An unmanned aerial vehicle cluster formation control method and system based on attractors

Abstract

The application provides a UAV cluster formation control method and system based on an attractor manifold, and the method comprises the following steps: constructing a formation topological structure of a UAV cluster; acquiring state information of itself and state information of adjacent UAVs in real time through an airborne sensor and a communication module; for each UAV, constructing a distributed control law based on an attractor manifold plasticity control method; and applying control input calculated by each UAV according to the distributed control law to a flight control system of the UAV, so that the UAV cluster moves to a target as a whole under the premise of maintaining formation and obstacle avoidance. The application integrates formation maintenance, overall maneuvering and obstacle avoidance safety into the same mathematical system, avoids separate design of different targets by different tools in a traditional method, and simplifies system design. Normal shrinkage and natural decomposition of a tangential task are realized through a projection operator, normal control guarantees exponential convergence of the formation structure, and tangential control realizes a maneuvering task without interference.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) swarm control, specifically to a method and system for UAV swarm control based on an attractive manifold. Background Technology

[0002] In recent years, drone swarms have been widely used in military reconnaissance, disaster relief, environmental monitoring, and logistics delivery. Compared with single drones, multi-drone collaboration can significantly expand mission coverage, improve system redundancy, and shorten mission completion time, demonstrating irreplaceable potential in complex environments. Existing research has systematically analyzed issues such as collaborative perception, collaborative planning, and collaborative control, and proposed various technical solutions. However, in actual deployment, swarms often need to flexibly avoid obstacles while maintaining a specific formation structure to ensure mission accuracy and flight safety. Therefore, how to simultaneously meet these two requirements within a unified control framework, and theoretically guarantee the stability and convergence of the system, has become one of the core challenges currently facing research.

[0003] The conflict between formation maintenance and obstacle avoidance stems from their different requirements on individual behavior. Formation maintenance requires individuals to maintain fixed relative positions or distances to form a stable geometric structure. Obstacle avoidance, on the other hand, requires individuals to temporarily deviate from their desired positions based on local environmental information to avoid obstacles, a process that inevitably disrupts the consistency of the formation structure. Existing methods often use different mathematical tools to model this problem separately, leading to coupling between multiple objectives. This coupling often makes it difficult for researchers to conduct joint design and overall stability analysis within a single system. For example, virtual structure methods can accurately maintain rigid formations but are difficult to adapt to dynamic obstacle avoidance requirements. The navigator-follower method increases flexibility through tracking relationships but is highly dependent on the reliability of the navigator and lacks autonomous obstacle avoidance capabilities. Consistency methods, while having a good graph theory foundation, do not inherently include obstacle avoidance mechanisms and lack an explicit relationship between perturbation amplitude and formation error. Behavioral methods are intuitive and flexible but lack theoretical guidance due to the conflict of multiple behaviors, making it difficult to guarantee overall stability. Artificial potential field methods can handle both types of requirements uniformly but are prone to getting trapped in local minima and formation error cannot be quantitatively controlled.

[0004] In recent years, optimization frameworks based on control Lyapunov functions and obstacle control functions, along with distributed model predictive control, have made unified design possible. However, these methods typically rely on online solutions of quadratic programming or nonlinear optimization, which imposes a heavy computational burden in distributed implementations and makes it difficult to directly derive the analytical bound between disturbance amplitude and formation error. Especially when obstacle avoidance requirements conflict with formation accuracy, quantifying the impact of obstacle avoidance actions on formation error and ensuring bounded error in dynamic environments remains an unsolved problem. It should be noted that existing methods often employ a hierarchical superposition of formation and obstacle avoidance terms, whose stability and error bounds vary with specific combinations, lacking a unified quantitative relationship for error disturbances, thus introducing additional complexity to system design and parameter tuning. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a UAV swarm formation control method based on an attracting manifold. This method considers the outer-loop position dynamics of the UAVs within a two-dimensional Euclidean space, models the desired collective behavior as a smooth attracting manifold in the state space, and achieves a natural separation of structural stability and mission maneuverability through normal-tangential decomposition. The technical solution provided by this invention is as follows:

[0006] A method for controlling UAV swarm formation based on attracting manifolds includes the following steps:

[0007] Step 1: Construct the formation topology of the drone swarm. The formation topology is based on a connected graph and is used to describe the positional relationships between the drones in the swarm.

