A UAV Swarm Trajectory Tracking Control Method Based on Virtual Containers and Ellipsoid Estimation

Abstract

This invention discloses a UAV swarm trajectory tracking control method based on virtual containers and ellipsoid estimation, belonging to the field of automatic control technology. The steps are as follows: generating a parameterized reference curve for the target; establishing a state nonlinear dynamic model to obtain the nominal state trajectory and calculating the nominal control input; generating the nominal trajectory, modeling a bounded uncertainty vector to obtain a time-varying linear dynamic model of the target state; obtaining an inner control ellipsoid based on the control deviation constraint set, and obtaining a time-varying outer uncertainty ellipsoid based on the state deviation; establishing a UAV swarm dynamic model to obtain the UAV swarm constraint set; defining a time-varying solvable set and constructing a solvable set ellipsoid tube; designing a boundary feedback control law; generating and synchronously implementing control commands for each UAV in the swarm to complete the UAV swarm trajectory tracking control. This invention solves the problem of reliably and safely controlling UAV swarms to perform collaborative tasks in complex environments.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology, and in particular relates to a method for tracking and controlling the trajectory of a drone swarm based on virtual containers and ellipsoid estimation. Background Technology

[0002] With the widespread application of UAV swarm technology in missions such as regional reconnaissance, search and rescue, and light shows, achieving high-precision motion control of multiple UAVs along predetermined trajectories has become crucial for improving mission efficiency. Traditional UAV swarm control methods often employ trajectory tracking or path tracking strategies and rely to some extent on global positioning information and a relatively stable motion environment. These traditional control methods are typically based on two fundamental assumptions: first, the UAVs can continuously acquire reliable global position feedback; and second, the target trajectory or formation path is a low-speed, smooth, or predictable pattern, allowing the use of predefined fixed formation configurations such as linear formations or grid distributions during control. Traditional control methods are effective in open spaces, with good communication, and where target motion is simple.

[0003] However, when the mission environment transforms into a complex space with dense obstacles, signal interference, or the need to traverse narrow passages, while simultaneously requiring the UAV swarm to strictly track complex three-dimensional curves and meet real-time obstacle avoidance and collision prevention requirements, traditional control methods reveal significant shortcomings. Specifically, traditional control methods generally employ simplified dynamic models, failing to fully consider the inherent nonlinearity and strong coupling characteristics of quadrotor UAVs, as well as actuator physical constraints. This leads to control commands being difficult to execute effectively in practical systems and may even cause instability. Furthermore, most control methods lack unified handling of state constraints such as attitude safety range, thrust limiting, and swarm collision avoidance, often employing local optimization or heuristic rules, making it difficult to satisfy global constraints while ensuring real-time performance. In the presence of model uncertainties and external disturbances, traditional open-loop or simplified feedback control methods exhibit poor robustness, easily leading to accumulated tracking errors or even mission failure. In addition, existing methods suffer from low computational efficiency when dealing with high-dimensional systems and multi-constraint coupled problems, making it difficult to support online real-time planning and control of large-scale swarms, severely limiting their application potential in dynamic and complex scenarios. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a UAV swarm trajectory tracking and control method based on virtual containers and ellipsoid estimation, which solves the problem of difficulty in controlling UAV swarms to reliably and safely perform collaborative tasks in complex environments.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: This invention provides a method for tracking and controlling the trajectory of a UAV swarm based on virtual containers and ellipsoid estimation, comprising the following steps: S1. Based on the 3D map data of the mission environment and the heuristic function of the improved hybrid A*, generate a parameterized reference curve for the target based on the initial virtual container; S2. Establish a nonlinear dynamic model of the state, and generate a virtual guide point trajectory based on the target parameterized reference curve to derive the nominal state trajectory in reverse, and obtain the nominal control input through inverse dynamics calculation; S3. Generate a nominal trajectory based on the nominal state trajectory and nominal control input, and perform a first-order Taylor expansion on the nonlinear dynamic model of the state near the nominal trajectory, and model a bounded uncertainty vector to obtain a time-varying linear dynamic model of the target state. S4. Approximate the interior of the control deviation constraint set as a time-varying inscribed control ellipsoid, and perform minimum volume circumscribed ellipsoid approximation and convex optimization on the uncertainty polyhedron model based on the uncertainty set modeling according to the state deviation, to obtain the time-varying circumscribed uncertainty ellipsoid. S5. Establish a dynamic model of the UAV swarm, and construct a time-varying scaling virtual container based on the initial virtual container and the virtual guide point trajectory. Vertically stack the virtual container constraints, anti-collision constraints and state deviation constraints of the UAV swarm to obtain the UAV swarm constraint set. S6. Based on the UAV swarm dynamics model and UAV swarm constraint set, a time-varying solvable set is defined, and a reverse recursive calculation is performed from the terminal time until the initial time to obtain the time-varying solvable set ellipsoid sequence, which constitutes the solvable set ellipsoid tube. S7. Based on the solvable ellipsoid tube, construct the Lyapunov function of the solvable ellipsoid distance, and design the boundary feedback control law based on the time-varying uncertainty ellipsoid. S8. Generate control commands for each UAV in the UAV swarm based on the boundary feedback control law, and use a distributed execution architecture to enable each UAV in the UAV swarm to implement the control commands synchronously, thereby completing the trajectory tracking control of the UAV swarm.

[0006] The beneficial effects of this invention are as follows: The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation provided by this invention introduces a term penalizing the distance of the state deviating from the container center into the heuristic function of the traditional A* algorithm, and adopts a multi-layer heuristic function fusion strategy. During path search, it simultaneously considers geometric distance, dynamic cost, and virtual container constraints, improving the search efficiency and success rate for safe and feasible paths in complex three-dimensional space. This invention employs a precise 12-dimensional state nonlinear dynamic model and time-varying linearization technology, comprehensively considering the UAV's position, velocity, Euler angles, and angular velocity, and models a bounded uncertainty vector, thus obtaining... The time-varying linear dynamics model for reaching the target state significantly improves the accuracy and adaptability of UAV tracking control. This invention transforms nonlinear constraint control into a computable ensemble evolution problem through virtual containers and ellipsoidal computation methods, providing a systematic solution for UAV swarm cooperative control. This invention proposes methods for control constraint ellipsoidization and uncertainty ellipsoid delimitation, and designs a boundary feedback control law based on a solvable set ellipsoidal tube, achieving efficient control command generation and strong robustness while ensuring safety. This invention effectively balances computational complexity and real-time requirements through a combination of offline computation and online control, making it suitable for practical engineering applications.

