Unmanned aerial vehicle adaptive maneuvering control method and system based on dubins path planning

Abstract

The application belongs to the technical field of unmanned aerial vehicle control, and discloses an unmanned aerial vehicle adaptive maneuvering control method and system based on Dubins path planning. A Dubins path with curvature and pitch constraints is constructed, a desired maneuvering trajectory with path length as a parameter is generated, a Rodrigues parameter is used to establish an attitude error model, a hierarchical position and attitude controller is designed, and a filter gradient update law and mass and moment of inertia adaptive estimation are combined to realize deep integration and coupling of Dubins path planning and maneuvering control, so that the unmanned aerial vehicle can directly and accurately track the planned path, effectively overcome the problems of control discontinuity and large tracking error, and significantly improve the large-angle maneuvering capability, trajectory tracking accuracy and flight stability in complex environments of the unmanned aerial vehicle. Deep integration and coupling of Dubins path planning and maneuvering control are realized, so that the unmanned aerial vehicle can directly and accurately track the planned path, and effectively overcome the problems of control discontinuity and large tracking error.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) control technology, and particularly relates to an adaptive maneuver control method and system for UAVs based on Durbins path planning. Background Technology

[0002] Durbins path planning can generate optimal feasible flight paths under curvature and turning radius constraints, but traditional solutions only perform geometric planning, requiring additional path conversion into time trajectories, resulting in redundancy and poor real-time performance. Furthermore, UAVs are affected by perturbations of airframe parameters and external gusts during flight, leading to decreased tracking accuracy and stability, necessitating adaptive control to improve robustness. Currently, the industry generally suffers from a disconnect between planning and control, making direct Durbins path tracking impossible and prone to tracking lag and uneven transitions. Therefore, there is an urgent need for an integrated UAV flight control solution that combines Durbins path planning and adaptive maneuver control to achieve high-precision direct path tracking without trajectory conversion.

[0003] Existing UAV technology suffers from significant drawbacks: planning and control are decoupled, making it impossible to directly track Dubins paths; path-to-track transitions result in system redundancy, tracking lag, and poor coordination; conventional attitude control suffers from lock-up and jitter issues, leading to poor stability during large-angle maneuvers; traditional control relies on fixed models, making it difficult to compensate for perturbations in airframe parameters and external wind disturbances, and existing adaptive algorithms lack integrated design and have poor real-time performance. Overall, it fails to balance path optimization, smooth control, and robustness against disturbances, severely limiting the maneuverability of UAVs in complex environments. Summary of the Invention

[0004] To overcome the problems existing in related technologies, the present invention discloses an adaptive maneuver control method and system for unmanned aerial vehicles (UAVs) based on Durbins path planning, specifically involving a UAV three-dimensional path planning, attitude stabilization and robust adaptive maneuver control method.

[0005] The technical solution is as follows: an adaptive maneuver control method for UAVs based on Durbins path planning, comprising the following steps: S1. Input the UAV's starting and ending poses, maximum turning radius, and pitch angle constraints. Solve for both externally and internally tangent CSC-type Durbins candidate paths and select the global shortest path. Construct a 3D reference path with height-uniform velocity constraints along the arc length parameter. ; S2. Establish a quaternion-based UAV translational and rotational dynamics model. Onboard sensors collect the UAV's current position, linear velocity, attitude quaternion, and three-axis angular velocity flight status in real time; directly read the three-dimensional reference path. With arc length parameter As a reference for drones to conduct maneuvering flights along predetermined routes; S3. Design an attitude planner to convert the underactuated UAV system into an equivalent all-drive control form. Based on the virtual control force output from the outer loop, calculate the total thrust and desired attitude orientation. Combine the flight yaw angle to synthesize the desired attitude quaternion and send it to the attitude inner loop to complete the maneuver attitude orientation. S4. Construct position and velocity errors, and establish an error dynamics model; design a translational displacement stabilization function to obtain the desired virtual control force. ; S5. Construct attitude error and angular velocity error, and establish an attitude error model based on Rodriguez parameters; design an angular velocity stabilization function to output a continuous and smooth torque control quantity. ; S6. Implement dynamic adjustment of path speed by executing the maneuver update rate: dynamically update the path arc length parameter and maneuver speed according to the path curvature and tracking error, match the speed distribution with the path shape, achieve smooth and stable maneuvering, and feed back the update amount to the outer loop position controller in real time to complete the closed-loop adjustment of maneuvering. S7. Execute the maneuvering filter gradient update law and complete adaptive parameter correction: Combining position error, attitude error and maneuvering speed information, the maneuvering filter gradient update law is used to estimate the mass and moment of inertia parameters of the UAV online, adaptively compensate for system parameter perturbations and external disturbances, and correct the inner and outer loop control quantities in real time with the estimation results.

[0006] Another object of the present invention is to provide an adaptive maneuver control system for unmanned aerial vehicles (UAVs) based on Durbins path planning. This system implements the aforementioned adaptive maneuver control method for UAVs based on Durbins path planning. The system includes: The 3D Durbins reference path generation module is used to generate 3D Durbins reference paths with curvature and pitch angle constraints. The module for establishing UAV translational and rotational dynamics models is used to establish UAV translational and rotational dynamics models based on quaternions and to acquire real-time UAV status data. The attitude planner design module is used to design an attitude planner based on the quaternion-based UAV translational and rotational dynamics model. This planner transforms the UAV underactuated system into an all-drive system and combines the yaw angle to synthesize the desired quaternion for inner-loop attitude error synthesis and tracking control. A module for obtaining the desired virtual control force is used to construct position and velocity errors and establish an error dynamics model; a translational displacement stabilization function is designed to obtain the desired virtual control force. ; The attitude error construction module is used to construct attitude error and angular velocity error. Based on the design of an attitude error-free model, it designs an angular velocity stabilization function and outputs a continuous and smooth torque control quantity. ; The maneuver update rate enables the path speed dynamic adjustment module, which dynamically updates the path arc length parameter and maneuver speed according to the path curvature and tracking error, matches the speed distribution with the path shape, achieves smooth and stable maneuvering, and feeds back the update amount to the outer loop position controller in real time to complete the closed-loop maneuvering adjustment. The filter gradient update law constitutes an adaptive parameter correction module, which integrates position, attitude and velocity errors to identify the body mass and moment of inertia online, compensates for parameter perturbations and external disturbances in real time, corrects inner and outer loop control quantities, realizes the integrated coupling of Dubins path planning and maneuver control, and ensures accurate flight path tracking.

