A dynamic gliding flight trajectory planning method for a fixed-wing aircraft

Abstract

The present application relates to the technical field of aircraft trajectory planning, in particular to a dynamic gliding flight trajectory planning method for fixed-wing aircraft, comprising: establishing an optimal control problem model with the minimum system energy consumption as the objective function; obtaining a nonlinear programming problem model; obtaining a single optimal trajectory and corresponding flight state data corresponding to the minimum system energy consumption in the unpowered gliding flight stage and powered recovery flight stage; and obtaining a multi-section dynamic gliding flight trajectory. The present application avoids the iterative process of solving nonlinear equations, significantly reduces the computational burden of single iteration, greatly improves the solution efficiency and robustness of the entire optimal control problem, and realizes stable periodic energy-gaining gliding flight by designing a multi-section dynamic gliding flight strategy for the unpowered gliding flight stage and the powered recovery flight stage to accurately compensate for the energy deficit of flight.

Description

Technical Field

[0001] This invention relates to the field of aircraft trajectory planning technology, and more specifically to a method for dynamic gliding flight trajectory planning for fixed-wing aircraft. Background Technology

[0002] In the context of the low-altitude economy, unmanned aerial vehicles (UAVs), as carriers of flight missions, are increasingly widely used in surveying, monitoring, and communication relay, making the demand for long endurance and extended flight time more urgent. Small and medium-sized UAVs mostly rely on batteries or fuel, and their flight time is limited by their onboard energy storage capacity, making it difficult to meet the long-term operational requirements of complex tasks. Given the limited onboard energy supply of UAVs, acquiring energy from the natural environment in real time during flight has become crucial to overcoming the endurance bottleneck.

[0003] Wind fields, as a widely existing renewable energy source in the atmosphere, offer potential for continuous flight of drones. Changes in wind speed represent air movement, and to a certain extent, these changes in wind speed characterize changes in air energy, which can be utilized by drones. Drawing inspiration from the principles of birds soaring through wind fields, the capture of wind energy through dynamic gliding has been theoretically and experimentally verified.

[0004] The idealized unpowered gliding process in existing technologies, which can maintain energy balance and achieve an ideal cycle without losing airspeed, is based on the premise that the aircraft itself has extremely high aerodynamic efficiency (i.e., high lift-to-drag ratio) and strong attitude transformation capabilities. For example, gliders designed specifically for gliding or the specific configuration of birds such as biomimetic albatrosses usually have the characteristics of high aspect ratio wings, slender fuselages, single power plants, and low load capacity.

[0005] However, in the context of the low-altitude economy, various fixed-wing UAVs with different configurations and sizes are designed and developed based on flight missions. They do not have the special flight capabilities of high maneuverability and large lift-to-drag ratio required for wind field energy acquisition, and generally carry payloads of a certain size / weight. For conventional fixed-wing UAVs whose aerodynamic parameters are not optimized for dynamic gliding and whose attitude change capabilities are poor, relying solely on unpowered gliding to complete a round of travel will inevitably cause unavoidable airspeed (i.e. kinetic energy) loss due to aerodynamic drag, thus making it impossible to maintain periodic flight motion. Secondly, the existing dynamic gliding flight strategies are designed for unpowered gliding aircraft under ideal wind field conditions. Although the wind field energy acquisition efficiency is extremely high, it cannot be extended to general fixed-wing aircraft flight in actual wind field environments. That is, the existing technology has two constraints on efficient wind field energy acquisition flight: (1) the wind field of the flight environment is an ideal gradient wind field; (2) the flight strategy and trajectory are strictly constrained, and the trajectory presents a standard figure-eight or S-shape. In practice, it is assumed that the aircraft has excellent maneuverability such as agile turning and rapid climbing, without considering whether the dynamic performance of the aircraft can achieve it. However, the wind field in the actual low-altitude flight environment is a time-varying wind field, with the wind size and direction changing with time and location. In addition, most small and medium-sized general-purpose fixed-wing aircraft are designed for low-speed flight missions, with limited maneuverability and various strict dynamic behavior constraints, making it impossible to fly strictly according to a standard figure-eight or S-shaped trajectory, and thus unable to effectively capture wind energy.

[0006] Therefore, existing dynamic gliding flight technology for aircraft is only designed for ideal wind field conditions and ideal gliding aircraft. When facing real low-altitude wind field environments, conventional fixed-wing aircraft find it difficult to obtain energy from the wind field of the flight environment when directly using dynamic gliding flight methods.

[0007] Therefore, there is a need to provide a dynamic gliding flight trajectory planning method for fixed-wing aircraft to solve the above problems. Summary of the Invention

[0008] To address the problem that conventional fixed-wing aircraft struggle to extract energy from wind fields when directly using dynamic gliding flight methods in real low-altitude wind environments, this invention provides a dynamic gliding flight trajectory planning method for fixed-wing aircraft to solve the existing problems.

[0009] The present invention provides a dynamic gliding flight trajectory planning method for a fixed-wing aircraft, the method employing the following technical solution, including:

[0010] A three-degree-of-freedom flight dynamics model of an aircraft in a gradient wind field is established based on an exponential wind field model in the northeast-northeast coordinate system. A wind field flight energy consumption assessment model is constructed based on the three-degree-of-freedom flight dynamics model and the power chain model of the energy system, electronic governor, motor and propeller in the aircraft. The system energy consumption is evaluated using the wind field flight energy consumption assessment model. According to the flight performance constraints and flight boundary constraints of the aircraft in the northeast-northeast coordinate system, an optimal control problem model with the minimum system energy consumption as the objective function is established.

[0011] The Legendre-Gauss-Radow collocation method is used to numerically transform the optimal control problem model into a nonlinear programming problem model.

[0012] The propeller speed, airflow roll angle, and angle of attack are used as control variables in the algorithm for solving the nonlinear programming problem. Numerical optimization algorithms such as sequential quadratic programming are used to solve the nonlinear programming problem model, resulting in a set of optimal control variable sequences that satisfy all flight performance constraints and flight boundary constraints and minimize system energy consumption. The optimal control variable sequence is used as the optimal control command for the current unpowered gliding flight phase. Flight simulation is performed based on the optimal control command, and the three-degree-of-freedom flight dynamics model is solved by integration to obtain the single optimal trajectory and its corresponding flight state data when the system energy consumption is minimized in the unpowered gliding flight phase and the powered recovery flight phase.

[0013] The flight status data at the end of the previous flight phase is used as the starting flight boundary constraint for the trajectory planning of the next flight phase of the same flight phase. The flight trajectory with the minimum system energy consumption is replanned until the flight status data of the aircraft reaches the preset flight termination boundary. Then the optimal flight trajectory for each flight phase is planned. The optimal flight trajectory of the unpowered gliding flight phase and the flight trajectory of the powered recovery flight phase are combined to obtain a multi-segment dynamic gliding flight trajectory.

[0014] In the powered flight recovery phase: the propeller speed constraint is relaxed from zero to within its physically feasible operating range; a path constraint with propeller thrust greater than zero is added; and in the flight boundary constraints, the aircraft's flight status data is restored to the initial state value at the beginning of the current unpowered gliding cycle.

