Leader following multi-robot sliding simulation launching formation control method based on event triggering under hybrid attack

Abstract

According to the leader following multi-robot gliding simulation launching formation control method based on event triggering under the mixed attack, distributed control, an affine transformation mechanism and an anti-attack robust control strategy are fused, and a multi-robot formation control framework with high maneuverability, high robustness and communication safety is constructed. The method is suitable for hybrid network attack scenes with communication interference, information tampering or denial of service, and belongs to the technical field of intelligent cooperative control and safety control of a multi-robot system. The invention aims to solve the problems of formation rigidity, low control precision, weak anti-interference capability and the like of a traditional formation control method in dynamic task execution, and further enhance the adaptive cooperative control capability of the system in a complex communication environment. The method supports various affine transformation forms, such as zooming, rotation, shearing, coplane and collinear, and has good environmental adaptability and system security.

Description

Technical Field

[0001] This invention belongs to the technical field of the integration of multi-robot system control and network security. Specifically, it relates to a continuous adaptive integral sliding mode leader-follower multi-robot affine formation control method based on an event-triggered mechanism. This method is suitable for multi-agent collaborative control tasks in the presence of communication uncertainty and network attack interference (such as denial of service attacks, false data injection, and data loss). This method is particularly suitable for achieving high-precision, low-communication, and high-robust collaborative formation control under constrained network conditions in scenarios such as drone swarms, underwater robots, and ground mobile robots. Background Art

[0002] In recent years, multi-robot collaborative control has been widely applied in fields such as intelligent manufacturing, environmental monitoring, and disaster relief. Affine formation control technology has become a research hotspot to improve task efficiency and spatial adaptability. However, existing methods generally rely on stable communication conditions and are unable to cope with the real-world threats of attacks and data loss in communication networks.

[0003] In open or untrusted networks, multi-robot systems are vulnerable to mixed network attacks such as DoS, FDI, and malicious packet loss or delays, which can rapidly amplify system state errors, cause control command failures, and even lead to system-wide instability. While traditional sliding mode control offers robustness, its fixed-gain strategy and high-frequency jitter limit its application in safety-sensitive scenarios.

[0004] Therefore, it is urgent to design a distributed formation control method with adaptive capabilities, continuous control structure and anti-attack mechanism, and combine it with event triggering strategy to reduce the communication burden while ensuring control accuracy, so as to achieve safe formation control of complex dynamic tasks. Summary of the Invention

[0005] The purpose of the present invention is to provide an event-triggered leader-follower multi-robot sliding mode shooting formation control method under hybrid attacks, which integrates distributed affine geometric control, attack-aware adaptive compensation, robust sliding mode regulation and low-frequency control update mechanism, while ensuring the system accuracy and convergence, effectively improving the security and robustness of the system in the face of hybrid network attacks.

[0006] The present invention discloses a method for controlling a leader-follower multi-robot sliding shooting formation based on event triggering under a hybrid attack, and the specific steps are as follows:

[0007] The steps are as follows:

[0008] S1. Construction of an affine hierarchical control framework: Based on the leader-follower model, the multi-robot formation structure is determined, the leader and follower roles are divided, and the nominal formation configuration and cluster communication topology are constructed. Through stress matrix calculation, the localizable modeling of affine geometric relationships is achieved, providing structural support for follower trajectory estimation.

[0009] S2. Distributed Estimator Design and Attack Perception Fusion: A distributed estimator is constructed by combining the stress matrix with neighbor information, enabling each follower to locally calculate the target trajectory. An attack detection mechanism is also introduced to perform residual analysis and trust assessment on neighbor state changes, including mixed attack signals such as DoS, FDI, or abnormal packet loss. State prediction and compensation are implemented to ensure stable operation of the estimator.