[0007] Other advantages of the present invention will be analyzed in more detail in the following embodiments. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating the steps of a drone swarm trajectory tracking and control method based on virtual container and ellipsoid estimation in an embodiment of the present invention. Detailed Implementation

[0010] 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0011] like Figure 1 As shown, in one embodiment of the present invention, the present invention provides a method for tracking and controlling the trajectory of a UAV swarm based on virtual containers and ellipsoid estimation, comprising the following steps: S1. Based on the 3D map data of the mission environment and the heuristic function of the improved hybrid A*, generate a parameterized reference curve for the target based on the initial virtual container; S1 includes the following steps: S11. Obtain 3D map data of the mission environment, including obstacle locations and mission area boundaries; S12. Based on the 3D map data of the task environment, define shape and size constraints to obtain a static convex polyhedron as the initial virtual container. The calculation expression for the initial virtual container is as follows: , , , in, Represents the initial virtual container. Represents a position vector in three-dimensional space. Indicates belonging to, Represents the set of real numbers. Indicates that, Let represent the normal vector matrix of each plane of the convex polyhedron. Represents the offset vector. Indicates the number of planes in a convex polyhedron; In this scheme, the initial virtual container includes the expected range of motion of the drone and reserves sufficient safety margin to cope with errors. As a global safety corridor, it can constrain the executable space for subsequent path search. S13. Based on the heuristic function of the improved hybrid A*, a path search is performed in the three-dimensional state space based on the initial virtual container to obtain discrete paths; S13 includes the following steps: S131, Define the path search state as ,in, The X-axis coordinate represents the position in three-dimensional space. The Y-axis coordinate represents the position in three-dimensional space. The Z-axis coordinate represents the position in three-dimensional space. Indicates the yaw angle of the drone; S132. Based on the path search state, construct a set of continuous trajectory segments as motion primitives based on the differential flatness theory, wherein the initial state of the motion primitives is... for The final state of the motion primitive for ,in, The X-axis coordinates representing the starting position of the trajectory. The Y-axis coordinate representing the starting position of the trajectory. The Z-axis coordinate represents the starting position of the trajectory. This indicates the yaw angle of the drone at the start of the trajectory. The X-axis coordinates representing the end position of the trajectory. The Y-axis coordinate representing the end position of the trajectory. The Z-axis coordinate representing the end position of the trajectory. Indicates the yaw angle at the end of the trajectory; In this scheme, each motion element corresponds to a flat output trajectory that is optimal or energy-optimal over a certain period of time. The flat output trajectory is obtained by solving the optimization model. S133. Construct a trajectory optimization model for motion primitives; The calculation expression for the trajectory optimization model is as follows: , in, This indicates taking the minimum value. This represents the time duration corresponding to the motion primitive. Indicates jerk. Represents the square of the norm. Indicates the rotation weighting coefficient. Indicates yaw acceleration. Represents the time infinitesimal element; In this scheme, the trajectory optimization model based on motion minimizes the weighted square integral of the rate of change of acceleration and the yaw angle acceleration, so that the motion primitives are optimized to be smooth, energy-efficient, feasible and safe under the premise of satisfying boundary conditions, container constraints, collision avoidance constraints and dynamic constraints. S134. The heuristic function of the hybrid A* algorithm is improved to obtain the improved hybrid A* heuristic function. In this scheme, the heuristic function improves the search efficiency and safety of complex three-dimensional curve paths by integrating geometric, dynamic and container space information. The computational expression for the improved hybrid A* heuristic function is as follows: , , , in, This represents an improved hybrid A* heuristic function. This indicates taking the maximum value. Indicating geometric distance inspiration, Indicates the minimum time cost. Indicates deviation from the weighting coefficient. This indicates the distance the penalty state deviates from the center of the container. Represents the L2 norm, This represents the position vector of the target point in three-dimensional space. Indicates the maximum speed of the drone. This represents the position vector of the container's center point in three-dimensional space. In this plan, This represents the minimum time cost estimated based on the Reeds-Shepp extended model; This scheme introduces a term that penalizes the state deviating from the center of the virtual container into the heuristic function of the traditional hybrid A* algorithm, and adopts a multi-layer heuristic function fusion strategy. This allows for the simultaneous consideration of geometric distance, dynamic cost, and virtual container constraints during path search, thereby improving the search efficiency and success rate of safe and feasible curved paths in complex 3D space. S135. By replacing the heuristic function in the hybrid A* algorithm with the improved hybrid A* heuristic function, the improved hybrid A* algorithm is obtained. S136. Based on the trajectory optimization model of the motion primitives and the improved hybrid A* algorithm, the nodes are iteratively expanded from the starting point until the target state region is reached or the preset maximum number of iterations is exceeded, so as to obtain a discrete path point sequence from the starting point to the ending point, which is used as the discrete path.

[0012] In this scheme, during the iterative expansion of nodes, the control input constraints, attitude safety constraints, collision avoidance constraints, and virtual container constraints are continuously checked.

[0013] S14. Perform spline fitting on the discrete path, and generate an initial smooth reference curve through curvature constraints, ascent angle constraints, and curve continuity constraints based on smoothness weights. S14 includes the following steps: S141. Take each discrete path point in the discrete path as the initial control point and fit it with a uniform B-spline curve to obtain the initial parameterized curve; in this scheme, the discrete path points in the discrete path refer to the starting point, ending point and nodes generated by the iterative expansion of the discrete path. S142. Based on the curvature constraint, the ascent angle constraint, and the curve continuity constraint based on the smoothness weight, the control points of the initial parameterized curve are optimized to obtain the initial smooth reference curve. The calculation expressions for the curvature constraint, the ascent angle constraint, and the curve continuity constraint based on smoothness weights are as follows: , , , in, Represents the curvature of the curve. Represents the tangent vector of the curve. The normal vector of the curve. Represents the cube of the modulus. Indicates the maximum curvature threshold. This represents the derivative of the position with respect to the Z-axis. This represents an infinitesimal increment along the direction of the curve parameter. This represents the tangent value of the maximum climb angle. Represents the set of control points to be optimized. Take the minimum value. Indicates the first One control point to be optimized Indicates the first One initial control point, Represents the square of the modulus. This represents the smoothing weights. In this scheme, It can reflect the curvature energy of a curve.

[0014] S15. Perform dense sampling on the initial smoothed reference curve to obtain a set of sampling points; S16. Perform dual verification on the sampling point set based on the virtual container inclusiveness verification model and the safe distance verification model. If the verification passes, the target parameterized reference curve is set; otherwise, the smoothing weight is adjusted and the process returns to S14. The calculation expressions for the virtual container inclusiveness verification model and the safe distance verification model are as follows: , in, Represents the first point in the set of sampling points. One sampling point, Represents a set of obstacle locations Obstacle locations Take the minimum value. This represents the minimum safe distance threshold between the drone and the obstacle, where, , This represents the total number of sampling points in the sampling point set.

