Four-rotor unmanned aerial vehicle cluster sliding mode active-disturbance-rejection control method based on differential game
By combining differential game theory and sliding mode control, the active disturbance rejection method solves the problem of cooperative formation of UAV swarms under complex threats, achieving high-precision and robust cooperative control suitable for complex open environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUHAN UNIV
- Filing Date
- 2026-01-23
- Publication Date
- 2026-05-01
AI Technical Summary
When facing complex threats such as disinformation injection attacks and high-frequency signal interference, existing control methods for drone swarms suffer from insufficient controller adaptability and reduced formation coordination, making it difficult to achieve high-precision and robust cooperative formation in complex and open environments.
A proactive disturbance rejection control method based on differential game theory and sliding mode control is adopted. By constructing an attack-defense game model, designing a robust controller and a hierarchical distributed control architecture, active defense against false data injection attacks and high-frequency interference is achieved, and cooperative formation is maintained in unstructured environments.
It achieves proactive defense against complex threats in complex environments, improves control precision and dynamic performance, enhances the collaborative intelligence and fault tolerance of the cluster, and is suitable for unstructured scenarios with GPS denial and limited environmental awareness.
Smart Images
Figure CN121956541A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) application technology, specifically relating to a sliding mode active disturbance rejection control technology scheme for quadrotor UAV swarms based on differential game theory. Background Technology
[0002] With the rapid development of computer and communication technologies, the collaboration and control of UAV swarms has become a research hotspot in UAV control systems. UAV swarm systems are often deployed in open environments to perform various complex tasks, frequently facing multiple information security and dynamic control challenges. Especially when facing malicious attacks such as the injection of false information, ensuring that UAV swarms can achieve autonomous passage and cooperative formation while maintaining efficiency and safety has become an important research direction in this field.
[0003] In practical applications, unmanned aerial vehicle (UAV) systems are not only susceptible to high-frequency signal interference but also need to cope with information attacks such as False Data Injection (FDI). Although robust methods such as sliding mode control have been extensively studied, their performance often depends on the precise setting of control parameters, making them difficult to adapt to the highly dynamic characteristics of single UAV systems. Furthermore, in multi-UAV cooperative formation processes, limited environmental perception capabilities restrict their adaptability and anti-interference ability in unstructured environments, affecting the stability and consistency of formation control.
[0004] To address the aforementioned issues, researchers in recent years have attempted to introduce differential game theory, constructing offensive and defensive game models to optimize controller design and enhance the system's adaptability to attacks and environmental disturbances. Simultaneously, by combining visual perception with a distributed predictive compensation mechanism, the positioning and path planning capabilities of UAVs in environments without GPS signals have been further improved, providing a new approach for achieving reliable multi-aircraft cooperative control.
[0005] However, existing research largely focuses on addressing single-type threats (such as FDI attacks alone). In real-world, complex, open environments, UAV swarms face a complex threat of both malicious attacks and high-frequency, strong interference. Existing solutions suffer from insufficient controller adaptability and decreased formation coordination when dealing with such complex and dynamic threats. They also fall short in integrating game theory and robust control to achieve coordinated formation of multiple UAVs in complex interference environments. For example, the combination of differential game theory and robust control (such as sliding mode) may not be deep enough, often resulting in a simple superposition and failing to form an organically integrated self-disruption mechanism. In formation control, static error feedback is frequently used, lacking distributed prediction and estimation capabilities of the leader's dynamic intentions, leading to slow dynamic response and weak anti-interference capabilities.
[0006] In summary, there is an urgent need in this field to develop integrated control methods and system architectures that can balance security, real-time performance, and robustness. Summary of the Invention
[0007] This invention addresses the robust control problem of single quadrotor UAVs encountering signal attacks and high-frequency signal interference. It proposes a quadrotor UAV active disturbance rejection control scheme based on a combination of differential game theory and sliding mode control. The scheme aims to solve the robust control and cooperative formation challenges faced by single UAVs and UAV swarms in complex open environments where false information injection attacks and high-frequency signal interference coexist. It can effectively resist both false data injection attacks and unmodeled high-frequency interference, and achieve high-precision, robust cooperative formation quadrotor UAV swarm control in unstructured environments.
