Adaptive antenna trajectory planning method for secure communication of unmanned aerial vehicle

Abstract

The application discloses a secure communication trajectory planning method for unmanned aerial vehicles with integrated control of an adaptive antenna, constructs an air-ground secure communication model containing rigid body dynamics constraints, and determines that the attitude of the unmanned aerial vehicle body is uniquely determined by the translational acceleration vector and the gravity acceleration; for horizontal-horizontal (HH) and vertical-vertical (VV) two kinds of airborne antenna configurations, an explicit coupling model of the antenna gain with respect to the acceleration is established; a non-convex trajectory optimization problem is constructed to maximize the average secrecy capacity; a sequential convex approximation combined with a convex difference programming strategy is adopted for solving, wherein the implicit function differentiation method is adopted to solve the gradient singularity problem of the VV antenna null point; and finally, a flight strategy containing an optimal acceleration sequence is output. The application utilizes the active change of the flight attitude of the unmanned aerial vehicle to realize mechanical beamforming, significantly improves the secrecy capacity through "active drift" or "null alignment" maneuvering, and the generated trajectory strictly satisfies the physical feasibility.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a secure communication trajectory planning method for an integrated communication and control UAV with an adaptive antenna. Background Technology

[0002] With the rapid development of unmanned aerial vehicle (UAV) technology, using UAVs as aerial base stations or relay nodes has become an important application scenario in the field of wireless communication. However, due to the broadcast characteristics of wireless channels, the downlink of UAVs is vulnerable to eavesdropping by unauthorized ground nodes, highlighting the growing importance of physical layer security. Existing research on secure UAV communication trajectory planning typically suffers from the following limitations:

[0003] (1) Simplified point mass model assumptions: Most existing works treat UAVs as ideal "point masses," assuming they maintain a horizontal attitude throughout flight, or that the antenna gain is isotropic / fixed vertically downward. However, according to the aerodynamic principles of rotorcraft UAVs, the UAV must tilt its fuselage to generate horizontal acceleration. This fuselage tilt (roll and pitch) inevitably causes the antenna fixed to the fuselage to deflect, thus significantly changing the beam direction and gain distribution. Ignoring this dynamic coupling characteristic can lead to the planned trajectory unexpectedly pointing the beam at an eavesdropper during actual flight, causing serious safety hazards.

[0004] (2) Reliance on expensive hardware beamforming: In order to achieve interference suppression or signal isolation against eavesdroppers, existing technologies often rely on multi-antenna arrays for electronic beamforming. This not only increases the payload weight and energy consumption of the UAV, but also increases the hardware cost and complexity of the system, making it unsuitable for small UAV platforms that are sensitive to endurance and cost.

[0005] (3) Insufficient physical feasibility: The trajectory optimized based on the mass model often implies sharp turns or instantaneous attitude changes that exceed the maneuverability of the UAV, which makes the theoretical "optimal trajectory" impossible to execute in the actual physical system, or communication interruption due to attitude limitations during execution.

[0006] Therefore, how to leverage the inherent flight dynamics of UAVs and actively adjust the antenna beam direction by utilizing changes in flight attitude without increasing additional hardware costs to achieve efficient physical layer secure communication is a pressing technical challenge that needs to be addressed. Summary of the Invention

[0007] Purpose of the Invention: The purpose of this invention is to provide an adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) integrating communication and control. It aims to overcome the limitations of the traditional point mass model by jointly optimizing the UAV's flight trajectory and acceleration (i.e., attitude), utilizing the "mechanical beamforming" effect caused by fuselage tilting to actively enhance the quality of legitimate links and suppress eavesdropping links, thereby maximizing the system's security capacity.

[0008] Technical solution: The present invention provides a secure communication trajectory planning method for an integrated communication and control UAV with an adaptive antenna, comprising the following steps:

[0009] Step 1: Construct an air-to-ground safety communication system model with rigid body dynamics constraints, and establish the rigid body dynamics coupling relationship between the UAV's fuselage attitude vector, translational acceleration vector, and gravitational acceleration;

[0010] Step 2: Based on the type of antenna carried by the UAV, establish an explicit function model of antenna gain with respect to the UAV's acceleration vector; the antenna types include horizontal-horizontal HH configuration and vertical-vertical VV configuration;

[0011] Step 3: With the goal of maximizing the average confidentiality capacity within the mission cycle, and with constraints such as the quality of service for legitimate users, the upper limit of the rate of eavesdropping users, and the physical limitations of UAV dynamics, construct a trajectory optimization problem with acceleration sequences as the core variable.