[0008] Step 2: Each UAV acquires its own status information and the status information of neighboring UAVs in real time through onboard sensors and communication modules. The status information includes position and speed.

[0009] Step 3: For each drone, construct a distributed control law based on the attraction-prevailing plasticity control method;

[0010] Step 4: Each UAV applies the control input calculated by the distributed control law to its own flight control system, so that the UAV swarm can move toward the target as a whole while maintaining formation and obstacle avoidance.

[0011] Preferably, the drone swarm achieves the following three objectives through control input:

[0012] Formation maintains target: the distance between adjacent individuals converges to the target distance. Furthermore, the speeds of all individuals tend to be consistent;

[0013] Overall maneuvering target: UAV swarm centroid tracking target point ;

[0014] Obstacle avoidance safety goal: To maintain a safe distance between individuals and circular obstacles. .

[0015] Preferably, the distributed control law is constructed based on the attractive manifold plastic control method, which uniformly models the desired collective behavior of the UAV swarm as a smooth attractive manifold. The system dynamics are designed to make the UAV state converge to the smooth attractive manifold and evolve on the smooth attractive manifold to perform maneuvering tasks. The system dynamics include normal dynamics and tangential dynamics. Normal dynamics pull the UAV swarm toward the manifold to ensure the stability of the formation structure, while tangential dynamics drive the overall motion of the UAV swarm without destroying the manifold invariance.

[0016] Preferably, the obstacle avoidance safety target is achieved based on the normal dynamics, by generating additional control components along the normal direction of the UAV to cause the UAV to deviate from its original path in order to avoid collision.

[0017] Preferably, the distributed control law is as follows:

[0018]

[0019] in, The control law of drone i is represented. Represents the set of neighbors of drone i; Position gain is used to control the convergence strength of the distance error between adjacent UAVs in the formation; This is a speed gain, used to make the speeds of adjacent drones tend to be consistent, thus achieving speed synchronization of the cluster; This is a self-damping gain, used to provide independent velocity negative feedback for each UAV, enhancing system stability; This is the target position gain, used to drive a single UAV toward the target point; The target velocity damping gain is used to provide damping for the center of mass tracking motion, prevent oscillations caused by an excessively large proportional term, and ensure smooth overall maneuvering. As an obstacle avoidance correction term, when drone i approaches a circular obstacle, an additional control component is generated, forcing the drone to deviate from its original path to maintain a safe distance. .

[0020] Secondly, a drone swarm formation control system based on an attraction manifold includes multiple drones, each equipped with:

[0021] The airborne sensor module is used to acquire its own status information and the status information of neighboring drones;

[0022] The communication module is used to exchange information with neighboring drones, broadcast its own status information and receive status information from neighboring drones;

[0023] The flight control module is used to execute flight commands and output control signals to the UAV's power system;

[0024] The formation control calculation module is equipped with the distributed control law in the UAV swarm formation control method based on the attraction manifold, and is used to calculate the control input based on its own state information and the state information of its neighbors, and transmit the control input to the flight control module.

[0025] Compared with existing technologies, the beneficial effects achieved by this invention are as follows: This invention integrates formation maintenance, overall maneuvering, and obstacle avoidance safety into the same mathematical system, avoiding the separate design of different tools for different targets in traditional methods, thus simplifying system design. The projection operator achieves the natural decomposition of normal contraction and tangential tasks; normal control ensures the exponential convergence of the formation structure; and tangential control enables maneuvering tasks without interference.