[0008] The technical solution of this invention is a sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory, used in a complex threat environment with spoofed data injection attacks and high-frequency unmodeled interference, comprising the following steps: Establish a dynamic model of a quadcopter UAV; The false data injection attack signal is defined as the attacker's strategy, the feedback controller is defined as the defender's strategy, and an attack and defense cost function representing the comprehensive cost of both sides is constructed. Based on the dynamic model and the attack and defense cost function, a Hamiltonian function is constructed and the saddle point of the differential game is solved to obtain the optimal game strategy for both the attacker and the defender. Design a robust controller based on a terminal sliding surface and including a nonlinear compensation term for compensating for unmodeled high-frequency disturbances; A hierarchical distributed control architecture is adopted to realize the collaborative formation control of the UAV swarm: the upper-level control generates the expected speed of each following UAV through a virtual navigator and a consensus protocol; the lower-level control integrates a feedback controller designed based on the optimal game strategy and the robust controller to drive each following UAV to track its own expected speed.
[0009] Moreover, the attack and defense cost function is constructed by the weight matrix of the system state vector, the weight matrix of the control input vector, and the weight matrix of the attack signal vector.
[0010] Moreover, the Hamiltonian function is composed of the time derivative of the Lyapunov function, the attack and defense cost function, and a penalty term for the attack signal.
[0011] Furthermore, in the robust controller, the terminal sliding surface is composed of the velocity tracking error and its integral; the nonlinear compensation term is a compensation term designed based on the power-law approaching law.
[0012] Furthermore, when generating the desired speed in the upper-level control, a distributed dynamic estimation term for the virtual navigator's state is introduced for each following drone.
[0013] Moreover, the distributed dynamic estimation term is generated by combining the navigator acceleration feedforward term with the consistency feedback term based on the relative position error between neighboring UAVs.
[0014] Moreover, the method enables the drone swarm to maintain cooperative formation capabilities in complex, unstructured environments lacking global positioning signals.
[0015] On the other hand, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements the above-described sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory.
[0016] On the other hand, the present invention provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described above.
[0017] On the other hand, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described above.
[0018] This invention provides an integrated control scheme that organically combines differential game theory with robust control, achieving high-precision and robust collaborative formation of clusters in complex interference environments under a hierarchical distributed architecture. This overcomes the shortcomings of existing technologies, which often employ discrete or simply serial control strategies when dealing with complex dynamic threats, failing to deeply integrate the optimal game theory approach for attack defense with robust control for interference resistance. Furthermore, existing technologies often rely on centralized information transmission or static feedback protocols for formation coordination, lacking distributed, predictive collaborative intelligence. Compared to existing technologies, this invention offers the following significant advancements: 1) Proactive defense capability against complex threats: By adopting a differential game equilibrium strategy based on a new form of cost function, the controller can optimally balance the relationship between countering FDI attacks and maintaining system performance at the design level, thus achieving an upgrade from passive compensation to proactive optimal defense.
[0019] 2) Higher control accuracy and dynamic performance: The terminal sliding surface ensures finite-time convergence, and the sliding self-disturbance rejection structure (nonlinear compensation term) effectively suppresses complex high-frequency interference and reduces chattering. Together, they ensure the control accuracy and rapid stability recovery of the single machine under extreme disturbances.
[0020] 3) Superior cluster collaborative intelligence and fault tolerance: The layered distributed architecture and distributed leader estimation strategy enable the cluster to achieve efficient collaboration without relying on a central node. Even if some nodes are damaged or communication is interrupted, the remaining nodes can still maintain formation through local information, demonstrating powerful distributed intelligence, fault tolerance, and scalability.
