Attack detection and stability control method for bilateral teleoperation system with network attacks

Abstract

The present invention discloses a bilateral teleoperation system attack detection and stability control method with network attack. The method comprises the following steps: Step 1: Establishing the dynamic equation of the bilateral teleoperation manipulator system; Step 2: Establishing the packet loss and network attack model in the network, and using the least squares algorithm to detect the network attack; Step 3: Designing an adaptive controller based on the detection result to eliminate the influence of the network attack on the stability of the system. The present invention accurately describes the packet loss and false data injection attack in the network, and successfully detects the false data injection attack in the bilateral teleoperation system, and designs a controller to eliminate the influence of the network attack on the stability of the bilateral teleoperation system. The present invention improves the anti-interference ability of the bilateral teleoperation system under network attack, and has important significance in practical application.

Description

Technical Field

[0001] The invention belongs to the field of bilateral remote operation control, and in particular relates to a bilateral remote operation system attack detection and stable control method with network attack. Background Art

[0002] With the development and progress of social economy and science and technology, the scope of human scientific research is also expanding. For some complex and difficult tasks, humans alone cannot complete them. The research and development and production of teleoperation robots can greatly simplify the complexity of the above tasks and improve work efficiency. At present, there are more and more research results on the transparency of teleoperation. Delay and packet loss have a great impact on the stability of bilateral teleoperation systems. Reference 1 (S. Huang, Y. Zhang, T. Zhu, and C. Fang, "Stability analysis of bilateral teleoperation system based on data sampling with time delay," in 2017 Eighth International Conference on Intelligent Control and Information Processing (ICICIP), pp. 287–292, 2017.) In order to eliminate the influence of delay, a zero-order keeper is used to ensure that the master and slave receive the data packets from the opposite end at the same time. When the network communication between the master and slave ends is attacked by false data injection, Reference 2 (Y. Guan and X. Ge, “Distributed attack detection and secure estimation of networked cyber-physical systems against false data injection attacks and jamming attacks,” IEEE Transactions on Signal and Information Processing over Networks, vol. 4, no. 1, pp. 48–59, 2018.) proposed a resilient attack detection estimator to detect false data injection attacks. In order to achieve the robust operability of the bilateral teleoperation system, Reference 3 (CC Hua, Y. Yang, and X. Guan, “Neural network-based adaptive position tracking control for bilateral teleoperation under constant time delay,” Neurocomputing, vol. 113, pp. 204–212, 2013.) proposed a neural network-based controller to use acceleration signals to eliminate the errors in the position and velocity tracking performance of the master and slave robots.

[0003] In order to solve the stability problem of bilateral teleoperation system with time delay and network attack, this paper sets a zero-order holder to reduce the impact of time delay, detects network attack at the same time, and designs an adaptive controller to ensure the tracking stability of master and slave manipulators. Summary of the invention

[0004] In order to solve the above technical defects in the prior art, the present invention proposes a bilateral teleoperation system attack detection and stability control method with network attack.

[0005] The technical solution to achieve the purpose of the present invention is: a bilateral teleoperation system attack detection and stability control method with network attack, comprising the following steps:

[0006] Step 1: Establish the dynamic equations of the bilateral teleoperated manipulator system;

[0007] Step 2: Establish a model of packet loss and network attacks in the network, and use the least squares algorithm to detect network attacks;

[0008] Step 3: Design an adaptive controller based on the network attack detection results.

[0009] Preferably, the dynamic equation of the bilateral teleoperated manipulator system established in step 1 is the Lagrangian dynamic equation of the n-th order bilateral teleoperated manipulator system, which is as follows:

[0010]

[0011]

[0012] Where i = m, s represents the master and slave robotic arms, The vector representing the joint position, A vector representing the joint velocity, A vector representing the joint acceleration; is the inertia matrix, are the centripetal and Coriolis matrices, is the gravitational torque; is the operator’s force vector, is the environmental force vector, is the controller input vector, represents a real vector, represents a real matrix, and the equation satisfies the following properties and assumptions:

[0013] Property 1: For any q, the inertia matrix M(q) is a symmetric positive definite matrix;

[0014] Feature 2: M i (q) and The following relationship exists: for any matrix Represents a real matrix

[0015] Property 3: There exists a positive scalar β i , so that U i (q i )≥β i , where U i (q i ) is the potential energy of the robot, satisfying the relationship