[0007] Combining all the above technical solutions, the beneficial effects of this invention are as follows: Addressing the shortcomings of traditional UAV control methods, such as disconnect between planning and control, discontinuous control, and poor disturbance rejection and parameter adaptation capabilities, this invention proposes a Durbins path planning and adaptive integrated maneuver control method. This scheme integrates constrained Durbins path modeling, singularity-free attitude control, hierarchical control, and parameter adaptive identification to achieve deep coupling between planning and control, accurately track paths, eliminate control jitter, and improve the UAV's large-angle maneuver performance and flight stability. The algorithm is lightweight and adaptable to airborne applications, meeting the requirements of high-speed maneuvering, obstacle avoidance, and trajectory change. It is suitable for scenarios such as inspection, penetration, and search and rescue, effectively suppressing parameter perturbations and gust disturbances, and reducing flight risks. This invention breaks through the limitations of traditional separate fixed parameter designs, integrating arc length correction, dual-parameter identification, and disturbance compensation to suppress parameter drift and solve problems such as high-speed maneuver attitude oscillation, arc length drift, and wind disturbance coupling, constructing an integrated control architecture adapted to strong maneuvering conditions. Attached Figure Description

[0008] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the disclosure of this invention and, together with the description, serve to explain the principles of this disclosure; Figure 1 This is a flowchart of the UAV adaptive maneuver control method based on Durbins path planning provided in an embodiment of the present invention; Figure 2 This is a simulation structure diagram provided by the present invention; Figure 3 This is the UAV position error diagram provided by the present invention; Figure 4 This is the UAV attitude error diagram provided by the present invention; Figure 5 This is the UAV control input diagram provided by the present invention; wherein, (a) is the UAV thrust diagram, and (b) is the UAV torque diagram; Figure 6 This is an adaptive map of the UAV provided by the present invention; wherein, (a) is a mass estimation map and (b) is an inertial matrix estimation map; Figure 7This is the path speed diagram provided by the present invention. Detailed Implementation

[0009] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0010] The purpose of this invention is to overcome the shortcomings of existing UAV control technologies, such as the disconnect between path and maneuver, discontinuous control, and difficulty in handling parameter perturbations and external disturbances. It provides a UAV maneuver control method and system based on Durbins path planning and adaptive control. The innovation of this invention lies in: constructing a Durbins path with curvature and pitch constraints, generating a desired maneuver trajectory with path length as a parameter, establishing an attitude error model using Rodrigues parameters, designing hierarchical position and attitude controllers, and combining a filter gradient update law with adaptive estimation of mass and moment of inertia. This achieves deep integration and coupling of Durbins path planning and maneuver control, enabling the UAV to directly and accurately track the planned path, effectively overcoming problems such as discontinuous control and large tracking errors, and significantly improving the UAV's large-angle maneuverability, trajectory tracking accuracy, and flight stability in complex environments.

[0011] Example 1.

[0012] like Figure 1 As shown, the UAV adaptive maneuver control method based on Durbins path planning provided by this invention includes the following steps: S1. Input the UAV's starting and ending poses, maximum turning radius, and pitch angle constraints. Solve for both externally and internally tangent CSC-type Durbins candidate paths and select the global shortest path. Construct a 3D reference path with height-uniform velocity constraints along the arc length parameter. ; S2. Establish a quaternion-based UAV translational and rotational dynamics model. Onboard sensors collect the UAV's current position, linear velocity, attitude quaternion, and three-axis angular velocity flight status in real time; directly read the three-dimensional reference path. With arc length parameter As a reference for drones to conduct maneuvering flights along predetermined routes; S3. Design an attitude planner to convert the underactuated UAV system into an equivalent all-drive control form. Based on the virtual control force output from the outer loop, calculate the total thrust and desired attitude orientation. Combine the flight yaw angle to synthesize the desired attitude quaternion and send it to the attitude inner loop to complete the maneuver attitude orientation. S4. Construct position and velocity errors, and establish an error dynamics model; design a translational displacement stabilization function to obtain the desired virtual control force. ; S5. Construct attitude error and angular velocity error, and establish an attitude error model based on Rodriguez parameters; design an angular velocity stabilization function to output a continuous and smooth torque control quantity. ; S6. Implement dynamic adjustment of path speed by executing the maneuver update rate: dynamically update the path arc length parameter and maneuver speed according to the path curvature and tracking error, match the speed distribution with the path shape, achieve smooth and stable maneuvering, and feed back the update amount to the outer loop position controller in real time to complete the closed-loop adjustment of maneuvering. S7. Execute the maneuvering filter gradient update law and complete adaptive parameter correction: Combining position error, attitude error and maneuvering speed information, the maneuvering filter gradient update law is used to estimate the mass and moment of inertia parameters of the UAV online, adaptively compensate for system parameter perturbations and external disturbances, and correct the inner and outer loop control quantities in real time with the estimation results.

[0013] For example, in S1, generating a 3D Durbins reference path with curvature and pitch angle constraints includes: Based on the initial pose, final pose, curvature, and pitch angle constraints, a CSC path composed of circular arcs and straight line segments is generated; external and internal Dubins paths are calculated separately, and the global shortest path is selected; uniform motion is adopted in the vertical direction to generate a three-dimensional Dubins reference path with path length as a parameter.

[0014] For example, given an initial pose and termination pose The shortest path satisfying curvature constraints between points is a path composed of three curve segments. The candidate paths include four CSC paths, where C represents an arc and S represents a straight line segment. For ease of representation, the following symbols are defined: Indicates external incision. Indicates incision, where, This indicates that both the starting and ending arcs are counter-clockwise. This indicates that both the starting and ending arcs are clockwise. This indicates that the starting arc is counterclockwise and the ending arc is clockwise. This indicates that the starting arc is clockwise and the ending arc is counterclockwise. These represent the starting points and their positions along the three axes of the world coordinate system. The initial heading angle is the starting point. These represent the three axes of the endpoint in the geodetic coordinate system. The heading angle for the final target.

[0015] Assumption 1: In order to achieve the desired motion of the UAV, the main physical constraint (1) is required; ; In the formula, For the real-time curvature of the path, The maximum permissible curvature for the drone. The path pitch angle, This is the maximum permissible pitch angle for the drone.

[0016] For example, the following focuses on path calculation in the horizontal plane, analyzing the construction methods of Dubins paths for external and internal tangency, as well as the selection of the globally optimal path.

[0017] Where, externally tangent; the coordinate systems are defined as the world coordinate system. and the initial coordinate system (by (with the center of the circle). Rotate and translate to the coordinate system. (by (with the center of the circle) translated to the coordinate system (by (with the circle as the center), rotate and translate to the final coordinate system. (by (centered at the center). All coordinate systems are... Coordinate system (with tangent vector as) (Right-handed system of axes). Introducing sequentially from... arrive coordinate transformation ( ), and define from arrive coordinate transformation .

[0018] This invention innovatively introduces the following parameters: ; for and Coordinates: ; Similarly, ; In the formula, Starting position The center of the starting arc tangent point The central angle formed; End point Termination arc center tangent point The central angle formed; The tangent points of two circular arcs , Length of the straight line segment between them; Starting from the heading The constructed homogeneous coordinate rotation transformation matrix is ​​used to transform the local coordinate system to the world coordinate system; The inverse coordinate transformation matrix corresponding to the endpoint.

[0019] The angle and length of the vector connecting the two centers are as follows: ; in, .

[0020] Therefore, we can obtain: ; Center of the starting arc Pointing to the center of the terminating arc The two-dimensional vector connecting the centers of circles; The azimuth angle corresponding to the vector connecting the centers of the circle. This represents the straight-line distance between the centers of the two circles. , indicating the normalization of the angle difference.

[0021] Define the following coordinate transformation: ; ; in, The total central angle of the starting arc with the turning symbol. The total central angle of the terminating arc with the turning symbol; The homogeneous matrix for the local coordinate system rotation transformation of the initial circular arc segment; The homogeneous transformation matrix for translating the middle straight line segment; This is the homogeneous coordinate rotation matrix corresponding to the terminating arc. (Based on path length) The parameter is the horizontal component of the externally tangent Dubins path ( The coordinates are represented in three segments as follows: when Corresponding to the initial turning arc segment, The total arc length of the initial arc. arc length The corresponding real-time turning center angle; The desired horizontal coordinates of the path corresponding to the current arc length are given by the following formula: ; This segment's real-time expected heading meets... In the formula, The expected course for the path.

