A continuous-time ARIS phase offset and unmanned aerial vehicle trajectory joint optimization method

Abstract

This invention discloses a joint optimization method for continuous-time ARIS phase offset and UAV trajectory. A joint optimization model integrating occlusion perception channel, UAV dynamics, energy consumption, and obstacle avoidance constraints is constructed. An alternating optimization framework is employed to decouple the original non-convex problem into sub-problems of ARIS phase offset optimization and UAV trajectory optimization. Coherent superposition of received signals is achieved through a phase-aligned closed-form solution. Furthermore, by combining B-spline control parameterization, constraint transformation, and smooth approximation techniques, the infinite-dimensional trajectory optimal control problem is transformed into a finite-dimensional nonlinear programming problem, which is then efficiently solved using a sequential quadratic programming algorithm. This invention can generate dynamically feasible, continuously smooth, and abrupt UAV flight trajectories that effectively avoid obstacles, significantly improving the overall reachability and reliability of the communication system.

Description

Technical Field

[0001] This invention relates to a method for joint optimization of continuous-time ARIS phase shift and UAV trajectory, belonging to the interdisciplinary field of air-to-ground integrated wireless communication, UAV trajectory planning and intelligent reflector technology. Background Technology

[0002] In recent years, with the development of sixth-generation (6G) mobile communication technology, wireless communication in urban environments has faced serious challenges. Due to the dense distribution of high-rise buildings, the line-of-sight path between base stations and ground users is easily blocked, leading to a decline in communication link quality or even interruption.

[0003] Unmanned aerial vehicles (UAVs) have demonstrated a wide range of applications in emergency communications, IoT data collection, and other scenarios due to their high mobility and flexible deployment capabilities. By moving flexibly in three-dimensional space, UAVs can establish line-of-sight (LoS) links, thereby effectively mitigating the performance degradation caused by obstruction and path loss in ground communications.

[0004] Reconfigurable Smart Surfaces (RIS) can construct "virtual line-of-sight links" in non-line-of-sight (NLoS) scenarios by controlling the reflection of incident signals. Deploying RIS on UAV platforms to form an Airborne RIS system (ARIS) can further combine the maneuverability of UAVs with the channel modulation capabilities of RIS, thereby significantly improving communication performance. However, existing ARIS-assisted UAV communication optimization methods have the following drawbacks:

[0005] (1) Most UAV trajectory optimization methods use time discretization modeling, which transforms the continuous flight trajectory into a position optimization problem over a finite number of time slots, ignoring the continuous dynamic constraints of the UAV, resulting in the obtained trajectory being physically unrealizable;

[0006] (2) In urban environments, the switching between LoS and NLoS caused by building occlusion is discontinuous, which makes the optimization problem non-differentiable, limits the application of gradient-based optimization algorithms, and increases the difficulty of solving the problem.

[0007] (3) Existing methods fail to uniformly consider the coupling relationship between complete dynamic constraints, occlusion effects and communication performance;

[0008] (4) The joint optimization problem is highly non-convex and infinite-dimensional. Existing methods converge slowly and have suboptimal performance, making it difficult to simultaneously consider communication efficiency, complete dynamics, energy consumption and obstacle avoidance constraints.

[0009] Therefore, developing a joint optimization method for UAV continuous-time trajectory and phase based on aerial reconfigurable smart surfaces that takes into account complete UAV dynamics, occlusion perception, smooth trajectory, and low computational complexity has become the key to improving urban air-to-ground communication performance. Summary of the Invention

[0010] This invention provides a method for joint optimization of continuous-time ARIS phase shift and UAV trajectory. In urban building-occupied environments, it jointly optimizes the continuous-time three-dimensional trajectory of the UAV and the ARIS phase to maximize the total reachability while satisfying practical constraints such as UAV complete dynamics, obstacle avoidance, energy consumption, and control boundaries. This addresses the problems disclosed in the background technology.

[0011] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0012] A joint optimization method for continuous-time ARIS phase shift and UAV trajectory:

[0013] Based on the pre-constructed UAV-equipped ARIS-assisted communication obstruction perception channel model, UAV continuous-time dynamics model, and UAV obstacle avoidance constraint model, a joint optimization problem is established with the goal of maximizing the total reachability rate, integrating fixed-wing UAV dynamics, altitude, speed, heading angle constraints, control vector constraints, energy consumption constraints, obstacle avoidance constraints, and ARIS phase offset constraints.

[0014] The joint optimization problem is decoupled into an ARIS phase offset optimization subproblem and an UAV trajectory optimization subproblem;

[0015] The optimal phase offset matrix is ​​obtained by solving the ARIS phase offset optimization subproblem.

[0016] Solve the UAV trajectory optimization subproblem to obtain the optimal UAV trajectory;

[0017] The optimal phase offset matrix and the optimal UAV trajectory are jointly optimized using an alternating optimization framework, and the jointly optimized ARIS phase offset matrix and UAV trajectory are output.

[0018] Furthermore, the method for constructing a UAV-equipped ARIS-assisted communication obstruction perception channel model includes: establishing a Cartesian coordinate system in three-dimensional space, where BS represents the base station with a fixed position; GU represents the ground user, which is in a low-speed moving state; and the UAV equipped with ARIS maneuvers in three-dimensional space, with the ARIS consisting of uniformly arranged... It consists of several reflective elements, each with a phase offset. exist Internally continuously adjustable The location of the ARIS center changes in real time with the drone;

[0019] The BS-GU direct link is modeled as a Rayleigh fading channel, and the BS-ARIS link and ARIS-GU link are modeled as LosS path loss channels.