[0026] This invention unifies distributed approximation and obstacle avoidance intervention into a bounded perturbation model. It theoretically proves that the system maintains exponential attractiveness under perturbation and provides a quantitative upper bound for formation error. The normal deviation caused by obstacle avoidance is incorporated into the perturbation analysis framework, eliminating the need to redesign the main controller and ensuring compatibility between safety and formation performance. Under the controller's action, all state variables automatically remain bounded, requiring no additional assumptions or saturation constraints. Attached Figure Description

[0027] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0028] Figure 1 This is the main flowchart of the present invention;

[0029] Figure 2 These are curves showing the formation and target tracking results in an unobstructed environment, where (a) is the formation error curve, (b) is the speed consistency error curve, and (c) is the target tracking error curve.

[0030] Figure 3 This is a typical trajectory curve of a drone swarm traversing a static obstacle area;

[0031] Figure 4 This is a graph showing the average minimum safe distance for drone swarms to traverse static obstacles.

[0032] Figure 5 This is a graph showing the average formation error of a drone swarm traversing static obstacles.

[0033] Figure 6 This is a snapshot of the dynamic obstacle avoidance of a drone swarm;

[0034] Figure 7 This is a curve diagram of the dynamic obstacle avoidance formation of a drone swarm. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] To make the above-mentioned objectives, features and effects of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] Example 1: A method for controlling UAV swarm formation based on attracting manifolds, such as... Figure 1 As shown, it includes the following steps:

[0038] Step 1: Construct the formation topology of the drone swarm. The formation topology is based on a connected graph and is used to describe the positional relationships between the drones in the swarm.

[0039] Step 2: Each UAV acquires its own status information and the status information of neighboring UAVs in real time through onboard sensors and communication modules. The status information includes position and speed.

[0040] Step 3: For each drone, construct a distributed control law based on the attraction-prevailing plasticity control method;

[0041] Step 4: Each UAV applies the control input calculated by the distributed control law to its own flight control system, so that the UAV swarm can move toward the target as a whole while maintaining formation and obstacle avoidance.

[0042] This invention proposes an Attractive Manifold Plastic Control (AMSC) method to construct distributed control laws. The desired collective behavior is uniformly modeled as a smooth attracting manifold M in the state space. The system dynamics are designed to converge the state exponent to M and evolve within M to execute maneuvering tasks. In this design, normal dynamics pulls the system towards the manifold, ensuring the stability of the formation structure, while tangential dynamics drives the overall motion without violating manifold invariance, achieving goal-oriented maneuvers. This decomposition incorporates formation maintenance and maneuvering tasks into the same mathematical analysis framework, allowing two objectives that would otherwise require different tools to be designed collaboratively within the same system. Furthermore, this decomposition provides natural theoretical support for handling obstacle avoidance problems. When an individual approaches an obstacle, control is applied to deviate it from its original path to avoid a collision. This deviation is essentially an additional control component generated along the normal direction. Since normal dynamics itself is responsible for pulling the system back to the manifold, as long as the magnitude of this additional component is bounded, its influence can be analyzed within the AMSC framework.

[0043] The drone swarm system model is set as a cluster of N isomorphic particles, each moving in a two-dimensional plane, and the dynamic model of each particle is in the form of a second-order integrator:

[0044]

[0045] in , and Representing the position, velocity, and control input of the i-th particle, respectively, all are two-dimensional state vectors. The overall state of the UAV swarm is:

[0046]

[0047] Where X is the state space.

[0048] Design a distributed control law to achieve the following three objectives: Group maintenance: [Based on a connected graph] The defined distance between adjacent individuals converges to the target distance. And all individuals tend to have the same speed, the maximum degree of the connected graph G is Overall maneuver: The centroid of the UAV swarm tracks the target point. Obstacle avoidance safety: Individuals and circular obstacles (center) ,radius Maintain a safe distance ,Right now .

[0049] The attraction current is modeled based on the formation structure objective, and this attraction current is jointly defined by position constraints and velocity constraints. The position constraints are defined based on a connected rigid graph, with linear residuals defined by side lengths.

[0050]

[0051] Speed ​​constraints are based on the speed consistency definition:

[0052]

[0053] Definition of total constraint mapping:

[0054]

[0055] Popularity is defined as:

[0056]

[0057] At the desired configuration, The Jacobian matrix has full row rank and the null space dimension is 5, therefore M is a 5-dimensional smooth embedded submanifold.

