Unmanned aerial vehicle formation event triggering sliding mode tracking control method and system
Through the sliding mode tracking control method triggered by the drone formation event, the impact of playback attack on the drone formation control is solved, the system stability and anti-interference ability are improved, and the formation coordination and execution are ensured.
Patent Information
- Application Number
- CN202411569034.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-05
- Publication Date
- 2025-02-14
AI Technical Summary
When facing a playback attack, the control instructions are no longer accurate, affecting the coordination and execution of the formation, and may even paralyze the entire system.
Using the sliding mode tracking control method for drone formation event triggering, through dynamic model construction based on graph theory, the translation and rotational motion theory is defined, linearized models in hover state are constructed, and replay attack models and switching event triggering are introduced. Mechanism, design drone observer and event-triggered sliding mode surface based on observer, and finally build a control strategy based on sliding mode surface.
Effectively reduce the impact of replay attacks on the drone formation, improve the stability and anti-interference ability of the system, reduce the burden of communication and computing, and ensure the coordination and execution of the formation.
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Figure CN119440097A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of unmanned aerial vehicle formation control, and in particular to an unmanned aerial vehicle formation event-triggered sliding mode tracking control method and system. Background Art
[0002] In recent years, drones have been widely used in reconnaissance, search, and rescue missions. However, due to their openness to the external environment and their reliance on wireless communication networks, they are vulnerable to network attacks, especially replay attacks, which can cause system control instability or failure by retransmitting past communication data.
[0003] Replay attacks are a common form of network attacks. Attackers disrupt the normal operation of the system by intercepting and resending past legitimate communication data packets. In drone formation control systems, replay attacks are particularly threatening because drones rely on wireless communication networks to exchange control commands and status information. Once an attacker successfully launches a replay attack, the system may make wrong decisions, resulting in inaccurate control commands, which in turn affects the coordination and execution of the formation and may even paralyze the entire system.
[0004] The danger of a replay attack is that it does not modify the data content directly, but rather uses the system's trust in old data to disguise itself as normal communication. This type of attack is usually difficult to detect, especially when a drone is performing a mission. When the attacker replays past status information or control instructions, the drone will respond based on outdated data, resulting in flight trajectory deviation, position offset, or formation structure failure. To this end, we propose a sliding mode tracking control method and system for drone formation events. Summary of the invention
[0005] The purpose of the present invention is to provide a UAV formation event-triggered sliding mode tracking control method to solve the problems raised in the above-mentioned background technology.
[0006] According to a first aspect of the present invention, in order to achieve the above-mentioned purpose, the present invention provides the following technical solution: a sliding mode tracking control method triggered by an event of a UAV formation, comprising the following steps:
[0007] Construct a dynamic model of a quadrotor drone based on graph theory, including defining the translational motion theory or the rotational motion theory, and constructing a linearized model in the hovering state;
[0008] Construct the UAV system model, including defining the UAV dynamic equations and defining the UAV tracking error;
[0009] Build a replay attack model;
[0010] Build a switching event trigger mechanism;
[0011] Designing drone observers;
[0012] Constructing observer-based event-triggered sliding surface;
[0013] Construct a control strategy based on event-triggered sliding surface.
[0014] Further, the translational motion theory is defined or the rotational motion theory is defined as follows:
[0015] (1) Define the theory of translational motion:
[0016] Using Newton's second law, we get:
[0017]
[0018] Where u to is the total thrust of the drone, m and g r are the mass and gravity acceleration of the drone respectively; in the world coordinate system, the east, north, and down positions of the drone are represented by Y r , X r and Z r , and W tr It is a transition matrix, which is used to realize the coordinate transformation from the drone body coordinate system to the world coordinate system;
[0019] Among them, u to The specific representation is as follows:
[0020] u to =F1+F2+F3+F4
[0021] where F p (p=1,2,3,4) represents the lift generated by the four motors;
[0022] Transition matrix W tr The specific definition of is:
[0023]
[0024] Where θ, φ, ψ represent the pitch angle, roll angle and yaw angle of the drone respectively; c(g) and s(g) represent the cosine and sine functions respectively;
[0025] W tr Substituting into the translational motion formula, we get:
[0026]
[0027] middle u to is the total thrust of the drone, m and g r are the mass and gravity acceleration of the drone respectively; in the world coordinate system, the east, north, and down positions of the drone are represented by Y r , Xr and Z r , and W tr It is a transition matrix, which is used to realize the coordinate transformation from the drone body coordinate system to the world coordinate system;
[0028] (2) Define the theory of rotational motion:
[0029] Using Euler's formula, we get:
[0030]
[0031] Where γ represents the angular velocity of the UAV in its fixed coordinate system, τ is the total torque of the UAV, and I is the inertia tensor matrix, which is regarded as a diagonal matrix due to the symmetry of the quadrotor UAV layout;
[0032] The specific expression of γ is as follows:
[0033] γ=[r x r y r z ] T
[0034] Where r x ,r y ,r z Respectively represent the angular velocity of the drone around the x-axis, y-axis, and z-axis of its body coordinate system, [] T Represents the transposed matrix of this matrix.