[0021] 4) Expanding application capabilities in complex scenarios: The combination of the above technical features makes the solution of the present invention particularly suitable for unstructured scenarios with GPS denial and limited environmental perception (such as autonomous indoor navigation and formation flying among dense obstacles), solving the problem of insufficient adaptability of existing solutions in such scenarios. Attached Figure Description
[0022] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0023] Figure 1 This is a diagram of the anti-disturbance control structure of a dual-layer UAV according to an embodiment of the present invention.
[0024] Figure 2 This is an undirected graph representing the communication architecture between the virtual navigator and the following drones in a drone formation according to an embodiment of the present invention.
[0025] Figure 3 This is a three-dimensional motion curve diagram set for the virtual navigator in an embodiment of the present invention.
[0026] Figure 4 Is Figure 3 A schematic diagram of the x-axis position error of the following trajectory of six follower drones under the virtual navigator motion curve.
[0027] Figure 5 Is Figure 3 A schematic diagram of the y-axis position error of the following trajectory of six follower drones under the virtual navigator motion curve.
[0028] Figure 6 Is Figure 3 A schematic diagram of the z-axis position error of the following trajectory of six follower drones under the virtual navigator motion curve. Detailed Implementation
[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.
[0030] Example 1 See Figure 1 This invention provides a sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory, comprising the following steps: Step 1: Establish the dynamic model of the quadcopter drone: This invention further proposes to construct a dynamic model of the UAV and transform it into a state-space equation.
[0031] In step 1 of the embodiment, the state of the quadcopter UAV is divided into position and attitude. Position is described using the three-axis coordinates (x, y, z) of the UAV's body coordinate system origin in the inertial coordinate system (Earth coordinate system), with both coordinate systems following the right-hand rule. Attitude is expressed using the quadcopter UAV's Euler angles: yaw. , up and down , roll The three Euler angles are defined as the three-axis rotation angles of the UAV's body coordinate system relative to the inertial coordinate system. The purpose of establishing the quadcopter UAV model is to analyze its position and attitude changes under external forces and torques. The total rotation matrix R is:
[0032] in, These represent yaw. , looking up , roll The rotation matrix, total thrust Along the ZB axis of the body coordinate system, the thrust of the quadcopter UAV is provided by its four propellers, and its direction is always the normal vector of the propeller's plane of rotation, perpendicular to the (XOB) direction of the body coordinate system. Therefore, the total thrust vector is... Represented as:
[0033] Multiplying the total thrust vector by the rotation matrix R on the left, the total thrust of the UAV quadcopter is calculated. Transform to inertial coordinate system, the result after transformation is used express:
[0034] Expanding the third column of R (i.e., R(:,3)) shows the forces acting on the quadcopter UAV in the x, y, and z directions in the inertial coordinate system:
[0035] In an inertial coordinate system, calculate the accelerations in the x, y, and z directions of the quadcopter drone according to Newton's second law, where the drone is subject to its own gravity in the z direction:
[0036] in, Let represent the accelerations of the drone in the x, y, and z directions, respectively; m represent the mass of the drone; and g represent the acceleration due to gravity. Ignoring other forces such as friction and disturbances acting on the drone, the accelerations in the x, y, and z directions are calculated from the propeller thrust and gravitational acceleration of the quadcopter.
[0037] After processing, the acceleration input is obtained, where These represent the dynamic equations of the UAV in the x, y, and z directions in the inertial coordinate system, ignoring other frictional forces and disturbances acting on the UAV:
[0038] Considering a quadcopter UAV with nonlinear dynamic characteristics, it can be represented as:
[0039] in For acceleration control input, This refers to the actual speed of the drone. The actual acceleration of the drone, The linear velocity is the air damping coefficient. The total disturbance represents the impact of internal parameter uncertainties and external disturbances on the linear velocity and yaw rate of the UAV along the x, y, and z axes. Let represent the total desired speed of the drone, and let represent the speed of the i-th drone as the control objective. asymptotic tracking of the expected speed of the i-th drone , These represent the expected tracking speeds of the UAV in the x, y, and z directions, respectively.