[0058] To achieve overall cluster maneuverability (such as centroid tracking), a task vector field is defined to act on the velocity components:

[0059]

[0060] in, Center of mass, For the target location, It is a vector of all 1s. and For gain.

[0061] To ensure that the target manifold M is a smooth embedded submanifold and that the subsequent tangent space and projection operators are well defined, it is necessary to verify that the constraint mapping h satisfies the regularity condition in the vicinity of M. Define the set... In a connected graph It is the minimum rigidity, and the target distance is... The corresponding configuration, assuming rigidity, has a constant. , , , so that for any have: , , ; The normal singular values ​​satisfy ;in Maximum degree, number of edges, and target distance of the graph Explicit correlation, It is determined by the minimum singular value of the rigid graph.

[0062] M has a tubular neighborhood ,Pick Then the nearest point projection Smoothness is defined. Furthermore, there exists a constant... Makes any have:

[0063]

[0064] Where the constant and The value of is derived from the estimation of the constraint mapping h in the tubular neighborhood:

[0065] Upper Realm By the mean value theorem, we obtain ,and Therefore ,Right now ;

[0066] The Lower World This is derived through first-order expansion and the lower bound of the normal singular values. Within the tubular neighborhood, the normal singular values ​​of Dh are at least... , project h at the point Expand at the location and utilize the upper bound of the remaining terms. Combined with neighborhood radius , can be obtained ,therefore .

[0067] Due to location constraints For control input The relative order is 2, directly relative to The design of a first-order dynamic approach is not feasible. To address this issue, a dynamic extension is introduced, defining the extended position error as follows:

[0068]

[0069] in As design parameters, the expanded total error variable is:

[0070]

[0071] in , .

[0072] right Differentiation yields:

[0073]

[0074] in:

[0075]

[0076]

[0077] In the tubular neighborhood Inside, The row is full rank and has a constant. Make

[0078]

[0079] Define the Gram matrix: Its smallest eigenvalue Define the orthogonal projection operator:

[0080]

[0081] Easy to know satisfy ,Right now Projected to .

[0082] The desired dynamic range of the expanded error is set as follows:

[0083]

[0084] Depend on It can be seen that this expected dynamic is equivalent to the linear equation:

[0085]

[0086] because If the row is full rank, equation (17) has a solution, and its minimum norm solution (located in...) )for:

[0087]

[0088] This component is called normal control because it precisely achieves the desired error dynamics. To achieve the task without interfering with normal contraction, the task vector field is... Projected to Upward, tangential control is obtained:

[0089]

[0090] because The tangential term does not affect Therefore, the ideal structured control law is:

[0091]

[0092] Will Substitution ,use From formula (18), we get:

[0093]

[0094] That is, formula (16) holds strictly, therefore the expanded error e converges exponentially:

[0095]

[0096] Depend on We can obtain:

[0097]

[0098] This is a For state, with For a linear system as input. Because The exponential convergence to zero is known from the input-to-state stability (ISS). It also converges exponentially to zero, combined with velocity constraints. The convergence of the original constraint h can be obtained from equation (8). The exponential convergence.

[0099] To ensure that the system state always remains within the regular neighborhood Within this set, construct a positive invariant set. Consider the Lyapunov function. Along the ideal trajectory:

[0100]

[0101] Take constant Make:

[0102]

[0103] but Under ideal control, the positive value remains constant. Meanwhile, from Established on the boundary, It is also positive and unchanging.

[0104] In practical systems, due to the inability to obtain global information such as average velocity and center of mass position, the ideal structured control law (20) is difficult to implement accurately. Let the actual control input be... The total disturbance is defined as:

[0105]

[0106] The actual propagation error dynamics are then:

[0107]

[0108] Disturbance This includes implementation errors of the normal term, leakage of the tangential term, and the impact of obstacle avoidance intervention.