[0020] Model the building's occlusion area as a convex polyhedron, and define the first... The area obstructed by the building, :

[0021] ,

[0022] in, Represents any point in three-dimensional space. For the set of all the planes that make up the building, Indicates the first The building The normal vector of each face. For based on The plane offset of the viewpoint;

[0023] Defining the first from GU's perspective The area obstructed by a building, :

[0024] ,

[0025] in, For the set of all the planes that make up the building, Indicates the first The building The normal vector of each face. This is the planar offset based on the GU's perspective;

[0026] Based on the occlusion region, the Loss indication functions for the BS-ARIS link and the ARIS-GU link are defined as follows:

[0027] ,

[0028] ,

[0029] in, This is the center position of the ARIS reflector unit; This represents the union of the BS-ARIS link's blocked regions. Represents the union of the ARIS-GU link's blocked regions;

[0030] By combining the channel coefficients of the direct link and the reflected link with the LoS indicator function, the received signal-to-noise ratio at the user end is obtained:

[0031] ,

[0032] in, This refers to the base station signal transmission power. For noise power, Let be the magnitude of the complex channel gain at time t. This represents the channel coefficient of the BS-GU link. This represents the channel vector of the BS-ARIS link. This represents the conjugate transpose of the ARIS-GU link channel vector. Denotes the ARIS phase offset matrix, where, e It is a natural constant. The imaginary unit, This represents the negative exponential phase rotation factor. Indicates the first Each reflective unit in Phase shift at any given moment;

[0033] Accordingly, duration The total reachable rate within is:

[0034] ;

[0035] in, Indicates time The instantaneous achievable speed, This represents the time differential.

[0036] Furthermore, the method for constructing the continuous-time dynamics model of the UAV is as follows:

[0037] The UAV carrying ARIS is modeled as a three-dimensional point mass, and the system state vector is defined. , Indicates the three-dimensional position of the drone, Indicates flight speed, Indicates heading angle, Indicates the track angle;

[0038] Define control vector , Represents the rate of change of velocity. Indicates the rate of change of heading angle. Rate of change of track angle;

[0039] According to the flight dynamics model, the motion of the UAV is described by a nonlinear state equation:

[0040] ,

[0041] The energy consumption of drones is generated by the work done by the propulsion system, over a period of time. The total energy consumption within is expressed as:

[0042] ,

[0043] in, For thrust, For flight speed, This represents the time differential.

[0044] Furthermore, the method for constructing the drone obstacle avoidance constraint model includes: modeling the drone and obstacles as a spherical safe region, and constraining the Euclidean distance between the drone and each obstacle to be no less than a preset safety threshold.

[0045] ;

[0046] in, Indicates the first The location of the center of the obstacle. and These are respectively the safe radius of the drone and the first The safe radius of an obstacle This represents the number of obstacles.

[0047] Furthermore, the joint optimization problem is:

[0048] ;

[0049] ,

[0050] ,

[0051] ,

[0052] ,

[0053] ,

[0054] ,

[0055] ,

[0056] in, For continuous dynamic constraints of UAVs, Constraints on the drone's altitude, speed, and heading angle. The minimum safe flight altitude for drones, The minimum flight speed for the drone, The maximum flight speed of the drone, The minimum flight path angle for the UAV. The maximum flight path angle of the drone. For control vector constraints, For the minimum rate of change of the drone's speed, Maximum rate of change of drone speed This represents the minimum rate of change of the UAV's heading angle. This represents the maximum rate of change of the UAV's heading angle. This represents the minimum rate of change of the UAV's flight path angle. The maximum rate of change of the UAV's flight path angle. Due to energy consumption constraints, This represents the maximum available total energy consumption of the drone's battery. To avoid obstacles and constraints, For ARIS phase offset constraints.

[0057] Furthermore, methods for solving the ARIS phase offset optimization subproblem to obtain the optimal phase offset matrix include:

[0058] Given control vector and task duration By adjusting the phase of each reflection unit, the total phase of the ARIS reflection path is made consistent with the phase of the direct link, thus achieving coherent signal superposition. Based on the phase alignment principle, the first... The optimal closed-form solution for the phase offset of each reflecting unit is:

[0059] ,

[0060] The optimal ARIS phase offset matrix is ​​expressed as follows: ;

[0061] in, For the small-scale fading coefficient of the direct link, For the phase of the direct link, For carrier wavelength, For the location of ground users, for No. The center position of each reflective unit This indicates the location of the base station.

[0062] Furthermore, methods for solving the UAV trajectory optimization subproblem to obtain the optimal UAV trajectory include:

[0063] With a fixed optimal phase offset matrix Subsequently, the joint optimization problem degenerates into a UAV trajectory optimization subproblem:

[0064] ,

[0065] ,

[0066] By jointly optimizing the control vector With task duration Maximize the total reachable rate ;

[0067] Variable task duration can be scaled using time scaling. Normalization to a fixed interval This achieves decoupling between trajectory shape and task duration; a normalized time variable is defined. The nonlinear state equation describing the motion of the UAV is transformed into:

[0068] ,

[0069] The objective function is normalized to:

[0070] ,

[0071] in, This refers to the base station signal transmission power. For the equivalent complex channel gain, d s For time differential components;

[0072] Energy consumption constraints are normalized to:

[0073] ;

[0074] in, This is the energy consumption function per unit time.

[0075] By using B-splines to parameterize the control variables, the infinite-dimensional continuous control function is transformed into a finite-dimensional optimization problem.

