Dynamic displacement feedback attack and analysis method and device

Abstract

The invention relates to a dynamic displacement feedback attack and analysis method and device, and belongs to the technical field of multi-agent system control. The dynamic displacement feedback attack method comprises the following steps: acquiring a linear dynamic model of a target robot formation and a formation controller equation of the target robot formation constructed based on the linear dynamic model; intercepting a control vector sent by a first robot to a second robot in the target robot formation, and designing an attack vector for the control logic of the target robot formation based on the control vector, the incomplete dynamic model and the formation controller equation; and sending the attack vector to the second robot as a pseudo control vector. The invention provides a novel attack mode with relatively high attack precision, which is convenient for researchers to research the security of the multi-agent system.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system control, and particularly to a dynamic displacement feedback attack, analysis method and device. Background Art

[0002] A multi-agent system consists of a group of intelligent agents that cooperate or compete through a network to complete common or individual tasks. As a basic application of multi-agent systems, swarm control algorithms aim to ensure that a group of agents can move to a desired position while maintaining a predefined swarm shape. Formation control algorithms have been widely studied due to their various applications. For unmanned aerial vehicles, formation control can be used in intelligent agriculture or drone delivery. In the case of unmanned ships, formation control can be used for search and rescue, port security, or hydrological monitoring, etc.

[0003] When formation control is applied to robots to perform tasks, communication between robots is required. Different from traditional industrial systems with wired networks, due to their mobility characteristics, formation control in many applications requires wireless networks. The air propagation characteristics of wireless networks are more vulnerable to attacks than wired networks because both legitimate and malicious users can access wireless networks. Although technicians have never stopped researching the security of multi-agent systems, there is a lack of research on the attacks themselves, and the existing attack methods only include denial-of-service (DoS) attacks and false data injection (FDi) attacks. The singularity of the attack methods leads to an incomplete security analysis of multi-agent systems.

[0004] It can be seen that due to the few attack methods for multi-agent systems, the security analysis of multi-agent systems is not comprehensive enough. Summary of the Invention

[0005] In view of this, it is necessary to provide a dynamic displacement feedback attack, analysis method and device to solve the problem that the security analysis of multi-agent systems is not comprehensive enough due to the few attack methods for multi-agent systems.

[0006] To solve the above problems, in a first aspect, the present invention provides a dynamic displacement feedback attack method, including: Obtaining the linear dynamics model of a target robot formation and the formation controller equation of the target robot formation constructed based on the linear dynamics model; Intercepting the control vector sent from a first robot to a second robot in the target robot formation, and designing an attack vector for the control logic of the target robot formation based on the control vector, the non-holonomic dynamics model and the formation controller equation; And sending the attack vector as a pseudo control vector to the second robot.

[0007] In a possible implementation, obtaining the linear dynamics model of the target robot formation includes: Construct the non - holonomic dynamics model of the i - th robot in the target robot formation composed of n differentially - driven robots as follows:

[0008] Where, is the inertial position of the i -th robot in the Cartesian coordinate system, and the subscripts xi and yi represent the horizontal coordinate and vertical coordinate of the i -th robot respectively, is the linear velocity of the i -th robot, is the angular velocity of the i -th robot, is the direction angle of the i -th robot, is the moment of inertia, is the applied force, is the applied torque; Based on the non - holonomic dynamics model, the hand position of the i -th robot can be determined as:

[0009] Where, is the hand position of the i -th robot, is the straight - line length between point and point , and is not zero; Based on the hand position of the i - th robot, the linear dynamics model of the i - th robot can be determined as:

[0010] Where, and represent the manipulator position and the velocity of the manipulator position of robot i respectively, and is the controller input.

[0011] In a possible implementation, the formation controller equation of the target robot formation is:

[0012] Where, , is the displacement information in the formation pattern, , , , , are all symmetric positive definite matrices, represents the i desired hand position in the formation pattern of the robot, represents the connection between robot i and robot j, represents no connection between robot i and robot j.