[0012] Step 4: Solve the trajectory optimization problem using an algorithm that combines sequential convex approximation and convexity planning. During the solution process, the rigid body attitude coupling constraint is linearized, the signal-to-noise ratio of the legal link is approximated by a concave lower bound, the eavesdropping link rate is approximated by a convex upper bound, and the gradient of the antenna gain with respect to acceleration is calculated.

[0013] Step 5: Output the optimized acceleration sequence as the confidential flight control strategy for the UAV.

[0014] Furthermore, in step 1, the rigid body dynamics coupling relationship is specifically manifested as follows: the attitude vector of the UAV is determined as the normalized direction of the vector sum of the translational acceleration vector and the gravitational acceleration vector; by changing the magnitude or direction of the translational acceleration vector, the attitude vector of the UAV is changed, thereby causing the antenna fixed on the UAV to deflect.

[0015] Furthermore, in step 2, the explicit function model construction includes: when using an HH configuration antenna, establishing a gain model positively correlated with the absolute value of the off-axis angle cosine, and using lateral maneuvering generated by acceleration to deviate the main lobe of the beam from the eavesdropper, thereby achieving an active drift strategy; when using a VV configuration antenna, establishing a gain model positively correlated with the off-axis angle sine, and using attitude tilt generated by acceleration to suppress the eavesdropping link using the antenna axial null, thereby achieving a null alignment strategy; the off-axis angle is defined as the angle between the fuselage attitude vector and the line-of-sight vector from the UAV to the ground node.

[0016] Furthermore, the specific calculation logic of the gain model is as follows: For HH configuration: the antenna gain is determined by the absolute value of the cosine of the off-axis angle multiplied by the maximum gain. The cosine value is calculated by the ratio of the inner product of the line-of-sight vector and the effective thrust vector, where the effective thrust vector is the sum of the translational acceleration vector and the gravitational acceleration vector; For VV configuration: the antenna gain is determined by the sine of the off-axis angle multiplied by the maximum gain, or it can be expressed as the maximum gain multiplied by 1 minus the square root of the square of the cosine of the off-axis angle.

[0017] Furthermore, in step 3, the construction of the trajectory optimization problem includes:

[0018] The objective function is configured as follows: maximize the average difference between the legal rate and the eavesdropping rate across all time slots;

[0019] The constraints include:

[0020] Legitimate rate constraint: requires that the communication rate of legitimate users is not lower than a preset minimum rate threshold;

[0021] Eavesdropping rate constraint: requires that the communication rate of the eavesdropping user does not exceed a preset maximum rate threshold;

[0022] Dynamic constraints: The flight speed of the UAV must not exceed the maximum speed limit, and the total thrust generated by the UAV must not exceed the maximum thrust limit of the rotor system. The total thrust is determined by the magnitude of the combined vector of acceleration vector and gravitational acceleration.

[0023] Furthermore, in step 4, the algorithm combining sequence convex approximation and convex difference programming is as follows: for the legal rate, a linear lower bound of its signal-to-noise ratio is constructed using a first-order Taylor expansion, and a convex constraint condition for the legal rate is constructed based on this linear lower bound; for the eavesdropping rate, a first-order Taylor expansion is directly performed on its logarithmic rate expression to construct a linear upper bound of its rate; the original non-convex objective function is transformed into the form of maximizing the legal rate calculated based on the linear lower bound minus the eavesdropping rate calculated based on the linear upper bound.

[0024] Furthermore, in step 4, the calculation of the gradient of antenna gain with respect to acceleration specifically involves: firstly calculating the Jacobian matrix of the body attitude vector with respect to acceleration, wherein the Jacobian matrix represents the change in attitude direction caused by the change in acceleration, and its calculation is based on the difference between the identity matrix and the outer product matrix of the current attitude vector.

[0025] Furthermore, in step 4, after approximating the eavesdropping link rate with a convex upper bound, the implicit function differential method is used to calculate the regularized gradient to address the gradient singularity problem of the VV antenna gain function at the null point. Specifically, an implicit function equilibrium equation describing the relationship between gain and the cosine of the off-axis angle is constructed; using the implicit function theorem, the gradient is regularized using the gain value at the current iteration point, and the derivative of the gain with respect to the cosine of the off-axis angle is calculated; combining the chain rule, the above derivative is multiplied by the derivative of the cosine of the off-axis angle with respect to acceleration to obtain the final acceleration gradient, thereby avoiding the gradient singularity problem of zero denominator caused by direct differentiation at the antenna null point.

[0026] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0027] The present invention also discloses a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method of the present invention.

