributed non-overlapping cylindrical NFZs. Assume that none of the U users are in the NFZ. Define the user set as No-fly zone collection Assume T is a flight period, which is divided into N time slots with a time slot length of δ t =T / N, and the time slot set is Based on the three-dimensional Cartesian coordinate system, the coordinate of user u can be set to w u =(x u ,y u ,0) T ; Use the time discrete method to express the coordinates of the drone in time slot n q[n] = (x[n], y[n], z[n]) T , where H min ≤z[n]≤H max , H min and H max are the minimum and maximum altitudes allowed for UAV flight, respectively; the central horizontal coordinates and radius of NFZs are denoted by c m =(x m ,y m ) and R m ; In each time slot n, the UAV flight speed is v[n] = (v x [n],v y [n],v z [n]) T , the acceleration is a[n]=(a x [n],a y [n],a z [n]) T , where v x [n],v y [n],v z [n] are the three-axis speeds, a x [n],a y [n],a z [n] are the three-axis accelerations respectively; the coordinates of the drone are expressed as: 2) Communication model: The Euclidean distance between the drone and user u is expressed as: d u [n]=||q[n]-w u || Since the flying altitude of the UAV is much higher than that of the ground terminal users, the influence of the non-line-of-sight channel formed by ground obstacles and other reasons is ignored, and the wireless channel between the user and the UAV is a line-of-sight channel; the UAV knows the location information of the ground user equipment to obtain the channel state information between them; the wireless channel between the UAV and user u is regarded as a free space path loss model, and its channel gain is expressed as follows: In the formula, h0 is the channel power gain per unit distance; further, according to the Shannon formula, the data transmission rate between the drone and user u is expressed as: In the formula, B represents the communication bandwidth, P u is the constant transmission power of user u, σ 2 is the Gaussian noise power; In step 4, the objective function of the UAV trajectory planning is constructed, which includes the following: (1) Minimize the length of the UAV’s flight path to reduce flight time and energy consumption; (2) Minimize altitude changes during flight to maintain flight stability; (3) Maximizing user transmission rates and, used to improve communication efficiency and quality; Among them, the cost function of the UAV flight path length is expressed as: The flight altitude change cost function is expressed as: The user transmission rate and function are expressed as: The objective function of UAV trajectory planning is comprehensively expressed as the weighted sum of the above three cost functions: In the formula, The three cost functions f are length 、f alt 、f vel The weight coefficient is used to balance the priority and relative importance among the three objectives; Construct constraints as follows: 1) Existing constraint model: The maximum flight speed and acceleration of the drone are v max and a max , the velocity and acceleration need to satisfy the following constraints: During the flight, the drone must completely avoid the no-fly zone NFZ; the existing time discretization method can only ensure that the drone does not enter the NFZ at certain discrete points, namely q[n-1] and q[n], which can be expressed as: It cannot be guaranteed that when transitioning from q[n-1] to q[n], the distance between the flight trajectory at each location and the center of the NFZ is always greater than or equal to the radius of the NFZ. In view of this limitation, it is optimized; 2) Add constraint model: Divide the actual flight trajectory of the UAV between q[n-1] and q[n] into K equal parts, and get K+1 points, denoted as in Corresponding to the starting point q[n-1], Corresponding to the end point q[n]; the flight trajectory of the drone presents a typical quadratic curve feature of a parabola in each time slot and changes continuously in time. The straight line approximation method is used to approximate its path; the first-order Taylor expansion of the drone flight trajectory equation is performed at this K+1 point: We get K+1 tangent line equations, where f(x k ) is the y value of the time slot, x k That is, the x value of the corresponding time slot; since x, y are parametric equations about t, for It can be found by the chain rule; the tangent equation constitutes a piecewise linear approximation of the actual flight trajectory of the drone, and each approximation segment closely fits the local form of the original trajectory in the corresponding interval, thereby achieving an effective simulation of the overall trajectory; the tangent equations of two adjacent tangents are combined: Solve for K intersection points, denoted as In order to completely avoid the no-fly zone, a new constraint is added so that all the K intersection points are outside the NFZ, that is, the condition is satisfied: Through the constraints, the UAV in this time slot can completely avoid the NFZ.

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