[0035] Furthermore, a linearized model in the hovering state is constructed as follows:
[0036] When the drone is close to hovering, u to =mg r ,φ≈0,θ≈0, Get the linearized model of the quadrotor drone near the hovering state:
[0037]
[0038] In the formula, u to is the total thrust of the drone, m and g r are the mass and gravitational acceleration of the UAV, θ, φ, ψ represent the pitch angle, roll angle and yaw angle of the UAV, c(g) and s(g) represent the cosine and sine functions, respectively.
[0039] Furthermore, the UAV system model is constructed, including defining the UAV dynamics equation and defining the UAV tracking error, as follows:
[0040] (1) Define the UAV dynamics equation:
[0041] Establish a drone formation, which includes a virtual leader, marked as the 0th drone, and N followers, marked as 1, 2, 3, ..., N;
[0042] definition:
[0043]
[0044] Where x i (t) represents the state variable of the i-th UAV at time t; v i (t) represents the position and speed of the UAV, respectively, [] T represents the transposed matrix of the matrix;
[0045] Then, the dynamic equations of the 0th UAV and the i-th follower UAV are described as:
[0046]
[0047] Where u i (t) is the control input of the ith UAV, U is a real constant matrix;
[0048] The specific definitions of A and B are as follows:
[0049]
[0050] Nonlinear function d i (t) represents a collection of various nonlinear behaviors that satisfy the following conditions:
[0051] ||d i (t)||2≤||Fx i (t)||2 (9)
[0052] Among them, the specific definition of F is:
[0053]
[0054] (3) Define UAV tracking error:
[0055] The directed communication topology F has a directed spanning tree with the 0th drone as its root node, representing the leader. The time-varying structure of the follower drones is described by the following formula:
[0056]
[0057] Where g i (t) is a continuously differentiable formation vector, g i (t) is defined as follows:
[0058]
[0059] In the formula represents the position of the i-th UAV, g iv (t) represents the speed of the ith UAV, and
[0060] The tracking error of the i-th UAV is defined as:
[0061]
[0062] in, w ij and a i The specific definition is as follows:
[0063]
[0064] The derivative formula of the tracking error formula is as follows:
[0065]
[0066] Where u ηi (t) is the formation control input, Bu ηi (t) and The specific definition is as follows:
[0067]
[0068] Nonlinear functions and tracking error η i The relationship between (t) satisfies the following constraints:
[0069]
[0070] In the formula is a given constant matrix.
[0071] Furthermore, a replay attack model is constructed as follows:
[0072] Each replay attack cycle is divided into a dormant period and an active period. The replay attack can be modeled by using a switching system:
[0073] Let h be the sampling step of the i-th drone state, then the data with replay attack transmitted through the network It is expressed as:
[0074]
[0075] Where T n Indicates the starting time of the nth attack, S n Indicates the duration of the replay attack, represents the actual transmitted data, and ε represents the delay time of replay;
[0076] definition:
[0077]
[0078] In (0, t), the number of switch transitions of the replay attack is expressed as M(t), which is given by and The synthesized attack signal satisfies the following attack frequency constraints:
[0079]
[0080] Where c = 1, e m =5.
