A Safety and Energy-Saving Trajectory Solution for Unmanned Aerial Vehicles Based on Vertically Polarized Antennas

Abstract

This invention discloses a safe and energy-saving trajectory solution method for UAVs based on vertically polarized antennas, integrating communication and control. First, a high-precision communication constraint model with attitude perception is established, revealing the antenna gain attenuation mechanism caused by lateral maneuvers. Then, using rigid body dynamics principles, the antenna pointing direction and acceleration vector are explicitly coupled. By introducing intermediate variables and dynamic decoupling projection techniques, the roll and pitch constraints, originally non-convex in Euler angle space, are accurately transformed into second-order cone constraints and linear polyhedral cone constraints in acceleration space, respectively. Finally, a second-order cone programming model with the goal of minimizing mechanical energy consumption is constructed and iteratively solved using a sequential convex approximation algorithm. This invention minimizes the mechanical energy consumption of UAVs during high-maneuverability flight while automatically avoiding antenna communication blind spots, solving the problem of difficult traditional non-convex optimization solutions. It is suitable for UAV application scenarios with high requirements for communication reliability and real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of interdisciplinary technology of UAV trajectory planning and wireless communication, and particularly relates to a safe and energy-saving trajectory solution method for UAV communication and control based on a vertically polarized antenna. Background Technology

[0002] With the booming development of the low-altitude economy, rotary-wing UAVs, with their vertical take-off and landing and flexible maneuverability, have been widely used in various complex scenarios such as logistics transportation, power line inspection, and base station communication relay. In these applications, maintaining a high-quality air-to-ground wireless communication link is crucial to ensuring the safe execution of missions and real-time data transmission. However, existing UAV trajectory planning technologies typically employ a simplified "point mass model," neglecting the impact of UAV attitude changes on the communication antenna gain.

[0003] In reality, most commercial drones are equipped with vertically polarized (VV) antennas (such as dipole antennas), whose radiation patterns exhibit typical "omnidirectional" characteristics. However, there is a gain null along the antenna axis (i.e., the vertical direction of the drone). When a drone performs large-angle rolls or pitches to achieve rapid maneuvers, the tilt of the fuselage causes the antenna null area to point towards the ground user, resulting in a sharp signal attenuation or even communication interruption. Existing planning methods based on the omnidirectional antenna assumption cannot predict and avoid this physical phenomenon, making it difficult to guarantee communication reliability during high-speed flight.

[0004] Furthermore, if attitude constraints related to Euler angles (roll and pitch) are directly introduced into trajectory planning, the complex inverse trigonometric nonlinear coupling between the angles and the control variables (acceleration) will result in a highly nonconvex optimization problem. Traditional nonconvex optimization algorithms often face challenges such as high computational complexity, slow convergence speed, and a tendency to get trapped in local optima when dealing with this type of problem, making it difficult to implement online trajectory replanning that meets real-time requirements on airborne platforms with limited computing power. Therefore, there is an urgent need for a trajectory optimization method that can accurately describe antenna attitude constraints and is easy to solve efficiently. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to provide a safe and energy-efficient trajectory solving method for unmanned aerial vehicles (UAVs) based on vertically polarized antennas. Addressing the communication blind zone characteristics of vertically polarized antennas in rotary-wing UAVs, this invention introduces intermediate variables and dynamic decoupling projection techniques to precisely transform the non-convex flight attitude constraints in Euler angle space into second-order cone (SOC) constraints and linear polyhedral cone constraints in acceleration space. This transforms the complex non-convex trajectory planning problem into an efficiently solvable convex optimization problem. This invention ensures minimal mechanical energy consumption during high-maneuverability flight of the UAV while strictly limiting the fuselage attitude to the safe envelope of the antenna gain, achieving coordinated optimization of communication quality assurance and flight dynamics control. This meets the dual requirements of efficient computation and secure communication for UAVs in complex application scenarios.

[0006] Technical solution: The present invention provides a safe and energy-saving trajectory solving method for unmanned aerial vehicles (UAVs) based on vertically polarized antennas, comprising the following steps:

[0007] Step 1: For communication scenarios using vertically polarized antennas, establish the geometric mapping relationship between antenna gain and UAV body attitude angle, and introduce dynamic coupling to derive an explicit function of antenna gain with respect to position and acceleration.