[0076] ,

[0077] in, For the control points to be optimized, for k Second-rate B spline basis functions;

[0078] use B The spline convex hull property allows control constraints to be applied directly to the control points:

[0079] ,

[0080] ,

[0081] in, For acceleration control points, For the rate of change of heading angle, The control point is the rate of change of the track angle;

[0082] Introducing a set of control points System dynamics constraints Represented as:

[0083] ,

[0084] constrain C2 and The unified representation is:

[0085] ,

[0086] Transform into an equivalent integral form:

[0087] ,

[0088] because Since the function is not differentiable, we introduce a local smoothing function for approximation:

[0089] ,

[0090] in, The smoothing parameter controls the smoothness of the function;

[0091] Introducing constraint tolerance If the hard constraints are relaxed, then the constraints... and Represented as:

[0092] ;

[0093] The Sigmoid function is used to smooth the LosS indicator functions of the BS-ARIS and ARIS-GU links:

[0094] ,

[0095] ,

[0096] in, The sigmoid smoothing parameter controls the degree of LoS approximation. The approximate indicator function becomes a binary function; the objective function is smoothed to... Among them, the smoothed instantaneous rate ,in, The smoothed channel amplitude;

[0097] The drone trajectory optimization subproblem is transformed into a finite-dimensional nonlinear programming problem:

[0098] ,

[0099] ,

[0100] ,

[0101] ,

[0102] ,

[0103] ;

[0104] Furthermore, methods for solving finite-dimensional nonlinear programming problems include:

[0105] The gradient of the objective function is calculated by the inverse integral of the costate variable equation, and its expression is:

[0106] ,

[0107] in, These are the costate variables of the objective function; Indicates the normalized time after smoothing. The instantaneous achievable speed; Represents the state variable The partial derivatives;

[0108] Terminal boundary conditions Below, the gradients of the objective function with respect to the control points and the task duration are respectively:

[0109] ,

[0110] ,

[0111] in, Indicates the control variable The partial derivatives;

[0112] The energy-constrained gradient is also calculated by inverse integration of the costate equation:

[0113] ,

[0114] in, For energy-constrained costate variables; under boundary conditions The gradients of energy consumption with respect to the control point and task duration are as follows:

[0115] ,

[0116] ;

[0117] The algorithm solution process is as follows: Initialize control points With duration And set the initial smoothing parameters. Constraint tolerance Each round uses sequential quadratic programming to solve the optimization problem, obtaining the current solution. If the solution does not satisfy the constraints, then the solution is narrowed down. And continue solving; if the constraints are satisfied, then gradually reduce the smoothing parameter and tolerance parameter: , Repeat the above process until... The system outputs the optimal control point and mission duration, thereby obtaining the optimal flight trajectory of the UAV.

[0118] Furthermore, the method for jointly optimizing the phase offset and UAV trajectory using an alternating optimization framework, and outputting the optimal ARIS phase offset matrix and UAV trajectory after joint optimization, is as follows:

[0119] Initialize UAV control vectors With task duration And set the number of iterations. =0;

[0120] In the In this iteration, the following steps are performed:

[0121] fixed and Update the optimal solution based on the phase closed-form solution. Phase offset matrix ;

[0122] Fixed phase offset matrix Update the control vector based on the solution results of the UAV trajectory optimization subproblem. With task duration ;

[0123] Calculate the total reachability rate of the current iteration. ,when If the algorithm converges, it is determined that the algorithm has converged, and the jointly optimized ARIS phase offset matrix and UAV trajectory are output; otherwise, another... Continue iterating.

[0124] The beneficial effects achieved by this invention are as follows: This invention can actively avoid building-occluded areas through occlusion perception modeling, maintain a line-of-sight link throughout the process, eliminate communication interruptions, and significantly improve reachability; Utilizing continuous-time B-spline control parameterization, it can generate smooth, abrupt trajectories that satisfy the complete dynamic constraints of the UAV, and can be directly applied to real UAVs; Constraint transcription and target smoothing make the problem continuously differentiable, and combined with SQP solution, it can achieve rapid convergence with far fewer iterations than traditional methods such as discrete SCA; It uniformly considers rate maximization, dynamic feasibility, obstacle avoidance, and energy consumption constraints, making it suitable for complex urban occlusion environments and highly practical in engineering. Attached Figure Description

[0125] Figure 1 A schematic diagram of the ARIS-assisted drone communication system;

[0126] Figure 2 A diagram illustrating the convergence performance comparison of different algorithms;

[0127] Figure 3 A comparative illustration of three-dimensional flight trajectories generated by different methods;

[0128] Figure 4 A diagram comparing the smoothness of control variables generated by different methods;

[0129] Figure 5 This is a schematic diagram comparing trajectories with and without obstacle avoidance constraints;

[0130] Figure 6 A schematic diagram comparing the perceived trajectory with and without occlusion;

[0131] Figure 7 A schematic diagram comparing time-varying reachability rates in different scenarios;

[0132] Figure 8 A diagram showing the comparison of total reachability in different scenarios;

[0133] Figure 9 A schematic diagram comparing the average rates of different numbers of reflective units; Detailed Implementation

[0134] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0135] The invention proposes a joint optimization method for continuous-time ARIS phase shift and UAV trajectory, comprising the following steps:

[0136] Step 1, as follows Figure 1 As shown, a UAV-assisted perception and communication channel model in three-dimensional space is constructed. The specific steps are as follows:

[0137] Step 101: Establish a coordinate system in three-dimensional space. The base station (BS) is a fixed single-antenna node, and its location... Ground users (GUs) are single-antenna mobile nodes, located... The drone is equipped with the ARIS (Airborne Intelligent Reflector) to fly in three-dimensional space. ARIS includes... There are 1 reflective element, each reflective element having a size of 1. Phase offset of each reflective unit exist Continuously adjustable within, the first The center location of each ARIS unit is:

[0138] ;

[0139] Step 102: The BS-ARIS channel vector is represented as follows:

[0140] ,

[0141] Under line-of-sight (LoS) conditions, BS to the first The channel coefficients of an ARIS unit can be modeled as follows:

[0142] ,

[0143] in, For a 1m reference path loss, This is the path loss index. Represents Euclidean distance. The phase delay of the BS-ARIS link is expressed as:

[0144] ,

[0145] in, For carrier wavelength, and The azimuth and elevation angles are respectively the arrival azimuth and the arrival elevation angle. It is a plane wave vector. Equivalent to Euclidean distance Then the phase delay can be simplified to:

[0146] ,

[0147] Similarly, The channel vector is represented as:

[0148] ,

[0149] Under line-of-sight (LoS) conditions, the first The channel coefficients from each ARIS unit to the GU can be modeled as follows:

[0150] ,

[0151] in, For a 1m reference path loss, This is the path loss index. The phase delay of the ARIS-GU link is expressed as:

[0152] ,

[0153] in, For carrier wavelength, and These are the azimuth and elevation angles, respectively. For a plane wave vector, the phase delay can be simplified to:

[0154] ,

[0155] Due to the obstruction of urban buildings, the BS-GU link is modeled as a Rayleigh fading channel, with the channel coefficients as follows:

[0156] ;

[0157] in, For a 1m reference path loss, This represents the small-scale fading coefficient. This is the path loss index.

[0158] Step 103: To characterize the occlusion of city buildings, model the occluded area of ​​each building as a convex polyhedron.

[0159] Define the first from the perspective of base station (BS) The obstruction area of ​​a building :

[0160] ,

[0161] in, Represents any point in three-dimensional space. For the set of all the planes that make up the building, Indicates the first The building The normal vector of each face. This is the planar offset based on the BS viewpoint;

[0162] Define the first from the perspective of ground users (GU) The obstruction area of ​​a building :

[0163] ,

[0164] in, For the set of all the planes that make up the building, Indicates the first The building The normal vector of each face. This is the planar offset based on the GU's perspective;

[0165] Define based on the occlusion area Link and Link's Loss Indicator Function:

[0166] ,

[0167] ,

[0168] in, This is the center position of the ARIS reflector unit; This represents the union of the BS-ARIS link's blocked regions. Represents the union of the ARIS-GU link's blocked regions;

[0169] These LoS conditions are equivalent to the ARIS location having a positive sign distance to each occluded region, i.e.:

[0170] ,

[0171] ,

[0172] in, and These represent the positions of ARIS from the perspectives of BS and GU, respectively. Symbol distance of each occluded area:

[0173] ,

[0174] ,

[0175] Step 104: Combining the channel coefficients of the reflected link and the direct link, and the Loss indicator function, the received signal of the ground user can be obtained:

[0176] ,

[0177] in, For the signal base station's transmission power, This represents the channel coefficient of the BS-GU link. This represents the channel vector of the BS-ARIS link. This represents the conjugate transpose of the ARIS-GU link channel vector. Represents the ARIS phase offset matrix. For the launch symbol, It is Gaussian white noise.

[0178] Therefore, the received signal-to-noise ratio at GU is:

[0179] ,

[0180] in, Let be the magnitude of the complex channel gain at time t. This represents noise power.

[0181] Duration The total reachable rate within is:

[0182] ;

[0183] in, Indicates time The instantaneous achievable speed, This represents the time differential.

[0184] Step 2: Construct a continuous-time dynamics model of the fixed-wing UAV and define the system state vector. , Indicates the three-dimensional position of the drone, Indicates flight speed, Indicates heading angle, Indicates the track angle;

[0185] Define three-dimensional control vector , Represents the rate of change of velocity. Indicates the rate of change of heading angle. Rate of change of track angle;

[0186] Based on the flight dynamics model, the motion of the UAV can be described as a nonlinear state equation:

[0187] ,

[0188] This model fully describes the changes in position, velocity, and attitude of the UAV, making the physical realization of its flight trajectory possible. The UAV's energy consumption is primarily generated by the work done by its propulsion system, over a period of time. The total energy consumption within can be expressed as:

[0189] ,

[0190] in, For thrust, For flight speed, Representing the time differential component. Substituting into the thrust expression:

[0191] ,

[0192] in, For the weight of the drone, For gravitational acceleration, the coefficient is... and ,in, air density, For reference wing area, The parasitic drag coefficient, For induced drag coefficient, load factor

[0193] .

[0194] The total energy consumption of the drone can be obtained as follows:

[0195] .

[0196] Step 3: Construct an obstacle avoidance constraint model, modeling both the drone and obstacles as spherical safe regions, and constraining the Euclidean distance between the drone and each obstacle to be no less than a preset safety threshold, i.e.: ;

[0197] in, Indicates the first The location of the center of the obstacle. and These are respectively the safe radius of the drone and the first The safe radius of an obstacle The number of obstacles is a constraint that is continuously satisfied throughout the entire mission cycle, enabling collision-free flight throughout the entire mission.

[0198] Step 4: Establish a joint optimization problem with the objective of maximizing the total reachability rate, integrating UAV dynamics, altitude and speed, pitch angle constraints, control constraints, energy consumption limits, obstacle avoidance constraints, and ARIS phase constraints:

[0199] ;

[0200] ,

[0201] ,

[0202] ,

[0203] ,

[0204] ,

[0205] ,

[0206] ,

[0207] in, For continuous dynamic constraints of UAVs, Constraints on the drone's altitude, speed, and heading angle. The minimum safe flight altitude for drones, The minimum flight speed for the drone, The maximum flight speed of the drone, The minimum flight path angle for the UAV. The maximum flight path angle of the drone. For control vector constraints, For the minimum rate of change of the drone's speed, Maximum rate of change of drone speed This represents the minimum rate of change of the UAV's heading angle. This represents the maximum rate of change of the UAV's heading angle. This represents the minimum rate of change of the UAV's flight path angle. The maximum rate of change of the UAV's flight path angle. Due to energy consumption constraints, This represents the maximum available total energy consumption of the drone's battery. To avoid obstacles and constraints, The problem is a non-convex, infinite-dimensional continuous-time optimal control problem with an objective function containing a non-differentiable line-of-sight indicator function, which is difficult to solve directly. Therefore, an alternating optimization (AO) framework is used to decouple the problem into two sub-problems: ARIS phase offset optimization and UAV trajectory optimization.