[0022] when The path coordinates are expressed as: ; The course remains constant during this segment, satisfying... .

[0023] when The path coordinate expression for the corresponding terminating turning arc segment is: ; The heading formula for this section is: ; Total length of external cut ,in, . The total path length of the externally tangent CSC type Durbins path is expressed as the sum of the lengths of the three path segments; The central turning angle corresponding to the turning arc at the starting point of the externally tangent configuration. The maximum bending rate of the drone, The length of the straight segment connecting the two curved arcs. The central turning angle corresponding to the turning arc at the end of the externally tangent configuration. These correspond to the arc lengths of the two turning arcs; subscript For turning direction identification parameters, The drone, with its externally tangent configuration, adopts a counter-clockwise turning mode. This indicates that the UAV in the external tangent configuration adopts a clockwise turning mode.

[0024] For example, internal tangency; the coordinate system definition of an internally tangent Dubins path is the same as that of an externally tangent path, that is, the world coordinate system. Starting coordinate system (by (with the circle as the center), rotate and translate to the coordinate system. (by (with the center of the circle) translated to the coordinate system (by (with the center as the coordinate system), rotate and translate to the final coordinate system. (by (centered at the center). All coordinate systems are... Coordinate system (with tangent vector as) (Right-handed linkage of the axis).

[0025] First, we introduce from... arrive coordinate transformation and define from arrive coordinate transformation .

[0026] This invention innovatively introduces the following parameters: ; In the formula, The point of tangency of the initial arc in the inscribed Dubins path. Point to the tangent point of the terminating arc A directed line segment, This represents the length of the straight line segment between the two points, corresponding to the geometric total length of the straight line segment in the middle of the CSC configuration path. For and Coordinates: ; Similarly, ; The angle and length of the vector connecting the two centers are as follows: ; in, Therefore, we get: ; ; For example, the coordinate transformation matrix corresponding to the internal path is defined as follows: ; ; In the formula, The total central angle of the starting arc with the turning indicator under the inscribed configuration. Used to characterize the reverse turning mode of two internally tangent circular arcs; This represents the offset / translation amount within the internal path. The turning radius of the path; It is the homogeneous transformation matrix of the local coordinate system rotation of the inscribed initial circular arc; The translation transformation matrix is ​​the inner intermediate line segment; This is the coordinate rotation homogeneous matrix corresponding to the inscribed terminating arc.

[0027] By path length As parameters, the horizontal component of the internal Dubins path is represented in three segments as follows: taking the path length... As a parameter, when Corresponding to the initial turning arc segment, The total arc length of the initial arc. arc length The corresponding real-time turning center angle, The coordinate solution is as follows: ; This segment's real-time expected heading meets... In the formula, For the expected course of the path, This represents the cumulative heading deflection along the arc length. Characterizes the opposing directions of the two circular arcs in the inscribed configuration. The maximum constraint curvature of the path; when When the path coordinates are expressed as: ; The course remains constant during this segment, satisfying... .

[0028] when When the path coordinates are expressed as: ; The heading formula for this section is: Total length of internal tangent ,in, The total length of the CSC-type Dubins path in the inscribed configuration, subscript For steering combination identification parameters, This represents the initial arc turning counterclockwise and the final arc turning clockwise under the inscribed configuration. This represents the starting arc turning clockwise and the ending arc turning counterclockwise under the inscribed configuration; The central turning angle corresponding to the turning arc at the starting point of the inscribed configuration. The central turning angle corresponding to the turning arc at the end of the inscribed configuration; These correspond to the arc lengths of the two turning arcs, respectively.

[0029] Final global shortest path length for: ; For example, in the vertical direction, the present invention employs uniform motion, that is, it is defined as follows: ; In the formula, The vertical altitude coordinates of the drone's flight start point. The vertical altitude coordinates of the drone's flight endpoint. This is the real-time arc length parameter for the path. The total length of the globally shortest Durbins path. arc length The corresponding expected vertical height, Vertical height with respect to arc length The first rate of change, Vertical height with respect to arc length The second derivative of is always 0 under uniform longitudinal motion.

[0030] Finally, the three-dimensional Durbins expected path is defined. : Using the path arc length The complete three-dimensional expected path of the independent variable is given by the plane Dubins horizontal coordinates. , With the above longitudinal height Combination structure; when the arc length is taken as the total global path length hour, The corresponding end point of the path.

[0031] For example, step S2 specifically includes: establishing a quaternion-based UAV translational and rotational dynamics model and acquiring real-time UAV status data; The translational and rotational dynamics model of the UAV based on quaternions is as follows: ; In the dynamic model formula, Let U be the three-dimensional position vector of the UAV in the inertial frame. Let the first derivative of the UAV's position with respect to time satisfy... , representing the linear velocity of the drone's motion, therefore the equation only reflects differential relationships and does not explicitly contain... ; For the inertial speed of the drone, The linear acceleration in the inertial frame of the UAV is the inertial velocity. The first derivative with respect to time; This represents the quaternion multiplication operator, used to perform vector coordinate transformations between the body coordinate system and the inertial coordinate system. For attitude quaternions The corresponding quaternion inverse, Let gravitational acceleration be constant. This represents the total external disturbance experienced by the UAV's translational path. To augment the quaternion form of angular velocity quaternions, The scalar part is 0, and the vector part is the angular velocity of the three axes of the machine. Here is the moment of inertia matrix in the UAV's body coordinate system. For the attitude quaternion of the UAV; This is the vertically upward unit basis vector of the inertial frame, used for thrust coordinate transformation of the UAV; The variation law of UAV attitude with random body angular velocity; For the angular acceleration of the drone body, For the overall quality of the drone, The three-axis angular velocities of the drone body. The control torques for the three axes of roll, pitch, and yaw of the UAV are generated by the differential rotation speed of the UAV rotor. The physical meanings of the two are completely consistent with those of the UAV thrust and torque mentioned later. The total external disturbance experienced by the UAV's rotation path. This is the total scalar thrust of the quadcopter of the UAV, used to control the translational motion of the UAV.

[0032] Let the unit quaternion representing the attitude deviation be... ,in, The real part of the quaternion scalar. The imaginary part of the quaternion three-dimensional vector satisfies the unit quaternion normalization constraint. .right Take the Rodrigues vector: ; The first derivative of the Rodrigues vector attitude error with respect to time is: ; Given the desired path and dynamic allocation, the maneuver problem consists of two tasks: (1) Geometric task; for any continuous function Forced output Converging to the desired path : ; (2) Speed ​​allocation; forced path speed speed of convergence to the expected value : ; in, Path arc length parameter The first derivative with respect to time characterizes the tangential travel rate of the UAV along the reference path; For the pre-configured time-varying desired path speed, uniform or variable speed timing commands can be set according to flight mission requirements.

[0033] Control objective: To design thrust and torque This enables the drone to move from its initial pose at the desired speed along a feasible and reasonable path. Flight to final pose And complete the geometry task and velocity allocation task.

[0034] For example, step S3 specifically includes: designing an attitude planner based on the UAV translational and rotational dynamics model based on quaternions to transform the UAV underactuated system into a fully driven form, calculating the total thrust and desired attitude direction from the desired virtual control force, completing attitude extraction through quaternion square root operation, and combining the yaw angle to synthesize the desired quaternion for inner loop attitude error synthesis and tracking control.