[0081] Furthermore, a switching event trigger mechanism is constructed, as follows:
[0082] The triggering conditions of the switching event triggering mechanism are designed as follows:
[0083] W1(t)+W2(t)-W3(fh)<0 (19)
[0084] in,
[0085]
[0086] Where v i ∈[0,1) represents a weight factor, k i =0.2,Φ i,σ(t) =diag(5,10,8) is the weight matrix, and are the release moments of the nth sleep stage and the nth active stage, respectively. represents the tracking error sampling signal at the initial moment, represents the current tracking error sampling signal, fh represents the adjustment amount, and the trigger mechanism does not include the leader drone; h represents the update frequency of the control signal;
[0087] The switching signal σ(t) is used to distinguish between two types of replay attacks during the attack period: active attack or dormant attack; s(t) = 1 means that the replay attack is in the interval When s(t) = 2, the trigger condition W1(t) + W2(t) - W3(fh) < 0, where W3(fh) ≠ 0, will result in a larger execution interval, so less data can be transmitted during the active period of the replay attack. It should be noted that k i The value of will affect the data publishing rate;
[0088] Definition, the event-triggered sampling state is expressed as:
[0089]
[0090] in,
[0091]
[0092] Furthermore, the UAV observer is designed as follows:
[0093] Definition, the design of the i-th UAV observer is as follows:
[0094]
[0095] Among them, H σ(t) (σ(t)∈{1,2}) is the observer gain to be designed;
[0096] Definition, observation error is expressed as:
[0097]
[0098] Combining the observation error formula (22) with the observer design formula (21), we get:
[0099]
[0100] Furthermore, an observer-based event-triggered sliding surface is constructed as follows:
[0101] The observer-based event-triggered sliding surface is defined as:
[0102]
[0103] Where K σ(t) , (σ(t)∈{1,2}) is the profit matrix of sliding mode control;
[0104] The specific definition of D is:
[0105] D = {2,3,1.5}
[0106] Order i (t) = 0, we get the equivalent observer-based sliding mode control law:
[0107]
[0108] Among them, the sliding mode gain matrix K σ(t) The choice directly affects the stability and response speed of the system;
[0109] Substituting (25) into (21), we can obtain the sliding dynamics formula:
[0110]
[0111] Combining equations (23) and (26), the matrix of a single UAV system is expanded to the entire multi-UAV system through the Kronecker product, and the following overall system dynamics equation is obtained:
[0112]
[0113] in:
[0114]
[0115] δ η (t) = col N {δ ηi (t)}
[0116]
[0117] V(t)=col N {V i (t)}
[0118] V(t-ε)=col N {V i (t-ε)}
[0119]
[0120] in, represents the tracking error vector; δ i (t) represents the observation error; V i (t) is the event error trigger signal; Represents the tracking error sampling signal at the initial moment; represents the current tracking error sampling signal, fh represents the adjustment amount; ε represents the delay time of playback; col N {} represents the column vector of the vector;
[0121] The coefficient matrix is defined as follows:
[0122]
[0123] Among them I N is the N×N identity matrix;
[0124] System Matrix A l , B l , U l and C l Defined as:
[0125]
[0126] Where l = 1, 2, and d(t) = ε + τ(t-ε) represents the time delay and disturbance of the system state; H1, H2 are observer gains to be designed; U is a real constant matrix.
[0127] Furthermore, a control strategy based on sliding surface is constructed as follows:
[0128] Under the framework of the switching event trigger mechanism and the observer, the sliding surface s shown in formula (24) is selected i (t), in order to enable the trajectory of the system to be driven to the sliding surface s i (t), the controller u is designed ηi (t), which is expressed as follows:
[0129]
[0130] The controller contains several items, each of which corresponds to a different control function:
[0131] This term includes the sliding mode gain K σ(t) and the dynamic compensation term H σ(t) , which act together on the state variables estimated by the observer Used to adjust the intensity of control input to ensure that the system responds quickly and approaches the sliding surface;
[0132] (a i +o i (t))S(s i (t)):coefficient r i =5, used to determine the size of the sliding surface attraction, is the compensation term based on the observer error;
[0133] in:
[0134]
[0135] Where β i =0.5 is a threshold value that determines the form of the sliding mode function;
[0136] When ||s i (t)||greater than or equal to the threshold β i When ||s i (t)|| is less than the threshold β i When , the controller adjusts the input to prevent the system state from leaving the sliding surface.
[0137] According to a second aspect of the present invention, the present invention provides a UAV formation event-triggered sliding mode tracking control system, which is used to implement the above-mentioned UAV formation event-triggered sliding mode tracking control method, comprising:
[0138] The first building module is used to build a dynamic model of the quadrotor drone based on graph theory, specifically including defining a translational motion theory or a rotational motion theory, and building a linearized model in a hovering state;
[0139] The second building module is used to build the UAV system model, including defining the UAV dynamic equation and defining the UAV tracking error;
[0140] The third building module is used to build a replay attack model;
[0141] The fourth building block is used to build a switching event trigger mechanism;
[0142] Design module, used to design drone observers;
[0143] A fifth building module, for building an observer-based event-triggered sliding surface;
[0144] The sixth building block is used to build a control strategy based on event-triggered sliding surface.
[0145] The present invention has at least the following beneficial effects:
[0146] 1. The present invention uses graph theory to construct a dynamic model of a quadrotor drone, and defines translation and rotation motions in detail. The model is linearized in the hovering state to achieve accurate analysis and control of the drone's motion state, forming a complete system model. In order to deal with replay attacks, a replay attack model is also introduced, and a switching event trigger mechanism is designed. By real-time monitoring of the system status and dynamically adjusting the control strategy, the impact of the attack can be effectively reduced.
[0147] 2. The present invention proposes an observer-based state estimation method, which improves the accurate evaluation of the system state, and constructs an event-triggered sliding surface based on this. Based on the designed sliding surface, a UAV formation control strategy is proposed. Combining the robustness of sliding mode control and the efficiency of event triggering mechanism, it not only reduces the communication and computing burden, but also improves the stability and anti-interference ability of the system.
[0148] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS
[0149] Figure 1 The figure is a schematic diagram of the process of the method of the present invention. DETAILED DESCRIPTION
[0150] The following will be combined with the drawings in the embodiments of the present disclosure to clearly and completely describe the technical solutions in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, rather than all the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.