[0010] S3. Design of a continuous adaptive integral sliding mode controller (with anti-attack function): An integral sliding mode surface is constructed based on the velocity error, a non-monotonic adaptive gain law is introduced, and a σ-correction mechanism is combined to dynamically adjust the control parameters. Robust compensation terms are designed into the control law to cope with model uncertainty and abnormal network disturbances. An event trigger mechanism integrates security perception information and adjusts the trigger threshold when the system detects a change in the attack level, thereby dynamically controlling the controller update frequency and ensuring a balance between control performance and communication load.

[0011] Furthermore, in a preferred embodiment, the multi-robot formation and stress matrix to be formed in S1 are defined as:

[0012] There are n robots to be formed. Two coordinate systems are introduced to describe the motion of the robots. The nonlinear kinematic and dynamic models of each robot are simplified as follows:

[0013]

[0014] Among them, x i and y i represents the coordinates, θ i represents the orientation of the ith robot relative to the inertial frame; the linear velocity and angular velocity of the ith robot in its body fixed frame are represented by v i and ω i Represented. A multi-robot system consists of n robots. The communication between n robots can be described by an undirected graph G = (N, ε, A), where N = {0, 1, n} is the set of robots, Edge Set, is the adjacency matrix. When a ij >0, otherwise a ij= 0. The configuration of the nominal formation is constructed as follows: l and f represent the leader and follower, and r represents the position of the n robots in the nominal formation. Based on the communication topology and the configuration of the nominal formation, the nominal formation of the multi-robot system is obtained as (G, r).

[0015] Furthermore, the stress matrix of the nominal formation is calculated using a linear matrix inequality solution method in S1. Furthermore, the specific steps of calculating the stress matrix of the nominal formation using a linear matrix inequality solution method are as follows:

[0016] Step S1-1, assign any direction to each edge of the undirected graph G, using B∈R n×m represents the incidence matrix of the undirected graph G, and the incidence matrix is defined as follows:

[0017]

[0018] Step S1-2: yes The i-th column of

[0019] definition:

[0020]

[0021] in, Defined as:

[0022]

[0023] Let z1,…,z q ∈R m yes A set of bases;

[0024] Step S1-3: Perform singular value decomposition to obtain

[0025] Let U = [U1, U2], where U1 contains the first d+1 columns of U;

[0026] definition:

[0027]

[0028] Step S1-4, solve the following linear matrix inequality to obtain the equilibrium stress of the nominal formation

[0029]

[0030] where c1,…,c q Satisfies the linear matrix inequality:

[0031]

[0032] Step S1-5: Using the equilibrium stress of the nominal formation obtained Solve for the equilibrium stress matrix:

[0033]

[0034] Where Ω is the equilibrium stress matrix.

[0035] Compared with the prior art, the advantages of the present invention are:

[0036] 1. This technology implements affine formation control for a multi-robot system based on a leader-follower control model. By constructing a follower-tracking multi-robot affine formation control strategy, followers track the leader's movements and automatically adjust their relative positions within the formation based on the leader's cluster configuration. This approach enables a multi-robot system to manage the entire cluster through the coordinated control of a small number of key pilot nodes, enabling the formation to generate, track, and transform while moving along different trajectories.

[0037] 2. This multi-robot affine formation control method based on the leader-follower model has good scalability and applicability in large-scale multi-robot formation control tasks, in which the overall shape of the formation can be determined by the configuration of the leader subsystem.

[0038] 3. By designing a distributed estimation mechanism, followers can locally compute their own reference trajectories based on the leader's position information. The reference trajectory is derived by time-transforming the nominal configuration, generating the desired position and attitude (especially yaw angle) in real time without the need for a centralized path planner. Each follower relies solely on information from its neighbors to track the reference trajectory, achieving fully distributed control.

[0039] 4. A distributed leader-follow multi-robot control strategy based on a continuous adaptive integral sliding mode for followers achieves the following key benefits: This strategy ensures that the follower robots accurately converge to their desired relative position or trajectory with respect to the leader within a finite time. Thanks to the inherent robustness of sliding mode control, this method is highly robust against model uncertainties within the robots themselves and external environmental disturbances, significantly improving formation tracking accuracy and stability. The non-singular terminal sliding mode ensures that the tracking error not only converges to zero within a finite time but also avoids the singularity issues that can arise with traditional terminal sliding modes, ensuring the boundedness of the control input and the good performance of the entire closed-loop system.