[0028] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0029] Significantly Enhanced Security Capacity: This invention achieves a beamforming-like effect by actively adjusting the beam direction using flight attitude. Simulations show that in the HH antenna scenario, the "active drift" strategy can improve security capacity by more than 25%; in the VV antenna scenario, the "zero-dip alignment" strategy can suppress the eavesdropping signal-to-noise ratio to an extremely low level, improving security capacity by more than 40% (or even higher).

[0030] Zero hardware cost gain: This invention utilizes only the flight dynamics characteristics of the UAV itself (tilted fuselage), without the need to install additional multi-antenna arrays or phase shifters, significantly enhancing physical layer security without increasing load and energy consumption, and is particularly suitable for small and medium-sized rotary-wing UAVs.

[0031] Ensuring physical feasibility: This invention directly introduces maximum thrust constraints based on acceleration and rigid body dynamics models during the optimization process, ensuring that the generated trajectory and attitude commands are always within the physical performance envelope of the UAV, thus avoiding the problem that the trajectory cannot be actually executed in traditional methods.

[0032] The algorithm is robust: Different gradient calculation methods are designed for different antenna types (HH / VV), especially for the implicit function processing of the zero point of VV antenna, which effectively avoids the gradient explosion problem in numerical calculation and ensures the fast convergence and stability of the optimization algorithm. Attached Figure Description

[0033] Figure 1 A flowchart illustrating a secure communication trajectory planning method for unmanned aerial vehicles (UAVs) based on antenna radiation characteristics and rigid body dynamics.

[0034] Figure 2 A schematic diagram of the vertical antenna beamline of a UAV;

[0035] Figure 3 A schematic diagram of the horizontal antenna beamline of a UAV;

[0036] Figure 4 An optimized flight trajectory diagram for a drone in a vertical-vertical antenna scenario;

[0037] Figure 5 A diagram illustrating the secure communication performance of unmanned aerial vehicles (UAVs) in a vertical-vertical antenna scenario.

[0038] Figure 6 A diagram of UAV flight control parameters in a vertical-vertical antenna scenario;

[0039] Figure 7 An optimized flight trajectory diagram for a drone in a horizontal-horizontal antenna scenario;

[0040] Figure 8 A diagram illustrating the secure communication performance of unmanned aerial vehicles (UAVs) in a horizontal-to-horizontal antenna scenario.

[0041] Figure 9 This is a diagram of UAV flight control parameters in a horizontal-horizontal antenna scenario. Detailed Implementation

[0042] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0043] This invention provides a method for planning secure communication trajectories for unmanned aerial vehicles (UAVs) based on antenna radiation characteristics and rigid body dynamics, comprising the following steps:

[0044] Step 1, construct an air-to-ground secure communication system model with rigid body dynamics constraints: establish a communication scenario including rotary-wing UAVs, legitimate users and eavesdroppers, and introduce rigid body dynamics coupling constraints for UAVs, clarifying that the fuselage attitude vector is uniquely determined by the current translational acceleration vector and gravitational acceleration.

[0045] Step 2, Explicit Gain-Acceleration Coupling Modeling Based on Antenna Type: For two typical airborne antenna configurations, horizontal-horizontal (HH) and vertical-vertical (VV), explicit function models of antenna gain with respect to the UAV acceleration vector are established. For the HH antenna, the lateral gain characteristics are modeled using a cosine function; for the VV antenna, the axial null characteristics are modeled using a sine function.

[0046] Step 3, Construct a trajectory optimization problem that maximizes the security capacity: With the objective of maximizing the average security capacity within the mission cycle, and constrained by the Quality of Service (QoS) of legitimate users, the maximum flight speed of the UAV, the maximum thrust, and the rigid body attitude dynamics, construct a non-convex trajectory optimization problem.

[0047] Step 4: Design a solution algorithm based on Sequence Convex Approximation (SCA) and Convexity Programming:

[0048] Step 4.1: Perform a first-order Taylor expansion on the rigid body attitude coupling constraints, calculate the Jacobian matrix of attitude with respect to acceleration, and realize the linearization of dynamic constraints.

[0049] Step 4.2: For a valid link, use the chain rule to calculate the composite gradient, which includes the rigid body geometric derivative and the antenna radiation derivative, to construct a linear lower bound for the signal-to-noise ratio.

[0050] Step 4.3: For the eavesdropping link, the concept of convexity programming is introduced to construct a linear upper bound for the eavesdropping rate.

[0051] In step 4.4, specifically, to address the gradient singularity problem of the VV antenna gain function at the zero trap, the implicit function differentiation method is used to calculate the regularized gradient, ensuring the numerical stability of the algorithm.

[0052] Step 4.5 transforms the original non-convex problem into a series of second-order cone programming (SOCP) subproblems for iterative solution.