[0008] Step 2: Establish a six-degree-of-freedom rigid body dynamics model of the rotorcraft UAV based on the Newton-Euler equations, and clarify the coupling constraints between the fuselage attitude and the current acceleration vector and gravity vector;

[0009] Step 3: Construct the original trajectory optimization problem with the goal of minimizing the flight energy consumption of the UAV. The problem includes communication service quality (QoS) constraints and flight attitude safety boundary constraints.

[0010] Step 4: Using the continuous convex approximation SCA technique, the non-convex communication QoS constraints in the original trajectory optimization problem are transformed into linear inequality constraints;

[0011] Step 5: Establish acceleration decoupling projection in the body coordinate system, and transform the non-convex Euler angle flight attitude safety boundary constraint into a convex constraint in the acceleration space; among them, the roll angle constraint is transformed into a second-order cone SOC constraint, and the pitch angle constraint is transformed into a linear polyhedral cone constraint.

[0012] Step 6: Combining the transformed linear communication QoS constraints and attitude convex constraints, construct a second-order cone programming SOCP trajectory optimization model;

[0013] Step 7: Solve the SOCP trajectory optimization model using an iterative algorithm based on sequence convex approximation to obtain the optimal acceleration sequence, and then use the inverse solution to generate flight control commands that satisfy communication and dynamic constraints.

[0014] Furthermore, in step 1, establishing the geometric mapping relationship between antenna gain and UAV body attitude angle specifically involves: defining the off-axis angle as the angle between the UAV body's vertical axis and the line-of-sight vector; establishing a mathematical model based on the characteristics of vertically polarized antennas, where the antenna gain is proportional to the sine value of the off-axis angle; using the vector inner product to express the off-axis angle as the geometric relationship between the body axis vector and the normalized line-of-sight vector; and, based on the rigid body dynamics coupling lemma, representing the body's vertical axis as a vector uniquely determined by the current acceleration vector and gravitational acceleration.

[0015] Furthermore, in step 4, the non-convex communication QoS constraint is transformed into a linear inequality constraint by: rearranging the signal-to-noise ratio constraint based on the Friis transmission formula into a coupled form of distance and thrust; at the iterative working point, performing a first-order Taylor expansion on the convex function part of the constraint, and introducing slack variables or adopting a differential convex programming form for the non-convex part to obtain a set of linear constraints that satisfy dynamic feasibility.

[0016] The signal-to-noise ratio (SNR) of the communication link must meet a minimum threshold. Based on Friis's transmission formula and the gain model, the QoS constraint is expressed as:

[0017]

[0018] in, For transmission power, The reference channel power gain is G0, the maximum antenna gain coefficient is d[n], the line-of-sight vector is u[n], the acceleration vector is g, and the g-force acceleration is g.

[0019] Linearization is performed using the continuous convex approximation (SCA) technique, and the inequality is rearranged as follows:

[0020]

[0021] In the Next iteration point At this point, a first-order Taylor expansion is performed on the convex function part on the left side of the formula, and slack variables are introduced or a difference convex programming form is adopted for the non-convex part on the right side, ultimately transforming the complex physical coupling constraint into a set of linear inequality constraints:

[0022]

[0023] in To target position based on current flight status and acceleration The calculated gradient coefficients, is the constant term after Taylor expansion.

[0024] Furthermore, in step 5, the establishment of the acceleration decoupled projection in the body coordinate system specifically includes: constructing an intermediate heading coordinate system, and using a rotation matrix to decouple and project the horizontal acceleration in the inertial coordinate system into a longitudinal acceleration component along the fuselage longitudinal axis and a lateral acceleration component along the fuselage transverse axis; wherein, the longitudinal acceleration component corresponds to the fuselage pitch maneuver, and the lateral acceleration component corresponds to the fuselage roll maneuver;

[0025] Among them, the yaw angle of the drone Determined by the mission path tangential or planned separately, to independently control roll and pitch, the horizontal acceleration in the inertial frame is... Projected onto the coordinate system of the heading of the aircraft head;

[0026] Define a two-dimensional rotation matrix :

[0027]

[0028] Calculate the acceleration components along the longitudinal axis of the fuselage. and acceleration components along the fuselage transverse axis Its physical meaning is: Generated by the fuselage pitch, used to control forward and backward movement; Generated by the fuselage roll, used to control lateral movement, the projection formula is as follows:

[0029]

[0030] Through linear transformation, the acceleration originally coupled on the x and y axes is decoupled into longitudinal and lateral components that are directly related to the attitude angle.