[0151] Embodiment 1:
[0152] See also Figure 1 The present invention provides a technical solution: a sliding mode tracking control method triggered by an event of a UAV formation, comprising the following steps:
[0153] S1. Construct a dynamic model of a quadrotor drone based on graph theory, including defining the translational motion theory or the rotational motion theory and constructing a linearized model in the hovering state, as follows:
[0154] (S11) Define the theory of translational motion:
[0155] Using Newton's second law, we get:
[0156]
[0157] Where u to is the total thrust of the drone, m and g r are the mass and gravity acceleration of the drone respectively; in the world coordinate system, the east, north, and down positions of the drone are represented by Y r , X r and Z r , and W tr It is a transition matrix, which is used to realize the coordinate transformation from the drone body coordinate system to the world coordinate system;
[0158] Among them, u to The specific representation is as follows:
[0159] u to =F1+F2+F3+F4
[0160] where F p (p=1,2,3,4) represents the lift generated by the four motors;
[0161] Transition matrix W tr The specific definition of is:
[0162]
[0163] Where θ, φ, ψ represent the pitch angle, roll angle and yaw angle of the drone respectively; c(g) and s(g) represent the cosine and sine functions respectively;
[0164] Wtr Substituting into the translational motion formula, we get:
[0165]
[0166] Where Y r , X r and Z r Respectively represent the east, north, and down positions of the UAV; θ, φ, ψ represent the pitch angle, roll angle, and yaw angle of the UAV; c(g) and s(g) represent the cosine and sine functions, respectively; u to is the total thrust of the drone; m and g r are the mass and gravitational acceleration of the drone respectively.
[0167] (S12) Define the theory of rotational motion:
[0168] Using Euler's formula, we get:
[0169]
[0170] Where γ represents the angular velocity of the UAV in its fixed coordinate system, τ is the total torque of the UAV, and I is the inertia tensor matrix, which is regarded as a diagonal matrix due to the symmetry of the quadrotor UAV layout;
[0171] The specific expression of γ is as follows:
[0172] γ=[r x r y r z ] T
[0173] Where r x ,r y ,r z Respectively represent the angular velocity of the drone around the x-axis, y-axis and z-axis of its body coordinate system; [] T Represents the transposed matrix of this matrix.
[0174] (S13) Constructing a linearized model in the hovering state, specifically as follows:
[0175] When the drone is close to hovering, u to =mg r ,φ≈0,θ≈0, Get the linearized model of the quadrotor drone near the hovering state:
[0176]
[0177] In the formula, u to is the total thrust of the drone, m and g rare the mass and gravitational acceleration of the UAV, θ, φ, ψ represent the pitch angle, roll angle, and yaw angle of the UAV, c(g) and s(g) represent the cosine and sine functions, respectively;
[0178] It can be seen that the control of the drone, including its own altitude and three-axis attitude control, is completely decoupled, which allows the quadrotor drone system to independently control its flight and formation;
[0179] S2. Construct the UAV system model, including defining the UAV dynamic equation and defining the UAV tracking error, as follows:
[0180] (S21) Define the UAV dynamics equation:
[0181] Establish a drone formation, which includes a virtual leader, marked as the 0th drone, and N followers, marked as 1, 2, 3, ..., N;
[0182] definition:
[0183]
[0184] Where x i (t) represents the state variable of the i-th UAV at time t; v i (t) represents the position and speed of the UAV respectively; [] T represents the transposed matrix of the matrix;
[0185] Then, the dynamic equations of the 0th UAV and the i-th follower UAV are described as:
[0186]
[0187] Where u i (t) is the control input of the ith UAV, U is a real constant matrix;
[0188] The specific definitions of A and B are as follows:
[0189]
[0190] Nonlinear function d i (t) represents a collection of various nonlinear behaviors that satisfy the following conditions:
[0191] ||d i (t)||2≤||Fx i (t)||2 (37)
[0192] Among them, the specific definition of F is:
[0193]
[0194] (S22) Define the drone tracking error:
[0195] The directed communication topology F has a directed spanning tree with the 0th drone as its root node, representing the leader. The time-varying structure of the follower drones is described by the following formula:
[0196]
[0197] Where g i (t) is a continuously differentiable formation vector, g i (t) is defined as follows:
[0198]
[0199] In the formula represents the position of the i-th UAV, g iv (t) represents the speed of the ith UAV, and
[0200] The tracking error of the i-th UAV is defined as:
[0201]
[0202] in, w ij and a i The specific definition is as follows:
[0203]
[0204] The derivative formula of the tracking error formula is as follows:
[0205]
[0206] Where u ηi (t) is the formation control input, Bu ηi (t) and The specific definition is as follows:
[0207]
[0208] Nonlinear functions and tracking error η i The relationship between (t) satisfies the following constraints:
[0209]
[0210] In the formula is a given constant matrix;
[0211] S3. Construct a replay attack model, as follows:
[0212] Each replay attack cycle is divided into a dormant period and an active period. The dormant period indicates that the signal transmission is normal, while the active period indicates that the attacker replaces the current packet with a packet from a certain period in the past. The replay attack can be modeled by using a switching system:
[0213] Let h be the sampling step of the i-th drone state, then the data with replay attack transmitted through the network It is expressed as:
[0214]
[0215] Where T n Indicates the starting time of the nth attack, S n Indicates the duration of the replay attack, represents the actual transmitted data, and ε represents the delay time of replay;
[0216] definition:
[0217]
[0218] In (0, t), the number of switch transitions of the replay attack is expressed as M(t), which is given by and The synthesized attack signal satisfies the following attack frequency constraints:
[0219]
[0220] Where c = 1, e m =5;
[0221] S4. Construct a switching event trigger mechanism, as follows:
[0222] In order to save the resources of the drone communication network, the triggering conditions of the switching event triggering mechanism are designed as follows:
[0223] W1(t)+W2(t)-W3(fh)<0 (47)
[0224] in,
[0225]
[0226] Where v i ∈[0,1) represents a weight factor, k i =0.2,Φ i,σ(t) =diag(5,10,8) is the weight matrix, and are the release moments of the nth sleep stage and the nth active stage, respectively. represents the tracking error sampling signal at the initial moment, represents the current tracking error sampling signal, fh represents the adjustment amount, and the trigger mechanism does not include the leader drone; h represents the update frequency of the control signal;
[0227] The switching signal σ(t) is used to distinguish between two types of replay attacks during the attack period: active attack or dormant attack; s(t) = 1 means that the replay attack is in the interval When s(t) = 2, the trigger condition W1(t) + W2(t) - W3(fh) < 0, where W3(fh) ≠ 0, will result in a larger execution interval, so less data can be transmitted during the active period of the replay attack. It should be noted that k i The value of will affect the data publishing rate;
[0228] Definition, the event-triggered sampling state is expressed as:
[0229]
[0230] in,
[0231]
[0232] S5. Design the drone observer as follows:
[0233] Definition, the design of the i-th UAV observer is as follows:
[0234]
[0235] Among them, H σ(t) (σ(t)∈{1,2}) is the observer gain to be designed;
[0236] Definition, observation error is expressed as:
[0237]
[0238] Combining the observation error formula (22) with the observer design formula (21), we get:
[0239]
[0240] S6. Construct an event-triggered sliding surface based on an observer, as follows:
[0241] The definition of sliding surface aims to design control strategy by observing and integrating the system state, so as to achieve effective control of the system. The event-triggered sliding surface based on observer is defined as:
[0242]
[0243] Where K σ(t) , (σ(t)∈{1,2}) is the profit matrix of sliding mode control;
[0244] The specific definition of D is:
[0245] D = {2,3,1.5}
[0246] Order i (t) = 0, we get the equivalent observer-based sliding mode control law:
[0247]
[0248] Among them, the sliding mode gain matrix K σ(t) The choice directly affects the stability and response speed of the system;
[0249] Substituting (25) into (21), we can obtain the sliding dynamics formula:
[0250]
[0251] Combining equations (23) and (26), the matrix of a single UAV system is expanded to the entire multi-UAV system through the Kronecker product, and the following overall system dynamics equation is obtained:
[0252]
[0253] in:
[0254]
[0255] δ η (t) = col N {δ ηi (t)}
[0256]
[0257] V(t)=col N {V i (t)}
[0258] V(t-ε)=col N {V i (t-ε)}
[0259]
[0260] in, represents the tracking error vector; δ i (t) represents the observation error; V i (t) is the event error trigger signal; Represents the tracking error sampling signal at the initial moment; represents the current tracking error sampling signal, fh represents the adjustment amount; ε represents the delay time of playback; col N {} represents the column vector of the vector;
[0261] The coefficient matrix is defined as follows:
[0262]
[0263] Among them I N is the N×N identity matrix;
[0264] System Matrix A l , B l , U l and C l Defined as:
[0265]
[0266] Where l = 1, 2, and d(t) = ε + τ(t-ε) represents the time delay and disturbance of the system state; H1, H2 are observer gains to be designed; U is a real constant matrix.