[0016] Assumption 1: Assume that the human operator and the environment are passive and can be described as

[0017] Preferably, step 2 establishes a model of packet loss and network attacks in the network, and the specific steps of using the least squares algorithm to detect network attacks are:

[0018] Step 2-1 establishes the packet loss and network attack models in the network, which are as follows:

[0019] The attack model of network attack is:

[0020] q i (t) = q i (t)+E i (t),|E i (t)|>E

[0021] Where i = m, s represents the master and slave robotic arms, q i (t) represents the position vector of the joint, E i (t) represents a false data injection attack, and E is a positive constant;

[0022] Use Bernoulli distribution variables to describe the packet loss model. Specifically, two Bernoulli distribution variables φ are selected. i (t) and γ i (t) to describe the model:

[0023] φ i (t) = 1 means there is no false data injection attack;

[0024] φ i (t) = 0 indicates a false data injection attack;

[0025] Where i = m, s represents the master and slave robotic arms,

[0026] γ i (t) = 1 means no packet loss;

[0027] γ i (t) = 0 means packet loss;

[0028] Where i = m, s represents the master and slave robotic arms,

[0029] Step 2-2 uses the difference equation to describe the dynamic behavior of the bilateral teleoperation system:

[0030] A(z -1 )q i (k) = B(z -1 )τ i (k)+e(k)

[0031] Where A(z -1 )=1+a1z -1 +...+a n z -n ,q i (k) represents the position vector of the joint, τ i (k) represents the control law of the robot arm, i = m, s represents the master and slave robot arms, B(z -1 )=b0+b1z -1 +...+b n z -n ; a1,...,a n ,b0,...,b n is an undetermined constant, e(k) is a white noise with zero mean;

[0032] Step 2-3 uses the least squares method to identify situations where there is no network attack or packet loss:

[0033] The kinetic difference equation can be written in standard least squares form:

[0034] Q i =Φθ+e

[0035] Where Q i =[q i (n+1),q i (n+2),…,q i (n+N)] T ,θ=[a1,a2,…,a n ,b0,b1…,b n ] T , e=[e(n+1),e(n+2),…,e(n+N)] T ,q i (n) represents the position vector of the joint, τ i (n) represents the control law of the robot, i=m, s represents the master and slave robots, e is white noise, n and N are positive integers, representing the nth sampling value and the total number of samples N respectively;

[0036] Using the least squares method, the following parameter identification is performed:

[0037] θ LS =(Φ T Φ)- 1 Φ T Q i

[0038] Where Q i =[q i (n+1),q i (n+2),…,q i (n+N)] T ,

[0039] q i (n) represents the position vector of the joint, τ i (n) represents the control law of the robot, i = m, s represents the master and slave robots;

[0040] The bilateral teleoperation system performs the same motion j times without being attacked by the network, and samples the state to obtain

[0041]

[0042] if and The variance of is within the error range, then

[0043]

[0044] Where h represents the sampling time, k represents the kth sampling;

[0045] Step 2-4: The system performs the same movement under the false data injection attack, and uses the least squares method to estimate the system parameters that have been attacked. To perform system identification:

[0046]

[0047] It is a positive number, indicating the attack detection threshold. r>g means the system is under attack.

[0048] Preferably, the specific steps of step 3 of designing an adaptive controller based on the network attack detection results are:

[0049] Step 3-1: Update the controller data packet based on the identification results of the network attack:

[0050] When the communication channel or When attacked, the corresponding φ m(t) or φ s (t) is 0, the data packet is discarded, and the zero-order holder keeps the state of the previous packet. When the data packet is not attacked or discarded, the controller updates the data packet;

[0051] The controller's data package is updated as follows:

[0052]

[0053]

[0054] Among them, φ m (t) and φ s (t) is the false data injection attack coefficient of the master and slave manipulators, γ m (t) and γ s (t) is the packet loss coefficient of the master and slave manipulators, is the position vector received from the controller; is the position vector received by the main controller, is the velocity vector received from the slave controller; is the velocity vector received by the main controller; represents the time delay, where d(t) = t-kh, t∈(kh,kh+h), where h represents the sampling time and k represents the kth sampling;

[0055] Step 3-2 Design an adaptive PD controller to eliminate the impact of network attacks on system stability:

[0056]

[0057]

[0058] The gain matrix k i and α i The adaptive law is:

[0059]

[0060]

[0061] Where, C1 = [1 0], C2 = [0 1], k m , k s , α m , α s is the gain of the PD controller, q m (t), q s (t) are the joint position vectors of the master and slave manipulators, a, b, c, d are the parameters of the adaptive law, Respectively represent the joint velocity vectors of the master and slave manipulators, Represents the data packets of the master and slave ends respectively.