[0015] S2. Establish a nonlinear dynamic model of the state, and generate a virtual guide point trajectory based on the target parameterized reference curve to derive the nominal state trajectory in reverse, and obtain the nominal control input through inverse dynamics calculation; S2 includes the following steps: S21. Based on the physical parameters and kinematic principles of the UAV, establish a nonlinear dynamic model of the state; The calculation expression for the state nonlinear dynamic model is as follows: , in, Represents the state vector of the drone. The derivative representing the position of the UAV in the X-axis direction in the inertial coordinate system. This represents the velocity of the UAV along the X-axis in the inertial coordinate system. The derivative representing the position of the UAV in the Y-axis direction in the inertial coordinate system. This represents the velocity of the UAV along the Y-axis in the inertial coordinate system. The derivative representing the position of the UAV in the Z-axis direction in the inertial coordinate system. This represents the velocity of the UAV along the Z-axis in the inertial coordinate system. Indicates the quality of the drone. This represents the acceleration of the UAV along the X-axis in the inertial coordinate system. This indicates the total pull of the drone. Indicates the roll angle of the drone. Indicates the drone's climb angle. This represents the acceleration of the UAV along the Y-axis in the inertial coordinate system. This represents the acceleration of the UAV along the Z-axis in the inertial coordinate system. Represents gravitational acceleration. The derivative of the roll angle, Indicates the roll angle and angular velocity. Indicates the angular velocity of the climb angle. Indicates yaw angle and angular velocity. The derivative representing the yaw angle. The derivative of the ascent angle, This represents the inertia tensor along the X-axis in the body coordinate system. Indicates roll acceleration. This indicates the horizontal distance from the drone's center of mass to each motor. This represents the rolling torque component of the drone. This represents the inertia tensor along the Z-axis in the body coordinate system. This represents the inertia tensor along the Y-axis in the body coordinate system. Indicates yaw acceleration. This represents the yaw moment component of the drone. Indicates the angular acceleration of the climb. This represents the pitch moment component of the drone; In this plan, , and The inertial tensor diagonal matrix that can form the body coordinate system ; S22. Extract the tangent vector of the target parameterized reference curve; The expression for calculating the tangent vector of the target parameterized reference curve is as follows: , in, This represents the tangent vector of the target parameterized reference curve. This represents the differential of the target parameterized reference curve with respect to the direction of the curve parameters. This represents the derivative of the target parameterized reference curve along the X-axis. This represents the derivative of the target parameterized reference curve along the Y-axis. This represents the derivative of the target parameterized reference curve along the Z-axis. S23. Define the curve arc length function; The expression for calculating the arc length function of the curve is as follows: , in, Represents the arc length function. This represents the cumulative path length from the starting point to the current point. This represents the minimum value of the curve parameter. Represents the path element. This represents the differential of the path element along the X-axis. This represents the differential of the path element along the Y-axis. This represents the differential of the path element along the Z-axis. There are speed constraints at the virtual guide point; The calculation expression for the velocity constraint is as follows: , , in, This represents the derivative of time at the virtual guide point. express The derivative of the parametric function of the time-time curve. express The drone speed at any given time; since the curve parameter function has a monotonically increasing property, then based on the curve parameter function... The nonlinear differential equation expression and arc length function can be obtained. , The differential of the arc length function is represented by the differential equation of the arc length parameter obtained from the velocity constraint. The arc length trajectory is obtained by calculating the arc length function and integrating the UAV velocity. The trajectory of the virtual guide point can be obtained by solving the inverse function. S24. Based on the curve arc length function and the tangent vector of the target parameterized reference curve, and based on the velocity constraint at the virtual guide point, the trajectory of the virtual guide point is calculated; in this scheme, the generated virtual guide point trajectory is used as the spatiotemporal reference for the cluster's cooperative motion. The calculation expression for the virtual guide point trajectory is as follows: , , in, Represents the trajectory of the virtual guide point. Represents the reference curve function. This represents a function of arc length that varies with time. This represents finding the inverse function of the arc length function that varies with time. This represents the derivative of time at the virtual guide point. express The derivative of the parametric function of the time-time curve. express The speed of the drone at any given moment The derivative of the arc length function; S25. Based on the theory of differential flatness, use a drone to track the trajectory of a virtual guide point and derive the nominal state trajectory in reverse. In this scheme, the nominal state trajectory satisfies dynamic constraints. The formula for calculating the UAV's position in the nominal state trajectory is as follows: , in, express The drone's location at any given time; According to the theory of differential flatness, all states and control inputs of the UAV can be expressed as algebraic functions of several flat outputs and their derivatives; due to the yaw angle at the virtual guide point... Already by If the direction is determined, the roll angle can be adjusted by changing the yaw angle. and Complies with attitude safety constraints; According to rotational dynamics, the body angular velocity is the vector sum of the angular velocities of each rotation in the body coordinate system. By numerically differentiating the Euler angles, the nominal body angular velocity can be obtained. The nominal trajectory is generated under the assumption of ideal, disturbance-free, and precise tracking, providing an ideal reference for subsequent control. However, in actual systems, there are model errors, linearization errors, and external disturbances.

[0016] S26. Based on the nominal state trajectory and the state nonlinear dynamic model, inverse dynamics calculation is performed to obtain the nominal control input. In this scheme, the nominal control input corresponds to the nominal thrust of the motor, and the nominal thrust of the motor can provide a benchmark for linearization and constraint processing. The calculation expression for the nominal control input is as follows: , , , , , , in, Indicates the nominal control input. This represents the inverse of the mapping matrix between the nominal control input and the motor. Indicates nominal controllability. This represents the mapping matrix between the nominal control input and the motor. This indicates the minimum threshold of motor thrust. Indicates the first The thrust of each motor This indicates the maximum threshold of motor thrust. This indicates the maximum threshold for roll angle. This represents the maximum threshold for the climb angle, where, In this plan, and All angles are much smaller than 90° to prevent the drone from entering an uncontrollable state or an Euler angle singularity.

[0017] S3. Generate a nominal trajectory based on the nominal state trajectory and nominal control input, and perform a first-order Taylor expansion on the nonlinear dynamic model of the state near the nominal trajectory, and model a bounded uncertainty vector to obtain a time-varying linear dynamic model of the target state. S3 includes the following steps: S31. Generate the nominal trajectory based on the nominal state trajectory and the nominal control input. ; In this embodiment, based on the nonlinear dynamic system and initial state conditions, a trajectory optimization or reference planning algorithm is used to generate a nominal trajectory to provide a linearized reference benchmark. S32. Perform a first-order Taylor expansion on the nonlinear dynamic model of the state near the nominal trajectory to obtain a time-varying linear dynamic model of the state. The calculation expression for the time-varying linear dynamics model is as follows: , , , , , , in, The derivative of the UAV's state vector. The derivative of the nominal state trajectory. Represents the system matrix. Indicates state deviation, Represents the input matrix, Indicates control deviation. This represents the sum of the higher-order Taylor remainder and the unmodeled dynamics. Represents the nominal trajectory property function. This represents the partial derivative of the nominal trajectory property function with respect to the UAV's state vector. This represents the partial derivative of the nominal trajectory property function with respect to the control input. The state vector function of the UAV, Indicates the control input function; S33. Modeling bounded uncertainty vectors based on the sum of higher-order Taylor remainders and unmodeled dynamics. The linearized error system is obtained. In this scheme, error analysis and sensitivity calculation are used to identify and quantify the magnitude and statistical properties of the bounded uncertainty vector, thereby providing a basis for evaluating the robustness of the system. The calculation expression for the linearization error system is as follows: , , in, The derivative of the UAV's state vector. Represents the uncertainty impact matrix. The dimension of an uncertain vector. Representing an allowed set of uncertainties, This represents the derivative of the target parameterized curve with respect to the curve parameters. Indicates a known upper bound; In this embodiment, The value is 12, if Then, represents the bounded uncertainty vector of a single UAV, and the bounded uncertainty vector... The dimension is consistent with the state space, indicating that there is an error in each channel of position, velocity, and attitude; S34. Substitute the linearized error system into the state time-varying linear dynamics model to obtain the target state time-varying linear dynamics model; The calculation expression for the time-varying linear dynamics model of the target state is as follows: , , in, The derivative of the UAV state vector function, Indicates the nominal dynamic offset.