[0053] Step 5, Output the optimized secure flight strategy: The output includes a flight strategy containing the optimal position sequence and acceleration sequence. This strategy implicitly includes an "Active Drifting" maneuver for the HH antenna, which uses lateral acceleration to deflect the main lobe of the beam away from the eavesdropper; and a "Null Alignment" maneuver for the VV antenna, which adjusts the attitude to align the antenna null with the eavesdropper.

[0054] Example

[0055] This invention proposes a trajectory planning method for secure UAV communication based on antenna radiation characteristics and rigid body dynamics. This method overcomes the limitations of traditional UAV communication, which treats the UAV as a point mass and uses a constant antenna gain. By leveraging the dynamic characteristic that rotorcraft UAVs must generate acceleration by tilting their fuselage, it actively adjusts the flight attitude to change the antenna beam direction, thereby physically enhancing signal coverage for legitimate users and suppressing signal leakage to eavesdroppers.

[0056] like Figure 1 As shown, the method of the present invention specifically includes the following steps:

[0057] Step 1. Construct an air-to-ground safe communication system model that includes rigid body dynamics constraints.

[0058] In this embodiment, a downlink secure communication scenario is considered, which includes a rotorcraft drone (Alice), a legitimate ground user (Bob), and a ground eavesdropper whose location is known (Eve).

[0059] Define the task cycle as Discretize it into There are 1 time slot, and the length of each time slot is 1. Define drones in the first The state variables for each time slot include position. ,speed and acceleration The positions of ground nodes Bob and Eve are fixed as follows: and .

[0060] Based on the principle of underactuated rigid body dynamics of rotary-wing UAVs, the vertical axis direction of the UAV body (i.e., the attitude vector of the fuselage) It is not an independent control variable, but rather is controlled by its current translational acceleration vector. and gravitational acceleration The rigid body dynamic coupling constraint is uniquely determined.

[0061]

[0062] This formula shows that every acceleration, deceleration, or turning maneuver of the drone (changing...) All of these will force a change in the aircraft's attitude. This causes the antenna fixed to the fuselage to deflect.

[0063] Step 2. Gain-acceleration adaptive explicit coupling modeling based on antenna type

[0064] To achieve secure communication, it is essential to accurately calculate the impact of attitude changes on the gain of both the legitimate and eavesdropping channels. This invention establishes gain relationships with acceleration for two typical airborne antenna configurations—horizontal-horizontal (HH) and vertical-vertical (VV) configurations. The explicit function model.

[0065] Define the drone to ground node ( The line-of-sight vectors of Bob and Eve are respectively... The distance is Define the off-axis angle. For the body axis With line of sight vector The included angle.

[0066] Given the spatial anisotropy of the radiation pattern of airborne ultra-wideband (UWB) antennas, their gain distribution typically exhibits two main modes: horizontal gain-dominated (strong lateral radiation) and vertical gain-dominated (strong axial radiation). Based on existing research on antenna lobe characteristics, this invention establishes two general mathematical models: horizontal-horizontal (HH) and vertical-vertical (VV), to cover different antenna radiation configurations. In practical engineering applications, the system can adaptively match the appropriate modeling method according to the specific radiation parameters of the mounted antenna.

[0067] Example A: Modeling of HH Antenna (Directional Patch Antenna)

[0068] The HH configuration typically corresponds to a directional antenna mounted vertically downwards, with its gain primarily concentrated below the device, away from other components. Figure 2 As shown. Antenna gain It is approximately proportional to the cosine of the off-axis angle. Substituting formula (1) into the cosine calculation formula, we obtain the gain function:

[0069]

[0070] in This model shows that by controlling the acceleration, the maximum gain can be achieved. The direction (i.e., lateral maneuver) can make Deviating from Eve's direction, thus reducing This enables "ActiveDrifting" to avoid eavesdropping.

[0071] Example B: Modeling of VV antenna (omnidirectional dipole antenna)

[0072] The VV configuration corresponds to an omnidirectional antenna, whose gain diagram is shaped like a "donut." It has a null along the antenna axis (vertical to the aircraft), far from... Figure 3 As shown. Antenna gain It is approximately proportional to the sine of the off-axis angle. The gain function is modeled as follows:

[0073]

[0074] This model demonstrates that during flight, the pitch or roll angle can be adjusted to change the aircraft's axis. Pointing to Eve, the eavesdropper, using the null characteristic of the antenna (i.e. This is used to suppress eavesdropping links and achieve "NullAlignment".

[0075] Step 3. Construct a trajectory optimization problem that maximizes the confidentiality capacity.