[0013] In a possible implementation, the attack vector is:

[0014]

[0015] where, is the attack vector, is the state information of robot T, q is the control vector, is the error function, is a preset positive constant used to ensure that the denominator is not zero.

[0016] In a second aspect, the present invention also provides a dynamic displacement feedback attack analysis method for analyzing the dynamic displacement feedback attack method described in any of the foregoing embodiments, including: Obtaining the real-time formation controller equation and error function of the target robot formation after being subjected to the dynamic displacement feedback attack; Analyzing the real-time formation controller equation and error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation being subjected to the dynamic displacement feedback attack; Determining the degradation characteristics of the dynamic displacement feedback attack based on the attack accuracy, where the degradation characteristics are used to indicate the relationship between the attack accuracy of each robot in the target robot formation being subjected to the dynamic displacement feedback attack and the position of each robot in the target robot formation.

[0017] In a possible implementation, the obtaining the real-time formation controller equation and error function of the target robot formation after being subjected to the dynamic displacement feedback attack includes: Defining the total error function as follows:

[0018] where, , is positive, represents the connection between robot i and robot j, represents no connection between robot i and robot j; Then the controller equation of the robot R can be expressed as:

[0019] Wherein, ; According to the controller equation of the robot R, the real-time formation controller equation of the target robot formation after suffering a dynamic displacement feedback attack is determined as:

[0020] Wherein, , , ; The real-time formation controller equation and the error function are rewritten in a stacked form as:

[0021] Wherein, , , , ,

[0022] Wherein, L is the Laplacian function of the undirected graph G of the target robot formation and .

[0023] In a possible implementation manner, analyzing the real-time formation controller equation and the error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation suffering from the dynamic displacement feedback attack includes: Select the following Lyapunov function:

[0024] Taking the derivative of V gives:

[0025] Combining the real-time formation controller equation and the error function gives:

[0026] Since , , it can be obtained that:

[0027] Wherein, , According to the calculation result, determine q and the magnitude of the included angle between, based on the q and the magnitude relationship of the included angle between to determine the attack accuracy of each robot in the target robot formation suffering from the dynamic displacement feedback attack.

[0028] In a possible implementation manner, the determining the degradation characteristics of the dynamic displacement feedback attack based on the attack accuracy includes: Sort each robot in the target robot formation according to the magnitude of the attack accuracy of suffering from the dynamic displacement feedback attack; Combine the sorting result of the attack accuracy and the positions of each robot in the target robot formation to determine the degradation characteristics of the dynamic displacement feedback attack.

[0029] In a third aspect, the present invention further provides a dynamic displacement feedback attack device, which is characterized by including: A model construction module, configured to obtain the linear dynamics model of the target robot formation and the formation controller equation of the target robot formation constructed based on the linear dynamics model; An attack vector design module, configured to intercept the control vector sent by the first robot to the second robot in the target robot formation, and design an attack vector for the control logic of the target robot formation based on the control vector, the non-holonomic dynamics model, and the formation controller equation; An attack module, configured to send the attack vector as a pseudo control vector to the second robot.

[0030] In a fourth aspect, the present invention further provides a dynamic displacement feedback attack analysis device, which is characterized by being used to analyze the dynamic displacement feedback attack method described in any of the foregoing embodiments, including: A function construction module, configured to obtain the real-time formation controller equation and error function of the target robot formation after suffering from the dynamic displacement feedback attack; An attack accuracy determination module, configured to analyze the real-time formation controller equation and error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation suffering from the dynamic displacement feedback attack; A degradation characteristic analysis module, configured to determine the degradation characteristics of the dynamic displacement feedback attack based on the attack accuracy, and the degradation characteristics are used to indicate the relationship between the attack accuracy of each robot in the target robot formation suffering from the dynamic displacement feedback attack and the positions of each robot in the target robot formation.