[0018] S4. Approximate the interior of the control deviation constraint set as a time-varying inscribed control ellipsoid, and perform minimum volume circumscribed ellipsoid approximation and convex optimization on the uncertainty polyhedron model based on the uncertainty set modeling according to the state deviation, to obtain the time-varying circumscribed uncertainty ellipsoid. S4 includes the following steps: S41. Construct a set of control deviation constraints based on the control input constraints; The calculation expression for the set of control deviation constraints is as follows: , in, Represents the set of control deviation constraints. This represents the actual control input vector. Indicates the first The nominal control input of each motor. Indicates the first Control deviation of individual motors; S42. According to the ellipsoid calculation method, suppose there exists an inscribed ellipsoid inscribed within the set of control deviation constraints. ,in, Represents ellipsoidal functions, represents the center of the inscribed ellipsoid, The shape matrix representing the inscribed ellipsoid; The expression for calculating the shape matrix of the inscribed ellipsoid is as follows: , , , in, Represents a diagonal matrix. This represents the total tensile force deviation constraint coefficient of the UAV. The minimum envelope representing the motor thrust margin; It is a time-varying positive scalar. Indicates the first The current nominal thrust of each motor Distance from its upper bound The minimum distance to the lower bound 0. This indicates that the minimum distance among the four motors is taken; This solution directly reflects the available margin of the motor with the most strained thrust adjustment capability at the current moment; it maximizes... In this way, ensure that by The defined ellipsoid is strictly contained within the set of control deviation constraints, thus reserving the maximum correction space for feedback control; In this embodiment, the minimum envelope of the motor thrust margin is obtained by solving the minimum envelope optimization model; The calculation expression for the minimum envelope optimization model is as follows: , in, The minimum envelope representing the thrust margin of the motor. Represents a mapping. for The first in Standard basis vectors Indicates the ellipsoid at the th The square of the half-shaft length in each motor direction, This represents the matrix controlling the shape of the ellipsoid. Indicates arbitrary selection; In this scheme, by maximizing the minimum envelope of the motor thrust margin, the maximum correction space can be reserved for feedback control while ensuring that the motor is not saturated. S43. Using the center of the inscribed ellipsoid as the nominal control deviation, and maximizing the volume of the inscribed ellipsoid based on its shape matrix, the time-varying inscribed control ellipsoid is obtained. ; The calculation expression for the time-varying inner control ellipsoid is as follows: , in, Indicates that it is included in; Based on the control input constraints, this scheme uses an inscribed ellipsoid approximation algorithm to approximate the control deviation constraint set as a time-varying ellipsoid, thereby maximizing the preservation of control authority. In this scheme, the boundary of the bounded uncertainty vector is determined by the allowable ranges of state deviation and control deviation, where state deviation... The allowable range is determined by the upper bound of the attitude angle deviation. Upper bound of angular velocity deviation Decide; S44. Based on Taylor expansion remainder analysis and Lyapunov method, analyze each uncertainty component in the bounded uncertainty vector to obtain the time-varying range of each uncertainty component, where the uncertainty components constitute the uncertainty set. The expression for calculating the time-varying range of the uncertainty component is as follows: , in, Indicates the first The minimum value of the uncertainty component in each dimension. Indicates the first Uncertainty components in each dimension Indicates the first The maximum value of the uncertainty components in each dimension; S45. Model the set of uncertainties as an uncertainty polyhedron model, wherein the boundary of the uncertainty polyhedron model is determined by analyzing the quadratic terms of the state deviation and control deviation. The expression for calculating the boundary of the uncertain polyhedron is as follows: , in, Represents an uncertain polyhedron. Indicates the first The minimum value of the uncertainty components in each dimension. Indicates the first The uncertainty components in each dimension Indicates the first The maximum value of the uncertainty components in each dimension; S46. Approximate the uncertain polyhedron model from the outside using a circumscribed ellipsoid, such that the uncertain polyhedron is contained within the circumscribed ellipsoid even when the circumscribed ellipsoid is at its minimum volume. ,in, Indicates the center of the circumscribed ellipsoid. Let represent the shape matrix of the circumsphere, where the center of the uncertain polyhedral model coincides with the center of the circumsphere; In this embodiment, the calculation expression for the center of the circumscribed ellipsoid is as follows: , in, This represents the minimum value of the uncertainty component in the first dimension. This represents the maximum value of the uncertainty component in the first dimension. This represents the minimum value of the uncertainty component in the 12th dimension. This represents the maximum value of the uncertainty component in the first dimension; S47. Optimize the shape matrix of the circumscribed ellipsoid using a convex optimization model to obtain a time-varying circumscribed uncertain ellipsoid. ; The computational expression for the convex optimization model is as follows: , in, Let e ​​represent the logarithmic function with e as the base constant. Represents the determinant of a matrix. The inverse matrix representing the shape matrix of the circumscribed ellipsoid. Indicates about Take the minimum value. The first part of the uncertain polyhedral model represents the... One vertex, The dimension of the uncertainty vector. This represents the optimized ellipsoidal quadratic form matrix. This represents the transpose of the optimized ellipsoidal quadratic form matrix.

[0019] The calculation expression for the time-varying circumscribed uncertain ellipsoid is as follows: .