[0076] The objective of this invention is to maximize average confidentiality capacity while satisfying the Quality of Service (QoS) for legitimate users. According to Shannon's formula, nodes... In the The instantaneous achievable rate of a time slot is:

[0077]

[0078] in, For the drone's transmission power, The reference channel power gain per unit distance. The noise power spectral density at the receiver. This represents the spatial fading coefficient, which takes different values ​​depending on the channel conditions. The following acceleration sequence is established. Optimization problem with core optimization variables (P1):

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Wherein, the objective function is the legal rate. With eavesdropping rate The expected value of the difference; Equivalent to The function is positive; The minimum speed requirement for legitimate users, This represents the maximum acceptable eavesdropping rate for the user. Furthermore, The maximum permissible flight speed for the drone. The maximum total thrust that the rotor system can provide. For the mass of the drone's fuselage.

[0088] Step 4. Design of a trajectory solving algorithm based on Sequence Convex Approximation (SCA) and Convexity Programming

[0089] Since the objective function of the optimization problem (P1) is the difference between two logarithmic functions, and the channel gain... This problem involves a highly nonlinear composite function of position and acceleration, and is a non-convex NP-hard problem. This invention proposes a two-layer convexity strategy: the outer layer utilizes the SCA iterative framework, while the inner layer approximates the lower and upper bounds for legitimate links and eavesdropping links, respectively.

[0090] Step 4.1 Linearization of Rigid Body Attitude Coupling Constraints

[0091] Before constructing the convex optimization subproblem, the core rigid body dynamics non-convex equality constraint is first addressed. This constraint is a typical fractional nonlinear mapping, and directly substituting it into the optimization problem will lead to a non-convex feasible region. This invention employs a first-order Taylor expansion technique to transform this nonlinear mapping into a local affine constraint.

[0092] Define the effective thrust vector as In the first The working point of the next iteration At this location, the fuselage attitude vector It can be approximated as:

[0093]

[0094] in, Let be the Jacobian matrix of the attitude vector with respect to acceleration. The specific formula for calculating this matrix is ​​derived as follows, based on the rules of vector calculus:

[0095]

[0096] In the formula, It is a third-order identity matrix. This is the thrust vector from the previous iteration point.

[0097] Step 4.2 Reconstruction and Relaxation of the Security Capacity Objective Function

[0098] The original objective function is However, the function It is a non-convex function and cannot be directly differentiated. Therefore, a new objective function is defined. Let be the global infimum of the original objective function. The expected value of the original objective function can be maximized by maximizing the global infimum. To make it solvable, a sequence of auxiliary variables is introduced. , where represent the lower bound of the legal signal-to-noise ratio and the upper bound of the eavesdropping signal-to-noise ratio, respectively.

[0099] The original problem can be transformed into the following equivalent form:

[0100]

[0101]

[0102]

[0103] — .

[0104] in At this point, the first term of the objective function It is a concave function (easy to maximize), but the second term It is a convex function (difficult to maximize). Also, constraints... and Because it includes a coupling gain term It is a non-convex constraint.

[0105] Step 4.3 Approximation of the concave lower bound of the legal link gain (handling constraints) )

[0106] For the legitimate user Bob, this invention needs to obtain a linear lower bound on his signal-to-noise ratio.

[0107] make In the first Next iteration point At this point, a first-order Taylor expansion is performed on the nonlinear composite function.

[0108] because ( (This is about acceleration) and location The gradient of the function is calculated using the chain rule (chain rule) for finding the derivative of the composite function:

[0109]

[0110]

[0111] Based on the above gradient, construct an affine lower bound for the legitimate signal-to-noise ratio. :

[0112]

[0113] constraint Transformed into a convex constraint: .

[0114] Step 4.4 Refined calculation of gain gradient for HH / VV antenna

[0115] To construct an accurate convex approximation model in the SCA iteration, the channel gain must be calculated. Regarding optimization variables (especially acceleration) The gradient of the antenna is calculated. Since different antenna configurations correspond to different radiation functions, this embodiment designs a differentiated gradient calculation process.

[0116] Let intermediate variables The cosine value of the off-axis angle is defined as:

[0117]

[0118] According to the chain rule, the total gradient consists of two parts: the derivative of the antenna radiation pattern. Derivatives of rigid body geometry .

[0119] Step 4.4.1 General gradient calculation for rigid body geometry

[0120] Regardless of the type of antenna used, the off-axis angle cosine value Regarding acceleration The gradient structure is the same. Let the effective thrust vector... Using the rules of vector calculus, the geometric gradient can be obtained:

[0121]

[0122] This formula reveals how minute changes in acceleration cause nonlinear changes in the beam pointing angle.