[0035] The attitude planner is designed as follows: Position dynamic equations for all-wheel drive configuration: ; in, Treating it as a designable control, its desired control vector is introduced. And assume there exists a Make: ; in, It is to be designed. Once given, the thrust can be obtained. Therefore, we obtain the simplified form of the above equation: ; in, Desired control vector The direction vector.

[0036] Consider pose extraction methods, i.e. Given the information, define a transition quaternion: ; This transition quaternion is used to characterize the benchmark. Shaft steering desired direction The rotational mapping relationship is such that its scalar component is the result of the dot product of the reference axis and the target direction vector, and its vector component is the result of the cross product of the two vectors. consider The square root operation is to find... satisfy: ; say One square root.

[0037] In order to calculate Unfold the left end: ; Expand the right side of the equation: ; in, These are the unit vectors of the desired direction. Projected components on the X, Y, and Z axes of the body coordinate system.

[0038] Then we have: ; By yaw angle Defined quaternions: ; In the formula, Let be the scalar real part of this yaw quaternion. For the imaginary part of a three-dimensional vector, Represents the unit direction vector along the Z-axis of the machine body; This invention can synthesize expected quaternions containing yaw angles: ; This will be used as the output of the attitude planner to synthesize attitude errors.

[0039] For example, controller design: This invention will utilize the concept of hierarchical control to design hierarchical controllers from the outer loop position control and the inner loop attitude control respectively, to complete the maneuverability control task.

[0040] For example, in step S4, the process of performing outer-loop position control to solve for the virtual control force specifically includes: constructing the outer-loop position error and the outer-loop velocity error, establishing an error dynamics model; designing a translational displacement stabilization function, and obtaining the desired virtual control force. The path speed is dynamically allocated based on the path curvature, enabling adaptive adjustment of speed between turning and straight sections; the continuous total thrust is calculated from the virtual control force. This provides the desired direction command for attitude control; The desired path obtained from the three-dimensional Durbins program Define position error for: ; In the formula, For the desired path The three components; In the attitude error closed-loop subsystem, the rotational error is defined in quaternion form: ; In the formula, The attitude quaternion error of the UAV is given by the inverse of the desired attitude quaternion. Quaternions of the actual attitude of the machine The value obtained by performing quaternion multiplication represents the rotational deviation of the UAV's current actual attitude relative to its desired attitude.

[0041] Angular velocity error construction relationship: ; In the formula, The desired angular velocity of the UAV is obtained from the attitude loop planning. This is the equivalent desired angular velocity after attitude error quaternion coordinate transformation, used to complete coordinate system matching and solve for angular velocity deviation. ; Convert the quaternion attitude error into a singularity-free Rodrigues parameter form. The corresponding error kinematic equations are obtained: ; In the formula, The attitude error vector is expressed based on Rodrigues parameters, thus avoiding the entanglement singularity problem in quaternion attitude representation; The first derivative of the Rodriguez attitude error with respect to time characterizes the dynamic rate of change of the attitude deviation. The dynamic equation for angular velocity error is derived as follows: ; In the formula, Let the moment of inertia matrix be the rotational moment of inertia matrix of the UAV's airframe center. The time derivative of the angular velocity error vector represents the angular acceleration error. Equivalent desired angular velocity The first derivative with respect to time, For three-axis control torque input; An example is the point set of error unit quaternions. It is a stable equilibrium point and unstable equilibrium points The set of intermediate points, when the state Approaching this posture, quaternion-based control strategies need to consider whether to overshoot. This often requires the introduction of switching, leading to discontinuous control. This prompted the present invention to consider the error kinematic equation (15) based on the Rodrigues vector representation, since the point set of the error unit quaternion in equation (13) is different. This corresponds to the boundary of equation (15). Therefore, there is no need to switch within equation (15), and an almost globally smooth controller can be designed to achieve the control objective.

[0042] For example, this invention overcomes lock-up and avoids discontinuous control through computational efficiency. This invention can eliminate errors in Euler angles, rotation matrices, and quaternion representations, making it naturally reliant on the Rodrigues vector representation error system. At this point, the singularity is at infinity (i.e., ), and the equilibrium point is The distance between the equilibrium point and the singularity is maximized at a certain point, thus allowing attitude control to be designed so that the tracking error approaches zero, thereby completing attitude adjustment. This invention uses Rodrigues vectors to represent the attitude error system, which only approaches infinity when the attitude error is close to 180°. To address this characteristic, this invention handles such extreme cases pre-processed in the path planning stage: by providing a reasonable initial pose, the initial attitude error of the system is ensured to be much less than 180°; then, by constructing a Lyapunov function, the Rodrigues vector is guaranteed to remain bounded throughout subsequent flight, thereby avoiding singularities and ensuring control stability.

[0043] For example, specifically including: Step 1: Define the translational velocity error; ; In the formula: This is the velocity deviation vector between the actual translational velocity of the UAV and the desired reference velocity. The real-time actual three-dimensional translational velocity in the UAV body coordinate system; Translational displacement stabilization function specifically designed for this step.

[0044] Arc length parameter update law: ; In the formula, It is the path arc length parameter The first derivative with respect to time, , All are constants. This is an auxiliary adjustment function to be designed later, used to correct the dynamics of arc length and realize closed-loop distribution control of path speed.

[0045] Define the Lyapunov function for translational displacement: ; In the formula, This represents the position tracking error vector between the actual spatial position of the UAV and the expected position along the Durbins reference path. for transpose, It is a positive definite Lyapunov function, and the value of this function is always greater than or equal to zero; Its time derivative is: ; In the formula, For Lyapunov functions The first derivative with respect to time, The desired position of the Durbins reference path relative to the arc length parameter The first-order partial derivative.

[0046] Then, a translational displacement stabilization function is selected: ; In the formula, This is the positive definite control gain for the outer loop of the position.

[0047] derivative It becomes: ; besides: ; In the formula, Position tracking error vector The first derivative with respect to time.

[0048] Step 2: Rewrite equation (5) as follows: ; In the formula, The second derivative of the UAV position error vector with respect to time represents the acceleration dynamics of the position error; For Dubins' expected position vector The second derivative with respect to time represents the target acceleration corresponding to the desired trajectory; For the actual virtual control of drones With desired virtual control Control deviation between; This refers to the overall weight of the drone. Among them, , For the expected path total feedforward compensation term, The baseline travel speed for the path The first derivative with respect to time, will It is considered as all-wheel drive control.

[0049] The Lyapunov function of the translational error system is defined as follows: ; Its time derivative satisfies: ; In the formula, For the total Lyapunov function The first derivative with respect to time.

[0050] Depend on The definition knows: ; In the formula, This is the coordinate rotation matrix corresponding to the desired pose; The attitude error rotation matrix is ​​derived from the attitude quaternion error. Rodriguez attitude error Common characteristics; It is a third-order identity matrix. Further combining this with Euler's formula, we can obtain: ; In the formula, The attitude error vector The transpose of the row vector; It is a third-order identity matrix; The attitude error vector The corresponding antisymmetric cross product matrix; Let be the Euclidean norm of the attitude error vector.

[0051] because: ; In the formula, It is an antisymmetric cross product matrix The Frobenius norm.

[0052] in: ; ; Therefore, from equation (17) to equation (21), we know that: ; Therefore: ; In the formula, velocity error vector The transpose row vector For the actual virtual control of drones With desired virtual control Control deviation between; These are artificially introduced positive definite adjustable relaxation constraint parameters; This is a lumped vector obtained by integrating thrust amplitude, adjustable parameters, and attitude error related terms.