[0208] Step 5: Given the control vector and task duration The ARIS phase offset optimization subproblem aims to maximize the achievable rate. Since the achievable rate monotonically increases with respect to the signal-to-noise ratio (SNR), this problem is equivalent to maximizing the SNR, and further equivalent to maximizing the received signal power, i.e., the magnitude of the composite channel gain. By adjusting the phase of each reflection unit, the total phase of the ARIS reflection path is made consistent with the phase of the direct link, thereby achieving coherent superposition of the received signals. Based on the phase alignment principle, the following can be derived: The optimal closed-form solution for the phase offset of each reflecting unit is:

[0209] ,

[0210] Accordingly, the optimal phase offset matrix can be expressed as:

[0211] ;

[0212] in, For the small-scale fading coefficient of the direct link, For the phase of the direct link, The carrier wavelength is denoted as λ. It can be seen that this is determined solely by geometric positional relationships and is independent of the line-of-sight indicator function. The line-of-sight indicator function only controls the activation and deactivation of the reflection link, i.e., determines whether the reflection path participates in signal superposition.

[0213] Step 6: Fix the optimal phase offset matrix Subsequently, the joint problem degenerates into a trajectory optimization subproblem. Under the far-field approximation, the channel coefficient magnitudes can be simplified to:

[0214] ,

[0215] in, For a 1m reference path loss, This is the path loss index. For the small-scale fading coefficient of the direct link, .

[0216] This leads to the trajectory optimization subproblem:

[0217] ,

[0218] ,

[0219] This problem remains an infinite-dimensional optimal control problem, and it needs to be transformed into a finite-dimensional nonlinear programming (NLP) problem. The specific steps for the transformation are as follows:

[0220] Step 601: Eliminating the variable time length The influence of introducing a normalized time variable , change variable task duration from Normalized to a fixed time interval This achieves decoupling between trajectory shape and task duration. The dynamic equations are then transformed into:

[0221] ,

[0222] Accordingly, the objective function is normalized to:

[0223] ,

[0224] in, This refers to the base station signal transmission power. For the equivalent complex channel gain, d s This is the time differential.

[0225] Energy consumption constraints are normalized to:

[0226] ;

[0227] in, This is the energy consumption function per unit time.

[0228] Step 602: To transform the infinite-dimensional control function into a finite-dimensional variable, B-spline functions are used to parameterize the control variables:

[0229] ,

[0230] in, For the control points to be optimized, for k Second-rate B Spline basis functions are recursively calculated using the Cox-deBoor formula:

[0231] ,

[0232] ;

[0233] use B The spline convex hull property allows for direct constraint application to control points, transforming control constraints into:

[0234] ,

[0235] ,

[0236] in, For acceleration control points, For the rate of change of heading angle, The control point is the rate of change of the track angle;

[0237] Introducing a set of control points System dynamics constraints It can be represented as:

[0238] ,

[0239] This method transforms the original infinite-dimensional function optimization problem into a finite-dimensional parameter optimization problem, ensuring continuous trajectory quantization and reducing the optimization difficulty.

[0240] Step 603: Set state constraints Obstacle avoidance constraints It should be written as:

[0241] ,

[0242] in, Let be the number of obstacles. This constraint is a continuous inequality constraint and cannot be solved numerically directly. It is transformed into an equivalent integral form:

[0243] ,

[0244] because Since the function is not differentiable, we introduce a local smoothing function for approximation:

[0245] ,

[0246] in, The smoothing parameter controls the smoothness of the function;

[0247] Introducing constraint tolerance If the hard constraints are relaxed, then the constraints... and It can be represented as:

[0248] .

[0249] Step 604: The LosS indicator functions of the original BS-ARIS link and ARIS-GU link are binary ladder functions, which will cause the target to be non-differentiable and the gradient algorithm cannot be used. The Sigmoid function is used to smooth them:

[0250] ,

[0251] ;

[0252] in, The sigmoid smoothing parameter controls the degree of LoS approximation. The approximate indicator function becomes a binary function. Correspondingly, the objective function can be smoothed to... Among them, the smoothed instantaneous rate ,in, This represents the smoothed channel amplitude.

[0253] Step 605: After the above transformation, the infinite-dimensional non-convex optimization problem is finally transformed into a finite-dimensional nonlinear programming problem:

[0254] ,

[0255] ,

[0256] ,

[0257] ,

[0258] ,

[0259] .

[0260] Step 7: Solve the finite-dimensional nonlinear programming problem using Sequential Quadratic Programming (SQP). This requires calculating the objective and constraint pairs for the control points. , The specific steps for gradient calculation and SQP solution are as follows:

[0261] Step 701: The gradient of the objective function is calculated by the inverse integral of the costate variable equation, and its expression is:

[0262] ,

[0263] in, These are the costate variables of the objective function; Indicates the normalized time after smoothing. The instantaneous achievable speed;

[0264] Terminal boundary conditions Below, the gradients of the objective function with respect to the control points and the task duration are respectively:

[0265] ,

[0266] .

[0267] Step 702: The energy consumption constraint gradient is also calculated through inverse integration of the costate equation:

[0268] ,

[0269] in, For energy-constrained costate variables; under boundary conditions The gradients of energy consumption with respect to the control point and task duration are as follows:

[0270] ,

[0271] ;

[0272] The method for solving the gradient of the state constraint function is similar to that for energy consumption constraints.