[0020] S5. Establish a dynamic model of the UAV swarm, and construct a time-varying scaling virtual container based on the initial virtual container and the virtual guide point trajectory. Vertically stack the virtual container constraints, anti-collision constraints and state deviation constraints of the UAV swarm to obtain the UAV swarm constraint set. S5 includes the following steps: S51. Based on the state-space representation method, and using the time-varying linear dynamics model of the target state and the nominal state trajectory, establish a dynamics model of the UAV swarm. The calculation expression for the UAV swarm dynamics model is as follows: , , , , , , , , in, The derivative of the state vector function of the drone swarm. The system matrix representing a drone swarm, The state vector function representing the drone swarm. The input matrix represents the drone swarm. This represents the control input vector of the drone swarm. Represents the nominal dynamic offset vector of the drone swarm. The matrix representing the uncertainty impact of drone swarms This represents the bounded uncertainty vector of a drone swarm. Represents a block diagonal matrix. The system matrix represents the first drone. The system matrix represents the second drone. Indicates the first The system matrix of drones, This indicates the total number of drones in the drone swarm. This represents the input matrix for the first drone. This represents the input matrix for the second drone. Indicates the first The input matrix of the drone, This represents the uncertainty impact matrix for the first drone. This represents the uncertainty impact matrix of the second drone. Indicates the first Uncertainty impact matrix of drones This indicates the nominal dynamic offset of the first drone. This indicates the nominal dynamic offset of the second drone. Indicates the first The nominal dynamic offset of the drone. This represents the transpose of the state vector of the first drone. This represents the transpose of the state vector of the second drone. Indicates the first The transpose of the state vector of the drone. This represents the transpose of the control input vector of the first UAV. This represents the transpose of the control input vector of the second UAV. Indicates the first Transpose of the control input vector of the drone. Denotes the transpose of the bounded uncertainty vector of the first drone. Denotes the transpose of the bounded uncertainty vector of the second drone. Indicates the first The transpose of the bounded uncertainty vector of a drone. The dimension representing the uncertainty vector of the drone swarm; In this solution, virtual containers It is a time-varying convex polyhedron, i.e., the initial virtual container is Virtual Container Center If it always coincides with the virtual boot point, then ; S52. Based on the initial virtual container and the virtual guide point trajectory, construct a time-varying scaling virtual container with the virtual guide point as the center; The calculation expression for the time-varying scaling virtual container is as follows: , , , , , in, This represents a time-varying scaling virtual container. The constraint matrix represents the time-varying scaling virtual container. Represents the constraint vector of the time-varying scaling virtual container. Represents the time-varying scaling matrix The inverse matrix, Represents the selection matrix transpose, Indicates the virtual container center, This represents the constraint matrix of the initial virtual container. This represents the constraint vector of the initial virtual container. This represents the scaling factor of the time-varying scaling matrix along the X-axis. This represents the scaling factor of the time-varying scaling matrix along the Y-axis. This represents the scaling factor of the time-varying scaling matrix along the Z-axis. Represents a three-dimensional rotation group; In this scheme, a time-varying scaling matrix is ​​used. Through dynamic adjustment, the virtual container can shrink in narrow channels and expand in open areas, thus achieving self-adaptation to complex environments. Scaling and rotating the virtual container transforms the static virtual container, i.e., the initial virtual container, into a time-varying scaled virtual container. In the offline planning phase, the initial virtual container ensures the global feasibility of the reference curve; the initial virtual container in the offline planning phase forms the basis for the online time-varying scaled virtual container. S53. Based on the relative positions between any two UAVs in the nominal state trajectory, construct a nonlinear constraint for safe distance, and at the reference point... A first-order Taylor expansion is performed to transform the result into a linear constraint for the safety distance, where, Indicates the first Reference position for the drone Indicates the first Reference position for the drone; The calculation expression for the nonlinear constraint of the safety distance is as follows: , in, Indicates the first The position vector of the drone, Indicates the first The position vector of the drone, This indicates the calculation of the Euclidean distance. Indicates the safe distance threshold; In this scheme, it is assumed that the first... The drone and the first Reference relative position of the drone The distance is non-zero; this reference point is derived from the nominal state trajectory to ensure the gradient of the position vector. The definition is valid, thus avoiding singularities; The calculation expression for the linear constraint of the safety distance is as follows: , , , in, Indicates the first The drone and the first Transposition of the safety distance slack between drones Indicates the first The positional deviation of the drone Indicates the first The positional deviation of the drone Indicates the first The drone and the first The gradient of the position vectors between the drones. Indicates the first The drone and the first The slack in the safe distance between drones Indicates the first The drone and the first The relative position of the drone Indicates the safe distance threshold. Indicates the first The position vector of the drone, Indicates the first The position vector of the drone, Indicates the first The drone and the first The transpose of the gradient of the position vectors between the drones. Indicates the first The drone and the first The relative positional deviation between the drones; S54. Define the position selection matrix , making And based on time-varying scaling virtual containers, virtual container constraints for drone swarms are constructed, where, Indicates the first The position vector of the drone in three-dimensional space. Indicates the first The state vector of the drone; The calculation expression for the virtual container constraints of the drone swarm is as follows: , in, The virtual container constraint matrix representing the drone swarm. Represents the state vector of a drone swarm. Represents the virtual container constraint vector of the drone swarm. Represents the transpose of the constraint vector of a time-varying scaling virtual container; S55. Define the collision avoidance constraint selection matrix , making And based on the linear constraint of safe distance, anti-collision constraints for the drone swarm are constructed; The calculation expression for the collision avoidance constraints of the drone swarm is as follows: , in, This represents the collision avoidance constraint matrix of a drone swarm. This represents the collision avoidance constraint selection matrix between the first and second drones. This represents the collision avoidance constraint selection matrix between the first and third drones. Indicates the first The drone and the first The collision avoidance constraint selection matrix for unmanned aerial vehicles. This represents the collision avoidance constraint vector of the drone swarm. This indicates the slack in the safe distance between the first and second drones. This indicates the slack in the safe distance between the first and third drones. Indicates the first The drone and the first The slack in the safe distance between drones; S56. Construct state deviation constraints for the UAV cluster based on the state deviation constraint matrix and state deviation constraint vector of the UAV. The calculation expression for the state deviation constraint of the UAV cluster is as follows: , in, This represents the state deviation constraint matrix of the drone swarm. This represents the state deviation constraint matrix for a single UAV. This represents the state deviation constraint vector of the drone swarm. This represents the transpose of the state deviation constraint vector of the first UAV. This represents the transpose of the state deviation constraint vector of the second UAV. Indicates the first The transpose of the state deviation constraint vector of the UAV; S57. According to the unified linear inequality representation, the virtual container constraints, anti-collision constraints and state deviation constraints of the UAV swarm are vertically stacked to obtain the UAV swarm constraint set. The calculation expression for the set of constraints of the UAV swarm is as follows: , in, The matrix representing the set of combined constraints for a drone swarm. This represents the constraint set vector of a drone swarm.

[0021] In this scheme, the safe flight corridor formed by the time-varying scaling virtual container centered on the virtual guide point embodies the spatial coordination mechanism constrained by the virtual container, which can provide a smooth, continuous collective movement channel for the UAV swarm that meets collision avoidance requirements.