[0123] Step 4.4.2 Scenario A: Explicit gradient processing for HH antenna (horizontal-horizontal)

[0124] For the HH antenna, the gain function is: .

[0125] To avoid the problem of non-differentiability of the absolute value at zero during the optimization process, this invention assumes that the beam mainly operates on a single hemisphere within the effective communication range (i.e., ),at this time .

[0126] Therefore, the gain gradient of the HH antenna is calculated as a simple linear mapping:

[0127]

[0128] Substituting the above equation into the Taylor expansion of SCA, the drone can be driven to perform "active drift" maneuvers, enabling... The value (i.e., the cosine value) tends to 1 for legitimate users and 0 for eavesdroppers.

[0129] Step 4.4.3 Scenario B: Implicit function gradient processing for VV antenna (vertical-vertical)

[0130] For a VV antenna, the gain function is: .

[0131] Directly taking its derivative yields It can be observed that when When the antenna axis is aligned with the target and is at a null point, the denominator approaches zero, leading to gradient explosion and causing instability in numerical calculations.

[0132] To address this numerical sensitivity issue, this invention employs implicit function differentiation to construct a robust gradient calculation process:

[0133] Constructing auxiliary equilibrium equations .

[0134] By utilizing the implicit function theorem, we avoid directly calculating the square root term in the denominator and instead use the gain value at the current iteration point. To regularize the gradient:

[0135]

[0136] Combining the geometric gradient, the final acceleration gradient expression for the VV antenna is:

[0137]

[0138] Because this gradient direction contains a negative sign, it will guide the optimization algorithm to automatically adjust the acceleration. This makes it possible for legitimate users (Utilizing the horizontal maximum gain surface), while for eavesdroppers (By using axial zero traps for locking), the automatic generation of the "zero trap alignment" strategy is achieved at the mathematical level.

[0139] Step 4.5 Approximation of the convex upper bound of the eavesdropping link gain (handling constraints) (with objective function)

[0140] For the eavesdropper Eve, this invention needs to limit the upper limit of her signal-to-noise ratio. Since direct linearization leads to significant errors, this invention introduces an exponential transformation variable. At this point, the negative term in the objective function becomes This term is a concave function, which meets the requirements of convex optimization.

[0141] Regarding constraints ,Right now The lower bound of the right side is approximated using the Arithmetic-Geometric Mean (AGM) inequality or a first-order Taylor expansion, while the left side is approximated using... Maintaining the non-convex form is quite difficult.

[0142] A more efficient strategy is to directly target the objective function. This overall term is expanded using a first-order Taylor series as an upper bound (because this invention aims to maximize...). That is, minimize ).

[0143] In the At the next iteration point, the affine upper bound of the eavesdropping rate is:

[0144]

[0145] in They are respectively about and The gradient.

[0146] In this way, the non-convex objective function is transformed into a concave function maximization problem:

[0147]

[0148] Step 5: Construct the complete convex optimization subproblem

[0149] Based on the legal rate linear lower bound obtained in step 4.3 And the upper linear bound of the eavesdropping rate obtained in step 4.5 This invention can transform the original non-convex problem (P1) into the first non-convex problem. The convex optimization subproblem of the next iteration.

[0150] In this embodiment, to ensure the generated trajectory is physically executable, the invention explicitly introduces basic flight constraints based on rigid body dynamics into the optimization model. The constructed second-order cone programming (SOCP) model is as follows:

[0151]

[0152]

[0153]

[0154]

[0155] — .

[0156] In the above formula and Threshold constraints after simple mathematical transformation , Let be the radius of the trust region. In this model, the objective function is a linear function (affine lower bound minus affine upper bound), and all constraints are linear inequalities or second-order cone constraints (norm cone). Therefore, this subproblem belongs to a standard convex optimization problem and can be solved efficiently using interior-point solvers (such as MOSEK or CVX).

[0157] Step 6: SCA Iteration and Convergence Decision

[0158] Solve the th using the solver The optimal solution of the next iteration .

[0159] Update work point: Order .

[0160] Convergence check: Calculate the increment of the objective function value. ( This represents the objective function value obtained in the $k$-th iteration, i.e. ).like (Preset convergence threshold, such as) If the algorithm converges, stop iterating; otherwise, let... The gradient is recalculated using the new working point (steps 4.3 and 4.4), and the process returns to step 4.5 to continue solving.

[0161] Output: After the algorithm converges, the final acceleration sequence is output. This is the optimal strategy for secure flight of drones.