[0015] A further technical solution of the present invention is that the expressions for the flight performance constraints and flight boundary constraints of the aircraft in the northeast celestial coordinate system are as follows:

[0016] The flight performance constraints are as follows:

[0017]

[0018] In the formula, Indicates that the aircraft is in The height of a moment; Indicates the minimum altitude of the aircraft; Indicates the maximum altitude of the aircraft; Indicates that the aircraft is in Airspeed at any given moment; Indicates the minimum airspeed of the aircraft; This indicates the aircraft's maximum airspeed; Indicates that the aircraft is in The maximum airflow trajectory inclination at any given moment; Indicates that the aircraft is in Inclination angle of airflow trajectory at any given moment; Indicates that the aircraft is in Rate of change of airflow trajectory inclination angle at any given time; Indicates that the aircraft is in The rate of change of the maximum airflow trajectory inclination at any given moment; Indicates that the aircraft is in The azimuth angle of the maximum airflow trajectory at any given moment; Indicates that the aircraft is in Azimuth of the airflow trajectory at any given moment; Indicates that the aircraft is in Rate of change of azimuth angle of airflow trajectory at any time; Indicates that the aircraft is in The rate of change of the azimuth angle of the airflow trajectory at any given moment; Indicates in Angle of attack at any moment; Indicates the minimum angle of attack; Indicates the maximum angle of attack; Indicates in The airflow roll angle at any given moment; Indicates the maximum airflow roll angle; Indicates in The propeller rotation speed at any given moment; Indicates the minimum propeller speed; Indicates the maximum propeller speed;

[0019] The flight boundary constraints are as follows:

[0020]

[0021] In the formula, The horizontal coordinate indicates the position at the start of the flight phase; The horizontal coordinate indicates the position at the end of the flight phase; Indicates the flight altitude at the start of the flight phase; Indicates the flight altitude at the end of the flight phase; This indicates the airspeed of the aircraft at the start of the flight phase. This indicates the airspeed of the aircraft at the end of its flight phase. Indicates the inclination angle of the airflow path at the start of the flight phase; Indicates the inclination angle of the airflow path at the end of the flight phase; Indicates the azimuth angle of the airflow path at the start of the flight phase; Indicates the azimuth angle of the airflow track at the end of the flight phase; Indicates the end time of the flight phase; Indicates the start time of the flight phase.

[0022] A further technical solution of the present invention is to establish a wind farm flight energy consumption assessment model, and to obtain the energy consumption of the aircraft at each stage based on the wind farm flight energy consumption assessment model, wherein the expression of the wind farm flight energy consumption assessment model is:

[0023]

[0024]

[0025] In the formula, This indicates the energy consumption of the energy system when the aircraft is flying in a wind field; This indicates the output power of the energy system when the aircraft is flying in a wind field; Indicates the output voltage of the energy system; Indicates the output current of the energy system; Indicates the input voltage of the electronic speed controller; This indicates the input current of the electronic speed controller; This indicates the input voltage of the motor; This indicates the input current of the motor; Indicates the internal resistance of the electronic speed controller; This represents the correction factor; where, during the unpowered gliding flight phase... .

[0026] A further technical solution of the present invention is that the objective function is:

[0027]

[0028] In the formula, Represents the objective function value; This represents the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field. This represents the output power of the energy system when the aircraft is flying in a wind field. The system energy consumption of the aircraft is 0 when the flight phase is the unpowered gliding flight phase. Indicates the end time of the flight phase; Indicates the start time of the flight phase; This represents the rate of change of energy within the energy system itself, i.e., the output power of the energy system. It represents the displacement in the flight direction over the entire time period.

[0029] A further technical solution of the present invention is that the expression for the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field is:

[0030]

[0031] In the formula, This represents the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field. Indicates the airspeed of the aircraft; This indicates the rate of change of the aircraft's airspeed; Indicates the mass of the aircraft; Represents gravitational acceleration; Indicates propeller thrust; This indicates the drag experienced by the aircraft; Indicates the vertical velocity of the aircraft; This represents the energy power absorbed by the gradient wind field when the aircraft is flying in the gradient wind field.

[0032] A further technical solution of the present invention is that the expression for the energy power absorbed by the gradient wind field when the aircraft flies in the gradient wind field is:

[0033]

[0034] In the formula, Indicates reference altitude; Indicates the wind speed at the reference altitude; Indicates flight altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. Indicates the inclination angle of the airflow path; Indicates the azimuth angle of the airflow path; It represents a dimensionless power law exponent, the value of which is used to determine the shape and curvature of the wind speed profile.

[0035] A further technical solution of the present invention is that the expression of the three-degree-of-freedom flight dynamics model is:

[0036]

[0037] In the formula, This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; Indicates the mass of the aircraft; Indicates propeller thrust; This indicates the drag experienced by the aircraft; This indicates the lift force acting on the aircraft. Represents gravitational acceleration; Indicates the inclination angle of the airflow path; This represents the rate of change of the airflow trajectory inclination angle; Indicates the azimuth angle of the airflow path; This indicates the rate of change of the azimuth angle of the airflow path; Indicates the airspeed of the aircraft; This indicates the rate of change of the aircraft's airspeed; This indicates the airflow roll angle.

[0038] A further technical solution of the present invention is that the expressions for the drag and lift experienced by the aircraft are:

[0039]

[0040] In the formula, Indicates air density; Indicates the reference area of ​​the wing; Indicates the drag coefficient; This represents the lift coefficient.

[0041] A further technical solution of the present invention is that the expression for wind speed under a gradient wind field is:

[0042]

[0043] In the formula, This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; Represents flight altitude in gradient wind field Wind speed at the location; Indicates reference altitude; Indicates the wind speed at the reference altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. It represents a dimensionless power law exponent, the value of which is used to determine the shape and curvature of the wind speed profile.

[0044] A further technical solution of the present invention includes a trajectory planning step based on a combination of decoupled 3D path and inverse dynamics verification, which includes:

[0045] The starting pose of the multi-segment dynamic gliding flight trajectory of the aircraft in the wind field is taken as the starting target pose, and the ending pose of the flight trajectory is taken as the ending target pose.

[0046] In a horizontal two-dimensional plane, the starting pose of the aircraft is connected to the starting target pose, and the ending pose is connected to the ending target pose. By comparing various combinations of "circular arc-straight line-circular arc", the path with the shortest total length is selected as the optimal horizontal path.

[0047] Using the horizontal flight distance (optimal horizontal path) as a benchmark, the optimal vertical change profiles corresponding to the starting point altitude and climb angle to the target altitude and climb angle, and the ending point altitude and climb angle to the target altitude and climb angle are planned.

[0048] By fusing the optimal horizontal path and the optimal vertical change profile, a three-dimensional spatial kinematic trajectory that satisfies all start and end state constraints is reconstructed.

[0049] Inverse dynamics verification of the three-dimensional kinematic trajectory: By inversely solving the three-degree-of-freedom flight dynamics model of the aircraft, the control input sequence required to track the three-dimensional kinematic trajectory is calculated. If all control inputs in the control input sequence are within the flight performance constraints and flight boundary constraints of the aircraft, the three-dimensional kinematic trajectory is confirmed as a completely feasible trajectory. If all control inputs in the control input sequence exceed the flight performance constraints and flight boundary constraints, the approach and exit distances of the trajectory planning are increased to satisfy the constraints, and the three-dimensional kinematic trajectory is reacquired until the reacquired three-dimensional kinematic trajectory satisfies inverse dynamics.

[0050] The beneficial effects of this invention are:

[0051] 1. This invention establishes an exponential wind field model, which reflects the velocity gradient characteristics of a real wind field through a nonlinear function. By adjusting key parameters such as the power-law exponent and reference wind speed, it characterizes the wind field environment under different real-world scenarios. Secondly, based on the exponential wind field model, a three-degree-of-freedom flight dynamics model of the aircraft in a gradient wind field is derived using a three-degree-of-freedom dynamics model. This model is further coupled with a powertrain model including the energy system, electronic governor, motor, and propeller, thereby constructing a wind field flight energy consumption assessment model. This model is used to accurately calculate the nonlinear changes in energy system efficiency caused by dynamic changes in the power system load under complex flight profiles, achieving a high-precision assessment of system energy consumption. Finally, in the optimal control... In solving the optimal control problem, propeller speed is selected as the control variable to replace the traditional method of using thrust as the control variable. At the same time, the airflow roll angle and angle of attack are kept as other control variables. By using propeller speed as a direct control quantity, the calculation process from this speed to thrust and system power consumption becomes a forward explicit solution process. This avoids the iterative solution of nonlinear equations that must be performed to obtain the propeller speed that meets the specific thrust requirement, significantly reducing the computational burden of a single iteration and improving the overall efficiency and robustness of solving the optimal control problem. Through the method of this invention, the unpowered gliding flight stage and the powered recovery flight stage are further decoupled to form a multi-stage dynamic gliding flight strategy to accurately compensate for the flight energy deficit and achieve periodic and sustainable energy-saving flight.