[0062] Compared with the prior art, the present invention has the following significant advantages: the present invention can successfully detect network attacks in a bilateral teleoperation system with network attacks, and use an adaptive controller to eliminate the impact of network attacks. Compared with bilateral teleoperation systems that have been attacked by network attacks in the past, the present invention ensures the stability of the system under network attacks.

[0063] Other features and advantages of the present invention will be described in the following description, and part of them will become obvious from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0065] Figure 1 It is a bilateral control block diagram of a bilateral remote operation system with network attack proposed by the present invention.

[0066] Figure 2 It is the human operating force curve in the present invention.

[0067] Figure 3 It is the position tracking curve of the master robot arm and the slave robot arm proposed by the present invention.

[0068] Figure 4 It is the speed tracking curve of the master robot arm and the slave robot arm proposed by the present invention.

[0069] Figure 5 It is the position error curve of the master robot arm and the slave robot arm proposed by the present invention.

[0070] Figure 6 It is the speed error curve of the master robot arm and the slave robot arm proposed by the present invention.

[0071] Figure 7 It is the main robot arm control parameter variation curve proposed by the present invention.

[0072] Figure 8 It is the control parameter variation curve of the slave robot arm proposed by the present invention. DETAILED DESCRIPTION

[0073] It is easy to understand that according to the technical solution of the present invention, without changing the essential spirit of the present invention, a person skilled in the art can imagine various embodiments of the present invention. Therefore, the following specific embodiments and drawings are only exemplary descriptions of the technical solution of the present invention, and should not be regarded as the whole of the present invention or as a limitation or limitation of the technical solution of the present invention. On the contrary, the purpose of providing these embodiments is to enable those skilled in the art to understand the present invention more thoroughly. The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the innovative concept of the present invention.

[0074] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0075] A bilateral teleoperation system attack detection and stability control method with network attacks analyzes the structure of the bilateral teleoperation system with network attacks and describes the packet loss and false data injection attacks in the network;

[0076] Step 1: Establish the dynamic equations of the bilateral teleoperated manipulator system;

[0077] Step 2: Establish a model of packet loss and network attacks in the network, and use the least squares algorithm to detect network attacks;

[0078] Step 3: Design an adaptive controller based on the network attack detection results.

[0079] In a further embodiment, the step 1 establishes the dynamic equation of the bilateral teleoperated manipulator system:

[0080] Step 1-1 Establish the dynamic equations of the bilateral teleoperated manipulator system

[0081] The Lagrangian dynamics equation of the n-order bilateral teleoperated manipulator system is as follows:

[0082]

[0083]

[0084] Where i = m, s, The vector representing the joint position, A vector representing the joint velocity, A vector representing the joint acceleration; is the inertia matrix, are the centripetal and Coriolis matrices, is the gravitational torque; is the operator’s force vector, is the environmental force vector, Input vector for the controller.

[0085] Property 1: For any q, the inertia matrix M(q) is a symmetric positive definite matrix.

[0086] Feature 2: M i (q) and The following relationship exists: for any matrix

[0087] Property 3: There exists a positive definite scalar β i , so that U i (q i )≥β i . Among them, U i (q i ) is the potential energy of the robot, satisfying the relationship

[0088] Assumption 1: Assume that the human operator and the environment are passive and can be described as

[0089] In a further embodiment, the step 2 establishes a model of packet loss and network attack in the network, and uses a least squares algorithm to detect network attacks:

[0090] Step 2-1: Build a model of packet loss and network attacks in the network

[0091] In a network attack, the attacker's energy is not unlimited, so the data packets transmitted in the network are not always attacked. In a bilateral teleoperation system, the network attacker hijacks the communication network and changes the master and slave data packet information at the same time.