[0040] Furthermore, this method employs a leader-follow multi-robot affine formation control strategy based on a continuous adaptive integral sliding mode for the followers. This enables fast, accurate, and robust distributed formation tracking control for the follower robots in dynamically changing environments or when maneuvering with the leader. Furthermore, this control method inherently and conveniently implements various affine transformations, such as translation, rotation, scaling, and shearing, for the entire robot formation, significantly enhancing the flexibility of the formation's maneuvers.

[0041] 5. The anti-attack control law is adopted to realize the recognition and response of network attack scenarios on the basis of the leader-follower multi-robot affine formation control strategy based on continuous adaptive integral sliding mode. Through the organic integration of sliding mode feedback, adaptive gain and predictive compensation, while ensuring control accuracy and finite time convergence, the system's robustness and communication adaptability in malicious network environments are effectively enhanced. It is suitable for formation mission scenarios with high security requirements, such as search and rescue, air-ground coordination and complex environment monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the implementation flow of the continuous adaptive integral sliding mode leading-following multi-robot affine formation control method based on the event triggering mechanism of this embodiment.

[0043] Figure 2 Schematic diagram of the communication topology of seven robot clusters in a specific application embodiment.

[0044] Figure 3 is a comparison diagram of the mean square error convergence of the multi-robot system used in a specific application embodiment. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] like Figure 1 As shown, the steps of the event-triggered leader-follower multi-robot sliding shooting formation control method under hybrid attack in this embodiment include:

[0047] S1. Construction of an affine hierarchical control framework: Based on the leader-follower model, the multi-robot formation structure is determined, the leader and follower roles are divided, and the nominal formation configuration and cluster communication topology are constructed. Through stress matrix calculation, the localizable modeling of affine geometric relationships is achieved, providing structural support for follower trajectory estimation.

[0048] S2. Distributed Estimator Design and Attack Perception Fusion: A distributed estimator is constructed by combining the stress matrix with neighbor information, enabling each follower to locally calculate the target trajectory. An attack detection mechanism is also introduced to perform residual analysis and trust assessment on neighbor state changes, including mixed attack signals such as DoS, FDI, or abnormal packet loss. State prediction and compensation are implemented to ensure stable operation of the estimator.

[0049] S3. Design of a continuous adaptive integral sliding mode controller (with anti-attack function): An integral sliding mode surface is constructed based on the velocity error, a non-monotonic adaptive gain law is introduced, and a σ-correction mechanism is combined to dynamically adjust the control parameters. Robust compensation terms are designed into the control law to cope with model uncertainty and abnormal network disturbances. An event trigger mechanism integrates security perception information and adjusts the trigger threshold when the system detects a change in the attack level, thereby dynamically controlling the controller update frequency and ensuring a balance between control performance and communication load.

[0050] The design concept for forming robots is divided into a leader-follower system, employing a follower-leader architecture to achieve affine formation. The leader determines the formation's formation, while the followers use the leader's position and control methods to determine their desired positions. They then move from their current positions to the desired positions, bringing the entire formation into the target formation. By changing the relative position of the leader, the leader can implement affine formation transformations such as shearing, scaling, and rotation.