[0052] 2. Secondly, a trajectory planning method based on decoupled 3D path and inverse dynamics verification was established, which solved the problem of trajectory connection between UAVs and specific wind field entry points when transitioning from arbitrary cruise states. It integrates isolated gliding cycles into a complete end-to-end mission profile, thereby making the aircraft path planning clearly integrated into the flight process. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart illustrating a dynamic gliding flight trajectory planning method for a fixed-wing aircraft according to the present invention.

[0055] Figure 2 This is a schematic diagram of the dynamic gliding force analysis of the UAV in this invention;

[0056] Figure 3This is a flowchart of the trajectory planning steps based on the combination of decoupled 3D path and inverse dynamics verification in Embodiment 2 of the present invention;

[0057] Figure 4 This is a geometric schematic diagram of the fixed-wing unmanned aerial vehicle in Embodiment 2 of the present invention;

[0058] Figure 5 This is a graph showing the change of wind speed with height under different power-law exponents in Embodiment 2 of the present invention;

[0059] Figure 6 This is a graph showing the wind speed versus altitude at different reference wind speeds in Embodiment 2 of the present invention.

[0060] Figure 7 This is a schematic diagram of the three-dimensional spatial kinematic trajectory obtained by simulation using the method of Embodiment 2 of the present invention;

[0061] Figure 8 A graph showing the battery output power during the aircraft's gliding process;

[0062] Figure 9 A graph showing the cumulative energy consumed by the battery during the aircraft's gliding process;

[0063] Figure 10 This is a schematic diagram showing the variation of wind speed near the Earth's surface with altitude.

[0064] Figure 11 This is a schematic diagram showing how the magnitude of the wind gradient near the Earth's surface varies with altitude.

[0065] Figure 12 This is a schematic diagram of an aircraft gaining energy by gliding in a wind gradient. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Existing research has found that birds can obtain energy from environmental wind fields to sustain their flight. Subsequent studies have also shown that albatrosses can achieve long-distance, long-duration flights with almost no wing flapping, obtaining energy from updrafts on the leeward side of ocean waves and strong gradient wind fields near the sea surface, and even from atmospheric turbulence and gusts. Therefore, current research indicates that one important way for drones to increase flight time is to obtain energy from the widely existing wind fields in nature. The energy contained in wind fields is mainly utilized by drones in two forms: updrafts (such as thermal currents and mountain-based updrafts) and gradient winds. Updrafts are mainly found in plateau and mountainous areas, making them difficult to utilize. Wind gradients, however, are widely present in nature, and their range overlaps with the flight altitude of small and medium-sized drones, thus offering significant potential for utilization. A wind gradient refers to the form of wind field where horizontal wind speed varies with altitude. Due to factors such as atmospheric heat conduction and friction between the ground and sea surface, it exists widely above the ground and sea surface, in upper-level inversion layers, and even in hurricanes. Figure 10 and Figure 11 As can be seen, the wind gradient is very large near the Earth's surface, even reaching 6 s⁻¹, but it decreases rapidly with increasing altitude. The basic principle of birds or drones using wind gradients for energy harvesting is simple. When the horizontal wind speed increases with altitude, birds or drones climb against the wind to supplement their airspeed from the wind, thus harvesting energy. They then turn and descend with the wind to further harvest energy, forming a closed loop trajectory. When this closed loop achieves energy balance, it can be considered an energy closed loop. A complete flight cycle begins in the low-altitude region of the gradient wind field and mainly consists of four consecutive stages: (1) low-altitude headwind turn, where the aircraft first faces the wind direction and begins to turn sideways into the headwind with a certain roll angle; (2) headwind climb, using the energy provided by the oncoming wind to climb to the predetermined altitude; (3) high-altitude tailwind turn, making a turn in the opposite direction at high altitude so that the nose faces the wind direction; (4) tailwind glide, gliding from the high altitude to the initial low-altitude position with the wind, finally completing a cycle. The core feature of this mode is that after completing a cycle, the aircraft can return to the initial flight altitude and restore the initial airspeed and attitude angle, but gains a net displacement on the horizontal plane. This characteristic makes it extremely valuable for application, just as albatrosses use a similar strategy for long-distance migration. UAVs can also achieve long-distance navigation in a specific direction by continuously repeating this cycle according to mission requirements. Figure 12 As shown, Figure 12In the diagram, 1 represents the uphill climb against the wind, 3 represents the downhill descent with the wind, and 2 and 4 represent the turning process. Since gliding in a wind gradient requires birds or drones to constantly maneuver to acquire energy from the wind field that varies with altitude, gliding in a wind gradient is called "dynamic gliding." Based on this, this invention proposes:

[0068] Example 1

[0069] An embodiment of a dynamic gliding flight trajectory planning method for fixed-wing aircraft, such as... Figure 1 As shown, it includes:

[0070] S1. Establish an optimal control problem model with the objective function of minimizing system energy consumption;

[0071] Specifically, a three-degree-of-freedom flight dynamics model of the aircraft in a gradient wind field is established based on an exponential wind field model in the northeast-northeast coordinate system. A wind field flight energy consumption assessment model is constructed based on the three-degree-of-freedom flight dynamics model and the power chain model of the battery, electronic governor, motor and propeller in the aircraft. The wind field flight energy consumption assessment model is used to evaluate the system energy consumption. According to the flight performance constraints and flight boundary constraints of the aircraft in the northeast-northeast coordinate system, an optimal control problem model with the minimum system energy consumption as the objective function is established.

[0072] For example, in this embodiment, step S11, the step of constructing the gradient wind field model, is as follows:

[0073] Gradient wind field, also known as horizontal wind shear, is an atmospheric phenomenon where wind speed varies vertically along a given direction. This gradient of wind speed with altitude is a prerequisite physical condition for UAVs to perform dynamic gliding and continuously harvest energy from it. To conduct in-depth analysis of the energy harvesting mechanism during dynamic gliding and to carry out trajectory planning research, it is essential to first establish a mathematical model that accurately describes the characteristics of the gradient wind field. Under different atmospheric conditions, the variation of wind speed with altitude may exhibit linear or nonlinear characteristics. Various mathematical models have been proposed to approximate horizontal wind shear, among which the exponential model is the most widely used. This exponential model, also known as the power-law model of wind speed profile, is one of the most widely used nonlinear wind shear models in engineering and research, often used to describe wind speed profiles near the sea surface, ridges, or undulating surfaces. In this exponential model, the wind speed increases exponentially before reaching the free flow value, as expressed by:

[0074]

[0075] In the formula, Represents flight altitude in gradient wind field Wind speed at the location; Indicates reference altitude; Indicates the wind speed at the reference altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. The dimensionless power-law exponent is used to determine the shape and curvature of the wind speed profile; the expression for the wind shear gradient as a function of height in this exponential model is:

[0076]

[0077] In the formula, This represents the wind shear gradient.