[0267] S7. Construct a control strategy based on event-triggered sliding surface, as follows:
[0268] Under the framework of the switching event trigger mechanism and the observer, the sliding surface s shown in formula (24) is selected i (t), in order to enable the trajectory of the system to be driven to the sliding surface s i (t), the controller u is designed ηi (t), which is expressed as follows:
[0269]
[0270] The controller contains several items, each of which corresponds to a different control function:
[0271] This term includes the sliding mode gain K σ(t) and the dynamic compensation term H σ(t) , which act together on the state variables estimated by the observer To adjust the intensity of the control input to ensure that the system can respond quickly and approach the sliding surface;
[0272] (a i +o i (t))S(s i (t)): This term is mainly responsible for the dynamic behavior of the system near the sliding surface, and the coefficient r i =5, which determines the size of the attraction of the sliding surface, and is a compensation term based on the observer error, which further enhances the robustness of the controller;
[0273] in:
[0274]
[0275] Where β i =0.5 is a threshold value that determines the form of the sliding mode function;
[0276] When ||s i (t)||greater than or equal to the threshold β i When ||s i (t)|| is less than the threshold β i , the controller adjusts the input to prevent the system state from leaving the sliding surface.
[0277] To sum up, the technical solution of this embodiment uses graph theory methods to construct a dynamic model of a quadrotor drone, and defines translation and rotation motions in detail. The model is linearized in the hovering state to achieve accurate analysis and control of the drone's motion state, forming a complete system model. In order to deal with replay attacks, this embodiment introduces a replay attack model and designs a switching event trigger mechanism. By real-time monitoring of the system state and dynamically adjusting the control strategy, the impact of the attack is effectively reduced. At the same time, this embodiment proposes an observer-based state estimation method, which improves the accurate assessment of the system state and constructs an event-triggered sliding surface based on this. Finally, a drone formation control strategy is proposed based on the designed sliding surface. Combining the robustness of the sliding mode control and the efficiency of the event triggering mechanism, it not only reduces the communication and computing burden, but also improves the stability and anti-interference ability of the system.
[0278] Embodiment 2:
[0279] This embodiment provides a UAV formation event-triggered sliding mode tracking control system, which is used to implement the UAV formation event-triggered sliding mode tracking control method described in Embodiment 1, including:
[0280] The first building module is used to build a dynamic model of the quadrotor drone based on graph theory, specifically including defining a translational motion theory or a rotational motion theory, and building a linearized model in a hovering state;
[0281] The second building module is used to build the UAV system model, including defining the UAV dynamic equation and defining the UAV tracking error;
[0282] The third building module is used to build a replay attack model;
[0283] The fourth building block is used to build a switching event trigger mechanism;
[0284] Design module, used to design drone observers;
[0285] A fifth building module, for building an observer-based event-triggered sliding surface;
[0286] The sixth building block is used to build a control strategy based on event-triggered sliding surface.
[0287] Specifically, the above-mentioned first building module, second building module, third building module, fourth building module, design module, fifth building module and sixth building module can be embedded in a computer processing system, and the computer calls the above-mentioned modules to complete the task of tracking and controlling the drone formation according to the above-mentioned drone formation event-triggered sliding mode tracking control method; the above-mentioned first building module, second building module, third building module, fourth building module, design module, fifth building module and sixth building module can perform operations according to the specific steps given in the drone formation event-triggered sliding mode tracking control method.
[0288] It should be noted that it should be understood that the division of the various modules of the above system is only the division of logical functions. In actual implementation, they can be fully or partially integrated into one physical entity, or they can be physically separated, and these modules can all be implemented in the form of software calling through processing elements; they can also be all implemented in the form of hardware; some modules can also be implemented in the form of software calling through processing elements, and some modules can be implemented in the form of hardware. For example, the design module can be a separately established processing element, or it can be integrated in a certain chip of the above device. In addition, it can also be stored in the memory of the above device in the form of program code, and called and executed by a certain processing element of the above device. The implementation of other modules is similar. In addition, these modules can be fully or partially integrated together, or they can be implemented independently. The processing element described here can be an integrated circuit with signal processing capabilities. In the implementation process, each step of the above method or each module above can be completed by the hardware integrated logic circuit in the processor element or the instructions in the form of software.
[0289] For example, the above modules may be one or more integrated circuits configured to implement the above methods, such as one or more application specific integrated circuits (ASIC), or one or more digital singnal processors (DSP), or one or more field programmable gate arrays (FPGA). For another example, when a module is implemented in the form of a processing element scheduling program code, the processing element may be a general-purpose processor, such as a central processing unit (CPU) or other processors that can call program code. For another example, these modules may be integrated together and implemented in the form of a system-on-a-chip (SOC).
[0290] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.
[0291] For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. When an element is referred to as being "assembled on", "installed on", "fixed on" or "set on" another element, it can be directly on the other element or there can also be a centered element. When an element is considered to be "connected" to another element, it can be directly connected to the other element or there may be a centered element at the same time. The terms "vertical", "horizontal", "up", "down", "left", "right" and similar expressions used herein are only for illustrative purposes and are not intended to be the only implementation method.
[0292] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
[0293] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.