[0040] The design of differential game theory and state feedback controllers requires approximating the UAV as a linear system and obtaining the state-space equations. First, the constructed UAV dynamics model is linearized, and the control input variables are defined, where:
[0041] in, These represent the thrust of the four rotors of the drone. These represent the total thrust of the UAV and the forces that cause yaw, roll, and pitch to the UAV, respectively. Substitute these into the acceleration control inputs. The expression yields:
[0042] in, These represent the velocities of the drone in the x, y, and z directions, respectively.
[0043] The Euler angular velocities of the quadcopter drone are respectively... This indicates that the relationship between the UAV's angular velocity and attitude angle is expressed as follows:
[0044] in, , , Let represent the angular velocities of the drone's yaw, pitch, and roll angles, respectively. Under normal drone flight conditions, a small-angle approximation can be used, meaning the value of the drone's Euler angles is considered close to 0. The above formula can be simplified to:
[0045] Let the three axes of rotational inertia of the UAV be respectively , , The torques of each propeller of the drone during rotation are as follows: , , , The corresponding drag coefficient is According to the theorem of angular momentum, the rotation equation of the UAV can be obtained as follows:
[0046] in, , , For roll, pitch, and yaw, angular acceleration.
[0047] For simplicity of derivation, let parameters be set. . If we denote the corresponding lever arm, then it simplifies to:
[0048] We can obtain:
[0049] State-space equations are established from the above equation, denoted as state variables: , And assuming the UAV provides thrust along the z-axis to counteract gravitational acceleration, the state-space equations of the UAV can be obtained. ,in Let A be the derivative of the state variable, B be the state matrix, and u be the input.
[0050] Step 2: Define the FDI attack signal as the attacker and the feedback controller as the defender, and establish the attack and defense cost function; This invention defines a false data injection attack signal as the attacker's strategy, defines a feedback controller as the defender's strategy, and constructs an attack and defense cost function that characterizes the combined costs of the attacker and defender.
[0051] In this embodiment, considering the FDI attack signal received by the UAV, the system state-space equation of the UAV in step 2 should be:
[0052] in, This is the system state vector; To control input (defender's strategy); To interfere with the input (attacker's strategy). The input FDI coefficient matrix, This is the FDI coefficient matrix for the sensing end. Let n be the real number field, and v, p be the corresponding matrices. The dimension; This is a composite coefficient matrix representing the FDI attack signals applied simultaneously to both the input and sensing ends of the system. This indicates the equivalent FDI attack signal at the system input. This indicates the equivalent FDI attack signal at the system's sensing end.
[0053] Define the attack and defense cost function:
[0054] in This reflects the combined cost of system state, control input, and attack (hereinafter denoted by E), representing the dynamic relationship between the control input u applied by the defender through Y, the FDI signal w injected by the attacker through Z, and the system state. In the formula, parameter Ix is the state weight matrix, I is the identity matrix, reflecting the penalty for state deviation; Y is the control input weight matrix, reflecting the system's emphasis on control signals; and Z is the FDI attack weight matrix, describing the degree of impact of the attack on the system.
[0055] Define quadratic performance index To measure the combined impact of control and attack on output:
[0056] In the formula This is a penalty term for the attack signal, representing the level of interference suppression. For time derivative.
[0057] Step 3: Construct and optimize the Hamiltonian function for synthesizing the system dynamics equations and performance indices, and solve for the saddle point in the differential game; This step is the key improvement of the present invention. Based on the dynamic model and the attack and defense cost function, the Hamiltonian function is constructed and solved to obtain the optimal game strategy for both the attacker and the defender. Furthermore, the step of constructing and optimizing the Hamiltonian function includes constructing a Lyapunov function containing a positive definite Riccati matrix, constructing the Hamiltonian function based on the Lyapunov function and the attack and defense cost function, and obtaining the optimal game strategy of the attacking and defending parties by finding the extreme values of the Hamiltonian function with respect to the defense control input and the attack input.