[0078] For example, in this embodiment, step S12, establishing a three-degree-of-freedom flight dynamics model of the aircraft in a gradient wind field under the northeast-northeast coordinate system, is as follows:

[0079] To accurately analyze the mechanism and optimize the trajectory of a UAV's dynamic gliding process in a gradient wind field, it is first necessary to establish a three-degree-of-freedom flight dynamics model describing this process. For example... Figure 2 As shown, the forces acting on the spacecraft are analyzed in the northeast-central inertial coordinate system, and its complete nonlinear dynamic equations are derived. For ease of analysis, it is assumed that the Earth is a non-rotating plane, and the motion of the spacecraft is described by a set of state variables, including its position in the northeast-central inertial coordinate system. ,in This represents flight altitude. In addition, a key variable describing the motion of an aircraft also includes its airspeed relative to the air. airflow trajectory inclination and airflow trajectory azimuth Therefore, the system's state variables are: In a gradient wind field, the inertial velocity of the aircraft... It is airspeed With local wind speed The vector sum of wind speed Mainly related to flight altitude Related, wind speed Component form ,in, The inertial velocity is usually assumed to be zero. airspeed The relationship is:

[0080]

[0081] In the formula, This indicates the spacecraft's position in the northeast inertial coordinate system. The inertial velocity component along the axial direction (i.e., the velocity component of the aircraft along the axial direction) Ground velocity in the axial direction); This indicates the spacecraft's position in the northeast inertial coordinate system. The inertial velocity component along the axial direction (i.e., the velocity component of the aircraft along the axial direction) Ground velocity in the axial direction); This indicates the spacecraft's position in the northeast inertial coordinate system. The inertial velocity component in the axial direction (i.e., the vertical velocity of the aircraft). This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction.

[0082] like Figure 2 As shown, the aircraft is subjected to three forces: aerodynamics (lift) and resistance propeller thrust ,gravity Assuming no sideslip effects, and based on Newton's second law, decomposed in the airflow coordinate system, we can obtain the following set of differential equations describing the three-degree-of-freedom flight dynamics model of the aircraft:

[0083]

[0084] In the formula, This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; Indicates the mass of the aircraft; Indicates propeller thrust; This indicates the drag experienced by the aircraft; This indicates the lift force acting on the aircraft. Represents gravitational acceleration; Indicates the inclination angle of the airflow path; This represents the rate of change of the airflow trajectory inclination angle; Indicates the azimuth angle of the airflow path; This indicates the rate of change of the azimuth angle of the airflow path; Indicates the airspeed of the aircraft; This indicates the rate of change of the aircraft's airspeed; This indicates the airflow roll angle.

[0085] To facilitate state integration and control applications, the differential equations of the three-degree-of-freedom flight dynamics model of the aircraft can be rearranged to obtain explicit expressions describing the rate of change of airspeed, the rate of change of airflow trajectory inclination angle, and the rate of change of airflow trajectory azimuth angle:

[0086]

[0087] In the formula, This indicates the rate of change of the aircraft's airspeed; This represents the rate of change of the airflow trajectory inclination angle; This represents the rate of change of the azimuth angle of the airflow trajectory; according to the chain rule, the rate of change of wind speed can be expressed as:

[0088]

[0089] Due to the wind speed in the gradient wind field Flight altitude only The function, that is, in the gradient wind field along the northeast inertial coordinate system. The expression for wind speed under time gradient wind field in the axial direction is:

[0090]

[0091] In the formula, This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; Represents flight altitude in gradient wind field Wind speed at the location; Indicates reference altitude; Indicates the wind speed at the reference altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. The exponent represents a dimensionless power law, the value of which determines the shape and curvature of the wind speed profile. In this embodiment, it is assumed that the wind speed at any point in the gradient wind field is independent of time, thus the following derivation is obtained:

[0092]

[0093] In the formula, This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components.

[0094] In this embodiment, to simplify calculations, the lift of the aircraft is... and resistance The calculation is performed using a classic quadratic polynomial model, namely:

[0095]

[0096] In the formula, Indicates air density; Indicates the reference area of ​​the wing; Indicates the drag coefficient; The lift coefficient, drag coefficient, and thrust coefficient are key dimensionless parameters that determine aerodynamic lift and drag; their values ​​are primarily determined by the aircraft's angle of attack. (The unit is radians) Therefore, in this embodiment, the expressions for the drag coefficient and lift coefficient are:

[0097]

[0098] In the formula, Represents the zero angle of attack lift coefficient (i.e. (lift coefficient when = 0); Indicates the zero lift drag coefficient; This represents the slope of the lift line, i.e., the rate at which the lift coefficient changes with the angle of attack; This represents the induced resistance factor.

[0099] For example, in this embodiment, step S13, which involves constructing a wind farm flight energy consumption assessment model based on a three-degree-of-freedom flight dynamics model and a powertrain model of the battery, electronic speed controller, motor, and propeller in the aircraft, is as follows:

[0100] Step S131: The propeller of an aircraft is the core component that generates thrust in the power chain. Its aerodynamic characteristics are determined by the flight state and its own state. Based on the blade element momentum theory, the following can be derived:

[0101]

[0102]

[0103] In the formula, Indicates propeller thrust; Indicates propeller torque; Indicates the thrust coefficient of the propeller; Indicates air density; Indicates the propeller speed; Indicates the propeller diameter; This represents the propeller torque coefficient. Considering the influence of the incoming flow velocity on the thrust and torque coefficients, the advance ratio needs to be introduced for correction. The formula for calculating the advance ratio is:

[0104]

[0105] In the formula, Indicates the forward ratio; This represents the airspeed of the aircraft. According to the strip theory, the propeller's thrust coefficient... and the torque coefficient of the propeller Determined by the aircraft's airspeed and propeller speed, it can be fitted as a function of the forward ratio. Polynomial functions:

[0106]

[0107]

[0108] In the formula, Indicates the tension coefficient with respect to the advance ratio polynomial functions; Indicates the tension coefficient with respect to the advance ratio The coefficients of the quadratic term in a polynomial function; Indicates the tension coefficient with respect to the advance ratio The coefficient of the linear term in a polynomial function; Indicates the tension coefficient with respect to the advance ratio The constant in a polynomial function; This indicates the torque coefficient with respect to the forward ratio. polynomial functions; This indicates the torque coefficient with respect to the forward ratio. The coefficients of the quadratic term in a polynomial function; This indicates the torque coefficient with respect to the forward ratio. The coefficient of the linear term in a polynomial function; This indicates the torque coefficient with respect to the forward ratio. The constant in the polynomial function.

[0109] Step S132: The aircraft's motor is a brushless DC motor (BLDC). The brushless DC motor (BLDC) is the core energy conversion unit in the powertrain, responsible for converting electrical energy into mechanical work to drive the propeller. This embodiment aims to evaluate the energy loss of the UAV's power system throughout flight. Therefore, a simplified steady-state equivalent circuit model is used to describe its electrical characteristics, neglecting the motor's angular acceleration and assuming that the propeller's speed and torque are always equal to the motor's output speed and torque. Given the propeller speed and torque, the expressions for the motor's input voltage and input current are:

[0110]

[0111]

[0112] In the formula, This indicates the input voltage of the motor; This indicates the input current of the motor; This represents the motor speed constant; Indicates the rated no-load voltage of the motor; This indicates the motor's rated no-load current; Indicates the interphase internal resistance of the motor; , These are all inherent parameters of the motor, obtained from technical data provided by the manufacturer. Given the motor's input voltage and current, the propeller speed and torque can be expressed as:

[0113]

[0114]

[0115] Motor efficiency is the motor's output power. With input power The ratio, that is:

[0116]

[0117] In the formula, This indicates the motor efficiency.