[0051] In this embodiment, it is assumed that there are n robots in a plane, and the interactions between the robots are described by a fixed graph G∈(V,ε). is an affine formation. Among them, the leader's formation is The robots in the follower formation are affine formations. They include leaders and followers. The goal is to keep the followers and leaders at the same speed and in a stable formation. Assume there are n robots in a plane. The interactions between the robots are described by a fixed graph G∈(V,ε). This graph consists of a vertex set and an edge set ε∈V×V. An edge (i,j)∈ε indicates that robot i can receive information from robot j, and robot j is a neighbor of i. The neighbor set of vertex i is N i ={j∈V:(j,i)∈ε}. This invention only considers undirected graphs, that is, assuming that the first n l The robot is the leader, and the remaining n f The robots are followers, where n f =nn l , then V l ={1,...,n l} and V f =V / V lare the sets of leaders and followers respectively. Let it be an affine formation. Among them, the leader's formation is and the follower's formation is a formation (G,p) represents a one-to-one mapping between the formation of the i-th robot and the i-th node in the graph G. A nominal formation corresponding to the graph G can be defined as (G,r), where the nominal formation is a constant. Affine transformation is a conventional linear transformation form, such as translation, rotation, reduction, shearing, and combinations of these transformations. Therefore, the affine mapping of the nominal formation r can be defined as:

[0052]

[0053] Among them I n represents the n×n identity matrix, represents the Kronecker product, 1 n is an n-dimensional column vector and its value is 1. A(t) and b(t) both represent 3-dimensional column vectors, representing 3×3-dimensional matrices. The affine transformation is recorded as (A, b). The matrices A(t) and b(t) are used to realize the robot's geometric transformation actions such as translation, rotation, scaling, and shearing.

[0054] For the formation, the stress corresponding to each side (i, j)∈ε{ω ij} (i,j)∈ε is a set of scalars. When there is attraction between i and j, ω ij >0, when there is repulsive force between i and j ω ij <0, in other cases ω ij =0, the relationship between stress and formation is described as:

[0055]

[0056] To make the expression more compact, ij} (i,j)∈ε Written as the following stress matrix:

[0057]

[0058] Rewrite the above formula as:

[0059]

[0060] in, represents the stress matrix of the navigator, represents the stress matrix of the navigator, represents the stress matrix between the leader and the follower, represents the stress matrix between the follower and the leader.

[0061] The distributed error expression for the i-th item is as follows:

[0062]

[0063] Rewrite the above formula as:

[0064]

[0065] in, represents the stress matrix of the navigator, represents the stress matrix of the navigator, represents the stress matrix between the leader and the follower, represents the stress matrix between the follower and the leader.

[0066] The distributed error expression for the i-th item is as follows:

[0067]

[0068] in, represents the position error, which reflects the local deviation of robot i in the formation position configuration. The introduction of the stress matrix ensures the rigid constraint of the formation against affine transformations (rotation, scaling, translation, shear). θ represents the posture error, which reflects the local deviation of robot i in the formation posture configuration. This error is used to ensure that the posture of all robots is consistent with the expected movement direction of the formation. i represents the posture of the i-th robot.

[0069] The virtual control rates of linear velocity and angular velocity are designed as follows:

[0070]

[0071] Among them, J i J represents the position transformation matrix of the i-th robot, describing the velocity transformation relationship from the body coordinate system to the earth-fixed coordinate system. i v j K represents the velocity vector of the jth neighbor robot in the earth-fixed coordinate system. i1p With K i2p is a diagonal positive definite matrix, K i1θ Represents the proportional gain of the yaw angle error, which is a positive constant used to adjust the convergence speed of the yaw angle error. K i2θ The integral gain of the yaw angle error is a positive constant used to eliminate the steady-state error of the yaw angle error. represents the time derivative of the desired yaw angle of the ith robot.

[0072] To make the expression more compact, iv =(α ip ,α iθ ) T, then the velocity tracking error vector expression is as follows:

[0073] v ie =e i -α iv .

[0074] The controller detects attacks by analyzing indicators such as event trigger interval fluctuations and neighbor state residuals. The state residual between node i and neighbor j is defined as:

[0075]

[0076] If r ij (t) is continuously greater than the threshold δ r , then the attack flag is triggered.

[0077] To enhance control continuity, a state predictor is introduced when the neighbor state is unavailable:

[0078]

[0079] Predicted state Used to replace failure data in estimation and control calculations.

[0080] The continuous adaptive integral sliding mode manifold of the velocity tracking error vector can be described as:

[0081]

[0082] Among them, K i3 is a positive definite matrix.