[0031] Furthermore, in step 5, the transformation of the non-convex Euler angle flight attitude safety boundary constraint into a convex constraint in the acceleration space specifically involves: establishing a dynamic relationship between the lateral acceleration component and the roll angle and total thrust modulus based on the dynamic lateral projection; utilizing the monotonicity of the sine function within the safety range, transforming the roll angle interval constraint into a second-order cone constraint form with respect to the three-dimensional acceleration vector; the form of the second-order cone constraint is: the product of the Euclidean norm of the lateral acceleration component and a preset coefficient is less than or equal to the sum of the vertical acceleration component and the gravitational acceleration.

[0032] Furthermore, in step 5, the roll angle constraint is transformed into a second-order cone SOC constraint, and the pitch angle constraint is transformed into a linear polyhedral cone constraint. Specifically, based on the dynamic longitudinal projection, the ratio of the tangent value of the pitch angle to the longitudinal acceleration and the vertical resultant external force is established; using the monotonicity of the tangent function and the positive definiteness condition of lift, the pitch angle interval constraint is transformed into a set of linear inequalities in the three-dimensional acceleration space. The linear inequalities geometrically describe a polyhedral cone with the gravity vector starting point as its vertex.

[0033] Furthermore, in step 7, the iterative algorithm specifically includes the following steps:

[0034] Step 7.1: Generate initial trajectory guesses using linear interpolation based on the task start and end points;

[0035] Step 7.2: Construct an SOCP subproblem at the current iteration point that includes linearized communication constraints and precise attitude convex constraints, and introduce trust region constraints to limit the update step size;

[0036] Step 7.3: Solve the SOCP subproblem using the interior point method solver and update the trajectory solution;

[0037] Step 7.4: Determine whether the difference between the objective functions of two adjacent iterations satisfies the convergence tolerance. If it does, output the optimal solution; otherwise, return to step 7.2 to continue iterating.

[0038] 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.

[0039] 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.

[0040] The present invention also discloses a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the method of the present invention.

[0041] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0042] (1) This invention proposes a method for transforming the safe boundary of UAV flight attitude into a convex cone and solving the trajectory. By introducing intermediate variables and dynamic decoupling projection technology, the flight attitude constraints that are originally non-convex in Euler angle space are accurately transformed into second-order cone (SOC) constraints and linear polyhedral cone constraints in acceleration space. This method achieves coordinated optimization of UAV mechanical energy consumption and communication quality while taking into account the refined modeling of the quality of service (QoS) of vertical polarized antennas. It is applicable to various attitude-sensitive rotary-wing UAV application scenarios such as logistics transportation and power line inspection.

[0043] (2) This invention solves the problem in the prior art of communication interruption caused by the "top blind zone" of the vertically polarized antenna due to the tilt of the fuselage during high-maneuver flight of rotary-wing UAVs, as well as the problem of trajectory planning being difficult to solve due to the non-convex characteristics of traditional six-degree-of-freedom rigid body attitude constraints. By establishing an explicit coupling model of attitude-gain-acceleration, it ensures that the UAV can automatically limit the tilt angle to avoid the antenna null zone when generating the trajectory, which significantly improves the communication coverage stability and flight safety of the UAV during the execution of dynamic tasks.

[0044] (3) This invention employs a method combining precise convex transformation and sequential convex approximation (SCA) to solve the trajectory. In particular, it losslessly transforms complex trigonometric function attitude constraints into standard convex constraints, avoiding physical errors caused by traditional approximations. Compared with general non-convex optimization algorithms, this invention utilizes an efficient interior-point method to solve the trajectory, significantly improving the computation speed while ensuring global optimality and physical feasibility. This effectively reduces the occupation of limited airborne computing resources and meets the needs of online real-time trajectory replanning for UAV systems. Attached Figure Description

[0045] Figure 1 A flowchart of a method for transforming a convex cone into a safe boundary for the flight attitude of an unmanned aerial vehicle (UAV) and solving its trajectory;

[0046] Figure 2 For different methods of flight trajectory routes;

[0047] Figure 3 A comparison of the final energy consumption of different methods. Detailed Implementation

[0048] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0049] This invention proposes a method for transforming the flight attitude safety boundary of a UAV into a convex cone and solving its trajectory. This method is not limited to specific communication scenarios and is applicable to various rotary-wing UAV applications, including logistics transportation, power line inspection, and base station communication. Its core lies in introducing intermediate variables to transform the originally non-convex flight attitude constraints in Eulerian angle space into second-order cone (SOC) constraints and linear polyhedral cone constraints in acceleration space, thereby transforming the complex non-convex trajectory planning problem into an efficiently solvable convex optimization problem.