[0118] Step S133: The aircraft's Electronic Speed ​​Control (ESC) receives flight control commands (usually throttle signals). This refers to the power electronic equipment that drives the motor. To simplify the analysis, temperature and AC current factors are ignored, and it is modeled as a DC-DC converter. Its core function is to regulate the voltage and current output to the motor. Therefore, the output voltage of the electronic speed controller... Output current The relationship between the motor input voltage and current is:

[0119]

[0120]

[0121] In the formula, This indicates the internal resistance of the electronic speed controller; the ESC receives the throttle signal from the flight control system. Then, the DC voltage of the battery is converted into the pulse width modulation (PWM) voltage of the BLDC motor without speed feedback. The expression for this process is as follows:

[0122]

[0123]

[0124] In the formula, Indicates the battery's output voltage; Indicates the input voltage of the electronic speed controller; Indicates the battery output current; This indicates the input current of the electronic speed controller; This represents the correction factor.

[0125] In summary, the energy consumption assessment requirements of UAVs in wind farms can be simplified as follows: Based on the three-degree-of-freedom flight dynamics model and overall parameters, determine the thrust requirements under different operating conditions and use this as input to the power energy system model. If propeller speed is used as the control variable for trajectory optimization, then propeller speed is selected as the input to the power energy system model. In this embodiment, since the object is a small electric UAV, the energy system of the small electric UAV is the battery, thus the energy consumed by the battery can be calculated.

[0126] Given the propeller thrust required for an aircraft to fly in a wind field. Then, the propeller speed can be derived. propeller thrust Satisfy the equation:

[0127]

[0128] Given a flight airspeed, due to Follow Since the expression increases monotonically with increasing , the above equation has a unique solution and can be rewritten as:

[0129]

[0130] In the formula, It represents a nonlinear function of propeller rotational speed with respect to airspeed and propeller thrust.

[0131] The propeller torque can be derived as follows:

[0132]

[0133] In the formula, It represents a nonlinear function of propeller torque with respect to airspeed and propeller speed.

[0134] Rotate the propeller speed propeller thrust Substituting the expressions for the motor's input voltage and input current, we can obtain the motor's input current and input voltage as follows:

[0135]

[0136]

[0137] In the formula, This represents a nonlinear function of the motor input current with respect to the propeller torque. This represents a nonlinear function of the motor input voltage with respect to the propeller speed and the motor input current.

[0138] Given propeller thrust or propeller speed After selecting the models and specifications of the battery, electronic speed controller, motor, and propeller, the expression for the wind farm flight energy consumption assessment model is as follows:

[0139]

[0140]

[0141] In the formula, This indicates the energy consumption of the energy system when the aircraft is flying in a wind field; This indicates the output power of the energy system when the aircraft is flying in a wind field; Indicates the output voltage of the energy system; Indicates the output current of the energy system; Indicates the input voltage of the electronic speed controller; This indicates the input current of the electronic speed controller; This indicates the input voltage of the motor; This indicates the input current of the motor; Indicates the internal resistance of the electronic speed controller; This represents the correction factor; where, during the unpowered gliding flight phase... .

[0142] At this point, the system energy consumption can be obtained using the wind farm flight energy consumption assessment model.

[0143] For example, in this embodiment, step S14, obtaining the flight performance constraints and flight boundary constraints of the aircraft in the northeast-northeast coordinate system, is as follows:

[0144] Since the aircraft's state and control parameters must be maintained within safe and physically feasible limits throughout the flight, and considering the maneuverability limitations of the object studied in this embodiment, the rate of change of airflow trajectory angle is adjusted to ensure the physical realism and flyability of the simulation results. and airflow trajectory azimuth rate of change Additional restrictions are added; specifically, in this implementation, S141, the flight performance constraints are:

[0145]

[0146] In the formula, Indicates that the aircraft is in Flight altitude at any given moment; Indicates the minimum altitude of the aircraft; Indicates the maximum altitude of the aircraft; Indicates that the aircraft is in Airspeed at any given moment; Indicates the minimum airspeed of the aircraft; This indicates the aircraft's maximum airspeed; Indicates that the aircraft is in Maximum airflow trajectory inclination at any given moment; Indicates that the aircraft is in Inclination angle of airflow trajectory at any given moment; Indicates that the aircraft is in Rate of change of airflow trajectory inclination angle at any given time; Indicates that the aircraft is in The rate of change of the maximum airflow trajectory inclination at any given moment; Indicates that the aircraft is in The azimuth angle of the maximum airflow trajectory at any given moment; Indicates that the aircraft is in Azimuth of the airflow trajectory at any given moment; Indicates that the aircraft is in Rate of change of azimuth angle of airflow trajectory at any time; Indicates that the aircraft is in The rate of change of the azimuth angle of the airflow trajectory at any given moment; Indicates in Angle of attack at any moment; Indicates the minimum angle of attack; Indicates the maximum angle of attack; Indicates in The airflow roll angle at any given moment; Indicates the maximum airflow roll angle; Indicates in The propeller rotation speed at any given moment; Indicates the minimum propeller speed; This indicates the maximum propeller speed.

[0147] For example, in one specific embodiment, in order to find a sustainable and repeatable gliding cycle, periodic constraints are typically imposed on the initial and terminal states. Some states are free, while others are required to return to the initial value at the end of the cycle. A complete multi-segment dynamic gliding requires, in the northeast-northeast coordinate system with the origin at (0,0,0), the x-axis... Flight altitude ,airspeed airflow trajectory inclination and airflow trajectory azimuth It is periodic; this means that after completing one cycle, the aircraft must return to its initial horizontal coordinate position, altitude, airspeed, and flight attitude. The position is not subject to periodic constraints, allowing the aircraft to achieve net displacement (travel) in the Y-axis direction, and allowing its airspeed to change at the end of the period. That is, in this embodiment, S142, the flight boundary constraint condition is:

[0148]

[0149] In the formula, The horizontal coordinate indicates the position at the start of the flight phase; The horizontal coordinate indicates the position at the end of the flight phase; Indicates the flight altitude at the start of the flight phase; Indicates the flight altitude at the end of the flight phase; This indicates the airspeed of the aircraft at the start of the flight phase. This indicates the airspeed of the aircraft at the end of its flight phase. Indicates the inclination angle of the airflow path at the start of the flight phase; Indicates the inclination angle of the airflow path at the end of the flight phase; Indicates the azimuth angle of the airflow path at the start of the flight phase; Indicates the azimuth angle of the airflow track at the end of the flight phase; Indicates the end time of the flight phase; Indicates the start time of the flight phase.

[0150] It should be noted that during trajectory planning, the dynamic behavior of the system must always follow a system of nonlinear differential equations. ; where, state vector and control vector Defined as:

[0151]

[0152]

[0153] Where: propeller speed The upper and lower boundaries are determined by the stage in which the aircraft is located, and the angle of attack. The range is calculated inversely based on the desired lift coefficient CL range to ensure it is within the effective aerodynamic range. According to the high-precision energy system model, if the propeller thrust... If we set this as a control variable, then when calculating power consumption in each optimization step, we must solve a system of nonlinear equations to obtain the corresponding propeller speed. In optimization frameworks like GPOPS-II, which rely on collocation methods, this embedded nonlinear solution process makes the calculation of the Jacobian matrix exceptionally complex, leading to a sharp drop in algorithm convergence speed and a significant increase in solution time. Conversely, by using propeller rotation speed... As a direct control variable, given the current flight state (such as airspeed)... Under the condition of ), propeller thrust The solution can be obtained directly and explicitly through forward computation, completely avoiding the iterative process of solving nonlinear equations. This approach greatly simplifies the mathematical structure of the problem, significantly reduces the computational burden of a single iteration, and thus greatly improves the solution efficiency and robustness of the entire optimal control problem.