[0058] In step 3 of this embodiment, a Hamiltonian function is constructed to synthesize the system's dynamic equations and performance indicators. The game control strategy is solved by optimizing this function. The system dynamic equations and performance indicators measure the combined cost of control and attack, and represent the penalty for attack signals. The Hamiltonian function unifies the control objective (minimizing the performance indicator) and the attack objective (maximizing destruction) into a single optimization problem. By solving for the extrema of the Hamiltonian function, the optimal game strategy for both the attacker and defender is found. The speed control system of the i-th quadcopter UAV can be described as follows:
[0059] in Let i represent the three-dimensional linear acceleration of the i-th UAV. Represents the three-dimensional acceleration input of the drone , Let i represent the three-dimensional linear velocity of the i-th UAV. and Let represent the combined uncertainties caused by external disturbances and internal uncertain parameters affecting the linear velocity and yaw rate of the i-th UAV along the x, y, and z axes, respectively. The value represents the velocity drag coefficient, and m is the mass of the UAV.
[0060] Define the speed tracking error of each drone in a drone formation. for
[0061]
[0062] in, Let i be the expected speed of the i-th drone. For the velocity tracking error along the x, y, and z axes, First, consider the case with only external disturbances (i.e.) )of Speed control system, for error The derivative is denoted as . :
[0063] in, The derivative of the desired velocity, This is the speed drag coefficient. It represents the sum of uncertain disturbances such as FDI attack signals and air resistance that the system is subjected to.
[0064] The following section uses differential game theory to solve for the feedback controller in this system. For ease of solution, the above equation is first converted into matrix form.
[0065] in, , This is an FDI attack signal. Let there be a coefficient matrix. , , , , ( (where is a 3x3 identity matrix), then the above equation can be written as:
[0066] The following will Treated as an FDI attacker, Design a differential game feedback controller for the defender side of the controller.
[0067] First, construct the Lyapunov function. :
[0068] Where P represents the Riccati matrix, which is positive definite, and the Hamiltonian function is constructed. As follows, here it is recorded as :
[0069] in, The weighting coefficients representing the attack signal. Let V represent the derivative of the Lyapunov function V with respect to time. For the cost function of the offensive and defensive game, , These are the weight matrices for the defender and the FDI attacker, respectively.
[0070] The attacker in the Hamiltonian function respectively and the defending side Take the partial derivative, and denote the result as... and ,Right now:
[0071] The superscript T indicates the transpose of the matrix.
[0072] For ease of representation, the following matrix is further defined:
[0073] in The elements of each block are:
[0074] Solving the simultaneous equations, we get:
[0075] in, As the optimal defense signal, This is the optimal attack signal.
[0076] Finding the extreme points represents the optimal defense controller. and attack signals To obtain the optimal game strategy for both the attacker and defender.
[0077] in To simplify the matrix
[0078] Unlike existing methods that construct cost functions, this invention constructs attack and defense cost functions and performance indicators by directly defining the weight matrices of state, control, and attack. This parameterization method more intuitively reflects different trade-off strategies for system state deviation, control energy consumption, and attack destructive power, and obtains optimal feedback gains with different structures through the trade-off strategy, thereby achieving a more targeted optimal balance between control performance and security defense.
[0079] Step 4: Design a robust controller for the unmodeled high-frequency disturbances experienced by the UAV system, incorporating the sliding mode control concept. In step 4 of the embodiment, in view of the uncertainty in the system and the impact of external unmodeled high-frequency interference on the system itself, this feedback controller is combined with the robustness of sliding mode control. Taking advantage of the strong robustness of sliding mode control, a sliding mode controller for the lower-level speed tracking control of the quadcopter UAV is designed.