[0053] Therefore, the desired full-drive control can be selected: ; In the formula, This represents the positive definite feedback gain of the outer velocity loop.

[0054] It can be deduced that: ; In the formula, To define the lumped coefficient vector The transpose of the row vector.

[0055] Post-synthetic subsystem: ; ; Equation (24) shows The subsystem, equation (25) is based on As input, with It is a strictly passive system for output.

[0056] It can be seen from formula (17) that Δ is related to F. It can be seen in the expression that it is related to This relates to F. Compared to linear feedback, this invention employs the aforementioned nonlinear form because linear feedback cannot accurately characterize Δ and F. , The nonlinear correlation between them can easily lead to insufficient or overcompensated compensation; however, the aforementioned nonlinear form corresponds perfectly to the structure of Δ, enabling effective compensation across the entire attitude error range and improving system robustness. In stability analysis, this invention can guarantee... It is bounded.

[0057] For example, in S5, executing the inner-loop attitude control to generate continuous torque commands includes: The attitude error and angular velocity error are constructed. Based on the singularity-free attitude error model (Rodrigues attitude error model), an angular velocity stabilization function is designed to output a continuous and smooth torque control quantity. In attitude control, a coupling compensation term is introduced to ensure that the control signal is jitter-free and seamless. Specifically, this includes: The attitude error system is as follows: ; ; Introducing angular velocity error: ; In the formula, For attitude outer loop virtual angular velocity stabilization reference commands, This refers to the inner loop angular velocity tracking error. Substituting into equation (26), we get: ; in, ; Define the attitude error Lyapunov function: ; Its derivative is equal to: ; By selecting the angular velocity stabilization function: ; Make: ; Considering Therefore, we can conclude that: ; Therefore, from equation (30), we have: ; From the second equation of equation (26) and equation (27), we can obtain: ; Select the Lyapunov function for the attitude system: ; Then its derivative along equation (31) satisfies: ; Torque control can be selected: ; It can be deduced that: ; Finally, the attitude error closed-loop subsystem is obtained: ; ; Equation (34) shows that - Subsystem formula (35) is based on As input, with It is a strictly passive system for output.

[0058] For example, in the above analysis, the term removed by this invention in the derivative term of the Lyapunov function is amplified. and These are all terms that contribute to posture stabilization. In (22), the coupling terms... Caused related items This appears as part of the dissipation rate in the position-free inequality (24). In equation (29)... The introduction of the term is to construct passive connections, and a dissipation term appears in the attitude passive inequality (34). This not only helps maintain composure by utilizing position, but also by maintaining composure by adopting a calm demeanor.

[0059] For example, in step S6, implementing dynamic path speed adjustment by executing the maneuver update rate includes: The path arc length parameter and maneuver speed are dynamically updated based on the path curvature and tracking error. The speed distribution is matched with the path shape to achieve smooth and stable maneuvering. The updated amount is fed back to the outer loop position controller in real time to complete the closed-loop adjustment of the maneuver.

[0060] Take the update law ; The core idea of ​​the trajectory tracking update law is to directly use the error between the actual trajectory and the desired trajectory as the driving signal to iteratively correct the controller parameters or estimates until the tracking error converges to zero. Its physical meaning is intuitive and easy to implement in engineering. This update law is directly related to the deviation between "actual output and desired output," requiring no complex mathematical derivation, thus lowering the design and debugging threshold. For example, in UAV trajectory tracking, the attitude angle command can be directly adjusted using the position error, making it easy for engineers to understand and verify.

[0061] Among them, the curvature and velocity were established in the outer loop controller, and the curvature-velocity coordinated adjustment mechanism was effectively demonstrated and verified in the simulation experiment.

[0062] It exhibits strong robustness and is insensitive to model simplification. It does not require a precise system dynamics model; even if the model contains unmodeled dynamics (such as aerodynamic damping errors), as long as the error signal effectively reflects the tracking deviation, the influence of model errors can be offset through iterative adjustments. It is suitable for complex nonlinear maneuvering systems (such as missiles and robots). The convergence speed is controllable and the response is fast. The error convergence rate can be directly controlled by adjusting the update gain. In scenarios that require rapid tracking of maneuvering targets or sudden trajectory commands (such as spacecraft rendezvous and docking, and emergency obstacle avoidance by autopilot), it can quickly respond to trajectory changes and reduce transient errors.

[0063] The overall controller can be summarized as follows: ; This yields the closed-loop error system used for stability analysis: ; Theorem 1: Under assumption 1 and initial values ​​satisfy... Under these conditions, by adjusting the design parameters, control equation (36) makes the closed-loop system equation (37) be based on... For input, It is a strictly passive system for output.

[0064] Proof: We choose the Lyapunov function of the entire system as the energy storage function: ; By the sourcelessness theorem: ; Thus, the closed-loop system has respect to the input. and output Strictly unpowered.

[0065] Theorem 2: Under initial values ​​satisfying Under the condition that, when And assume there exists a constant. and Make: ; By introducing a damping term into the controller (36) and appropriately adjusting the design (planning and control) parameters, all signals of the closed-loop system can be made bounded, and the output... Can be actually tracked When the noise is zero, the closed-loop system equation (38) is exponentially stable, and the output... Asymptotic tracking is possible .

[0066] Proof: Selection of design parameters Correcting the controller in (36) and for: ; The Lyapunov function satisfies: ; in, , .

[0067] therefore, ; In the formula, For the Lyapunov function at the initial time The corresponding values ​​characterize the magnitude of the total error energy of the initial position and velocity of the system, and are uniquely determined by the initial tracking error conditions of the system. The global exponential convergence coefficient is greater than zero. The exponential decay exponent is denoted by an exponentially decreasing exponent. Therefore, all signals in the closed-loop system are bounded. By selecting a sufficiently large exponent... and Make The limit of is arbitrarily small, which means that the output Can be actually tracked When the noise is zero, the system equation (37) is exponentially stable, and the output... Asymptotic tracking is possible .

[0068] To complete the proof, further explanation is also needed. and Well defined, that is: ; A sufficient condition for it is: ; in, ; For the ability to make In any plan, there is always a sufficiently small and large enough This makes equation (38) true.

[0069] To verify the rationality of the scheme, this paper extends the control strategy to adaptive scenarios. Addressing the uncertainty of the UAV's mass and moment of inertia due to load variations, this paper designs an adaptive trajectory tracking controller under extreme conditions with unknown parameters. This method does not rely on precise system parameters, is highly versatile, and easily extended and transferred. Specifically, it includes: Because in controller (36), and Relying on unknown parameters, direct adaptive control is employed to estimate the parameters in the controller; , The corresponding unknown parameters are defined as follows: The expression is: ; ; For the original Lyapunov function, augmenting the adaptive Lyapunov function terms yields: ; In the formula, Here is a globally adaptive Lyapunov positive definite function used for closed-loop stability analysis. Position error vector transpose, To adaptively update the gain for quality parameters, For quality identification error transpose, , To identify the discrepancy between the estimated mass and the actual mass of the drone. To adaptively update the gain for the moment of inertia parameter, Inertia vector identification error transpose, , The three-axis rotational inertia vector Parameter identification error, From the body Three-axis rotational inertia constitute, This is the squared term corresponding to the arc length auxiliary correction, used to suppress arc length parameter drift, auxiliary disturbance constraints, and stability derivation; Taking the derivative of equation (39), we have: ; in, ; ; ; It is evident that, within the gradient adaptive update framework, the natural and continuous excitation conditions brought about by path segmentation maneuvering ensure consistent convergence of the adaptive parameters, achieving stable parameter identification. This design approach, which relies on the inherent characteristics of the task trajectory to implement excitation constraints, differs from the traditional standard gradient descent method. It eliminates the need for additional auxiliary excitation modules, enhancing the system's autonomy and engineering practicality while ensuring identification convergence.