[0092] The attack model of network attack is as follows:

[0093] q i (t) = q i (t)+E i (t),|E i (t)|>E

[0094] Where i = m, s represents the master and slave robotic arms, q i (t) represents the position vector of the joint, E i (t) represents the false data injection attack, and E is a positive constant.

[0095] For packet loss in network communication, this paper proposes a Bernoulli distribution variable to describe the packet loss model. Whether the system loses normal data packets or attacked data packets, the Bernoulli packet loss model is applicable.

[0096] The present invention selects two Bernoulli distribution variables φ i (t) and γi (t) to describe the model.

[0097] φ i (t) = 1 means there is no false data injection attack

[0098] φ i (t) = 0 indicates a false data injection attack

[0099] Where i = m, s represents the master and slave robotic arms,

[0100] γ i (t) = 1 means no packet loss

[0101] γ i (t) = 0 means packet loss

[0102] Where i = m, s represents the master and slave robotic arms,

[0103] To detect the presence of false data injection attacks, we first study the case where the system is not subject to network attacks or packet loss. We sample the instantaneous state of the system from the beginning to equilibrium, and then use a least squares-based offline identification method to study the dynamic characteristics of the system.

[0104] Step 2-2 uses the difference equation to describe the dynamic behavior of the bilateral teleoperation system:

[0105] A(z -1 )q i (k) = B(z -1 )τ i (k)+e(k)

[0106] Where A(z -1 )=1+a1z -1 +...+a n z -n ,q i (k) represents the position vector of the joint, τ i (k) represents the control law of the robot arm, i = m, s represents the master and slave robot arms, B(z -1 )=b0+b1z -1 +...+b n z -n ; a1,...,a n ,b0,...,b n is an undetermined constant, and e(k) is a white noise with zero mean.

[0107] Step 2-3 uses the least squares method to identify situations where there is no network attack or packet loss:

[0108] The kinetic difference equation can be written in standard least squares form:

[0109] Q i =Φθe

[0110] Where Q i =[q i (n+1),q i (n+2),…,q i (n+N)] T ,θ=[a1,a2,…,a n ,b0,b1…,b n ] T , e=[e(n+1),e(n+2),…,e(n+N)] T ,q i (n) represents the position vector of the joint, τ i (n) represents the control law of the robot arm, i=m, s represents the master and slave robot arms, e is white noise, n and N are positive integers, representing the nth sampling value and the total number of samples N respectively.

[0111] Using the least squares method, the following parameter identification is performed:

[0112] θ LS =(Φ T Φ) -1 Φ T Q i

[0113] Where Q i =[q i (n+1),q i (n+2),…,q i (n+N)] T ,

[0114] q i (n) represents the position vector of the joint, τ i (n) represents the control law of the robot arm, i=m, and s represents the master and slave robot arms.

[0115] The bilateral teleoperation system performs the same motion j times without being attacked by the network, and samples the state to obtain

[0116]

[0117] if and The variance of is within the error range, then

[0118]

[0119] Where h represents the sampling time and k represents the kth sampling.

[0120] Finally, the least squares method is used to estimate the parameters of the unattacked system. To identify.

[0121] Step 2-4 uses the least squares method to identify packet loss or network attacks.

[0122] The system performs the same exercise under the false data injection attack, and uses the least squares method to estimate the system parameters that have been attacked. Perform system identification.

[0123]

[0124] is a positive constant, indicating the attack detection threshold. r>g means the system is under attack.

[0125] In a further embodiment, step 3 designs an adaptive controller based on the network attack detection results.

[0126] Step 3-1 Update the controller data packet based on the identification results of the network attack

[0127] When the communication channel or When attacked, the corresponding φ m (t) or φ s If (t) is 0, the packet is discarded and the zero-order holder keeps the state of the previous packet. The controller will update the packet only when the packet is not attacked or discarded.

[0128] The controller's data package is updated as follows:

[0129]

[0130]

[0131] Among them, φ m (t) and φ s (t) is the false data injection attack coefficient of the master and slave manipulators, γ m (t) and γ s (t) is the packet loss coefficient of the master and slave manipulators, is the position vector received from the controller; is the position vector received by the master controller. is the velocity vector received from the slave controller; is the velocity vector received by the master controller. represents the time delay, where d(t) = t-kh, t∈(kh,kh+h), where h represents the sampling time and k represents the kth sample.

[0132] Step 3-2 designs an adaptive PD controller to eliminate the impact of network attacks on system stability.