[0083] The event trigger mechanism is designed as follows:

[0084]

[0085] Among them, the trigger threshold parameter δ i Real-time adjustment based on attack status:

[0086]

[0087] Among them, η1 and η2 are fixed safety margins, which are used to increase the control update frequency and improve the reliability of the control response.

[0088] The adaptive continuous sliding mode control law is designed as follows:

[0089]

[0090] in, is the dynamic compensation term, is the linear feedback term; is a robust term (in the form of boundary layer function); It is an anti-attack compensation item. represents the nominal inertia matrix of the i-th robot, represents the nominal Coriolis and centripetal force matrices of the ith robot, ξ i represents the velocity vector of the i-th robot, represents the nominal damping matrix of the ith robot.

[0091] The non-monotonic adaptive gain law is designed as:

[0092]

[0093]

[0094] Among them, γ ij (j=0,1,2) represents the adaptive gain, a positive constant used to adjust the amplitude of the adaptive rate. The adaptive law dynamically updates the upper bound parameters of uncertainty, allowing the estimated value to gradually approach the true value. This design, based on the norms of the sliding surface vector and the velocity vector, can adjust the control strategy according to real-time operating conditions, effectively offsetting the effects of disturbances. The advantage of the adaptive law is that it does not require prior knowledge of the specific characteristics of the disturbance, reducing the control law's reliance on prior knowledge. This dynamic adjustment mechanism significantly improves the flexibility and environmental adaptability of the control law, enabling multi-robot formations to maintain stable performance in complex environments.

[0095] This paper addresses the collaborative control of multi-robot systems in complex dynamic environments and under untrusted communication conditions. It proposes a continuous adaptive integral sliding mode leader-follower affine formation control method based on an event-triggered mechanism. This method integrates a distributed control architecture, an affine transformation formation strategy, adaptive sliding mode control theory, and a cyberattack resistance mechanism to enhance the system's dynamic coordination, control accuracy, communication efficiency, and robustness. By constructing an affine hierarchical control framework, the leader and follower roles are partitioned and the formation geometry can be localized. A distributed trajectory estimator is designed incorporating stress matrix theory, enabling each robot to predict its local trajectory based solely on the states of its neighbors. In the controller design, an integral sliding mode surface is constructed, and a nonmonotonic adaptive gain law and σ-correction mechanism are introduced to dynamically adjust the sliding mode gain and suppress system disturbances. A continuous control law is also employed to mitigate the high-frequency chattering problem inherent in traditional sliding modes. In the face of hybrid cyberattacks, the controller features state residual monitoring and attack detection. When information is unavailable, a prediction compensation mechanism is activated to maintain stable operation of the estimator and control law. In addition, the event trigger mechanism adaptively adjusts the trigger threshold according to the sliding mode error and attack status, thereby effectively controlling the communication update frequency and ensuring control continuity and system consistency under attack and interference conditions.

[0096] Figure 2The communication topology of a multi-robot formation network is presented. This topology illustrates how information is exchanged between robots and is key to implementing distributed control strategies.

[0097] Figure 3 This paper demonstrates the comparative control performance of a continuous adaptive integral sliding mode control method based on an event-triggered mechanism in a multi-robot affine formation task under two communication environments: "no attack" and "mixed attack." Specifically, the mean squared evolution of the error is shown. In the no-attack scenario, the system error decreases rapidly, exhibiting a smooth and stable convergence trend. This aligns with the controller's design goals of excellent tracking performance and efficient convergence, as mentioned earlier. In the mixed-attack scenario, while the system still maintains convergence, the error curve exhibits some initial oscillation and a slower overall rate of descent than in the no-attack scenario, indicating that the attack perturbs the system and confirms the weakening effect of the attack models constructed earlier (such as DoS attacks, false data injection, and packet loss) on control performance. This perturbation forces the controller to rely on adaptive gain adjustment and sliding mode robust compensation mechanisms to mitigate the disturbance and maintain asymptotic convergence of the final error. Ultimately, both curves approach zero, demonstrating that the control method maintains a certain degree of robustness and stability even in the presence of mixed attacks. This also confirms the practical value of our previously designed controller structure based on σ-correction, event triggering, and non-monotonic adaptive law in complex environments.