[0050] like Figure 1 As shown, the method of the present invention specifically includes the following steps:

[0051] Step 1. Refined Modeling of Quality of Service (QoS) Based on Vertical Polarized Antenna Model

[0052] In this embodiment, a high-precision communication constraint model with attitude awareness is established for communication scenarios using vertically polarized (VV) antennas. VV antennas (such as dipole antennas) have a typical "omnidirectional" radiation pattern, with their gain being greatest in the horizontal plane and greatest in the antenna axis (i.e., the vertical axis of the aircraft). There is a "null" in the direction of the antenna. Therefore, the tilt of the drone's fuselage during maneuvering flight will significantly change the coverage area of ​​the antenna's main lobe.

[0053] Step 1.1 Establish the geometric mapping between antenna gain and attitude angle

[0054] Define drones in The location of the time slot is The fixed location of ground users is The line-of-sight (LoS) vector between the two is defined as follows: Its Euclidean distance is .

[0055] Define the off-axis angle. Vertical axis of the drone body With line of sight vector The angle between them. For a VV antenna, its gain It is directly proportional to the sine of the off-axis angle (i.e., inversely proportional to the square of the cosine), and its mathematical model can be expressed as:

[0056]

[0057] in This is the maximum gain coefficient of the antenna. From vector geometry, we know that... It can be determined by the body axis vector The inner product representation of the normalized line-of-sight vector:

[0058]

[0059] Step 1.2 Introducing dynamic coupling and acceleration substitution

[0060] According to the rigid body dynamics coupling lemma in step 1.1, the vertical axis of the body (i.e., antenna pointing) is determined by the current acceleration vector. and gravity The only certainty, that is Substituting this relationship into the equation and The antenna gain can be obtained with respect to the optimization variable (position). and acceleration Explicit functions of )

[0061]

[0062] The above formula This profoundly reveals the impact of attitude on communication: when a UAV accelerates laterally to generate horizontal displacement (i.e., to generate roll or pitch angles), The direction of the antenna axis is deflected, causing the antenna axis to... Deviating from the vertical line. For VV antennas, if... When the drone is tilted at a large angle so that its "top" is pointing at the user, the gain will drop sharply to zero. Therefore, the optimization algorithm must limit the direction of acceleration to keep the drone in an appropriate attitude.

[0063] Step 2: Coupled Modeling of UAV Dynamics and Attitude

[0064] Unlike the simplified point mass model, this invention considers the six-degree-of-freedom rigid body characteristics of a rotary-wing UAV based on the Newton-Euler equations. Let the mass of the UAV be... The acceleration due to gravity is The inertial coordinate system is The body coordinate system is The translational dynamics equations of a drone are determined by the net external force, namely the total thrust generated by the rotor. The resultant force with gravity:

[0065]

[0066] in, This is the linear acceleration vector of the drone; It is the perpendicular unit vector in the inertial frame; For the body coordinate system The direction vector of the axis in the inertial frame (i.e., the direction of the fuselage's vertical axis) directly determines the line-of-sight direction of the airborne antenna.

[0067] Introducing virtual control variables This represents the three-dimensional acceleration vector of the UAV. The equation... Deformation, separating the thrust term:

[0068]

[0069] For the formula Taking the Euclidean norm from both sides. Since unit direction vector ( The required total thrust can be obtained as follows:

[0070]

[0071] Will Substitute return This allows us to obtain the explicit attitude-acceleration coupling constraints:

[0072]

[0073] The above derivation shows that for underactuated UAVs, their fuselage attitude It is not an independent control variable, but rather is controlled by its current acceleration vector. and gravitational acceleration It is uniquely determined. This model provides the physical basis for subsequently converting angular constraints into acceleration constraints.

[0074] Step 3. Formulating the problem

[0075] In this embodiment, the goal is to minimize the energy consumption of the UAV in discrete time, and a primitive trajectory optimization problem based on rigid body dynamics is constructed. Let the total mission duration be... Discretize it into There are 1 time slot, and the length of each time slot is 1. Define the set of optimization variables. , representing the position sequence, velocity sequence, and acceleration sequence of the UAV in all time slots, respectively.