[0133]

[0134]

[0135] The gain matrix k i and α i The adaptive law is:

[0136]

[0137]

[0138] Where, C1 = [1 0], C2 = [0 1], k m , k s , α m , α s is the gain of the PD controller, q m (t), q s (t) are the joint position vectors of the master and slave manipulators, Respectively represent the joint velocity vectors of the master and slave manipulators, Represents the data packets of the master and slave ends respectively.

[0139] Using the Lyapunov functional method, sufficient conditions for the system to achieve global asymptotic stability under false data injection attacks are given. The specific proof is: Select the Lyapunov function as V

[0140]

[0141] Derivative of the Lyapunov function:

[0142]

[0143]

[0144]

[0145] in

[0146] From the theorem, we know that Therefore, the bilateral teleoperation control system is globally asymptotically stable.

[0147] In the present invention, the bypass system recognizes and divides data into normal data packets and attack data packets. The Bernoulli model can vividly describe the data packet loss and attack data packets.

[0148] Example 1

[0149] The present invention is to detect network attacks and packet loss in a bilateral teleoperation system with network attacks, and ensure that the master and slave ends can still achieve stable tracking under the influence of network attacks. The specific operation steps are as follows:

[0150] The bilateral teleoperation system consists of two two-degree-of-freedom robotic arm systems:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156] The system parameters are selected as follows:

[0157] m1=10kg, m2=5kg, l1=0.7m, l2=0.5m, g=9.82m / s 2 ,

[0158] h=0.02s,a j =b j =c j =d j =300(j=1,2)

[0159] Attack detection threshold g = 0.3; false injection data E i (t) = 2. When 1.5 < t < 15, the system is attacked. The initial condition of the bilateral teleoperation system: q m (0) = q s (0) = [0 0] T , Delay d(t)<0.02.

[0160] Finally, the above simulation results are summarized as follows: In a bilateral teleoperation system with network attacks, Figure 3-8 It shows the performance of the system when it is attacked by false data injection. Figure 3 and Figure 4 The performance of the master and slave position and speed synchronization is shown. Figure 5 and Figure 6 The error can be clearly seen in the figure. At about 5 seconds, the false data injection attack had a huge impact on the system. The attack detection successfully reduced the impact of the attack. The control parameters of the master and slave manipulators are as follows: Figure 7 , Figure 8 As shown. m Converges to (-185.5, -200.3), α m Converges to (-137.9, -170.2), k s Converges to (-162.1, -226.1), α s Converges to (-26.82, -36.38). Through adaptive control, it can be concluded that bilateral teleoperation is globally asymptotically stable.

[0161] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0162] It should be understood that in order to simplify the present invention and help those skilled in the art understand the various aspects of the present invention, in the above description of the exemplary embodiments of the present invention, the various features of the present invention are sometimes described in a single embodiment or described with reference to a single figure. However, the present invention should not be interpreted as the features included in the exemplary embodiments are all necessary technical features of the patent claims.