[0109] A constant exists depending only on the graph parameters, gain, and state boundary conditions. , Make it so that in the positive invariant set Established within:

[0110]

[0111] Specifically,

[0112]

[0113] in , and Let be a constant determined by the properties of a connected graph. For the average speed at The upper boundary inside, This is the upper bound of the correction magnitude for the control barrier function CBF.

[0114] make Suppose there exists a radius Make:

[0115]

[0116] If the initial value Then for all have ,and:

[0117]

[0118] therefore ,when When, formula (31) degenerates into formula (22).

[0119] Under the conditions of formula (8), there exists a constant. This makes it possible for all ,have and .

[0120] Based on the above design, the final distributed control law adopted is:

[0121]

[0122] in, The control law of drone i is represented. Represents the set of neighbors of drone i; Position gain is used to control the convergence strength of the distance error between adjacent UAVs in the formation; This is a speed gain, used to make the speeds of adjacent drones tend to be consistent, thus achieving speed synchronization of the cluster; This is a self-damping gain, used to provide independent velocity negative feedback for each UAV, enhancing system stability; This is the target position gain, used to drive a single UAV toward the target point; The target velocity damping gain is used to provide damping for the center of mass tracking motion, prevent oscillations caused by an excessively large proportional term, and ensure smooth overall maneuvering. As an obstacle avoidance correction term, when drone i approaches a circular obstacle, an additional control component is generated, forcing the drone to deviate from its original path to maintain a safe distance. This control law is a distributed approximation of the ideal control (20), and its deviation is controlled by the total disturbance. Absorption, and The upper bound of the perturbation is satisfied by formula (28). As can be seen from formula (8), as long as the parameter selection satisfies the stability condition, the robustness index of the system will converge to the bounded neighborhood of the target manifold.

[0123] To verify the effectiveness of the method of this invention, a multi-agent simulation platform was built based on the Python language. The platform uses the fourth-order Runge-Kutta method for numerical integration with an integration step size of 0.02s. The main simulation parameters are divided into three categories: system parameters, including cluster size, desired distance, neighbor topology, etc.; control gain, including normal contraction term and gain coefficient in task term; obstacle avoidance parameters and initial condition parameters.

[0124] First, consider an accessible scenario. The experiment sets up 60 individuals whose initial positions are randomly distributed within a disk centered at [-50, 0] with a radius of 15 m, and whose initial velocity is zero. The target point is set as... The simulation lasted 60 seconds.

[0125] In this scenario, the normal contraction term and the tangential target term work together, and the system is expected to quickly form a formation that satisfies the distance constraint and translate towards the target point while maintaining a consistent velocity. Twenty independent simulations were conducted, and the formation error was recorded. Speed ​​consistency error and target tracking error The mean curve and standard deviation band of the above errors are shown below. Figure 2 As shown.

[0126] Figure 2 (a) plots the formation errors recorded in 20 independent experiments. Mean curve. Formation error. Directly measure the actual distance between adjacent individuals and the expected value The deviation is a core indicator for verifying the attractiveness of the normal contraction term exponential. Figure 2 (a) It can be seen that the initial formation error is approximately 3.1m, which then continuously decreases under the influence of the normal term. Within the first 10 seconds of the simulation, the error rapidly decreases to 0.85m, after which the rate of decrease gradually slows down. It dropped to 0.7m, and finally at It then stabilized at around 0.5m. Statistical results from 20 independent simulations show that the mean steady-state formation error is... The value has not completely returned to zero. This phenomenon is due to the individual nature of the target tracking item. Instead of an ideal tangential global translation, the introduced normal perturbation prevents the system from converging precisely to the target manifold, causing it to stabilize within a bounded neighborhood of the manifold. This steady-state residual... This can be achieved by increasing the normal gain. Further reduction is possible, but the system's sensitivity to noise must be considered. Overall, the formation error decays exponentially, validating the effectiveness of the normal contraction term.