[0076] The original trajectory planning problem (denoted as...) The model is as follows:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] Wherein, objective function The physical meaning is to minimize the control input energy (mechanical energy consumption) during flight. The constraints encompass the discrete-time state update equations, the position and velocity requirements of the mission start and end points, and the maximum flight speed. and maximum thrust limit .

[0087] In particular, the original problem includes explicit Euler angle safety constraints: and These represent the current acceleration vectors respectively. The roll and pitch angles are determined. Due to the complex inverse trigonometric nonlinear coupling between these two angles and acceleration, the constraints are nonconvex, making the original problem... It is difficult to solve directly.

[0088] Step 4. Construct and transform non-convex QoS constraints

[0089] In actual flight, to ensure flight stability and safety, the attitude angles (roll angles) of the UAV must be controlled. and pitch angle Strict restrictions must be imposed, that is, the following conditions must be met. and However, directly introducing Euler angle constraints into the optimization problem leads to a non-convex problem that is difficult to solve. Therefore, this invention performs a convex transformation through the following steps.

[0090] The signal-to-noise ratio (SNR) of the communication link must meet a minimum threshold. Based on Friis's transmission formula and the gain model described above, the QoS constraint is expressed as:

[0091]

[0092] in For transmission power, This is the power gain for the reference channel.

[0093] Observational It can be seen that this constraint applies to the optimization variables. and It is highly non-convex. In order to solve it using second-order cone programming (SOCP) or convex optimization algorithms, this invention uses the continuous convex approximation (SCA) technique to linearize it.

[0094] First, the inequality is rearranged as follows:

[0095]

[0096] In the Next iteration point Location, relative to The convex function part on the left (the coupling term of distance and thrust) is expanded using a first-order Taylor series. For the non-convex part on the right, relaxation variables are introduced or a difference-of-convex (DC) programming form is adopted. Finally, this complex physical coupling constraint is transformed into a set of linear inequality constraints.

[0097]

[0098] in To target position based on current flight status and acceleration The calculated gradient coefficients, This is the constant term after Taylor expansion. This linear constraint is embedded in the optimization problem model of step 3 to ensure that the generated trajectory automatically avoids the "top blind zone" of the VV antenna while satisfying dynamic feasibility, thus achieving coordinated optimization of communication quality and flight maneuvers.

[0099] Step 5. Handling and transforming non-convex angle constraints

[0100] Step 5.1 Establish acceleration decoupling projection in the body coordinate system

[0101] To map the complex Euler angle constraints to the linear acceleration space, it is first necessary to establish the projection relationship between the inertial coordinate system and the intermediate heading coordinate system.

[0102] Euler angles of the drone (roll) , looking up ,yaw The yaw angle is defined based on the rotation order. In trajectory planning, the yaw angle... Typically determined by the tangential direction of the mission path or planned separately, it can be considered a known quantity. To independently control roll and pitch, the horizontal acceleration in the inertial frame needs to be considered. Projected onto the coordinate system of the heading of the machine head.

[0103] Define a two-dimensional rotation matrix :

[0104]

[0105] Calculate the acceleration components along the longitudinal axis of the fuselage. and acceleration components along the fuselage lateral axis (Lateral) Its physical meaning is: Primarily generated by fuselage pitch, used to control forward and backward movement; Primarily generated by fuselage roll, it is used to control lateral movement. The projection formula is as follows:

[0106]

[0107] Through the above linear transformation, the acceleration originally coupled on the x and y axes is decoupled into longitudinal and lateral components directly related to the attitude angle, laying the geometric foundation for subsequent convex transformation.

[0108] Step 5.2 Second-order cone convex relaxation transformation of roll angle (Roll) constraint

[0109] Roll angle The rotation of the airframe around the longitudinal axis is defined. Based on the force analysis of the rotary-wing UAV, the lateral acceleration... It is generated by the lateral component of the total thrust vector.

[0110] According to the projection of Newton's second law onto the side of the body, the following dynamic equation exists:

[0111]

[0112] in, For quality, This represents the total thrust modulus generated by the rotor. From step 2, we know that the normalized specific force modulus... Therefore, the formula It can be rewritten as:

[0113]

[0114] The original safety constraints required that the roll angle be limited to a safe range, i.e. Because in The constraint is equivalent to the following: The sine function is monotonically increasing within the interval.

[0115]

[0116] Will Substitution and noticed (The drone must generate thrust to maintain flight), so we can move the denominator to the right side of the inequality and get:

[0117]

[0118] make The constant coefficients, For three-dimensional vector variables. Formula The standard form fully conforms to the second-order cone (SOC) constraint. .