[0070] For terms without unknowns, the definition is exactly the same as that of the controller formula (36), while for terms with unknowns... and Change the unknown to an estimated value, and derive an adaptive law for the unknown: ; In the formula, This is the feedforward compensation term for the translational channel trajectory. For attitude channel coupling feedforward term, The damping coefficient is the adaptive law. for Convergence gain; You can then obtain: ; In the formula, For a globally adaptive Lyapunov function The first derivative with respect to time; The error systems used for analysis are summarized as follows: ; The following theorem shows that, for cases with uncertain parameters, the controller equation (36) satisfies the principle of necessary equivalence.

[0071] Theorem 3: For system equation (2), a nearly globally smooth control equation (40) is chosen such that the closed-loop system equation (42) is ultimately uniformly bounded, and the bounds can be adjusted to be sufficiently small by appropriately adjusting the parameter bounds. In particular, in the case of no disturbance, a selection is made... Control type (40) (excluding) This item makes the closed-loop system stable. It converges to zero, and the remaining signals are bounded.

[0072] Proof: Combining equations (39) and (41), it is easy to see that the closed-loop system equation (42) is ultimately uniformly bounded.

[0073] In the absence of interference, take By Barbara's lemma, it is easy to see The exponent converges to zero. The proof of the theorem can be completed by following the exact same proof as Theorem 1 and Theorem 2.

[0074] As can be seen from the above embodiments, the present invention proposes a UAV maneuver control architecture based on a Durbins path with curvature and pitch constraints, which realizes deep integration and coupling of path planning and maneuver control, and can achieve direct tracking without converting the path into a time-based trajectory, thus eliminating the system redundancy and tracking delay of traditional solutions.

[0075] This invention uses Rodrigues parameters to construct an attitude error dynamic model, which fundamentally avoids the defects of Euler angle attitude lock-up and quaternion control discontinuity.

[0076] This invention designs a hierarchical passive control structure with outer-loop position maneuver control and inner-loop attitude stabilization control, and introduces a maneuver-oriented filter gradient update law to improve path tracking accuracy and system stability.

[0077] This invention introduces an online adaptive estimation mechanism for mass and moment of inertia, which can compensate for parameter perturbations and external disturbances in real time, significantly enhancing the robustness and flight reliability of UAVs in complex environments.

[0078] This invention integrates Durbins path planning and maneuver control, enabling direct tracking of reference routes without path trajectory conversion. It utilizes Rodrigues parameters to eliminate Euler angle singularities and quaternion control discontinuities, smoothly achieving large-angle maneuvers. Combined with hierarchical control and a filtered gradient update law, it enhances tracking performance and adaptively identifies airframe mass and moment of inertia to suppress parameter disturbances and external interference. This algorithm has low computational cost, is easy to deploy onboard, and effectively enhances the robustness of UAVs in complex environments.

[0079] Example 2. The UAV adaptive maneuver control system based on Durbins path planning provided in this embodiment of the invention includes: The 3D Durbins reference path generation module is used to generate 3D Durbins reference paths with curvature and pitch angle constraints. The module for establishing UAV translational and rotational dynamics models is used to establish UAV translational and rotational dynamics models based on quaternions and to acquire real-time UAV status data. The attitude planner design module is used to design an attitude planner based on the quaternion-based UAV translational and rotational dynamics model. This planner transforms the UAV underactuated system into an all-drive system and combines the yaw angle to synthesize the desired quaternion for inner-loop attitude error synthesis and tracking control.

[0080] A module for obtaining the desired virtual control force is used to construct position and velocity errors and establish an error dynamics model; a translational displacement stabilization function is designed to obtain the desired virtual control force. ; The attitude error construction module is used to construct attitude error and angular velocity error. Based on the design of an attitude error-free model, it designs an angular velocity stabilization function and outputs a continuous and smooth torque control quantity. ; The maneuver update rate enables the path speed dynamic adjustment module, which dynamically updates the path arc length parameter and maneuver speed based on the path curvature and tracking error. It matches the speed distribution with the path shape to achieve smooth and stable maneuvering, and feeds back the update amount to the outer loop position controller in real time to complete the closed-loop maneuver adjustment.

[0081] The filter gradient update law constitutes an adaptive parameter correction module, which integrates position, attitude and velocity errors to identify the body mass and moment of inertia online, compensates for parameter perturbations and external disturbances in real time, corrects inner and outer loop control quantities, realizes the integrated coupling of Dubins path planning and maneuver control, and ensures accurate flight path tracking.

[0082] To further illustrate the effects of the embodiments of the present invention, the following simulation experiment was conducted. The simulation object was a quadcopter unmanned aerial vehicle (UAV) system model, and its actual physical parameters were set as follows: mass was... The moment of inertia matrix is: ; gravitational acceleration .

[0083] For the adaptive filter gradient update law, the desired path is generated by the Dubins path planning algorithm proposed in the path planning section. The starting pose and ending pose are set as follows: ; Path curvature constraint is Pitch angle constraint is The cruising speed is taken as .

[0084] The corresponding initial state of the drone is: position initial velocity value Initial value of angular velocity The initial values ​​of the attitude quaternions are determined by the initial yaw angle. Determined as ; Desired path tracking speed set to ; Control parameters are , , , , , .

[0085] Figure 2 This is a simulation structure diagram provided by the present invention; Figure 3 This is the UAV position error diagram provided by the present invention; Figure 4 This is the UAV attitude error diagram provided by the present invention; Figure 5 This is the UAV control input diagram provided by the present invention; Figure 6 This is the UAV adaptive map provided by the present invention; Figure 7 This is the path velocity diagram provided by the present invention. The simulation results are as follows: Figures 2 to 7 As shown, the effectiveness of the proposed control scheme is verified. Figure 3 The 3D trajectory of the drone was demonstrated, with minimal path tracking error, indicating that the designed algorithm can achieve accurate 3D trajectory tracking. Figure 4 It can be seen that the attitude error , , After a slight fluctuation in the initial stage, it quickly converged to near zero, verifying the fast response capability and stability of the attitude control loop. Figure 5 Given the control input curve and total thrust With torque After an initial rapid adjustment, it remains stable without continuous oscillation or divergence, meeting the system's physical constraints and stable operation requirements. Figure 6 Presents adaptive parameter estimation results, unknown parameters Fast convergence to steady-state value, parameter estimation error The gradual decay over time demonstrates the effectiveness of the adaptive algorithm. Figure 7 Display path speed The proposed control algorithm successfully tracked path speed, ensuring the completion of maneuverable tasks. Overall, the simulation results collectively validated the excellent performance and robustness of the proposed control algorithm in trajectory tracking, attitude stabilization, and parameter adaptation.