[0098] therefore, Figure 3 It was verified that the proposed control method can still ensure that the states of each robot in the system remain coordinated and consistent when facing hybrid network attacks, and enable the overall formation system to operate stably under the influence of disturbances without divergence or loss of control. This shows that the method has strong anti-interference ability and stability, can effectively suppress the error accumulation caused by attacks, and achieve finite-time consistency and robust convergence of the multi-robot system.

[0099] To achieve flexible transformations of nominal formations in multi-robot affine formations and enhance the system's stability and robustness in complex communication environments, this paper proposes a continuous adaptive integral sliding mode leader-follower multi-robot affine formation control method based on an event-triggered mechanism. This method introduces a continuous adaptive integral sliding mode controller to control the follower's motion. By constructing a sliding mode surface containing an integral term, the system state is guided to approach the ideal trajectory within a finite time. Furthermore, the controller incorporates a σ-correction strategy to design a non-monotonic adaptive gain law, enabling dynamic online adjustment of the sliding mode gain, thereby avoiding the high-frequency chattering problem caused by fixed or excessive gains in traditional sliding mode control. Furthermore, to address hybrid network attacks that may occur in actual communication networks, such as DoS, FDI, and packet loss, this paper further embeds an attack perception mechanism and a state prediction compensation module into the control structure. When neighbor information is interfered with or interrupted by an attack, the controller automatically activates a redundant state prediction model to ensure the continued effectiveness of trajectory estimation and control laws. In order to reduce the communication burden and improve system security, the present invention also designs an event trigger mechanism with attack perception capability, which dynamically adjusts the trigger threshold according to the sliding surface error and attack intensity, so that the control input is updated only when the system error is significant or affected by an attack. This ensures the convergence and consistency of the formation while effectively improving the system's robustness, communication efficiency and resource utilization capabilities in harsh network environments.

[0100] The above specific embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the scope of the technical solutions of the present invention, and all of these should be included in the scope of the claims of the present invention.

Claims

1. A method for controlling a leader-follow multi-robot sliding shooting formation based on event triggering under a hybrid attack, characterized in that: include: S1. Construction of an affine hierarchical control framework: Based on the leader-follower model, the multi-robot formation structure is determined, the leader and follower roles are divided, and the nominal formation configuration and cluster communication topology are constructed. Through stress matrix calculation, the localizable modeling of affine geometric relationships is achieved, providing structural support for follower trajectory estimation. S2. Distributed Estimator Design and Attack Perception Fusion: A distributed estimator is constructed by combining the stress matrix with neighbor information, enabling each follower to locally calculate the target trajectory. An attack detection mechanism is also introduced to perform residual analysis and trust assessment on neighbor state changes, including mixed attack signals such as DoS, FDI, or abnormal packet loss. State prediction and compensation are implemented to ensure stable operation of the estimator. S3. Design of a continuous adaptive integral sliding mode controller (with anti-attack functionality): An integral sliding mode surface is constructed based on the velocity error, a non-monotonic adaptive gain law is introduced, and a σ-correction mechanism is used to dynamically adjust the control parameters. Robust compensation terms are designed into the control law to cope with model uncertainty and abnormal network disturbances. The event trigger mechanism integrates security perception information and adjusts the trigger threshold when the system detects a change in the attack level, thereby dynamically controlling the controller update frequency and ensuring a balance between control performance and communication load.