[0119] Technical effect: Through the above derivation, the originally highly non-convex trigonometric function interval constraint is... The constraints are precisely and losslessly transformed into SOC constraints, a standard feature of convex optimization. This allows us to solve the problem directly using efficient interior-point solvers (such as MOSEK), ensuring the convergence and global optimality of the algorithm.

[0120] Step 5.3 Pitch-constrained linear polyhedral cone transformation

[0121] Pitch angle It defines the rotation of the aircraft around the transverse axis. It determines the proportion of the thrust vector distribution in the longitudinal and vertical directions.

[0122] According to dynamic geometry, the tangent of the pitch angle is equal to the ratio of the longitudinal acceleration to the net vertical force (vertical acceleration + gravity):

[0123]

[0124] The original pitch angle constraint is Considering the tangent function in The monotonicity of the expression is equivalent to the constraint that:

[0125]

[0126] In normal flight, drones must generate an upward lift component to counteract gravity, and therefore must meet physical constraints. Based on this positive definite condition, multiplying the denominator to both sides of the inequality while keeping the direction of the inequality signs unchanged, yields two linear inequalities:

[0127]

[0128] Combining the physical constraint of upward thrust, the pitch angle constraint is ultimately transformed into a set of linear constraints in three-dimensional acceleration space:

[0129]

[0130] in It is a constant.

[0131] Technical effect: Formula Geometrically, this describes a polyhedral cone with the gravity vector as its vertex. This transformation completely "reduces the dimensionality" of the original non-convex constraints, which included inverse trigonometric functions, into a simple set of linear inequalities. Computationally, the processing complexity of linear constraints is far lower than that of second-order cone constraints, which greatly reduces the computational load of the optimization problem, making real-time trajectory replanning possible on airborne platforms with limited computing power.

[0132] Step 6. Construct a trajectory optimization problem based on SOCP

[0133] Based on the above transformation, a general UAV trajectory optimization problem is constructed. To ensure that the generated trajectory is physically executable and meets mission requirements, constraints on flight start and end points, velocity boundary constraints, and thrust amplitude constraints must be introduced.

[0134] Establish the following second-order cone programming (SOCP) optimization model:

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] in, These are the start and end coordinates given for the task; The starting and ending speeds (usually set to zero, i.e., hovering takeoff and landing). The maximum total pulling force that the drone's power system can provide.

[0146] Step 7. Trajectory Iterative Solution Algorithm Based on Sequence Convex Approximation (SCA)

[0147] Since the communication QoS constraints established in step 4 contain non-convex terms, and in order to obtain an accurate energy-optimal solution, this invention designs an iterative optimization algorithm based on Sequential Convex Approximation (SCA). The core idea of ​​this algorithm is to transform the original non-convex problem into a series of locally convex approximation subproblems for solution. The attitude safety boundary constraints directly adopt the accurate convex forms (second-order cones and linear polyhedral cones) derived in steps 5.2 and 5.3, without approximation, thus ensuring strict satisfaction of physical feasibility.

[0148] The specific algorithm steps are as follows:

[0149] Step 7.1: Algorithm Initialization

[0150] Initialize the iteration counter Based on the task starting point and the end point Initial trajectory guess values ​​are generated using linear interpolation. Set the convergence tolerance. (like ) and maximum number of iterations .

[0151] Step 7.2: Constructing a convex approximation subproblem

[0152] In the In the next iteration, the non-convex communication QoS constraints in the original problem (formula) are addressed. ), at the current work point Perform a first-order Taylor expansion at the given point to construct a linear lower bound constraint:

[0153]

[0154] Meanwhile, to ensure the approximate accuracy of the Taylor expansion, a trust region constraint is introduced to limit the update step size in a single iteration:

[0155]

[0156] Step 7.3: Solve the second-order cone programming (SOCP) subproblem.

[0157] Construct the first The next iteration's convex subproblem. This subproblem combines the exact transformation of attitude constraints with linearized communication constraints, and its mathematical form is as follows:

[0158]

[0159] st — , , .

[0160] The SOCP subproblem described above can be solved using an interior-point solver (such as MOSEK or SDPT3) to obtain the optimal solution. .

[0161] Step 7.4: Iterative Update and Convergence Decision

[0162] Update the work point for the next iteration:

[0163]

[0164] Calculate the difference between the objective functions of two adjacent iterations. .