[0022] S6. Based on the UAV swarm dynamics model and UAV swarm constraint set, a time-varying solvable set is defined, and a reverse recursive calculation is performed from the terminal time until the initial time to obtain the time-varying solvable set ellipsoid sequence, which constitutes the solvable set ellipsoid tube. S6 includes the following steps: S61. Based on the reachability analysis theory, and using the UAV swarm dynamics model and the UAV swarm constraint set, define a time-varying solvable set. The calculation expression for the time-varying solvable set is as follows: , , , in, Represents the time-varying solvable set. express The state vector of the drone at time t, This indicates that it exists. This indicates the position feedback control law. This represents the set of permissible state feedback control laws. Indicates control input constraints. This represents the state vector of the UAV at the terminal moment. Represents the target set at the terminal time, where, ,in, Indicates the start time. Indicates the terminal time; in this scheme, satisfy ; S62. Based on the equal-interval discretization method and the time-varying solvable set, the planning time interval is divided into K equally intervald discrete time steps, and the solvable set at the terminal time is obtained by initializing the target constraint set at the terminal time. The expression for calculating the solvable set at the terminal moment is as follows: , , in, This represents the solvable set at the terminal time. Indicates the first The solvable set at each moment Indicates the first The set of target constraints at each moment This represents the set of combined constraints for the drone swarm at the terminal moment. This represents the constraint set vector of the drone swarm at the terminal moment. Indicates the initial time. Indicates the first moment. Indicates the first At that moment, Represents the discrete time step. Indicates the first At that moment, Indicates the first At that moment; In this scheme, since the UAV swarm dynamics model must fall into the target set at the terminal moment, the backward induction method is adopted to ensure that the solvable set at each moment is a safe predecessor of the target set at the previous moment, thereby constructing an updated model that obtains the solvable set. S63. Based on dynamic programming and reachability analysis theory, construct an update model for time-varying solvable sets using backward induction. The computational expression for the update model of the time-varying solvable set is as follows: , in, Indicates the first The solvable set at each moment Indicates the first The inverse of the solvable set at a given moment and the forward reachable set at that moment. Indicates intersection, Indicates the first The target set at each time point; in this embodiment... Defined from the first Starting from a certain moment, it can reach [the destination] within a discrete time step interval. The set of states; S64. Based on the ellipsoidal approximation set operation and the update model of the time-varying solvable set, construct the ellipsoidal recursive model. In this scheme, for any given moment Does there exist a solvable ellipsoid at that moment? satisfy ,in, express The center of the solvable set ellipsoid corresponding to the time step. express The shape matrix of the solvable ellipsoid at time t. express The transpose of the shape matrix of the solvable ellipsoid corresponding to the time step. Indicates that the matrix is ​​positive definite; When approximating an ellipsoid for a one-step forward reachable set, a linear dynamic transformation is first performed to obtain the intermediate state ellipsoid to be constrained and clipped. The calculation expression for the intermediate state ellipsoid is as follows: , , in, The center of the ellipsoid represents the intermediate state of the ellipsoid. The shape matrix representing the intermediate state of the ellipsoid. Denotes the inverse of the one-step forward reachable set. Represents the identity matrix. Indicates the first Discrete time steps Indicates the first The dynamic model matrix of the drone swarm at each moment. Indicates the first The control input matrix of the drone swarm at each moment. Indicates the first The nominal dynamic offset vector of the drone swarm at each moment. The matrix representing the uncertainty impact of drone swarms Indicates the first The center of the circumscribed uncertain ellipsoid at time t. Indicates the first The drone swarm input matrix at each time step, This represents the matrix controlling the shape of the ellipsoid. Indicates the first The transpose of the drone swarm input matrix at time t. Indicates the first The shape matrix of the circumscribed ellipsoid at time t. The transpose of the matrix representing the overall uncertainty impact of the drone swarm; By obtaining the geometric process of the ellipsoid at the current moment through linear transformation and intersection operation from the ellipsoid at the previous moment, we can discover the computational feasibility of ellipsoid approximation in set operations. The calculation expression for the ellipsoidal recursive model is as follows: , , , , , , in, Indicates the first The center of the ellipsoid with the largest volume at each moment. Indicates the first The shape matrix of the inscribed ellipsoid with the largest volume at each moment. The center of the ellipsoid represents the intermediate state of the ellipsoid. The shape matrix representing the intermediate state of the ellipsoid. Indicates the first The set of target constraints at each moment Indicates the first The center of the solvable set ellipsoid corresponding to each time step. Indicates the first The shape matrix of the solvable ellipsoid corresponding to each time step. The shape matrix representing the intermediate state of the ellipsoid. Indicates the first The polyhedron at moment n Offset of each face, Indicates the first The polyhedron at moment n The normal vector of each face. Indicates the first The polyhedron at moment n The inverse vector of the normal vector of each face. Indicates the first The transpose of the shape matrix of the solvable ellipsoid at each time step; In this scheme, the maximum volume inscribed ellipsoid is contained within both the known ellipsoid and the polyhedron. For the N planes of the polyhedron, the maximum volume inscribed ellipsoid is completely located within each half-space. This scheme can find the maximum ellipsoid volume that can be completely contained within the currently constrained polyhedron at any time, thus theoretically ensuring the low conservatism of the algorithm. S65. Based on the ellipsoidal recursive model, starting from the terminal time, the ellipsoid is set as the maximum inscribed ellipsoid of the terminal constraint set and the reverse recursive calculation is performed until the initial time, to obtain the time-varying solvable set ellipsoid sequence, which constitutes the solvable set ellipsoid tube. The time-varying solvable ellipsoid sequence includes solvable ellipsoids from the initial time to the terminal time.

[0023] The settable ellipsoid is composed of a series of elements inscribed within a time-varying settable. The sequence of solvable ellipsoids is used to computationally approximate the set of all feasible states that satisfy the set of UAV swarm constraints from the initial time to the terminal time.

[0024] In this scheme, the ellipsoid evolves gradually from the terminal moment to the initial moment by reversing the time sequence. This reflects the structural integrity of the solvable ellipsoid tube and shows that this scheme can provide a safe and controllable pipeline from the initial state to the target state for the UAV swarm dynamics model, and ensures the feasibility of the closed-loop system under all constraints.

[0025] S7. Based on the solvable ellipsoid tube, construct the Lyapunov function of the solvable ellipsoid distance, and design the boundary feedback control law based on the time-varying uncertainty ellipsoid. S7 includes the following steps: S71. Let the current time be... Based on the current state vector of the drone swarm Choose a solvable ellipsoid from the solvable ellipsoid tube. , making arrive To minimize the distance between them, and to construct the Lyapunov function for the distance of the solvable ellipsoid, where, This represents the center of the selected solvable ellipsoid. This represents the shape matrix of the selected solvable ellipsoid. The parameter index represents the ellipsoid of the solvable set; The Lyapunov function for the solvable set ellipsoidal distance is expressed as follows: , , in, This represents the weighted distance of the ellipsoidal isosurface of the ellipsoid that can be solved at the current moment. This represents the center of the solvable ellipsoid at the current moment. This represents the inverse matrix of the shape matrix of the solvable ellipsoid corresponding to the current time step. The shape matrix of the solvable ellipsoid corresponding to the current time step; S72. Based on the Lyapunov function of the distance to the solvable set ellipsoid and the extreme value analysis method, determine the direction of the worst-case uncertainty affecting stability based on the time-varying uncertainty ellipsoid. The expression for calculating the worst-case uncertainty direction of stability is as follows: , , , in, This indicates the direction of the worst-case effect of stability on uncertainty. Indicates the first The center of the circumscribed ellipsoid at each moment is subject to uncertainty. Indicates the first The shape matrix of the circumscribed ellipsoid at time t. Indicates the first The auxiliary vector at each time step. Indicates the first The transpose of the auxiliary vector at each time step. The transpose of the matrix representing the overall uncertainty impact of the drone swarm. Indicates the first Discrete time steps Indicates the first The dynamic model matrix of the drone swarm at each moment. Indicates the first The inverse matrix of the shape matrix of the solvable ellipsoid at time n. Indicates the first The center of the solvable ellipsoid at time t. Indicates the first The circumscribed ellipsoid of uncertainty at each moment; in this scheme, the auxiliary vector refers to the linear transformation between the UAV swarm dynamics model and the current state deviation; S73. Based on the control input constraints and the extreme point selection strategy, a boundary feedback control law is designed based on the time-varying inscribed control ellipsoid. In this scheme, the boundary feedback control law is used to offset the influence of the worst-case uncertainty direction of stability and to minimize the ellipsoid distance at the next time step. The calculation expression for the boundary feedback control law is as follows: , in, Indicates the first Boundary feedback control law at each time step Indicates the first The center of the inscribed control ellipsoid at each moment. Indicates the first Adaptive gain at each time step Indicates the first The shape matrix of the inscribed control ellipsoid at each time step. Indicates the first The transpose of the UAV swarm input matrix at each time step, where... While maximizing the boundary feedback control law, substituting it into the UAV swarm dynamics model after K discrete steps can satisfy the condition of decreasing Lyapunov function: ,in, Indicates the first Weighted distance of ellipsoidal isosurface at each time step Indicates the first The weighted distance of the ellipsoidal isosurface at each time step.