[0080] Design terminal sliding surface
[0081]
[0082] in, Denotes the sliding mode control coefficient of the i-th UAV. This represents the error between the actual speed and the expected speed of the i-th drone. Let t be the integral term, and t represent time. To stabilize the sliding mode control, the derivative with respect to the sliding surface is taken and set to 0, and a compensation term is designed to compensate for uncertainties in the system's internal parameters and external disturbances.
[0083] The equivalent control term for sliding mode is
[0084]
[0085] Design sliding mode control compensation items for
[0086] in, Let i represent the expected three-dimensional linear acceleration of the i-th UAV. For the compensation term coefficient, The proportionality coefficient for the compensation term, sig() is the sign function, and the parameter is... Guarantee convergence within a finite time.
[0087] By combining a sliding mode controller with a differential game controller, the acceleration control input of the disturbed velocity control system can be obtained. for
[0088] in, To simplify the matrix,
[0089] The sliding mode controller designed in this invention differs significantly from traditional integral or linear sliding mode control. First, it employs a terminal sliding surface, the structure of which is designed to ensure that the tracking error converges within a finite time, rather than asymptotically, thereby improving the system's dynamic response speed. Second, and most importantly, it introduces a nonlinear compensation term, employing a power-law approaching function. This term not only counteracts the total disturbance but also embodies the essence of extended state observation and nonlinear feedback in active disturbance rejection control. Combined with the strong robustness of sliding mode, it forms a unique sliding mode active disturbance rejection control structure that can more effectively suppress high-frequency unmodeled disturbances and weaken the chattering phenomenon inherent in traditional sliding mode control.
[0090] Step 5: Design a hierarchical distributed UAV formation control method that includes trajectory tracking and speed control: The formation is implemented using a hierarchical distributed control architecture. The upper layer generates the expected speed of each UAV through a virtual navigator and a consensus protocol. The lower layer integrates the optimal game strategy and the robust controller to drive each following UAV to track the expected speed, so as to jointly resist false data injection attacks and high-frequency disturbances.
[0091] This invention proposes upper-layer trajectory tracking control and lower-layer speed tracking control. The upper-layer trajectory tracking control sets a virtual navigator trajectory and calculates the expected speed of each following drone based on a consensus protocol. The lower-layer speed tracking control receives the expected speed and uses the optimal game strategy and the robust controller to enable each following drone to track its expected speed, while resisting false data injection attacks and unmodeled high-frequency disturbances.
[0092] In step 5 of the embodiment, the two-layer formation controller of the quadcopter drone swarm consists of an upper-layer trajectory tracking control and a lower-layer speed tracking control. The goal of drone formation control is to maintain a certain formation during flight. The upper-layer trajectory tracking control sets a virtual navigator, with each quadcopter drone acting as a follower. The trajectory of each follower drone is determined by a consistency control law, and the desired speed for each follower drone to maintain this trajectory is calculated and transmitted to the lower-layer speed tracking control. The lower-layer desired speed tracking control ensures that each follower drone's speed tracks the desired speed, while using differential game theory and sliding mode control to address the effects of external FDI attack signals and uncertain interference. The upper and lower layers work together to achieve cooperative anti-interference formation control of the quadcopter drone swarm.
[0093] In the drone formation algorithm, consider a drone formation system consisting of n follower drones and 1 virtual leader. The follower dynamics model is as follows:
[0094] in It is a position state vector. The velocity state vector, Input the speed of the i-th drone.
[0095] For each follower drone, the control method consists of two parts.