[0127] Figure 2 (b) plots the formation speed consistency error recorded in 20 independent experiments. The mean curve. Speed ​​consistency error. Used to measure the error between individual velocities and the group average velocity, it reflects the degree to which the common velocity degree of freedom is realized in the target manifold. From Figure 2 (b) It can be seen that the initial velocity error of the cluster is about 1.35 m / s, which decays rapidly under the action of distributed velocity feedback, that is, the sum of the velocity differences of the neighbors. The time error was reduced to 0.45 m / s. The speed is 0.25 m / s. It dropped to 0.15 m / s, then continued to decrease, eventually reaching... It then approaches zero. The mean velocity consistency error during the steady-state phase is... They were almost perfectly synchronized. Interestingly, in Within this range, the speed consistency error generates an overshoot fluctuation, a phenomenon stemming from the interaction between the speed synchronization rate and the target term perturbation. Smaller... This results in slow speed synchronization, and the system is insufficiently able to suppress speed disturbances caused by the objective term during the quasi-steady-state phase. Consequently, oscillations occur under continuous excitation by the objective term, manifesting as brief spikes in speed error. Larger [progress] It can quickly eliminate velocity differences and enhance the system's resistance to disturbances. Although overshoot fluctuations exist, the system can quickly recover and eventually return to zero, demonstrating the overall stability of normal contraction. This result shows that although the control law only uses local neighbor information instead of global average velocity, graph connectivity can still efficiently drive the entire system to achieve velocity consistency. The system successfully enters the common velocity subspace of the target manifold, verifying the theoretical feasibility of distributed implementation.

[0128] Figure 2 (c) plots the target tracking errors recorded in 20 independent experiments. Mean curve. Target tracking error. Used to evaluate the overall performance of the maneuver mission and quantify the impact of the tangential term design on the center of mass motion. Figure 2 (c) shows that the initial mass center is located at The target point is approximately 130m away. Driven by the target, the centroid moves towards the target at an approximately constant rate, and the error decreases linearly with time. The temperature dropped to 80m. The time is 35 m. The time is 5m. The time is 0.5 m. The time is 0 m. The mean steady-state target tracking error is The system reaches the target almost precisely. This evolutionary trend is consistent with the expectation of the ideal tangential term, proving that even if the individual target term is used instead of the overall translation, the system can still maintain the coordination of the overall motion, and the disturbance introduced by the target term is effectively suppressed by the normal contraction, resulting in a very small tracking error.

[0129] The obstacle avoidance capability and formation recovery performance under disturbance were then tested in a static obstacle environment. Twenty-five staggered circular obstacles were placed along the swarm's movement path. The radius of each obstacle was... Safety margin Radius of influence The obstacle coverage area is , Directional spacing Typical trajectories of a cluster traversing areas of static obstacles, such as... Figure 3 As shown.

[0130] Figure 3 The image demonstrates a typical trajectory of a swarm traversing a static obstacle area. The movement paths of 10 randomly selected individuals are plotted, with one location point displayed every two simulation steps to ensure image clarity. It is evident that the swarm automatically detours when approaching the obstacle, rejoins the formation after bypassing it, and the overall direction of movement is not significantly affected.

[0131] To further analyze the formation performance of the swarm when traversing static obstacles, the experiment also recorded the minimum safe distance data of the swarm when traversing obstacles. This experiment also conducted 20 independent trials, and the mean minimum safe distance of the swarm was plotted as a curve, as shown below. Figure 4 As shown.

[0132] Figure 4 The minimum safe distance is given. The mean curve and its standard deviation band. In the initial stage of moving away from the obstacle ( The minimum distance is approximately 28 m. After entering the dense obstacle area ( The mean value rapidly decreased to approximately 2.270 m, with a standard deviation of approximately 3.897 m, indicating significant differences in individual obstacle-crossing paths across different trials, resulting in considerable dispersion in the minimum distance. Although the lower edge of the standard deviation band was close to the safety threshold of 2.0 m, the minimum total distance recorded across all 20 independent trials was 2.100 m, strictly exceeding the safety threshold, thus verifying the effectiveness of the obstacle avoidance mechanism and demonstrating that the system could ensure collision-free operation.