[0154] For example, in one specific embodiment, step S15, constructing the objective function, is as follows:

[0155] Since the primary objectives of unpowered gliding are to verify feasibility and conserve energy as much as possible, its objective function is set to minimize energy consumption per unit distance traveled. Under unpowered conditions, with zero battery power consumption, this objective function is equivalent to maximizing the difference between the energy gained from the wind field and the energy dissipated to overcome air resistance per unit distance, thus guiding the optimizer to find the most efficient gliding path. The energy change of an aircraft in a gradient wind field is a complex process, mainly including the conversion of its own mechanical energy (potential and kinetic energy), the energy extracted from the wind field, and the energy dissipated to overcome air resistance. The dynamic energy relative to the air reflects its energy exchange with the surrounding flow field, consisting of its kinetic energy and gravitational potential energy relative to the air. In an inertial frame, the dynamic energy relative to the air is defined as:

[0156]

[0157] In the formula, Represents dynamic energy relative to the air; Indicates the mass of the aircraft; Represents gravitational acceleration; Indicates flight altitude; Let represent the airspeed of the aircraft. Then the rate of change of its dynamic energy relative to the air is:

[0158]

[0159] In the formula, This represents the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field. Indicates the airspeed of the aircraft; This indicates the rate of change of the aircraft's airspeed; Indicates the mass of the aircraft; Represents gravitational acceleration; Indicates propeller thrust; This indicates the drag experienced by the aircraft; Indicates the vertical velocity of the aircraft; This represents the energy power absorbed by the gradient wind field when the aircraft is flying in the gradient wind field.

[0160] The expression for the energy power absorbed by the gradient wind field when the aircraft flies in the gradient wind field is:

[0161]

[0162] In the formula, Indicates the wind speed at the reference altitude; Indicates flight altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. Indicates the inclination angle of the airflow path; Indicates the azimuth angle of the airflow path; It represents a dimensionless power law exponent, the value of which is used to determine the shape and curvature of the wind speed profile.

[0163] Since the objective function is to maximize the total flight time Within this context, the aircraft minimizes energy consumption per unit distance traveled; therefore, this embodiment sets the objective function as follows: Defined as:

[0164]

[0165] In the formula, Represents the objective function value; This represents the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field. This represents the output power of the energy system when the aircraft is flying in a wind field. The system energy consumption of the aircraft is 0 when the flight phase is the unpowered gliding flight phase. Indicates the end time of the flight phase; Indicates the start time of the flight phase; This represents the rate of change of energy in an energy system; It represents the displacement in the flight direction over the entire time period.

[0166] Thus, based on the flight performance constraints and flight boundary constraints, an optimal control problem model with the objective function of minimizing system energy consumption can be established.

[0167] S2. Obtain the nonlinear programming problem model;

[0168] Specifically, the Legendre-Gauss-Radow collocation method is used to numerically transform the optimal control problem model into a nonlinear programming problem model.

[0169] For example, in one specific embodiment, the specific steps for numerically transforming the optimal control problem using the Legendre-Gauss-Radau (LGR) collocation method include:

[0170] Step S21, Time Domain Discretization: Discretize the continuous time domain of a single gliding flight into a set of preset Legendre-Gauss-Lado collocations.

[0171] Step S22, Variable parameterization: Set the state variables (such as position, airspeed, airflow path inclination angle, airflow path azimuth angle) and control variables (such as angle of attack, airflow roll angle, propeller speed) of the aircraft at each set point as the optimization variables to be determined.

[0172] Step S23, Dynamic Constraint Transformation: Based on the three-degree-of-freedom flight dynamics model under the gradient wind field in step S1, the differential equations describing the aircraft motion are transformed into a set of algebraic equation constraints applied to each collocation point through collocation constraints. This process transforms the dynamic process into static constraints.

[0173] Step S24, Applying performance and boundary constraints: Apply the flight performance constraints and flight boundary constraints from step S1 to the corresponding collocation points to form additional algebraic equality or inequality constraints.

[0174] Thus, through the transformation from steps S21 to S24, the optimal control problem in step S1 has been transformed into a large-scale nonlinear programming (NLP) problem.

[0175] S3. Obtain the single optimal trajectory and its corresponding flight status data when the system energy consumption is minimized during the unpowered gliding flight phase and the powered recovery flight phase.

[0176] Specifically, propeller speed, airflow roll angle, and angle of attack are used as control variables in the algorithm for solving the nonlinear programming problem model. Numerical optimization algorithms such as sequential quadratic programming are used to solve the nonlinear programming problem model, resulting in a set of optimal control variable sequences that satisfy all flight performance constraints and flight boundary constraints while minimizing system energy consumption. The optimal control variable sequence is then used as the optimal control command for the current unpowered gliding flight phase. Flight simulation is performed based on the optimal control command, and the three-degree-of-freedom flight dynamics model is solved integrally to obtain the single optimal trajectory and its corresponding flight state data when the system energy consumption is minimized in the unpowered gliding flight phase and the powered recovery flight phase.

[0177] For example, in one specific embodiment, by solving this nonlinear programming problem, a set of optimal control variables can be directly obtained that minimizes system energy consumption (i.e., minimizes the objective function value) while satisfying all flight performance constraints and flight boundary constraints. Flight simulation is then performed based on this optimal control variable sequence, and the three-degree-of-freedom flight dynamics model under gradient wind field is integrally solved to obtain the single-cycle optimal trajectory and its corresponding flight state data corresponding to the minimum system energy consumption during the unpowered gliding flight phase and the powered recovery flight phase.

[0178] S4. Obtain multi-segment dynamic gliding flight trajectory;

[0179] Specifically, the flight status data at the end of the previous flight phase is used as the starting flight boundary constraint for the trajectory planning of the next flight phase of the same flight phase. The flight trajectory with the minimum system energy consumption for the next segment is replanned until the flight status data of the aircraft reaches the preset flight termination boundary. Then, the optimal flight trajectory for each flight phase is planned. The optimal flight trajectory of the unpowered gliding flight phase and the flight trajectory of the powered recovery flight phase are combined to obtain a multi-segment dynamic gliding flight trajectory.

[0180] For example, in this embodiment, such as Figure 3 As shown, to achieve long-endurance flight, taking the unpowered gliding flight phase as an example, this embodiment adopts an iterative planning strategy, namely:

[0181] Step S41, Setting initial conditions for iteration: Use the flight state data at the end of the last unpowered gliding (e.g., the state after taking into account the displacement in the Y direction and the loss of airspeed) as the initial boundary conditions for the unpowered gliding flight phase planning.

[0182] Step S42, Iterative Loop: Repeat steps S1 to S3, that is, replan the flight trajectory with the minimum system energy consumption for the next segment based on the new initial boundary conditions.

[0183] Step S43, Termination Condition: Continue iterative planning until the aircraft state reaches a preset threshold (i.e., the airspeed is less than the minimum airspeed), at which point the unpowered gliding flight phase stops.

[0184] It should be noted that, considering that fixed-wing UAVs inevitably dissipate energy due to aerodynamic drag during unpowered gliding, they cannot achieve a complete energy loop relying solely on wind energy, thus making indefinite sustainable gliding difficult. Therefore, this embodiment introduces a powered recovery flight phase, aiming to construct a sustainable cyclical flight mode of "multi-segment unpowered gliding + one-segment powered recovery." The goal of this powered recovery flight phase is: after multiple unpowered gliding segments, to employ an optimized low-energy thrust strategy to precisely compensate for the energy deficit during the flight cycle, restoring the aircraft's state to its initial value before the start of the gliding cycle (except for the continuous advancement of the heading distance Y), preparing for the next round of multi-segment unpowered gliding, and ultimately achieving efficient and sustainable long-distance flight. Specifically, in this embodiment, during the powered recovery flight phase: the propeller speed constraint is relaxed from zero to within its physically feasible operating range; a path constraint with propeller thrust greater than zero is added; and in the flight boundary constraints, the aircraft's flight state data is restored to the initial state value at the start of the current unpowered gliding cycle.