[0096]
[0097] In the formula Let k be the location input for the i-th drone. k represents the neighbor error feedback coefficient. Represents the adjacency matrix. Indicate the positions of the i-th and j-th drones. Indicates a collection of drones. This indicates the preset formation positions of the i-th and j-th drones. Let be the connection weight matrix between the i-th drone and the navigator. Let represent the speed of the i-th drone and the navigator. This is the navigator speed estimate, the navigator estimation term. Includes acceleration feedforward compensation (i.e., the known portion of the leader's acceleration). This is to offset the effect of leader acceleration on velocity and reduce estimation error. k is the gain coefficient, and the rest is the neighbor error feedback correction term, which is obtained through the local position error term. The system feeds back the positional differences between the follower drone, neighboring drones, and the leader drone into the velocity estimation. When the follower drone is ahead of its neighbors or the leader, the feedback term decreases, suppressing overshoot; when it lags, the feedback term increases, accelerating the catch-up with the virtual leader. The update of the leader estimation term depends on acceleration information and is also adjusted by local consistency error, forming a closed-loop estimation. By compensating for dynamic changes in advance during real-time corrections, tracking lag is significantly reduced.
[0098] The formation control of this invention employs a clear two-layer distributed architecture. The upper trajectory generation layer not only calculates the desired velocity, but its core function is to generate a localized leader velocity estimate for each follower. This estimate is not simply received from global information, but is dynamically updated, incorporating the leader's acceleration feedforward and feedback correction based on local neighbor position errors. This distributed prediction and estimation mechanism enables each UAV to proactively and in advance adapt to the leader's dynamic changes, significantly reducing communication dependence and tracking lag. Compared with the static error feedback protocols based on fixed gain commonly used in existing technologies, this significantly improves the formation's cooperative consistency, dynamic response speed, and overall robustness under disturbances and attacks.
[0099] This invention addresses the robust control problem of quadrotor UAVs encountering signal attacks and high-frequency signal interference, proposing an active disturbance rejection control (ADRC) method for quadrotor UAVs based on a combination of differential game theory and sliding mode control. The invention constructs a dynamic system and state-space equation model of the UAV. Within the framework of differential game theory, it defines the attack cost function (FDI attack signal as the attacker) and the cost function (feedback controller as the defender). A Hamiltonian function is constructed and optimized to synthesize the system's dynamic equations and performance indicators. The differential game feedback controller is designed by solving for the differential game saddle point (i.e., the Nash equilibrium solution). Furthermore, it incorporates sliding mode control principles to design a robust controller for unmodeled high-frequency disturbances affecting the UAV system, and constructs a Lyapunov function to analyze the stability of the controlled control system. Finally, a UAV dynamics and disturbance model is built in the Matlab / Simulink simulation environment, verifying the correctness of the theoretical results.
[0100] This invention also addresses the problem of cooperative anti-disturbance formation in quadrotor UAV swarms in open environments, proposing a hierarchical distributed formation control method that includes trajectory tracking and velocity control. In the upper-level trajectory tracking control, based on the consensus algorithm of the virtual leader, each following quadrotor UAV calculates its own desired velocity by estimating the unknown acceleration information of the virtual leader. In the lower-level desired velocity tracking control, considering the aforementioned interference and attack signals, a robust self-disturbance rejection controller for the single UAV system in the quadrotor UAV swarm formation is designed. Differential game theory is incorporated into the parameter design of the sliding mode control system, enabling each quadrotor UAV to track the desired trajectory transmitted by the upper-level trajectory tracking controller and maintain a certain swarm formation shape. By constructing Lyapunoy and Hamiltonian functions, sufficient conditions to ensure the stability of the UAV swarm formation control are given. Finally, UAV dynamics and disturbance models are built in Matlab / Simulink to verify the correctness of the above theoretical results.
[0101] To facilitate understanding of the technical effects of this invention, the sliding mode active disturbance rejection controller for quadrotor UAV swarms based on differential game theory described above was simulated and verified. A swarm of six follower UAVs and one virtual navigator was used to form a communication topology.
[0102] See Figure 2 This represents an undirected graph illustrating the communication architecture between the virtual navigator and the follower drones in a drone swarm.
[0103] Set a movement trajectory for the virtual navigator. Figure 3This represents the 3D motion curve set for the virtual navigator. The goal is to examine the effectiveness of the following drones' movement in tracking the formation target by establishing the virtual navigator's trajectory. Once set up, the drone swarm follows the virtual navigator, and the error between the actual trajectory of each following drone and the desired motion curve is observed.