[0133] Subsequently, as the cluster gradually moved away from the obstacle zone ( The minimum distance mean steadily recovered to the final time. However, the evolution of standard deviation exhibits two distinct phases: in to During this period, the standard deviation gradually increases to its peak value, and then rapidly narrows to its final value. This is because when the cluster just leaves the obstacle zone, the individuals are still affected by the perturbations during the crossing process, and the cluster configuration varies greatly in different trials, causing the absolute dispersion of the minimum distance to increase with the mean. Subsequently, with the continued effect of the normal contraction term, the system gradually converges to the target manifold, and the consistency between trials gradually recovers, thus in The standard deviation then decreases rapidly, eventually reaching a minimum. Throughout the process, the minimum distance remains above the safety threshold, demonstrating the robustness and safety of this invention in complex environments.

[0134] To further analyze the formation-keeping capability of the swarm during obstacle avoidance, this experiment recorded the formation error data from 20 independent experiments and plotted the average value as a formation error curve, as shown in the figure below. Figure 5 As shown.

[0135] Figure 5 For formation error The mean curve and its standard deviation band. The initial formation error is approximately 3.1m, which decreases rapidly under the influence of the normal contraction term. Before entering the obstacle area ( The formation error has been reduced to approximately 1.1 meters. During the process of traversing the obstacle zone ( Despite the continuous effect of obstacle avoidance forces on individual units, formation error fluctuated only slightly and continued to decrease at a slightly slower rate. The distance decreased to 0.75 m. This is due to the strong attraction of the normal contraction term. The obstacle avoidance force, as a bounded disturbance, was quickly suppressed by the system, and the system remained within the neighborhood of the target manifold. After leaving the obstacle region, the formation error further decreased, eventually reaching a minimum. Later stabilized Compared to the steady-state error (0.592 m) in the accessible scenario, the mean here is slightly larger, but the standard deviation is extremely small, indicating that the algorithm can still maintain a high degree of consistent formation accuracy under different random initial conditions.

[0136] Finally, a moving circular obstacle was placed on the cluster's movement path to test the robustness of the invention to time-varying perturbations. The initial position of the obstacle was... , radius is With speed The cluster moves at a constant speed along the positive x-axis. Starting from its initial position, the target point is... The moving obstacle needs to be avoided during movement. The obstacle's safety margin, radius of influence, and obstacle avoidance force parameters are consistent with the static scenario. A snapshot of the cluster's dynamic obstacle avoidance is shown below. Figure 6 As shown.

[0137] Figure 6 This shows a typical snapshot of the interaction process between the swarm and moving obstacles. At that time, the cluster starts from the initial position on the left, and the obstacle is located... As time progressed, the obstacle moved to the right. The cluster actively adjusted its path as it approached the obstacle, forming a local detour, and then continued moving towards the target. No collisions occurred throughout the entire process, and the obstacle avoidance success rate in 20 independent trials was 100%, verifying the algorithm's effective response to time-varying perturbations.

[0138] Figure 7 The formation error in 20 independent trials is given. The mean curve and its standard deviation band. In the initial stage, the formation error decreases rapidly. Time dropped to about When the cluster approaches a moving obstacle ( The formation error fluctuated significantly, reaching a peak of [missing information]. It then gradually recovered, until Time drops to Recovery time is approximately The error then continued to decrease slowly, eventually stabilizing at... The steady-state error compared to static obstacle scenarios ( Compared to moving obstacles, the final formation error caused by moving obstacles is slightly higher, but the standard deviation is extremely small, indicating that the algorithm can still maintain a high degree of consistent formation accuracy under different random initial conditions.

[0139] Example 2: A drone swarm formation control system based on an attraction manifold, comprising multiple drones, each drone equipped with:

[0140] An airborne sensor module, including a GPS receiver, an inertial measurement unit, and at least one relative positioning sensor, is used to acquire its own state information and the state information of neighboring drones.

[0141] The communication module is used to exchange information with neighboring drones, broadcast its own status information and receive status information from neighboring drones;

[0142] The flight control module is used to execute flight commands and output control signals to the UAV's power system;

[0143] The formation control calculation module, equipped with the distributed control law described in Embodiment 1, is used to calculate the control input based on its own state information and the state information of its neighbors, and transmit the control input to the flight control module.