[0026] In this scheme, based on nonsmooth analysis theory, the Lyapunov function of the closed-loop system trajectory and the maintenance of the system state within the solution set were verified using the boundary feedback control law and the distance to the solvable set ellipsoid: If If the set is sufficiently small and the time-varying solvable ellipsoidal sequence satisfies the reverse recurrence relation, then we can obtain: ,in, This represents the weighted distance of the ellipsoidal isosurface of the ellipsoid that can be solved at the next time step. To ensure that the Lyapunov function of the solution set ellipsoidal distance has strictly decreasing exponential convergence coefficients, The value is determined by , Eigenvalues ​​and UAV swarm dynamics model matrix The norm of the system is determined by the system state, ensuring that the system state approaches the center of the ellipsoid at each time step.

[0027] This scheme designs a boundary feedback control law with strict robustness guarantee by using a solvable ellipsoid tube and Lyapunov stability theory. It enables the state exponent of the UAV swarm dynamics model to converge to the center of the solvable ellipsoid and always satisfy the UAV swarm constraint set under the conditions of bounded uncertainty and control input constraints.

[0028] S8. Generate control commands for each UAV in the UAV swarm based on the boundary feedback control law, and use a distributed execution architecture to enable each UAV in the UAV swarm to implement the control commands synchronously, thereby completing the trajectory tracking control of the UAV swarm.

[0029] S8 includes the following steps: S81. Based on the boundary feedback control law, and the selected solvable ellipsoid and the state vector of the UAV cluster at the current moment, control commands for each UAV in the UAV cluster are generated. In this scheme, the generation of control commands for each UAV in the UAV cluster is used to offset the influence of the worst-case uncertainty direction of stability. S82. Through the UAV swarm communication network, the generated control commands are sent to each UAV in the UAV swarm, and the control commands are implemented synchronously using a distributed execution architecture to complete the UAV swarm trajectory tracking control.

[0030] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for tracking and controlling the trajectory of a UAV swarm based on virtual containers and ellipsoid estimation, characterized in that, Includes the following steps: S1. Based on the 3D map data of the mission environment and the heuristic function of the improved hybrid A*, generate a parameterized reference curve for the target based on the initial virtual container; S2. Establish a nonlinear dynamic model of the state, and generate a virtual guide point trajectory based on the target parameterized reference curve to derive the nominal state trajectory in reverse, and obtain the nominal control input through inverse dynamics calculation; S3. Generate a nominal trajectory based on the nominal state trajectory and nominal control input, and perform a first-order Taylor expansion on the nonlinear dynamic model of the state near the nominal trajectory, and model a bounded uncertainty vector to obtain a time-varying linear dynamic model of the target state. S4. Approximate the interior of the control deviation constraint set as a time-varying inscribed control ellipsoid, and perform minimum volume circumscribed ellipsoid approximation and convex optimization on the uncertainty polyhedron model based on the uncertainty set modeling according to the state deviation, to obtain the time-varying circumscribed uncertainty ellipsoid. S5. Establish a dynamic model of the UAV swarm, and construct a time-varying scaling virtual container based on the initial virtual container and the virtual guide point trajectory. Vertically stack the virtual container constraints, anti-collision constraints and state deviation constraints of the UAV swarm to obtain the UAV swarm constraint set. S6. Based on the UAV swarm dynamics model and UAV swarm constraint set, a time-varying solvable set is defined, and a reverse recursive calculation is performed from the terminal time until the initial time to obtain the time-varying solvable set ellipsoid sequence, which constitutes the solvable set ellipsoid tube. S7. Based on the solvable ellipsoid tube, construct the Lyapunov function of the solvable ellipsoid distance, and design the boundary feedback control law based on the time-varying uncertainty ellipsoid. S8. Generate control commands for each UAV in the UAV swarm based on the boundary feedback control law, and use a distributed execution architecture to enable each UAV in the UAV swarm to implement the control commands synchronously, thereby completing the trajectory tracking control of the UAV swarm.

2. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 1, characterized in that, S1 includes the following steps: S11. Obtain 3D map data of the mission environment, including obstacle locations and mission area boundaries; S12. Based on the 3D map data of the task environment, define shape and size constraints to obtain a static convex polyhedron as the initial virtual container. S13. Based on the heuristic function of the improved hybrid A*, a path search is performed in the three-dimensional state space based on the initial virtual container to obtain discrete paths; S14. Perform spline fitting on the discrete path, and generate an initial smooth reference curve through curvature constraints, ascent angle constraints, and curve continuity constraints based on smoothness weights. S15. Perform dense sampling on the initial smoothed reference curve to obtain a set of sampling points; S16. Perform dual verification on the sample point set based on the virtual container inclusiveness verification model and the safe distance verification model. If the verification passes, the target parameterized reference curve is obtained; otherwise, adjust the smoothing weights and return to S14.

3. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 2, characterized in that, The computational expression for the improved hybrid A* heuristic function in S13 is as follows: ， ， ， in, This represents an improved hybrid A* heuristic function. This indicates taking the maximum value. Indicating geometric distance inspiration, Indicates the minimum time cost. Indicates deviation from the weighting coefficient. This indicates the distance the penalty state deviates from the center of the container. Represents the L2 norm, Represents a position vector in three-dimensional space. This represents the position vector of the target point in three-dimensional space. Indicates the maximum speed of the drone. This represents the position vector of the container's center point in three-dimensional space.

4. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 3, characterized in that, S2 includes the following steps: S21. Based on the physical parameters and kinematic principles of the UAV, establish a nonlinear dynamic model of the state; S22. Extract the tangent vector of the target parameterized reference curve; S23. Define the curve arc length function; S24. Based on the curve arc length function and the tangent vector of the target parameterized reference curve, and based on the velocity constraint at the virtual guide point, calculate the trajectory of the virtual guide point. S25. Based on the differential flatness theory, use a drone to track the trajectory of a virtual guide point and derive the nominal state trajectory in reverse. S26. Perform inverse dynamics calculations based on the nominal state trajectory and the state nonlinear dynamics model to obtain the nominal control input.

5. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 4, characterized in that, S3 includes the following steps: S31. Generate a nominal trajectory based on the nominal state trajectory and the nominal control input; S32. Perform a first-order Taylor expansion on the nonlinear dynamic model of the state near the nominal trajectory to obtain a time-varying linear dynamic model of the state. S33. Based on the sum of the higher-order Taylor remainder and the unmodeled dynamics, a bounded uncertainty vector is modeled to obtain a linearized error system. S34. Substitute the linearized error system into the state-time-varying linear dynamics model to obtain the target state-time-varying linear dynamics model.

6. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 5, characterized in that, S4 includes the following steps: S41. Construct a set of control deviation constraints based on the control input constraints; S42. According to the ellipsoid calculation method, suppose there exists an inscribed ellipsoid inscribed in the set of control deviation constraints; S43. Using the center of the inscribed ellipsoid as the nominal control deviation, and maximizing the volume of the inscribed ellipsoid based on the shape matrix of the inscribed ellipsoid, the time-varying inscribed control ellipsoid is obtained. S44. Based on Taylor expansion remainder analysis and Lyapunov method, analyze each uncertainty component in the bounded uncertainty vector to obtain the time-varying range of each uncertainty component, where the uncertainty components constitute the uncertainty set. S45. Model the set of uncertainties as an uncertainty polyhedron model, wherein the boundary of the uncertainty polyhedron model is determined by analyzing the quadratic terms of the state deviation and control deviation. S46. Use the circumscribed ellipsoid to approximate the uncertain polyhedron model from the outside, and ensure that the uncertain polyhedron is contained within the circumscribed ellipsoid even when the circumscribed ellipsoid is at its minimum volume. S47. The shape matrix of the circumscribed ellipsoid is optimized by using a convex optimization model to obtain a time-varying circumscribed uncertain ellipsoid.

7. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 6, characterized in that, S5 includes the following steps: S51. Based on the state-space representation method, and using the time-varying linear dynamics model of the target state and the nominal state trajectory, establish a dynamics model of the UAV swarm. S52. Based on the initial virtual container and the virtual guide point trajectory, construct a time-varying scaling virtual container with the virtual guide point as the center; S53. Based on the relative positions between any two UAVs in the nominal state trajectory, construct a nonlinear constraint for safe distance, and at the reference point... A first-order Taylor expansion is performed to transform the result into a linear constraint for the safety distance, where, Indicates the first Reference position for the drone Indicates the first Reference position for the drone; S54. Define the location selection matrix and construct the virtual container constraints of the drone swarm based on the time-varying scaling virtual container; S55. Define the collision avoidance constraint selection matrix , making And based on the linear constraint of safe distance, anti-collision constraints for the drone swarm are constructed, where, Indicates belonging to, Represents the set of real numbers. This indicates the total number of drones in the drone swarm. Represents the state vector of a drone swarm. Indicates the first The drone and the first The gradient of the position vectors between the drones; S56. Construct state deviation constraints for the UAV cluster based on the state deviation constraint matrix and state deviation constraint vector of the UAV. S57. Based on the unified linear inequality representation, the virtual container constraints, anti-collision constraints, and state deviation constraints of the UAV swarm are vertically stacked to obtain the UAV swarm constraint set.

8. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 7, characterized in that, S6 includes the following steps: S61. Based on the reachability analysis theory, and using the UAV swarm dynamics model and the UAV swarm constraint set, define a time-varying solvable set. S62. Based on the equal-interval discretization method and the time-varying solvable set, the planning time interval is divided into K equally intervald discrete time steps, and the solvable set at the terminal time is obtained by initializing the target constraint set at the terminal time. S63. Based on dynamic programming and reachability analysis theory, construct an update model for time-varying solvable sets using backward induction. S64. Based on the ellipsoidal approximation set operation and the update model of the time-varying solvable set, construct the ellipsoidal recursive model. S65. Based on the ellipsoidal recursive model, starting from the terminal time, the ellipsoid is set as the maximum inscribed ellipsoid of the terminal constraint set and the reverse recursive calculation is performed until the initial time, to obtain the time-varying solvable set ellipsoid sequence, which constitutes the solvable set ellipsoid tube. The time-varying solvable ellipsoid sequence includes a solvable ellipsoid from the initial time to the terminal time.

9. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 8, characterized in that, S7 includes the following steps: S71. Let the current time be... Based on the current state vector of the drone swarm Choose a solvable ellipsoid from the solvable ellipsoid tube. , making arrive To minimize the distance between them, and to construct the Lyapunov function for the distance of the solvable ellipsoid, where, This represents the center of the selected solvable ellipsoid. This represents the shape matrix of the selected solvable ellipsoid. The parameter index represents the ellipsoid of the solvable set; The Lyapunov function for the solvable set ellipsoidal distance is expressed as follows: ， ， in, This represents the weighted distance of the ellipsoidal isosurface of the ellipsoid that can be solved at the current moment. This represents the center of the solvable ellipsoid at the current moment. This represents the inverse matrix of the shape matrix of the solvable ellipsoid corresponding to the current time step. The shape matrix of the solvable ellipsoid corresponding to the current time step; S72. Based on the Lyapunov function of the distance to the solvable set ellipsoid and the extreme value analysis method, determine the direction of the worst-case uncertainty affecting stability based on the time-varying uncertainty ellipsoid. The expression for calculating the worst-case uncertainty direction of stability is as follows: ， ， ， in, This indicates the direction of the worst-case effect of stability on uncertainty. Indicates the first The center of the circumscribed ellipsoid at each moment is subject to uncertainty. Indicates the first The shape matrix of the circumscribed ellipsoid at time t. Indicates the first The auxiliary vector at each time step. Indicates the first The transpose of the auxiliary vector at each time step. The transpose of the matrix representing the overall uncertainty impact of the drone swarm. Indicates the first Discrete time steps Indicates the first The dynamic model matrix of the drone swarm at each moment. Indicates the first The inverse matrix of the shape matrix of the solvable ellipsoid at time n. Indicates the first The center of the solvable ellipsoid at time t. Indicates the first The circumscribed ellipsoid of uncertainty at each moment; S73. Based on the control input constraints and the extreme point selection strategy, design the boundary feedback control law based on the time-varying inscribed control ellipsoid. The calculation expression for the boundary feedback control law is as follows: ， in, Indicates the first Boundary feedback control law at each time step Indicates the first The center of the inscribed control ellipsoid at each moment. Indicates the first Adaptive gain at each time step Indicates the first The shape matrix of the inscribed control ellipsoid at each time step. Indicates the first The transpose of the input matrix of the drone swarm at each moment. Let represent the identity matrix, where While maximizing the boundary feedback control law, substituting it into the UAV swarm dynamics model after K discrete steps can satisfy the condition of decreasing Lyapunov function: ,in, Indicates the first Weighted distance of ellipsoidal isosurface at each time step Indicates the first The weighted distance of the ellipsoidal isosurface at each time step.

10. The UAV swarm trajectory tracking and control method based on virtual container and ellipsoid estimation according to claim 9, characterized in that, S8 includes the following steps: S81. Based on the boundary feedback control law, and the selected solvable ellipsoid and the state vector of the UAV cluster at the current moment, generate control commands for each UAV in the UAV cluster. S82. Through the UAV swarm communication network, the generated control commands are sent to each UAV in the UAV swarm, and the control commands are implemented synchronously using a distributed execution architecture to complete the UAV swarm trajectory tracking control.

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