[0086] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. An adaptive maneuver control method for unmanned aerial vehicles based on Durbins path planning, characterized in that, The method includes the following steps: S1. Input the UAV's starting and ending poses, maximum turning radius, and pitch angle constraints. Solve for both externally and internally tangent CSC-type Durbins candidate paths and select the global shortest path. Construct a 3D reference path with height-uniform velocity constraints along the arc length parameter. ; S2. Establish a quaternion-based UAV translational and rotational dynamics model. Onboard sensors collect the UAV's current position, linear velocity, attitude quaternion, and three-axis angular velocity flight status in real time; directly read the three-dimensional reference path. With arc length parameter As a reference for drones to conduct maneuvering flights along predetermined routes; S3. Design an attitude planner to convert the underactuated UAV system into an equivalent all-drive control form. Based on the virtual control force output from the outer loop, calculate the total thrust and desired attitude orientation. Combine the flight yaw angle to synthesize the desired attitude quaternion and send it to the attitude inner loop to complete the maneuver attitude orientation. S4. Construct position and velocity errors, and establish an error dynamics model; design a translational displacement stabilization function to obtain the desired virtual control force. ; S5. Construct attitude error and angular velocity error, and establish an attitude error model based on Rodriguez parameters; design an angular velocity stabilization function to output a continuous and smooth torque control quantity. ; S6. Implement dynamic adjustment of path speed by executing the maneuver update rate: dynamically update the path arc length parameter and maneuver speed according to the path curvature and tracking error, match the speed distribution with the path shape, achieve smooth and stable maneuvering, and feed back the update amount to the outer loop position controller in real time to complete the closed-loop adjustment of maneuvering. S7. Execute the maneuvering filter gradient update law and complete adaptive parameter correction: Combine position error, attitude error and maneuvering speed information, use the maneuvering filter gradient update law to estimate the mass and moment of inertia parameters of the UAV online, adaptively compensate for system parameter perturbations and external disturbances, and correct the inner and outer loop control quantities in real time with the estimation results. In step S1, solving for the two types of CSC-type Dubins candidate paths, external and internal, and selecting the global shortest path includes: generating a CSC path composed of circular arcs and straight line segments based on the initial pose, final pose, curvature, and pitch angle constraints; calculating the external and internal Dubins paths respectively and selecting the global shortest path; and generating a three-dimensional Dubins reference path with the path length as a parameter by using uniform motion in the vertical direction. Combining external and internal Dubins paths, the shortest path is calculated for each type of path, and the global shortest path is finally selected as the expected path for the UAV; specifically defined as: Under the externally tangent configuration, the path length expression is defined as: ； In the formula, The total length of the externally tangent CSC type Durbins path, subscript For turning direction identification parameters, The drone, with its externally tangent configuration, adopts a counter-clockwise turning mode. The UAV with the external tangent configuration adopts a clockwise turning mode; The central turning angle corresponding to the turning arc at the starting point of the externally tangent configuration. The maximum bending rate of the drone, The length of the straight segment connecting the two curved arcs. The central turning angle corresponding to the turning arc at the end of the externally tangent configuration. These correspond to the arc lengths of the two turning arcs, respectively. pass Solving for the parameters that minimize the path length yields the desired result. And determine the path length corresponding to the shortest path under the externally tangent configuration. ; Under the inscribed configuration, the path length expression is defined as: ； In the formula, The total length of the CSC-type Dubins path in the inscribed configuration, subscript For steering combination identification parameters, This represents the initial arc turning counterclockwise and the final arc turning clockwise under the inscribed configuration. This represents the starting arc turning clockwise and the ending arc turning counterclockwise under the inscribed configuration; The central turning angle corresponding to the turning arc at the starting point of the inscribed configuration. The central turning angle corresponding to the turning arc at the end of the inscribed configuration; These correspond to the arc lengths of the two turning arcs, respectively. pass Solving for the parameters that minimize the path length yields the desired result. And determine the path length corresponding to the shortest path under the inscribed configuration. ; Total length of the shortest Dubins path globally for: 。 2. The UAV adaptive maneuver control method based on Durbins path planning according to claim 1, characterized in that, The vertical direction exhibits uniform motion, expressed as: ； In the formula, arc length The corresponding expected vertical height, The vertical altitude coordinates of the drone's flight endpoint. The vertical altitude coordinates of the drone's flight start point. This is the real-time arc length parameter for the path. Vertical height with respect to arc length The first rate of change, Vertical height with respect to arc length The second derivative of is always 0 under uniform longitudinal motion; Define the three-dimensional Durbins expected path : Using the path arc length The complete three-dimensional expected path of the independent variable is given by the plane Dubins horizontal coordinates. , and arc length Corresponding expected vertical height Combination structure; when the arc length is taken as the total global path length hour, The corresponding end point of the path.

3. The UAV adaptive maneuver control method based on Durbins path planning according to claim 1, characterized in that, In step S2, establishing the quaternion-based UAV translational and rotational dynamics model includes: acquiring real-time UAV state data, including real-time collected UAV position, velocity, attitude, and angular velocity data; the expression is: ； In the formula, Let be the first derivative of the drone's position with respect to time. For the inertial speed of the drone, The linear acceleration in the inertial frame of the UAV is the inertial velocity. The first derivative with respect to time; This represents the quaternion multiplication operator, used to perform vector coordinate transformations between the body coordinate system and the inertial coordinate system. For attitude quaternions The corresponding quaternion inverse, Let gravitational acceleration be constant. This represents the total external disturbance experienced by the UAV's translational path. To augment the quaternion form of angular velocity quaternions, The scalar part is 0, and the vector part is the angular velocity of the three axes of the machine. Here is the moment of inertia matrix in the UAV's body coordinate system. For the attitude quaternion of the UAV; This is the vertically upward unit basis vector of the inertial frame, used for thrust coordinate transformation of the UAV; The variation law of the angular velocity of the UAV attitude random body. ; For the angular acceleration of the drone body, For the overall quality of the drone, The three-axis angular velocities of the drone body. For the three-axis control torque of the UAV (roll, pitch, and yaw), The total external disturbance experienced by the UAV's rotation path. This is the total scalar thrust of the quadcopter of the UAV, used to control the translational motion of the UAV.

4. The UAV adaptive maneuver control method based on Durbins path planning according to claim 3, characterized in that, In step S3, the attitude planner is designed to convert the underactuated UAV system into an equivalent all-drive control form, including: The position dynamic equations for all-wheel drive configuration are: ； In the formula, is the equivalent virtual control force vector of the UAV, which is derived from the total thrust of the UAV. After the current attitude quaternion Obtained by rotation transformation; in, To design control, a desired control vector is introduced. Suppose that there exists , so that: ； In the formula, For the desired virtual control quantity, The desired attitude unit quaternion of the UAV obtained by the attitude planner is used to construct the desired virtual control quantity. This characterizes the target attitude that the UAV needs to achieve to track the reference flight path; For the desired pose quaternion The reverse; By setting get , Simplified to: ； In the formula, Desired control vector The direction vector; The expected quaternion containing the yaw angle is used as the output of the attitude planner to synthesize the attitude error; ； In the formula, To complete the vertical unit vector of the machine body Desired thrust direction to inertial frame Rotational transformation, This is the expected quaternion corresponding to the yaw angle.