Claims
1. The UAV formation event-triggered sliding mode tracking control method is characterized by: The following steps are involved: Construct a dynamic model of a quadrotor drone based on graph theory, including defining the translational motion theory or the rotational motion theory, and constructing a linearized model in the hovering state; Construct the UAV system model, including defining the UAV dynamic equations and defining the UAV tracking error; Build a replay attack model; Build a switching event trigger mechanism; Designing drone observers; Constructing observer-based event-triggered sliding surface; Construct a control strategy based on event-triggered sliding surface.
2. The UAV formation event-triggered sliding mode tracking control method according to claim 1, characterized in that: The definition of translational motion theory or the definition of rotational motion theory is as follows: (1) Define the theory of translational motion: Using Newton's second law, we get: Where u to is the total thrust of the drone, m and g r are the mass and gravity acceleration of the drone respectively; in the world coordinate system, the east, north, and down positions of the drone are represented by Y r , X r and Z r , and W tr It is a transition matrix, which is used to realize the coordinate transformation from the drone body coordinate system to the world coordinate system; Among them, u to The specific representation is as follows: u to =F1+F2+F3+F4 where F p (p=1,2,3,4) represents the lift generated by the four motors; Transition matrix W tr The specific definition of is: Where θ, φ, ψ represent the pitch angle, roll angle and yaw angle of the drone respectively; c(g) and s(g) represent the cosine and sine functions respectively; W tr Substituting into the translational motion formula, we get: Where Y r , X r and Z r They represent the east, north, and down positions of the drone, respectively; θ, φ, ψ represent the pitch, roll, and yaw angles of the drone, respectively; c(g) and s(g) represent the cosine and sine functions, respectively; u to is the total thrust of the drone, m and g r are the mass and gravitational acceleration of the drone respectively; (2) Define the theory of rotational motion: Using Euler's formula, we get: Where γ represents the angular velocity of the UAV in its fixed coordinate system, τ is the total torque of the UAV, and I is the inertia tensor matrix, which is regarded as a diagonal matrix due to the symmetry of the quadrotor UAV layout; The specific expression of γ is as follows: γ=[r x r y r z ] T Where r x ,r y ,r z Respectively represent the angular velocity of the drone around the x-axis, y-axis, and z-axis of its body coordinate system, [] T Represents the transposed matrix of this matrix.
3. The UAV formation event-triggered sliding mode tracking control method according to claim 2, characterized in that: Construct a linearized model in the hovering state as follows: When the drone is approaching a hovering state, Get the linearized model of the quadrotor drone near the hovering state: In the formula, u to is the total thrust of the drone, m and g r are the mass and gravitational acceleration of the UAV, θ, φ, ψ represent the pitch angle, roll angle and yaw angle of the UAV, c(g) and s(g) represent the cosine and sine functions, respectively.
4. The UAV formation event-triggered sliding mode tracking control method according to claim 3 is characterized in that: Construct the UAV system model, including defining the UAV dynamic equation and defining the UAV tracking error, as follows: (1) Define the UAV dynamics equation: Establish a drone formation, which includes a virtual leader, marked as the 0th drone, and N followers, marked as 1, 2, 3, ..., N; definition: Where x i (t) represents the state variable of the i-th UAV at time t; Respectively represent the position and speed of the drone; [] T represents the transposed matrix of the matrix; Then, the dynamic equations of the 0th UAV and the i-th follower UAV are described as: Where u i (t) is the control input of the ith UAV, U is a real constant matrix; The specific definitions of A and B are as follows: Nonlinear function d i (t) represents a collection of various nonlinear behaviors that satisfy the following conditions: ||d i (t)||2≤||Fx i (t)||2 (9) Among them, the specific definition of F is: (2) Define UAV tracking error: The directed communication topology F has a directed spanning tree with the 0th drone as its root node, representing the leader. The time-varying structure of the follower drones is described by the following formula: Where g i (t) is a continuously differentiable formation vector, g i (t) is defined as follows: In the formula represents the position of the i-th UAV, g iv (t) represents the speed of the ith UAV, and The tracking error of the i-th UAV is defined as: Where η i (t) represents the tracking error; in, w ij and a i The specific definition is as follows: The derivative formula of the tracking error formula is as follows: Where u ηi (t) is the formation control input, Bu ηi (t) and The specific definition is as follows: Nonlinear functions and tracking error η i The relationship between (t) satisfies the following constraints: In the formula is a given constant matrix.
5. The UAV formation event-triggered sliding mode tracking control method according to claim 4, characterized in that: Construct a replay attack model as follows: Each replay attack cycle is divided into a dormant period and an active period. The replay attack can be modeled by using a switching system: Let h be the sampling step of the i-th drone state, then the data with replay attack transmitted through the network It is expressed as: Where T n Indicates the starting time of the nth attack, S n Indicates the duration of the replay attack, represents the actual transmitted data, and ε represents the delay time of replay; The sleep period of the replay attack is expressed as: The active period of the replay attack is expressed as: In (0, t), the number of switch transitions of the replay attack is expressed as M(t), which is given by and The synthesized attack signal satisfies the following attack frequency constraints: Where c = 1, e m =5.