[0162] 7. Output the optimized secure flight strategy

[0163] The optimal acceleration sequence output by the algorithm of this invention It not only defines the drone's flight trajectory, but more importantly, it implicitly contains the optimal attitude control law for the current antenna configuration, thereby achieving physical layer security.

[0164] For HH antenna scenarios (active drift strategy):

[0165] Figure 4 shows the flight trajectory. When the drone flies over the eavesdropper, the algorithm automatically generates a large lateral acceleration component. Based on the dynamic coupling formula... This will cause the fuselage to roll and tilt significantly. At this time, the main lobe of the directional antenna fixed at the bottom of the fuselage will deflect, pointing away from the vertically downwards at the eavesdropper, and projecting a high-gain beam toward the legitimate user on the side, thus achieving "active drift" to avoid eavesdropping.

[0166] For VV antenna scenarios (zero-depression blocking strategy):

[0167] As shown in Figure 7, the algorithm adjusts the drone's flight altitude and pitch acceleration to ensure the drone's axis of rotation is aligned correctly. Dynamically aligns with the eavesdropper's location. Utilizing the axial radiation null characteristic of the dipole antenna, the signal-to-noise ratio of the eavesdropping link is minimized, achieving a "physical blockade" of the eavesdropper.

[0168] To verify the effectiveness of the method of the present invention, a comparative experiment was conducted in a simulation environment. The experimental parameters were set as follows: UAV flight altitude. m, task duration s, maximum speed m / s.

[0169] (1) Significantly improved confidentiality capacity

[0170] The method of this invention is compared with the traditional point-mass model (PMM) optimization method (which assumes the antenna is always vertically downward). Simulation results show:

[0171] like Figure 5 As shown, in the HH antenna scenario, due to the adoption of the "active drift" strategy, this invention effectively avoids eavesdroppers directly below, and the average security capability is improved by approximately 77% compared to traditional methods. Specific attitude angles and acceleration parameters are as follows: Figure 6 As shown.

[0172] like Figure 8 As shown, in the VV antenna scenario, thanks to the "zero-trap blocking" strategy, this invention suppresses the eavesdropping signal-to-noise ratio to an extremely low level, increasing the security capacity by approximately 900%. This is a fundamental improvement. Previously, drones could only fly horizontally, and security capacity could only be increased through distance, essentially unable to prevent eavesdropping. However, with attitude control, the eavesdropper can be placed in a zero-space position, achieving near-ideal secure communication. Specific attitude angles and acceleration parameters are as follows... Figure 9 As shown.

[0173] (2) Guarantee of physical feasibility

[0174] Traditional methods often generate trajectories that cannot be executed due to sharp turns (implying excessively large attitude angle requirements). This invention, however, directly introduces a maximum thrust constraint during optimization. This ensures that the output acceleration sequence is always within the capability range of the UAV's power system, and the generated trajectory has 100% physical executability.

[0175] 8. Hardware execution logic

[0176] The optimal acceleration sequence calculated by this invention It does not act directly on the motor, but is translated into low-level control commands through the following mapping:

[0177] The UAV's onboard computer performs the inverse transformation of formula (1) to... Decompose into the desired total thrust and expected posture quaternion The command is sent to the attitude loop controller of the flight control system, and is ultimately distributed to the four rotor motors through the Mixer algorithm, driving the UAV to accurately reproduce the planned "active drift" or "zero-trajectory alignment" maneuvers.

[0178] The above embodiments are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several improvements and equivalent substitutions without departing from the principle of the present invention. All such improvements and equivalent substitutions to the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A secure communication trajectory planning method for an integrated communication and control UAV with an adaptive antenna, characterized in that, Includes the following steps: Step 1: Construct an air-to-ground safety communication system model with rigid body dynamics constraints, and establish the rigid body dynamics coupling relationship between the UAV's fuselage attitude vector, translational acceleration vector, and gravitational acceleration; Step 2: Based on the type of antenna carried by the UAV, establish an explicit function model of antenna gain with respect to the UAV's acceleration vector; the antenna types include horizontal-horizontal HH configuration and vertical-vertical VV configuration; Step 3: With the goal of maximizing the average confidentiality capacity within the mission cycle, and with constraints such as the quality of service for legitimate users, the upper limit of the rate of eavesdropping users, and the physical limitations of UAV dynamics, construct a trajectory optimization problem with acceleration sequences as the core variable. Step 4: Solve the trajectory optimization problem using an algorithm that combines sequential convex approximation and convexity programming; In the solution process, the rigid body attitude coupling constraint is linearized, the signal-to-noise ratio of the legal link is approximated by a concave lower bound, the eavesdropping link rate is approximated by a convex upper bound, and the gradient of the antenna gain with respect to acceleration is calculated. Step 5: Output the optimized acceleration sequence as the confidential flight control strategy for the UAV.