[0163] It should be understood that the modules, units, components, etc. included in the device of an embodiment of the present invention can be adaptively changed to be set in a device different from the embodiment. The different modules, units, or components included in the device of the embodiment can be combined into one module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A bilateral teleoperation system attack detection and stability control method with network attack, characterized in that: The following steps are involved: Step 1: Establish the dynamic equations of the bilateral teleoperated manipulator system; Step 2: Establish a model of packet loss and network attacks in the network, and use the least squares algorithm to detect network attacks. The specific steps are as follows: Step 2-1 establishes the packet loss and network attack models in the network, which are as follows: The attack model of network attack is: q i (t)=q i (t)+E i (t),|E i (t)|>E Where i = m, s represents the master and slave robotic arms, q i (t) represents the position vector of the joint, E i (t) represents a false data injection attack, and E is a positive constant; Use Bernoulli distribution variables to describe the packet loss model. Specifically, two Bernoulli distribution variables φ are selected. i (t) and γ i (t) to describe the model: φ i (t) = 1 means there is no false data injection attack; φ i (t) = 0 indicates a false data injection attack; Where i = m, s represents the master and slave robotic arms, γ i (t) = 1 means no packet loss; γ i (t) = 0 means packet loss; Where i = m, s represents the master and slave robotic arms, Step 2-2 uses the difference equation to describe the dynamic behavior of the bilateral teleoperation system: Until -1 )q i (k)=B(z -1 )τ i (k)+e(k) Where A(z -1 )=1+a1z -1 +…+a n z -n ,q i (k) represents the position vector of the joint, τ i (k) represents the control law of the robot arm, i = m, s represents the master and slave robot arms, B(z -1 )=b0+b1z -1 +...+b n z -n ; a1,...,a n ,b0,...,b n is an undetermined constant, e(k) is a white noise with zero mean; Step 2-3 uses the least squares method to identify situations where there is no network attack or packet loss: The kinetic difference equation can be written in standard least squares form: Q i =Φθ+e Where Q i =[q i (n+1),q i (n+2),…,q i (n+N)] T ,θ=[a1,a2,…,a n ,b0,b1…,b n ] T , e=[e(n+1),e(n+2),…,e(n+N)] T ,q i (n) represents the position vector of the joint, τ i (n) represents the control law of the robot, i=m, s represents the master and slave robots, e is white noise, n and N are positive integers, representing the nth sampling value and the total number of samples N respectively; Using the least squares method, the following parameter identification is performed: i LS =(Φ T F) -1 F T Q i where Q i = [q i (n + 1), q i (n + 2), …, q i (n + N)] T , q i (n) represents the position vector of the joint, τ i (n) represents the control law of the robot, i = m, s represents the master and slave robots; The bilateral teleoperation system performs the same motion j times without being attacked by the network, and samples the state to obtain if and The variance of is within the error range, then Where h represents the sampling time, k represents the kth sampling; Step 2-4: The system performs the same movement under the false data injection attack, and uses the least squares method to estimate the system parameters that have been attacked. To perform system identification: is a positive constant, indicating the attack detection threshold, r>g means the system is under attack; Step 3: Design an adaptive controller based on the network attack detection results.

2. The bilateral teleoperation system attack detection and stability control method with network attack according to claim 1 is characterized in that: The dynamic equation of the bilateral teleoperated manipulator system established in step 1 is the Lagrangian dynamic equation of the n-th order bilateral teleoperated manipulator system, which is as follows: Where i = m, s represents the master and slave robotic arms, The vector representing the joint position, A vector representing the joint velocity, A vector representing the joint acceleration; is the inertia matrix, are the centripetal and Coriolis matrices, is the gravitational torque; is the operator’s force vector, is the environmental force vector, is the controller input vector, represents a real vector, represents a real matrix, and the equation satisfies the following properties and assumptions: Property 1: For any q, the inertia matrix M(q) is a symmetric positive definite matrix; Feature 2: M i (q) and The following relationship exists: for any matrix represents a real matrix; Property 3: There exists a positive definite scalar β i , so that U i (q i )≥β i , where U i (q i ) is the potential energy of the robot, satisfying the relationship Assumption 1: Assume that the human operator and the environment are passive and can be described as 3. The attack detection and stability control method of bilateral teleoperation system with network attack according to claim 1 is characterized in that: Step 3 The specific steps of designing an adaptive controller based on the network attack detection results are: Step 3-1: Update the controller data packet based on the identification results of the network attack: When the communication channel or When attacked, the corresponding φ m (t) or φ s (t) is 0, the data packet is discarded, and the zero-order holder keeps the state of the previous packet. When the data packet is not attacked or discarded, the controller updates the data packet; The controller's data package is updated as follows: Among them, φ m (t) and φ s (t) is the false data injection attack coefficient of the master and slave manipulators, γ m (t) and γ s (t) is the packet loss coefficient of the master and slave manipulators, is the position vector received from the controller; is the position vector received by the main controller, is the velocity vector received from the slave controller; is the velocity vector received by the main controller; represents the time delay, where d(t) = t-kh, Where h represents the sampling time, k represents the kth sampling; Step 3-2 Design an adaptive PD controller to eliminate the impact of network attacks on system stability: The gain matrix k i and α i The adaptive law is: Among them, C1=[1 0], C2=[01], k m , k s , α m , α s is the gain of the PD controller, q m (t), q s (t) are the joint position vectors of the master and slave manipulators, a, b, c, d are the parameters of the adaptive law, Respectively represent the joint velocity vectors of the master and slave manipulators, Represents the data packets of the master and slave ends respectively.

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