[0273] Step 703: The algorithm solution process is as follows: Initialize control points With duration And set the initial smoothing parameters. Constraint tolerance In each round, a sequential quadratic programming (SQP) problem is solved to obtain the current solution. If the solution does not satisfy the constraints, then the solution is narrowed down. And continue solving; if the constraints are satisfied, then gradually reduce the smoothing parameter and tolerance parameter: , Repeat the above process until... The system outputs the optimal control point and mission duration, thereby obtaining the optimal flight trajectory of the UAV.

[0274] Step 8: Joint optimization of UAV trajectory and phase is performed using an alternating optimization (AO) framework. The overall process is as follows:

[0275] Initialize UAV control vectors With task duration And set the number of iterations. =0;

[0276] In the In this iteration, the following steps are performed:

[0277] fixed and Update the optimal solution based on the phase closed-form solution. Phase offset matrix ;

[0278] Fixed phase offset matrix Update the control vector based on the solution results of the UAV trajectory optimization subproblem. With task duration ;

[0279] Calculate the total reachability rate of the current iteration. ,when If the algorithm converges, the jointly optimized algorithm is output. Phase offset matrix and optimal UAV trajectory; otherwise, another Continue iterating.

[0280] like Figures 2 to 9 As shown, the simulation results of the proposed continuous-time ARIS phase shift and UAV trajectory joint optimization method are presented. Figure 2 As shown, in an ARIS-assisted UAV communication scenario, the convergence curves of three methods—continuous B-spline parameterization, continuous control parameterization, and discrete successive convex approximation (SCA)—are compared. Simulation results indicate that the algorithm proposed in this invention converges the fastest, reaching stability within 4 iterations. This is because the inherent smoothness and differentiability of B-spline control parameterization, combined with the sigmoid smoothing of the line-of-sight indicator function, enables efficient optimization of gradient-based SQP solutions. The continuous control parameterization method converges more slowly, stabilizing after approximately 5 iterations. The discrete SCA method converges the slowest, requiring 9 iterations to stabilize. Furthermore, the algorithm proposed in this invention exhibits the highest total reachability rate after convergence, indicating that its trajectory better maintains an uninterrupted line-of-sight link. Therefore, it can be concluded that the method of this invention significantly outperforms existing methods in terms of convergence efficiency and performance optimization.

[0281] like Figure 3 As shown, in an ARIS-assisted UAV communication scenario, the 3D flight trajectories generated by three methods—continuous B-spline parameterization, continuous control parameterization, and discrete successive convex approximation (SCA)—are compared. Simulation results indicate that the discrete SCA method generates piecewise linear trajectories with sharp turns and abrupt altitude changes, violating the continuous dynamics constraints of the UAV and making it unsuitable for execution on actual aircraft. Both B-spline parameterization and continuous parameterization methods generate smooth trajectories that satisfy dynamic constraints and possess realistic physical flyability. Therefore, it can be concluded that discrete trajectory optimization disrupts the continuity of UAV motion, while continuous B-spline parameterization ensures dynamic feasibility of the trajectory, which is a necessary condition for safe flight and reliable communication of fixed-wing UAVs in urban environments.

[0282] like Figure 4As shown, in an ARIS-assisted UAV communication scenario, the time-varying control variable curves generated by continuous B-spline parameterization and continuous control parameterization methods are compared over time. Simulation results indicate that the B-spline method produces a continuous and smooth control quantity with gradual changes; the continuous control parameterization method exhibits abrupt changes in the control quantity, requiring a large number of time points to achieve the same smoothness, resulting in high computational costs. Therefore, it can be concluded that B-spline parameterization achieves smooth control with only a small number of control points, achieving an excellent balance between trajectory quality and computational complexity.

[0283] like Figure 5 As shown, in an urban obstacle environment, the optimized flight trajectories of the ARIS UAV are compared under two conditions: with and without obstacle avoidance constraints. Simulation results show that the trajectory without obstacle avoidance constraints will directly cross the obstacle safety zone and collide, lacking practical safety. With the addition of a spherical safety zone constraint, the optimized trajectory actively avoids obstacles, maintains a safe distance, and avoids collisions throughout the flight, making it directly applicable for safe urban flight deployment. Therefore, it can be concluded that integrating obstacle avoidance constraints into trajectory optimization can ensure the safety of the UAV throughout its flight without sacrificing communication speed, meeting the requirements for safe low-altitude flight in urban areas.

[0284] like Figure 6 As shown, the ARIS UAV trajectories are compared under two conditions: with and without occlusion perception optimization, in a building-occluded environment. Simulation results show that the trajectory without occlusion perception will enter the building-occluded area, causing the BS-ARIS or ARIS-GU link to be interrupted and degrade to a non-line-of-sight (NLoS) state. The trajectory with occlusion perception optimization can effectively avoid the occlusion areas of the base station and the user's viewpoint, always maintaining a dual-link line-of-sight (LoS) state, thus ensuring the continuous availability of the communication link. Therefore, it can be concluded that modeling urban building occlusion as a convex polyhedral constraint and incorporating it into trajectory optimization enables UAVs to actively avoid occlusion and maintain the reliability of the ARIS-assisted communication link.

[0285] like Figure 7 As shown, a comparison of time-varying achievable rates is presented for three scenarios: occlusion-sensing trajectory, unocclusion-sensing trajectory, and ideal unocclusion-sensing trajectory. Simulation results indicate that the ideal unocclusion-sensing scenario exhibits the highest and most stable rate; the unocclusion-sensing trajectory enters the occlusion zone mid-flight, causing the rate to drop sharply to zero within 10-13 seconds, resulting in communication interruption; the occlusion-sensing trajectory of this invention maintains a stable, non-zero rate throughout its entire flight without rate interruption; although its rate is slightly lower than the ideal scenario, it is far superior to the interruption-sustaining scheme. Therefore, it can be concluded that occlusion-sensing trajectory optimization can effectively eliminate communication interruption problems caused by building obstruction, providing more stable and reliable communication services in complex urban environments.