2. The adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) with integrated communication and control, as described in claim 1, is characterized in that... In step 1, the rigid body dynamics coupling relationship is specifically manifested as follows: the attitude vector of the UAV is determined as the normalized direction of the vector sum of the translational acceleration vector and the gravitational acceleration vector; by changing the magnitude or direction of the translational acceleration vector, the attitude vector of the UAV is changed, thereby causing the antenna fixed on the UAV to deflect.

3. The adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) with integrated communication and control, as described in claim 1, is characterized in that... In step 2, the explicit function model construction includes: when using an HH configuration antenna, establishing a gain model positively correlated with the absolute value of the off-axis angle cosine, and using lateral maneuvering generated by acceleration to deviate the main lobe of the beam from the eavesdropper, thus achieving an active drift strategy; when using a VV configuration antenna, establishing a gain model positively correlated with the off-axis angle sine, and using attitude tilt generated by acceleration to suppress the eavesdropping link using the antenna axial null, thus achieving a null alignment strategy; the off-axis angle is defined as the angle between the fuselage attitude vector and the line-of-sight vector from the UAV to the ground node.

4. The adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) with integrated communication and control, as described in claim 3, is characterized in that... The specific calculation logic of the gain model is as follows: For HH configuration: the antenna gain is determined by the absolute value of the cosine of the off-axis angle multiplied by the maximum gain. The cosine value is calculated by the ratio of the inner product of the line-of-sight vector and the effective thrust vector, where the effective thrust vector is the sum of the translational acceleration vector and the gravitational acceleration vector; For VV configuration: the antenna gain is determined by the sine of the off-axis angle multiplied by the maximum gain, or it can be expressed as the maximum gain multiplied by 1 minus the square root of the square of the cosine of the off-axis angle.

5. The adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) with integrated communication and control, as described in claim 1, is characterized in that... In step 3, the construction of the trajectory optimization problem includes: The objective function is configured as follows: maximize the average difference between the legal rate and the eavesdropping rate across all time slots; The constraints include: Legitimate rate constraint: requires that the communication rate of legitimate users is not lower than a preset minimum rate threshold; Eavesdropping rate constraint: requires that the communication rate of the eavesdropping user does not exceed a preset maximum rate threshold; Dynamic constraints: The flight speed of the UAV must not exceed the maximum speed limit, and the total thrust generated by the UAV must not exceed the maximum thrust limit of the rotor system. The total thrust is determined by the magnitude of the combined vector of acceleration vector and gravitational acceleration.

6. The adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) with integrated communication and control, as described in claim 1, is characterized in that... In step 4, the algorithm combining sequence convex approximation and convex difference programming is as follows: For the legal rate, a linear lower bound of its signal-to-noise ratio is constructed using a first-order Taylor expansion, and a convex constraint condition for the legal rate is constructed based on this linear lower bound; For the eavesdropping rate, a first-order Taylor expansion is directly performed on its logarithmic rate expression to construct a linear upper bound of its rate; The original non-convex objective function is transformed into the form of maximizing the legal rate calculated based on the linear lower bound minus the eavesdropping rate calculated based on the linear upper bound.

7. The adaptive antenna-based secure communication trajectory planning method for unmanned aerial vehicles (UAVs) with integrated communication and control, as described in claim 1, is characterized in that... In step 4, the calculation of the gradient of antenna gain with respect to acceleration specifically involves: firstly, calculating the Jacobian matrix of the body attitude vector with respect to acceleration. The Jacobian matrix represents the change in attitude direction caused by the change in acceleration, and its calculation is based on the difference between the identity matrix and the outer product matrix of the current attitude vector.

8. The method for secure communication trajectory planning of an integrated communication and control UAV with an adaptive antenna according to claim 1, characterized in that, In step 4, after approximating the eavesdropping link rate with a convex upper bound, the gradient singularity problem of the VV antenna gain function at the null point is addressed by using implicit function differentiation to calculate the regularized gradient. Specifically, this involves: constructing an implicit function equilibrium equation describing the relationship between gain and the cosine of the off-axis angle; using the implicit function theorem, regularizing the gradient with respect to the gain value at the current iteration point, and calculating the derivative of the gain with respect to the cosine of the off-axis angle; combining the chain rule, multiplying the above derivative with the derivative of the cosine of the off-axis angle with respect to acceleration to obtain the final acceleration gradient, thereby avoiding the gradient singularity problem of zero denominator caused by direct differentiation at the antenna null point.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of claim 1.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of claim 1.

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