6. The UAV formation event-triggered sliding mode tracking control method according to claim 4, characterized in that: Construct a switching event trigger mechanism, as follows: The triggering conditions of the switching event triggering mechanism are designed as follows: W1(t)+W2(t)-W3(fh)<0 (19) in, Where v i ∈[0,1) represents a weight factor, k i =0.2,Φ i,σ(t) =diag(5,10,8) is the weight matrix, and are the release moments of the nth sleep stage and the nth active stage, respectively. Represents the tracking error sampling signal at the initial moment, V i (t) is the event error trigger signal, represents the current tracking error sampling signal, fh represents the adjustment amount, and the trigger mechanism does not include the leader drone; h represents the update frequency of the control signal; The switching signal σ(t) is used to distinguish between two types of replay attacks during the attack period, active attack or dormant attack. s(t) = 1 means that the replay attack is in the interval When s(t) = 2, the trigger condition W1(t) + W2(t) - W3(fh) < 0, where W3(fh) ≠ 0, will result in a larger execution interval, so less data can be transmitted during the active period of the replay attack. It should be noted that k i The value of will affect the data publishing rate; Definition, the event-triggered sampling state is expressed as: in, 7. The UAV formation event-triggered sliding mode tracking control method according to claim 6, characterized in that: Design a drone observer as follows: Definition, the design of the i-th UAV observer is as follows: Among them, H σ(t) (σ(t)∈{1,2}) is the observer gain to be designed; Definition, observation error is expressed as: Combining the observation error formula (22) with the observer design formula (21), we get:
8. The UAV formation event-triggered sliding mode tracking control method according to claim 7, characterized in that: Construct an observer-based event-triggered sliding surface as follows: The observer-based event-triggered sliding surface is defined as: Where K σ(t) ,(σ(t)∈{1,2}) is the profit matrix of sliding mode control; The specific definition of D is: D＝{2,3,1.5} Order i (t) = 0, we get the equivalent observer-based sliding mode control law: Among them, the sliding mode gain matrix K σ(t) The choice directly affects the stability and response speed of the system; Substituting (25) into (21), we can obtain the sliding dynamics formula: Combining equations (23) and (26), the matrix of a single UAV system is expanded to the entire multi-UAV system through the Kronecker product, and the following overall system dynamics equation is obtained: in: V(t)=col N {V i (t)} V(t-ε)=col N {V i (t-ε)} in, represents the tracking error vector; δ i (t) represents the observation error; V i (t) is the event error trigger signal; Represents the tracking error sampling signal at the initial moment; represents the current tracking error sampling signal, fh represents the adjustment amount; ε represents the delay time of playback; col N {} represents the column vector of the vector; The coefficient matrix is defined as follows: Among them I N is the N×N identity matrix; System Matrix A l , B l , U l and C l Defined as: Where l = 1, 2, and d(t) = ε + τ(t-ε) represents the time delay and disturbance of the system state; H1, H2 are observer gains to be designed; U is a real constant matrix.
9. The UAV formation event-triggered sliding mode tracking control method according to claim 8, characterized in that: Construct a control strategy based on sliding surface as follows: Under the framework of the switching event trigger mechanism and the observer, the sliding surface s shown in formula (24) is selected i (t), in order to enable the trajectory of the system to be driven to the sliding surface s i (t), the controller u is designed ηi (t), which is expressed as follows: The controller contains several items, each of which corresponds to a different control function: This term includes the sliding mode gain K σ(t) and the dynamic compensation term H σ(t) , which act together on the state variables estimated by the observer Used to adjust the intensity of control input to ensure that the system responds quickly and approaches the sliding surface; (a i +o i (t))S(s i (t)):coefficient r i =5, used to determine the size of the sliding surface attraction, is the compensation term based on the observer error; in: Where β i =0.5 is a threshold value that determines the form of the sliding mode function; When ||s i (t)||greater than or equal to the threshold β i When ||s i (t)|| is less than the threshold β i , the controller adjusts the input to prevent the system state from leaving the sliding surface.
10. A UAV formation event-triggered sliding mode tracking control system, used to implement the UAV formation event-triggered sliding mode tracking control method according to any one of claims 1 to 9, characterized in that: include: The first building module is used to build a dynamic model of the quadrotor drone based on graph theory, specifically including defining a translational motion theory or a rotational motion theory, and building a linearized model in a hovering state; The second building module is used to build the UAV system model, including defining the UAV dynamic equation and defining the UAV tracking error; The third building module is used to build a replay attack model; The fourth building block is used to build a switching event trigger mechanism; Design module, used to design drone observers; A fifth building module, for building an observer-based event-triggered sliding surface; The sixth building block is used to build a control strategy based on event-triggered sliding surface.