[0104] Figure 4 Indicates in Figure 3 Under the virtual navigator motion curve, the x-axis position error of the following trajectory of the six following drones is respectively represented by... The results in the figure show that, with the initial x-axis distance error not being zero, the six following drones can quickly converge the error to zero by following the formation, meaning that the following drones can stably track the virtual navigator in the x-axis.
[0105] Figure 5 Indicates in Figure 3 Under the virtual navigator motion curve, the y-axis position errors of the following trajectories of the six following drones are respectively represented by... The results in the figure show that, with the initial y-axis distance error not being zero, the six following drones can quickly converge the error to zero by following the formation, meaning that the following drones can stably track the virtual navigator in the y-axis.
[0106] Figure 6 Indicates in Figure 3 Under the virtual navigator motion curve, the z-axis position errors of the following trajectories of the six following drones are respectively represented by... The results in the figure show that, with the initial formation z-axis distance error not being zero, the six following drones can quickly converge the error to zero by following the formation, meaning that the following drones can stably track the virtual navigator in the z-axis.
[0107] As shown in the figure, the position errors of each UAV in the x / y / z directions can quickly converge to near zero and maintain a bounded small range of fluctuations. This verifies that the present invention can still maintain high accuracy and strong stability in formation tracking under the presence of attacks and interference.
[0108] Example 2 Based on the same inventive concept, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described above.
[0109] Example 3 Based on the same inventive concept, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, it implements the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described above.
[0110] In another possible embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described above.
[0111] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.
[0112] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to replace them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.
Claims
1. A sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory, characterized in that, For environments with a combination of threats including fake data injection attacks and high-frequency unmodeled interference, the following steps are included: Establish a dynamic model of a quadcopter UAV; The false data injection attack signal is defined as the attacker's strategy, the feedback controller is defined as the defender's strategy, and an attack and defense cost function representing the comprehensive cost of both sides is constructed. Based on the dynamic model and the attack and defense cost function, a Hamiltonian function is constructed and the saddle point of the differential game is solved to obtain the optimal game strategy for both the attacker and the defender. Design a robust controller based on a terminal sliding surface and including a nonlinear compensation term for compensating for unmodeled high-frequency disturbances; A hierarchical distributed control architecture is adopted to realize the collaborative formation control of the UAV swarm: the upper-level control generates the expected speed of each following UAV through a virtual navigator and a consensus protocol; the lower-level control integrates a feedback controller designed based on the optimal game strategy and the robust controller to drive each following UAV to track its own expected speed.
2. The sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory according to claim 1, characterized in that: The attack and defense cost function is constructed by the weight matrix of the system state vector, the weight matrix of the control input vector, and the weight matrix of the attack signal vector.
3. The sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory according to claim 1, characterized in that: The Hamiltonian function consists of the time derivative of the Lyapunov function, the attack and defense cost function, and a penalty term for the attack signal.
4. The sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory according to claim 1, characterized in that: In the robust controller, the terminal sliding surface is composed of the velocity tracking error and its integral; the nonlinear compensation term is a compensation term designed based on the power-law approaching law.
5. The sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory according to claim 1, characterized in that: When generating the desired speed in the upper-level control, a distributed dynamic estimation term for the virtual navigator's state is introduced for each following drone.
6. The sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory according to claim 1, characterized in that: The distributed dynamic estimation term is generated by combining the navigator acceleration feedforward term with the consistency feedback term based on the relative position error between neighboring UAVs.
7. A sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory according to claim 1, characterized in that: The method enables the drone swarm to maintain coordinated formation capabilities in complex, unstructured environments lacking global positioning signals.
8. An electronic device comprising a memory, a processor, 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 sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described in any one of claims 1 to 7.
9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described in any one of claims 1 to 7.
10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the sliding mode active disturbance rejection control method for quadrotor UAV swarms based on differential game theory as described in any one of claims 1 to 7.