[0165] ·like If the algorithm converges, the final trajectory is output.

[0166] ·like and Then let Return to step 6.2 and continue iterating;

[0167] If the maximum number of iterations is reached, output the current optimal solution.

[0168] Step 7.5: Flight control command generation (inverse decoding output)

[0169] Obtain the final optimized acceleration sequence Then, using the reverse mapping relationship in steps 5.2 and 5.3, the attitude angle command to be executed in each time slot is calculated:

[0170]

[0171]

[0172] The above attitude command sequence and thrust command The data is sent to the underlying flight controller of the UAV to enable autonomous flight that meets safety communication and dynamic constraints.

[0173] like Figure 2 The diagram shows a comparison of trajectories obtained by the method proposed in this invention and traditional methods. It can be seen that the method proposed in this invention utilizes attitude control for direct flight, reducing detours and additional maneuvers, thus saving flight time and energy consumption. Figure 3 The diagram shows a comparison of energy consumption between the two methods. The method proposed in this invention can achieve a 24% reduction in energy consumption under the same constraints, which is a significant energy saving.

[0174] The method described in this embodiment achieves a significant improvement in computational efficiency and trajectory quality while ensuring that the UAV's flight attitude remains within the safety envelope. Compared to traditional non-convex optimization algorithms, this method improves the solution speed by several times and avoids the risk of getting trapped in local optima, making it particularly suitable for online trajectory planning systems for UAVs with high real-time requirements.

Claims

1. A vertical polarization antenna-based unmanned aerial vehicle control and management integrated safe energy-saving trajectory solving method, characterized in that, Includes the following steps: Step 1: For communication scenarios using vertically polarized antennas, establish the geometric mapping relationship between antenna gain and UAV body attitude angle, and introduce dynamic coupling to derive an explicit function of antenna gain with respect to position and acceleration. Step 2: Establish a six-degree-of-freedom rigid body dynamics model of the rotorcraft UAV based on the Newton-Euler equations, and clarify the coupling constraints between the fuselage attitude and the current acceleration vector and gravity vector; Step 3: Construct the original trajectory optimization problem with the goal of minimizing the flight energy consumption of the UAV. The problem includes communication service quality (QoS) constraints and flight attitude safety boundary constraints. Step 4: Using the continuous convex approximation SCA technique, the non-convex communication QoS constraints in the original trajectory optimization problem are transformed into linear inequality constraints; Step 5: Establish acceleration decoupling projection in the body coordinate system, and transform the non-convex Euler angle flight attitude safety boundary constraint into a convex constraint in the acceleration space; among them, the roll angle constraint is transformed into a second-order cone SOC constraint, and the pitch angle constraint is transformed into a linear polyhedral cone constraint. Step 6: Combining the transformed linear communication QoS constraints and attitude convex constraints, construct a second-order cone programming SOCP trajectory optimization model; Step 7: Solve the SOCP trajectory optimization model using an iterative algorithm based on sequence convex approximation to obtain the optimal acceleration sequence, and then use the inverse solution to generate flight control commands that satisfy communication and dynamic constraints.

2. The unmanned aerial vehicle control and safety integrated energy-saving trajectory solving method based on vertical polarization antenna according to claim 1, characterized in that, In step 1, establishing the geometric mapping relationship between antenna gain and UAV body attitude angle specifically involves: defining the off-axis angle as the angle between the UAV body's vertical axis and the line-of-sight vector; establishing a mathematical model based on the characteristics of vertically polarized antennas, where the antenna gain is proportional to the sine value of the off-axis angle; using the vector inner product to express the off-axis angle as the geometric relationship between the body axis vector and the normalized line-of-sight vector; and, based on the rigid body dynamics coupling lemma, representing the body's vertical axis as a vector uniquely determined by the current acceleration vector and gravitational acceleration. 3.The unmanned aerial vehicle control and safety energy-saving trajectory solving method based on vertical polarization antenna according to claim 1, wherein, In step 4, the non-convex communication QoS constraint is transformed into a linear inequality constraint by: rearranging the signal-to-noise ratio constraint based on the Friis transmission formula into a coupled form of distance and thrust; at the iterative working point, performing a first-order Taylor expansion on the convex function part of the constraint, and introducing slack variables or adopting a differential convex programming form for the non-convex part to obtain a set of linear constraints that satisfy dynamic feasibility. The signal-to-noise ratio, SNR, of the communication link needs to satisfy a minimum threshold According to the Friis transmission formula, in combination with the gain model, the QoS constraint is expressed as: ； wherein is the transmit power, is the reference channel power gain, G0is the antenna maximum gain coefficient, d[n] is the line-of-sight vector, u[n] is the acceleration vector, and g is the gravitational acceleration; Linearization is performed using the continuous convex approximation (SCA) technique, and the inequality is rearranged as follows: ； At the point of the first iteration , the first-order Taylor expansion is performed on the convex function part on the left side of the formula, and the relaxation variable is introduced or the difference convex programming form is adopted on the non-convex part on the right side, and finally the complex physical coupling constraint is converted into a set of linear inequality constraints: ； wherein is a gradient coefficient calculated based on the current flight state for the position and acceleration , is a constant term after Taylor expansion.