5. The UAV adaptive maneuver control method based on Durbins path planning according to claim 4, characterized in that, In step S4, position error and velocity error are constructed, and an error dynamics model is established; a translational displacement stabilization function is designed to obtain the desired virtual control force. This includes: dynamically allocating path speed based on path curvature to enable adaptive speed adjustment between turning and straight sections; and calculating the total scalar thrust of the continuous UAV quadcopter from virtual control force. This provides the desired direction command for attitude control; The desired path obtained from the three-dimensional Durbins program Define position error for: ； In the formula, For the desired path The three components; Rewritten in error form, we get: ； In the formula, The second derivative of the UAV position error vector with respect to time represents the acceleration dynamics of the position error. For Dubins' expected position vector The second derivative with respect to time represents the target acceleration corresponding to the desired trajectory; The actual virtual control force and the expected virtual control force of the drone The control deviation between them ; An outer-loop position stabilization controller is designed based on an error dynamics model. A stabilization-type Lyapunov function is constructed, starting with the translational displacement stabilization function. The expression is: ； In the formula, This is a translational displacement stabilization function used to preprocess position tracking errors and connect the recursive relationships between the position loop and the velocity loop; The position outer loop positive definite control gain, For Dubins' desired position relative to path arc length The first derivative, The linear velocity along the reference path; Based on this translational displacement stabilization function, the desired virtual control force of the outer loop control output is further derived: ； In the formula, For the positive definite control gain of the speed loop, These are positive definite adjustable constraint parameters. For speed tracking error, This is the total feedforward compensation term for the desired path; The modulus of the desired virtual control force is calculated, and the total thrust of the UAV is obtained by solving the problem. .

6. The UAV adaptive maneuver control method based on Durbins path planning according to claim 1, characterized in that, In step S5, attitude error and angular velocity error are constructed, and an attitude error model is established based on Rodriguez parameters; an angular velocity stabilization function is designed to output a continuous and smooth torque control quantity. This includes: constructing a closed-loop attitude error subsystem, and deriving continuous and smooth three-axis torque control quantities based on a backstepping recursive approach. To achieve UAV attitude tracking; in the attitude error closed-loop subsystem, the rotation error is defined in quaternion form: ； In the formula, The attitude quaternion error of the UAV is given by the inverse of the desired attitude quaternion. Quaternions of the actual attitude of the machine The value obtained by performing quaternion multiplication represents the rotational deviation of the UAV's current actual attitude relative to the desired attitude. Taking the time derivative of the attitude error quaternion, we obtain the kinematic equation of the attitude error: ； In the formula, The first derivative of the attitude error quaternion with respect to time describes the dynamic evolution of attitude deviation with respect to angular velocity error. This represents the three-axis angular velocity error vector of the aircraft. The relationship for angular velocity error is constructed as follows: ； In the formula, The desired angular velocity of the UAV is obtained from the attitude loop planning. This is the equivalent desired angular velocity after attitude error quaternion coordinate transformation, used to complete coordinate system matching and solve for angular velocity deviation. ; Convert the quaternion attitude error into a singularity-free Rodrigues parameter form. The corresponding error kinematic equations are obtained: ； In the formula, The attitude error vector is expressed based on Rodrigues parameters, thus avoiding the entanglement singularity problem in quaternion attitude representation; The first derivative of the Rodriguez attitude error with respect to time characterizes the dynamic rate of change of the attitude deviation. The dynamic equation for angular velocity error is derived as follows: ； In the formula, Let the moment of inertia matrix be the rotational moment of inertia matrix of the UAV's airframe center. The time derivative of the angular velocity error vector represents the angular acceleration error. Equivalent desired angular velocity The first derivative with respect to time, For three-axis control torque input; Select the angular velocity stabilization function: ； In the formula, This represents the positive definite control gain for the attitude loop. This is the coupling compensation coefficient term; attitude Rodriguez error Construct intermediate virtual states to complete the pre-design of attitude loop backstep recursion; Based on this angular velocity stabilization function, a three-axis torque control input is designed: ； In the formula, This is the positive definite control gain of the attitude angular velocity loop. For angular velocity tracking error, Angular velocity stabilization function The first derivative with respect to time, For attitude Rodriguez error The transpose obtained by construction.

7. The UAV adaptive maneuver control method based on Durbins path planning according to claim 6, characterized in that, In step S6, implementing dynamic path speed adjustment by executing the maneuver update rate includes: taking the update law. The overall controller is: ； A closed-loop error system for stability analysis is obtained: ； In step S7, executing the motor filter gradient update law and completing the adaptive parameter correction includes: , The corresponding unknown parameters are defined as follows: The expression is: ； ； In the formula, For the actual weight of the drone , is a parameter vector composed of the rotational inertia of the three axes of the machine body. For the drone to circle the body Roll axis moment of inertia For the drone to circle the body Pitch axis moment of inertia For the drone to circle the body Yaw axis moment of inertia; the three inertial elements form the diagonal rotational moment of inertia matrix of the UAV. ; For the original Lyapunov function, augmenting and adapting the corresponding Lyapunov function terms yields: ； In the formula, Here is a globally adaptive Lyapunov positive definite function used for closed-loop stability analysis. Position error vector transpose, To adaptively update the gain for quality parameters, For quality identification error transpose, , To identify the discrepancy between the estimated mass and the actual mass of the drone. To adaptively update the gain for the moment of inertia parameter, Inertia vector identification error transpose, , The three-axis rotational inertia vector Parameter identification error, From the body Three-axis rotational inertia constitute, This is the squared term corresponding to the arc length auxiliary correction, used to suppress arc length parameter drift, auxiliary disturbance constraints, and stability derivation; For terms without unknowns, use the exact same definition as the controller; for terms with unknowns... and Change the unknowns to estimated values ​​and derive an adaptive law for the unknowns: ； In the formula, This is the feedforward compensation term for the translational channel trajectory. For attitude channel coupling feedforward term, The damping coefficient is the adaptive law. for Convergence gain; get: ； In the formula, For a globally adaptive Lyapunov function The first derivative with respect to time; The error systems used for analysis are summarized as follows: 。 8. An adaptive maneuver control system for unmanned aerial vehicles based on Durbins path planning, characterized in that, The system implements the UAV adaptive maneuver control method based on Durbins path planning as described in any one of claims 1-7, and the system includes: The 3D Durbins reference path generation module is used to generate 3D Durbins reference paths with curvature and pitch angle constraints. The module for establishing UAV translational and rotational dynamics models is used to establish UAV translational and rotational dynamics models based on quaternions and to acquire real-time UAV status data. The attitude planner design module is used to design an attitude planner based on the quaternion-based UAV translational and rotational dynamics model. It transforms the UAV underactuated system into an all-drive system, calculates the total thrust and desired attitude direction from the desired virtual control force, extracts the attitude through quaternion square root operation, and combines the yaw angle to synthesize the desired quaternion for inner-loop attitude error synthesis and tracking control. A module for obtaining the desired virtual control force is used to construct position and velocity errors and establish an error dynamics model; a translational displacement stabilization function is designed to obtain the desired virtual control force. ; The attitude error construction module is used to construct attitude error and angular velocity error. Based on the design of an attitude error-free model, it designs an angular velocity stabilization function and outputs a continuous and smooth torque control quantity. ; The maneuver update rate enables the path speed dynamic adjustment module, which dynamically updates the path arc length parameter and maneuver speed according to the path curvature and tracking error, matches the speed distribution with the path shape, achieves smooth and stable maneuvering, and feeds back the update amount to the outer loop position controller in real time to complete the closed-loop maneuvering adjustment. The filter gradient update law constitutes an adaptive parameter correction module, which integrates position, attitude and velocity errors to identify the body mass and moment of inertia online, compensates for parameter perturbations and external disturbances in real time, corrects inner and outer loop control quantities, realizes the integrated coupling of Dubins path planning and maneuver control, and ensures accurate flight path tracking.

Images