[0185] At this point, the optimal flight trajectory for each flight phase can be planned. The optimal flight trajectory for the unpowered gliding flight phase and the flight trajectory for the powered recovery flight phase can be combined to obtain a multi-segment dynamic gliding flight trajectory.

[0186] Example 2

[0187] Building upon Example 1, Example 2 proposes a trajectory planning step combining decoupled 3D path and inverse dynamics verification. To ensure the application of the proposed dynamic gliding trajectory planning method for fixed-wing aircraft in practical missions, this example must address the precise transition from any cruise state to the gliding start point, and from the gliding end point to the mission endpoint. This involves establishing an efficient approach and exit transition trajectory planning model, integrating independent gliding cycles into a complete, end-to-end mission profile. To meet the stringent requirements for aircraft position, attitude, and velocity at the start of dynamic gliding, this example proposes a trajectory planning method combining decoupled 3D path and inverse dynamics verification. It should be noted that the core idea of ​​this proposed method is to decompose the complex 3D trajectory planning problem into two independent 2D path planning sub-problems in the horizontal and vertical planes. After generating the geometrically optimal trajectory, the dynamic feasibility of the trajectory is verified using an inverse dynamics model. Specifically, as follows... Figure 3As shown, the trajectory planning method based on the combination of decoupled 3D path and inverse dynamics verification has the following steps:

[0188] Step 1, attitude determination: The starting attitude of the multi-segment dynamic gliding flight trajectory of the aircraft in the wind field in Example 1 is taken as the starting target attitude, and the ending point of the flight trajectory is taken as the ending target attitude.

[0189] Step Two: Horizontal Path Planning: First, in the horizontal two-dimensional plane (XY plane), connect the aircraft's starting pose with the starting target pose, and the ending pose with the ending target pose. A key feature of this step is that the path turning radius is not a fixed value, but is dynamically calculated based on the aircraft's airspeed and maximum roll angle limits at the endpoints, thus ensuring that the planned path better reflects the aircraft's actual maneuverability. By comparing various "circular arc-straight line-circular arc" (CSC) combinations, the shortest total length is selected as the optimal horizontal path.

[0190] Step 3: Vertical Profile Planning: After obtaining the optimal horizontal path and its total length, the vertical profile (sh plane) is planned. This step uses the horizontal flight distance (optimal horizontal path) as a benchmark to plan the optimal vertical variation profile from the starting altitude and climb angle to the target altitude and climb angle, and from the ending altitude and climb angle to the target altitude and climb angle, thus defining the variation law of flight altitude with horizontal mileage.

[0191] Step 4, 3D Trajectory Reconstruction: Finally, the two-dimensional paths (optimal horizontal path and optimal vertical change profile) generated in Step 2 and Step 3 are merged to reconstruct a three-dimensional spatial kinematic trajectory that satisfies all start and end state constraints (which can be obtained by connecting the entry transition trajectory, the multi-segment dynamic gliding flight trajectory in the gradient wind field of this embodiment, and the exit transition trajectory).

[0192] Step 5, Dynamics Verification: To ensure the aircraft can actually execute the three-dimensional kinematic trajectory, inverse dynamics verification is performed. This involves solving the UAV's dynamic equations in reverse to calculate the necessary control input sequence (such as roll angle, angle of attack, and thrust) for accurately tracking the three-dimensional kinematic trajectory. If all control inputs are within the aircraft's flight performance constraints and flight boundary constraints, the three-dimensional kinematic trajectory is confirmed as a fully feasible three-dimensional kinematic trajectory (i.e., formed by the fusion of the approach transition trajectory, multi-segment dynamic gliding flight trajectory, and exit transition trajectory). If the control inputs exceed the flight performance constraints and flight boundary constraints, the distance between the approach and exit points is increased to satisfy the flight performance constraints and flight boundary constraints. The three-dimensional kinematic trajectory is then re-acquired until it satisfies inverse dynamics. Simultaneously, based on the thrust sequence in the control input sequence, the wind field flight energy consumption assessment model can be invoked to accurately calculate the energy consumption of this segment of the approach and exit transition trajectories. Through steps one through five, this embodiment can efficiently generate a geometrically optimal and dynamically feasible three-dimensional kinematic trajectory.

[0193] The present invention will be further described below with reference to specific data and accompanying drawings:

[0194] In this embodiment, for example... Figure 4 The overall performance parameters of the UAV are shown in Table 1.

[0195] Table 1

[0196]

[0197] Figure 5 Showing at reference height wind speed at the location Under the condition of constant 6 m / s, different power law exponents The influence of gradient wind field profile shape, from Figure 5 It can be clearly seen from the data that the power law exponent... This determines the degree of nonlinearity in the change of wind speed with height, i.e., the intensity of wind shear; Figure 6 This shows the power law exponent. With a fixed value of 1.0, different reference heights wind speed at the location The influence on the overall intensity of the gradient wind field profile, and The main difference lies in the profile "shape" and reference height. wind speed at the location This directly determines the "basic strength" of the wind field; Figure 7This embodiment visually demonstrates the three-dimensional spatial kinematic trajectory of the complete end-to-end multi-segment dynamic gliding mission profile constructed in this embodiment. This three-dimensional spatial kinematic trajectory is not an isolated gliding cycle, but a complete continuous flight path containing multiple different physical stages, consisting of an approach transition segment, a core gliding segment, and an exit transition segment.

[0198] like Figure 8 As shown, Figure 8 The data clearly reveals the energy demand characteristics of the mission profile: the approach and exit phases are characterized by stable cruise power, while the dynamic gliding phases exhibit periodic pulse sequences consisting of unpowered gliding and high-power recovery. For example... Figure 9 As shown, the cumulative energy consumption curve quantifies the energy proportion of each stage. According to the integral results, the dynamic gliding segment in this mission includes four macroscopic cycles of "unpowered + powered", with a total energy consumption of 2557.48J.

[0199] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for planning dynamic gliding flight trajectories for fixed-wing aircraft, characterized in that, include: A three-degree-of-freedom flight dynamics model of an aircraft in a gradient wind field is established based on an exponential wind field model in the northeast-north sky coordinate system. A wind farm flight energy consumption assessment model is constructed based on a three-degree-of-freedom flight dynamics model and a power chain model of the energy system, electronic governor, motor, and propeller in the aircraft. The wind farm flight energy consumption assessment model is used to evaluate the system energy consumption. Based on the flight performance constraints and flight boundary constraints of the aircraft in the northeast-northeast coordinate system, an optimal control problem model with the minimum system energy consumption as the objective function is established. The Legendre-Gauss-Radow collocation method is used to numerically transform the optimal control problem model into a nonlinear programming problem model. The propeller speed, airflow roll angle, and angle of attack are used as control variables in the algorithm for solving the nonlinear programming problem. A sequential quadratic programming numerical optimization algorithm is used to solve the nonlinear programming problem model, resulting in a set of optimal control variable sequences that satisfy all flight performance constraints and flight boundary constraints and minimize system energy consumption. The optimal control variable sequence is used as the optimal control command for the current unpowered gliding flight phase. Flight simulation is performed based on the optimal control command, and the three-degree-of-freedom flight dynamics model is solved by integration to obtain the single optimal trajectory and its corresponding flight state data when the system energy consumption is minimized in the unpowered gliding flight phase and the powered recovery flight phase. The flight status data at the end of the previous flight phase is used as the starting flight boundary constraint for the trajectory planning of the next flight phase of the same flight phase. The flight trajectory with the minimum system energy consumption is replanned until the flight status data of the aircraft reaches the preset flight termination boundary. Then the optimal flight trajectory for each flight phase is planned. The optimal flight trajectory of the unpowered gliding flight phase and the flight trajectory of the powered recovery flight phase are combined to obtain a multi-segment dynamic gliding flight trajectory. In the powered flight recovery phase: the propeller speed constraint is relaxed from zero to within its physically feasible operating range; a path constraint with propeller thrust greater than zero is added; and in the flight boundary constraints, the aircraft's flight status data is restored to the initial state value at the beginning of the current unpowered gliding cycle.

2. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 1, characterized in that, The expressions for the flight performance constraints and flight boundary constraints of the aircraft in the northeast-northeast coordinate system are as follows: The flight performance constraints are as follows: In the formula, Indicates that the aircraft is in The height of a moment; Indicates the minimum altitude of the aircraft; Indicates the maximum altitude of the aircraft; Indicates that the aircraft is in Airspeed at any given moment; Indicates the minimum airspeed of the aircraft; This indicates the aircraft's maximum airspeed; Indicates the maximum airflow trajectory inclination angle of the aircraft; Indicates that the aircraft is in The inclination angle of the airflow trajectory at any given moment; Indicates that the aircraft is in The rate of change of the airflow trajectory inclination angle at any given moment; Indicates that the aircraft is in The rate of change of the maximum airflow trajectory inclination at any given moment; Indicates that the aircraft is in The maximum azimuth angle of the airflow trajectory at any given moment; Indicates that the aircraft is in The azimuth angle of the airflow trajectory at any given moment; Indicates that the aircraft is in The rate of change of the azimuth angle of the airflow trajectory at any given time; Indicates that the aircraft is in The rate of change of the maximum azimuth angle of the airflow trajectory at any given moment; Indicates in Angle of attack at any moment; Indicates the minimum angle of attack; Indicates the maximum angle of attack; Indicates in The airflow roll angle at any given moment; Indicates the maximum airflow roll angle; Indicates in The propeller rotation speed at any given moment; Indicates the minimum propeller speed; Indicates the maximum propeller speed; The flight boundary constraints are as follows: In the formula, The horizontal coordinate indicates the position at the start of the flight phase; The horizontal coordinate indicates the position at the end of the flight phase; Indicates the flight altitude at the start of the flight phase; Indicates the flight altitude at the end of the flight phase; This indicates the airspeed of the aircraft at the start of the flight phase. This indicates the airspeed of the aircraft at the end of its flight phase. Indicates the inclination angle of the airflow path at the start of the flight phase; Indicates the inclination angle of the airflow path at the end of the flight phase; Indicates the azimuth angle of the airflow path at the start of the flight phase; Indicates the azimuth angle of the airflow track at the end of the flight phase; Indicates the end time of the flight phase; Indicates the start time of the flight phase.

3. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 1, characterized in that, A wind farm flight energy consumption assessment model is established. Based on this model, the energy consumption of the aircraft at each stage is obtained. The expression for the wind farm flight energy consumption assessment model is as follows: In the formula, This indicates the energy consumption of the energy system when the aircraft is flying in a wind field; This indicates the output power of the energy system when the aircraft is flying in a wind field; Indicates the output voltage of the energy system; Indicates the output current of the energy system; Indicates the input voltage of the electronic speed controller; This indicates the input current of the electronic speed controller; This indicates the input voltage of the motor; This indicates the input current of the motor; Indicates the internal resistance of the electronic speed controller; This represents the correction factor; where, during the unpowered gliding flight phase... .

4. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 1, characterized in that, The objective function is: In the formula, Represents the objective function value; This represents the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field. This represents the output power of the energy system when the aircraft is flying in a wind field. The system energy consumption of the aircraft is 0 when the flight phase is the unpowered gliding flight phase. Indicates the end time of the flight phase; Indicates the start time of the flight phase; This represents the rate of change of energy in an energy system; It represents the displacement in the flight direction over the entire time period.

5. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 4, characterized in that, The expression for the rate of change of an aircraft's dynamic energy relative to the air under a gradient wind field is: In the formula, This represents the rate of change of the dynamic energy of an aircraft relative to the air under a gradient wind field. Indicates the airspeed of the aircraft; This indicates the rate of change of the aircraft's airspeed; Indicates the mass of the aircraft; Represents gravitational acceleration; Indicates propeller thrust; This indicates the drag experienced by the aircraft; Indicates the vertical velocity of the aircraft; This represents the energy power absorbed by the gradient wind field when the aircraft is flying in the gradient wind field.

6. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 5, characterized in that, The expression for the energy power absorbed by the gradient wind field when an aircraft flies in the gradient wind field is: In the formula, Indicates reference altitude; Indicates the wind speed at the reference altitude; Indicates flight altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. Indicates the inclination angle of the airflow path; Indicates the azimuth angle of the airflow path; It represents a dimensionless power law exponent, the value of which is used to determine the shape and curvature of the wind speed profile.

7. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 1, characterized in that, The expression for the three-degree-of-freedom flight dynamics model is: In the formula, This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; This represents the wind speed in the wind field in the northeast-sky inertial coordinate system. Rate of change of axial components; Indicates the mass of the aircraft; Indicates propeller thrust; This indicates the drag experienced by the aircraft; This indicates the lift force acting on the aircraft. Represents gravitational acceleration; Indicates the inclination angle of the airflow path; This represents the rate of change of the airflow trajectory inclination angle; Indicates the azimuth angle of the airflow path; This indicates the rate of change of the azimuth angle of the airflow path; Indicates the airspeed of the aircraft; This indicates the rate of change of the aircraft's airspeed; This indicates the airflow roll angle.

8. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 7, characterized in that, The expressions for drag and lift experienced by the aircraft are: In the formula, Indicates air density; Indicates the reference area of ​​the wing; Indicates the drag coefficient; This represents the lift coefficient.

9. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 1, characterized in that, The expression for wind speed under gradient wind field is: In the formula, This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; This indicates the gradient wind field along the northeast-sky inertial coordinate system. In the axial direction Wind speed component in the axial direction; Represents flight altitude in gradient wind field Wind speed at the location; Indicates reference altitude; Indicates the wind speed at the reference altitude; This represents the height of the point where the wind speed is theoretically zero, relative to the ground. It represents a dimensionless power law exponent, the value of which is used to determine the shape and curvature of the wind speed profile.

10. The method for dynamic gliding flight trajectory planning for a fixed-wing aircraft according to claim 1, characterized in that, It also includes a trajectory planning step based on a combination of decoupled 3D path and inverse dynamics verification, which includes: The starting pose of the multi-segment dynamic gliding flight trajectory of the aircraft in the wind field is taken as the starting target pose, and the ending pose of the flight trajectory is taken as the ending target pose. In a horizontal two-dimensional plane, the starting pose of the aircraft is connected to the starting target pose, and the ending pose is connected to the ending target pose. By comparing various combinations of "circular arc-straight line-circular arc", the path with the shortest total length is selected as the optimal horizontal path. Using the horizontal flight distance as a benchmark, which is the optimal horizontal path, we plan the optimal vertical change profiles from the starting point altitude and climb angle to the target altitude and climb angle, and from the ending point altitude and climb angle to the target altitude and climb angle. By fusing the optimal horizontal path and the optimal vertical change profile, a three-dimensional spatial kinematic trajectory that satisfies all start and end state constraints is reconstructed. Inverse dynamics verification of the three-dimensional kinematic trajectory: By inversely solving the three-degree-of-freedom flight dynamics model of the aircraft, the control input sequence required to track the three-dimensional kinematic trajectory is calculated. If all control inputs in the control input sequence are within the flight performance constraints and flight boundary constraints of the aircraft, the three-dimensional kinematic trajectory is confirmed as a completely feasible trajectory. If all control inputs in the control input sequence exceed the flight performance constraints and flight boundary constraints, the approach and exit distances of the trajectory planning are increased to satisfy the constraints, and the three-dimensional kinematic trajectory is reacquired until the reacquired three-dimensional kinematic trajectory satisfies inverse dynamics.

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