[0286] like Figure 8As shown, the total reachable rate is compared under three scenarios: occlusion-aware trajectory, unocclusion-aware trajectory, and ideal unocclusion. Simulation results show that the ideal scenario has the highest total rate, while the unocclusion-aware scenario suffers a significant drop in total rate due to link interruption. The occlusion-aware scheme of this invention has a significantly higher total rate than the unocclusion-aware scheme, approaching ideal performance. Therefore, it can be concluded that in urban occlusion environments, ignoring occlusion constraints leads to a severe decline in actual communication performance, while occlusion-aware optimization can maximize reachable rate under both security and dynamic constraints.

[0287] like Figure 9 As shown, the average achievable speed varies with the number of reflector units under the configurations of Ground Intelligent Reflector (TRIS) and ARIS. Simulation results indicate that the speed of all schemes increases with the number of reflector units; the optimized ARIS speed is higher than most fixed-location TRIS, but slightly lower than the ideal TRIS deployed in the optimal location; the performance of fixed TRIS is heavily dependent on the deployment location, and the speed drops significantly if the location is poor; while ARIS is not limited by location, can dynamically establish and maintain line-of-sight links, and has better overall performance; at the same time, the optimal ARIS is significantly better than the continuously controlled parameterized and discrete ARIS schemes. Therefore, it can be concluded that ARIS, which combines trajectory and phase joint optimization, has better global optimization capabilities than fixed TRIS in complex environments.

[0288] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0289] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of the claims of the present invention pending approval.

Claims

1. A method for joint optimization of continuous-time ARIS phase shift and UAV trajectory, characterized in that: Based on the pre-constructed UAV-equipped ARIS-assisted communication obstruction perception channel model, UAV continuous-time dynamics model, and UAV obstacle avoidance constraint model, a joint optimization problem is established with the goal of maximizing the total reachability rate, integrating fixed-wing UAV dynamics, altitude, speed, heading angle constraints, control vector constraints, energy consumption constraints, obstacle avoidance constraints, and ARIS phase offset constraints. The joint optimization problem is decoupled into an ARIS phase offset optimization subproblem and an UAV trajectory optimization subproblem; The optimal phase offset matrix is ​​obtained by solving the ARIS phase offset optimization subproblem. Solve the UAV trajectory optimization subproblem to obtain the optimal UAV trajectory; The optimal phase offset matrix and the optimal UAV trajectory are jointly optimized using an alternating optimization framework, and the jointly optimized ARIS phase offset matrix and UAV trajectory are output. The method for constructing a UAV-equipped ARIS-assisted communication obstruction perception channel model includes: establishing a Cartesian coordinate system in three-dimensional space, where BS represents the base station with a fixed location; GU represents the ground user in a low-speed moving state; and the UAV equipped with ARIS maneuvers in three-dimensional space, with the ARIS consisting of uniformly arranged... It consists of several reflective elements, each with a phase offset. exist Internally continuously adjustable The location of the ARIS center changes in real time with the drone; The BS-GU direct link is modeled as a Rayleigh fading channel, and the BS-ARIS link and ARIS-GU link are modeled as LosS path loss channels. Model the building's occlusion area as a convex polyhedron, and define the first... The area obstructed by the building, : ， in, Represents any point in three-dimensional space. For the set of all the planes that make up the building, Indicates the first The building The normal vector of each face. For based on The plane offset of the viewpoint; Defining the first from GU's perspective The area obstructed by the building, : ， in, For the set of all the planes that make up the building, Indicates the first The building The normal vector of each face. This is the planar offset based on the GU's perspective; Based on the occlusion region, the Loss indication functions for the BS-ARIS link and the ARIS-GU link are defined as follows: ， ， in, This is the center position of the ARIS reflector unit; This represents the union of the BS-ARIS link's blocked regions. Represents the union of the ARIS-GU link's blocked regions; By combining the channel coefficients of the direct link and the reflected link with the LoS indicator function, the received signal-to-noise ratio at the user end is obtained: ， in, This refers to the base station signal transmission power. For noise power, Let be the magnitude of the complex channel gain at time t. This represents the channel coefficient of the BS-GU link. This represents the channel vector of the BS-ARIS link. This represents the conjugate transpose of the ARIS-GU link channel vector. ； Denotes the ARIS phase offset matrix, where, It is a natural constant. The imaginary unit, This represents the negative exponential phase rotation factor. Indicates the first Each reflective unit in Phase shift at any given moment; Accordingly, duration The total reachable rate within is: ； in, Indicates time The instantaneous achievable speed, Represents the time differential; The method for constructing the continuous-time dynamics model of an unmanned aerial vehicle (UAV) is as follows: The UAV carrying ARIS is modeled as a three-dimensional point mass, and the system state vector is defined. , Indicates the three-dimensional position of the drone, Indicates flight speed, Indicates heading angle, Indicates the track angle; Define control vector , Represents the rate of change of velocity. Indicates the rate of change of heading angle. Rate of change of track angle; According to the flight dynamics model, the motion of the UAV is described by a nonlinear state equation: ， The energy consumption of drones is generated by the work done by the propulsion system, over a period of time. The total energy consumption within is expressed as: ， in, For thrust, For flight speed, Represents the time differential; The method for constructing the drone obstacle avoidance constraint model includes: modeling the drone and obstacles as a spherical safe region, and constraining the Euclidean distance between the drone and each obstacle to be no less than a preset safety threshold. ； in, Indicates the first The location of the center of the obstacle. and These are respectively the safe radius of the drone and the first The safe radius of an obstacle The number of obstacles; The joint optimization problem is: ； ， ， ， ， ， ， ， in, For continuous dynamic constraints of UAVs, Constraints on the drone's altitude, speed, and heading angle. The minimum safe flight altitude for drones, The minimum flight speed for the drone, The maximum flight speed of the drone, The minimum flight path angle for the UAV. The maximum flight path angle of the drone. For control vector constraints, For the minimum rate of change of the drone's speed, Maximum rate of change of drone speed This represents the minimum rate of change of the UAV's heading angle. This represents the maximum rate of change of the drone's heading angle. This represents the minimum rate of change of the UAV's flight path angle. The maximum rate of change of the UAV's flight path angle. Due to energy consumption constraints, This represents the maximum available total energy consumption of the drone's battery. To avoid obstacles and constraints, For ARIS phase offset constraints.