2. The multi-robot affine formation control method based on the pilot-follower mode according to claim 1, characterized in that: In S1: In a communication topology diagram Contains a node set and an edge set A directed edge (i, j)∈ε is a path from node i to node j. The neighbor set of vertex i is given by Therefore, the adjacency matrix is defined as If (i,j)∈ε then otherwise Since there is no self-loop, Applicable. The Laplace matrix is defined as The expression is as follows: The affine mapping of the nominal formation is expressed as: The affine representation of the position set of a multi-robot formation based on the leader-follower method is: The required position stack p can be obtained by affine mapping * , the expression is as follows: in, represents the nominal configuration. The matrix are the gains associated with the rotation, scaling, and shear transformations, which control the entire formation to perform the desired maneuver with respect to r. The affine image includes all affine transformations of the nominal configuration. In addition, the desired position stack can be extracted from the affine image. For the formation The stress is defined as {ω ij } (i,j)∈E A scalar set of Assign to all edges. If a stress satisfies Condition, then the stress is classified as equilibrium stress and can be expressed in matrix form in represents a stress matrix that satisfies the following conditions: Rewrite the above formula as: definition and Denote the leader and follower respectively, and we get:

3. The multi-robot distributed affine formation control method based on a continuous adaptive integral sliding mode controller according to claim 2, characterized in that: In S2: The distributed error expression for the i-th item is as follows: The virtual control rates of linear velocity and angular velocity are designed as follows: To make the expression more compact, iv =(α ip ,α iθ ) T , then the velocity tracking error vector expression is as follows: v ie =e i -α iv 4. The multi-robot distributed affine formation control method based on a continuous adaptive integral sliding mode controller according to claim 3, characterized in that: In the S3: To address the potential mixed network attacks encountered in real-world communication networks, such as DoS, FDI, and packet loss, a robust and secure continuous adaptive integral sliding mode control law was designed. Building on the existing sliding mode control structure, this control law integrates attack detection, redundant state prediction, anti-attack compensation, and an attack-aware event triggering mechanism, effectively improving the control system's stability and convergence performance in non-ideal communication environments. The controller detects attacks by analyzing indicators such as event trigger interval fluctuations and neighbor state residuals. The state residual between node i and neighbor j is defined as: If r ij (t) is continuously greater than the threshold δ r , then the attack flag is triggered. To enhance control continuity, a state predictor is introduced when the neighbor state is unavailable: Predicted state Used to replace failure data in estimation and control calculations.

5. The multi-robot distributed affine formation control method based on continuous adaptive integral sliding mode controller according to claim 4, characterized in that: In the S3: The continuous adaptive integral sliding mode manifold of the velocity tracking error vector can be described as: Among them, K i3 is a positive definite matrix. The event trigger mechanism is designed as follows: Among them, the trigger threshold parameter δ i Real-time adjustment based on attack status: Where η1 and η2 are fixed safety margins, which are used to increase the control update frequency and improve the reliability of the control response. The adaptive continuous sliding mode control law is designed as follows: in, is the dynamic compensation term, is the linear feedback term; is a robust term (in the form of boundary layer function); It is an anti-attack compensation item. The non-monotonic adaptive gain law is designed as:

6. A method for controlling a leader-follow multi-robot sliding shooting formation based on event triggering under a hybrid attack, characterized in that: The method adopts the multi-robot formation controller construction method described in any one of claims 1 to 4 to design a corresponding controller implementation, and each robot to be formed is configured with an independently running formation controller. The specific process of the control method includes: each robot controller exchanges information with its neighbor nodes through a distributed communication network; the controller fuses the local state with the received neighborhood state data in real time, and solves the affine geometric constraints and the expected trajectory based on the constructed stress matrix; when there is a communication attack or information loss, the controller automatically enables the state prediction compensation mechanism and reconstructs the neighbor estimation information to maintain the continuity of the trajectory estimation; then, based on the estimation result, the speed tracking error is constructed and the integral sliding mode surface is generated, and the continuous sliding mode control law is updated to generate a control input with anti-disturbance and anti-attack capabilities by combining the non-monotonic adaptive gain adjustment law and the attack perception event triggering mechanism; the controller finally drives the robot to complete the affine formation action (including scaling, rotation, shearing, etc.) under the condition of local information, and ensures that the entire formation system still has finite time convergence and system dynamic consistency under the conditions of hybrid network attacks, external disturbances and communication delays.

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