[0144] Example 3: The computer-readable storage medium of this example stores a computer program that, when executed by a processor, implements the steps of the UAV swarm formation control method based on an attraction manifold in Example 1.

[0145] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0146] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0147] Example 4: The computer device of this example includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the UAV swarm formation control method based on an attraction manifold of Example 1.

[0148] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0149] Those skilled in the art will clearly understand that each implementation can be achieved using software plus the necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0150] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for controlling UAV swarm formation based on attracting manifolds, characterized in that, Includes the following steps: Step 1: Construct the formation topology of the drone swarm. The formation topology is based on a connected graph and is used to describe the positional relationships between the drones in the swarm. Step 2: Each UAV acquires its own status information and the status information of neighboring UAVs in real time through onboard sensors and communication modules. The status information includes position and speed. Step 3: For each drone, construct a distributed control law based on the attraction-prevailing plasticity control method; Step 4: Each UAV applies the control input calculated by the distributed control law to its own flight control system, so that the UAV swarm can move toward the target as a whole while maintaining formation and obstacle avoidance.

2. The UAV swarm formation control method based on attracting manifolds according to claim 1, characterized in that, Drone swarms achieve the following three objectives through control inputs: Formation maintains target: the distance between adjacent individuals converges to the target distance. Furthermore, the speeds of all individuals tend to be consistent; Overall maneuvering target: UAV swarm centroid tracking target point ; Obstacle avoidance safety goal: To maintain a safe distance between individuals and circular obstacles. .

3. The UAV swarm formation control method based on attracting manifolds according to claim 2, characterized in that, The distributed control law is constructed based on the attractive manifold plastic control method, which uniformly models the desired collective behavior of the UAV swarm as a smooth attractive manifold. The system dynamics are designed to make the UAV state converge to the smooth attractive manifold and evolve in the smooth attractive manifold to perform maneuvering tasks. The system dynamics include normal dynamics and tangential dynamics. Normal dynamics pulls the drone swarm toward the manifold, ensuring the stability of the formation structure, while tangential dynamics drives the overall motion of the drone swarm without violating the manifold invariance.

4. The UAV swarm formation control method based on attracting manifolds according to claim 3, characterized in that, The obstacle avoidance safety objective is achieved based on the normal dynamics, by generating additional control components along the normal direction of the UAV to deviate the UAV from its original path in order to avoid collision.

5. The UAV swarm formation control method based on attracting manifolds according to claim 4, characterized in that, The distributed control law is specifically as follows: ； in, The control law of drone i is represented. Represents the set of neighbors of drone i; Position gain is used to control the convergence strength of the distance error between adjacent UAVs in a formation; This is a speed gain, used to make the speeds of adjacent drones tend to be consistent, thus achieving speed synchronization of the cluster; This is a self-damping gain, used to provide independent velocity negative feedback for each UAV, enhancing system stability; This is the target position gain, used to drive a single UAV toward the target point; The target velocity damping gain is used to provide damping for the center of mass tracking motion, prevent oscillations caused by an excessively large proportional term, and ensure smooth overall maneuvering. As an obstacle avoidance correction term, when UAV i approaches a circular obstacle, an additional control component is generated, forcing the UAV to deviate from its original path to maintain a safe distance. .

6. A drone swarm formation control system based on an attractive manifold, characterized in that, This includes multiple drones, each equipped with: The airborne sensor module is used to acquire its own status information and the status information of neighboring drones; The communication module is used to exchange information with neighboring drones, broadcast its own status information and receive status information from neighboring drones; The flight control module is used to execute flight commands and output control signals to the UAV's power system; The formation control calculation module is equipped with the distributed control law in the UAV swarm formation control method based on the attraction manifold as described in any one of claims 1-5. It is used to calculate the control input based on its own state information and the state information of its neighbors, and transmit the control input to the flight control module.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the UAV swarm formation control method based on attraction manifold as described in any one of claims 1-5.

8. A computer device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the UAV swarm formation control method based on attraction manifold as described in any one of claims 1-5.

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