2. The continuous-time ARIS phase shift and UAV trajectory joint optimization method according to claim 1, characterized in that, Methods for solving the ARIS phase offset optimization subproblem to obtain the optimal phase offset matrix include: Given control vector and task duration By adjusting the phase of each reflection unit, the total phase of the ARIS reflection path is made consistent with the phase of the direct link, thus achieving coherent signal superposition. Based on the phase alignment principle, the first... The optimal closed-form solution for the phase offset of each reflecting unit is: ， The optimal ARIS phase offset matrix is ​​expressed as follows: ; in, For the small-scale fading coefficient of the direct link, For the phase of the direct link, For carrier wavelength, For the location of ground users, for No. The center position of each reflective unit This indicates the location of the base station.

3. The continuous-time ARIS phase shift and UAV trajectory joint optimization method according to claim 2, characterized in that: Methods for solving the UAV trajectory optimization subproblem to obtain the optimal UAV trajectory include: With a fixed optimal phase offset matrix Subsequently, the joint optimization problem degenerates into a UAV trajectory optimization subproblem: ， ， By jointly optimizing the control vector With task duration Maximize the total reachable rate ; Variable task duration can be scaled using time scaling. Normalization to a fixed interval This achieves decoupling between trajectory shape and task duration; a normalized time variable is defined. The nonlinear state equation describing the motion of the UAV is transformed into: ， The objective function is normalized to: ， in, This refers to the base station signal transmission power. For the equivalent complex channel gain, For time differential components; Energy consumption constraints are normalized to: ； in, This is the energy consumption function per unit time. By using B-splines to parameterize the control variables, the infinite-dimensional continuous control function is transformed into a finite-dimensional optimization problem. ， in, For the control points to be optimized, The basis functions are k-th degree B-spline functions; By utilizing the properties of the B-spline convex hull, control constraints can be directly applied to the control points: ， ， in, For acceleration control points, For the rate of change of heading angle, The control point is the rate of change of the track angle; Introducing a set of control points System dynamics constraints Represented as: ， Constraints 2 and The unified representation is: ， Transform into an equivalent integral form: ， because Since the function is not differentiable, we introduce a local smoothing function for approximation: ， in, The smoothing parameter controls the smoothness of the function; Introducing constraint tolerance If the hard constraints are relaxed, then the constraints... 2 and Represented as: ； The Sigmoid function is used to smooth the LosS indicator functions of the BS-ARIS and ARIS-GU links: ， ， in, The sigmoid smoothing parameter controls the degree of LoS approximation. The approximate indicator function becomes a binary function; the objective function is smoothed to... Among them, the smoothed instantaneous rate ,in, The smoothed channel amplitude; The drone trajectory optimization subproblem is transformed into a finite-dimensional nonlinear programming problem: ， ， ， ， ， 。 4. The continuous-time ARIS phase shift and UAV trajectory joint optimization method according to claim 3, characterized in that: Methods for solving finite-dimensional nonlinear programming problems include: The gradient of the objective function is calculated by the inverse integral of the costate variable equation, and its expression is: ， in, These are the costate variables of the objective function; Indicates the normalized time after smoothing. The instantaneous achievable speed; Represents the state variable The partial derivatives; Terminal boundary conditions Below, the gradients of the objective function with respect to the control points and the task duration are respectively: ， ， in, Indicates the control variable The partial derivatives; The energy-constrained gradient is also calculated by inverse integration of the costate equation: ， in, For energy-constrained costate variables; under boundary conditions The gradients of energy consumption with respect to the control point and task duration are as follows: ， ； The algorithm solution process is as follows: Initialize control points With duration And set the initial smoothing parameters. Constraint tolerance Each round uses sequential quadratic programming to solve the optimization problem, obtaining the current solution. If the solution does not satisfy the constraints, then the solution is narrowed down. And continue solving; if the constraints are satisfied, then gradually reduce the smoothing parameter and tolerance parameter: , Repeat the above process until... The system outputs the optimal control point and mission duration, thereby obtaining the optimal flight trajectory of the UAV.

5. The continuous-time ARIS phase shift and UAV trajectory joint optimization method according to claim 4, characterized in that, The method for jointly optimizing phase offset and UAV trajectory using an alternating optimization framework, and outputting the optimal ARIS phase offset matrix and UAV trajectory after joint optimization, is as follows: Initialize UAV control vectors With task duration And set the number of iterations. =0; In the In this iteration, the following steps are performed: fixed and Update the optimal solution based on the phase closed-form solution. Phase offset matrix ; Fixed phase offset matrix Update the control vector based on the solution results of the UAV trajectory optimization subproblem. With task duration ; Calculate the total reachability rate of the current iteration. ,when If the algorithm converges, it is determined that the algorithm has converged, and the jointly optimized ARIS phase offset matrix and UAV trajectory are output; otherwise, another... Continue iterating.

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