4. The unmanned aerial vehicle control and safety integrated energy-saving trajectory solving method based on vertical polarization antenna according to claim 1, characterized in that, In step 5, the establishment of the acceleration decoupled projection in the body coordinate system specifically includes: constructing an intermediate heading coordinate system, and using a rotation matrix to decouple and project the horizontal acceleration in the inertial coordinate system into a longitudinal acceleration component along the fuselage longitudinal axis and a lateral acceleration component along the fuselage transverse axis; wherein, the longitudinal acceleration component corresponds to the fuselage pitch maneuver, and the lateral acceleration component corresponds to the fuselage roll maneuver; wherein the yaw angle of the drone Decided by the tangent of the mission path or planned separately, for independent control of roll and pitch, the horizontal acceleration in the inertial system Projected into the nose heading coordinate system; Defining a two-dimensional rotation matrix : ； Acceleration component along the longitudinal axis of the fuselage Acceleration component along the lateral axis of the fuselage ; its physical meaning is: Generated by the pitch of the fuselage, used to control the advance and retreat; Generated by the roll of the fuselage, used to control the side shift, the projection formula is as follows: ； Through linear transformation, the acceleration originally coupled on the x and y axes is decoupled into longitudinal and lateral components that are directly related to the attitude angle.

5. The unmanned aerial vehicle control and safety integrated energy-saving trajectory solving method based on vertical polarization antenna according to claim 4, characterized in that, In step 5, the transformation of the non-convex Euler angle flight attitude safety boundary constraint into a convex constraint in the acceleration space specifically involves: establishing the dynamic relationship between the lateral acceleration component and the roll angle and total thrust modulus based on the dynamic lateral projection; utilizing the monotonicity of the sine function within the safety range, transforming the roll angle interval constraint into a second-order cone constraint form with respect to the three-dimensional acceleration vector; the form of the second-order cone constraint is: the product of the Euclidean norm of the lateral acceleration component and a preset coefficient is less than or equal to the sum of the vertical acceleration component and the gravitational acceleration.

6. The unmanned aerial vehicle control and safety integrated energy-saving trajectory solving method based on vertical polarization antenna according to claim 1, characterized in that, In step 5, the roll angle constraint is transformed into a second-order cone SOC constraint, and the pitch angle constraint is transformed into a linear polyhedral cone constraint. Specifically, based on the longitudinal projection of the dynamics, the ratio of the tangent of the pitch angle to the longitudinal acceleration and the resultant vertical external force is established; using the monotonicity of the tangent function and the positive definiteness of the lift, the pitch angle interval constraint is transformed into a set of linear inequalities in the three-dimensional acceleration space. The linear inequalities geometrically describe a polyhedral cone with the gravity vector starting point as its vertex.

7. The method for solving the integrated communication and control, safe and energy-saving trajectory of a UAV based on a vertically polarized antenna according to claim 1, characterized in that, Step 7, the iterative algorithm specifically includes the following steps: Step 7.1: Generate initial trajectory guesses using linear interpolation based on the task start and end points; Step 7.2: Construct an SOCP subproblem at the current iteration point that includes linearized communication constraints and precise attitude convex constraints, and introduce trust region constraints to limit the update step size; Step 7.3: Solve the SOCP subproblem using the interior point method solver and update the trajectory solution; Step 7.4: Determine whether the difference between the objective functions of two adjacent iterations satisfies the convergence tolerance. If it does, output the optimal solution; otherwise, return to step 7.2 to continue iterating.

8. 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.

9. 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.

10. A computer program product comprising a computer program / instructions, 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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