[0031] The beneficial effects of the present invention are as follows: The dynamic displacement feedback attack method provided by the present invention obtains the linear dynamics model of the target robot formation and the formation controller equation of the target robot formation constructed based on the linear dynamics model. According to the control logic of the target robot formation for the formation controller equation, it intercepts the control vector sent from the first robot to the second robot in the target robot formation, designs an attack vector based on the control vector, the non-holonomic dynamics model, and the formation controller equation of the target robot formation, and sends the attack vector as a pseudo-control vector to the second robot. Without knowing the system parameters, the attacker will only disrupt one communication channel between the two robots, providing a new attack method with high attack accuracy, which is convenient for researchers to study the security of multi-agent systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those skilled in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0033] Figure 1 Schematic flowchart of a dynamic displacement feedback attack method provided by an embodiment of the present invention; Figure 2 Schematic diagram of an attack vector provided by an embodiment of the present invention; Figure 3 Schematic diagram of a man-in-the-middle attack provided by an embodiment of the present invention; Figure 4 Schematic flowchart of a dynamic displacement feedback attack analysis method provided by an embodiment of the present invention; Figure 5 Schematic diagram of the first included angle provided by an embodiment of the present invention; Figure 6 Schematic diagram of the second included angle provided by an embodiment of the present invention; Figure 7 Schematic diagram of the first robot formation provided by an embodiment of the present invention; Figure 8 Schematic diagram of the second robot formation provided by an embodiment of the present invention; Figure 9 Schematic diagram of the third robot formation provided by an embodiment of the present invention; Figure 10 Schematic diagram of the fourth robot formation provided by an embodiment of the present invention; Figure 11 Schematic diagram of the fifth robot formation provided by an embodiment of the present invention; Figure 12 The sixth schematic diagram of robot formation provided by the embodiment of the present invention; Figure 13 The structural schematic diagram of a dynamic displacement feedback attack device provided by the embodiment of the present invention; Figure 14 The structural schematic diagram of a dynamic displacement feedback attack analysis device provided by the embodiment of the present invention. Specific implementation manners

[0034] The following will specifically describe the preferred embodiments of the present invention in conjunction with the accompanying drawings. The accompanying drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0035] The descriptions such as "first", "second", etc. involved in the embodiments of the present invention are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the quantity of the indicated technical features. Therefore, the technical features defined with "first" and "second" may explicitly or implicitly include at least one such feature.

[0036] Referring to "embodiment" herein means that the specific features, structures or characteristics described in connection with the embodiment may be included in at least one embodiment of the present invention. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will explicitly and implicitly understand that the embodiments described herein may be combined with other embodiments.

[0037] A specific embodiment of the present invention, as Figure 1 shown, discloses a dynamic displacement feedback attack method, including: S101, obtaining the linear dynamics model of the target robot formation and the formation controller equation of the target robot formation constructed based on the linear dynamics model.

[0038] In the embodiment of the present invention, the DFD (Dynamic Feedback displacement) attack refers to the dynamic displacement feedback attack, which is a new attack method provided by the present invention with high attack accuracy and can attack a multi-agent system to destroy the formation control of the multi-agent system.

[0039] In some embodiments, the obtaining the linear dynamics model of the target robot formation includes: Constructing the non-holonomic dynamics model of the i-th robot in the target robot formation composed of n non-holonomic differentially driven robots as follows:

[0040] Among them, is the inertial position of the robot i in the Cartesian coordinate system, and the subscripts xi and yi respectively represent the horizontal coordinate and the vertical coordinate of the i th robot. The linear velocity, angular velocity and direction angle of the i th robot are , and respectively. The mass of robot i is , and the moment of inertia is . The applied force and the applied torque are and respectively; The non-holonomic dynamic model can be rewritten as:

[0041] Among them, , , the function and the parameter can be deduced from the non-holonomic dynamic model; Define a point as the hand position of the th robot. is the straight-line length between the point and the point . is not equal to zero and can be defined in simulation or application cases. This line is perpendicular to the wheel axis and the end point is

[0042] The definition of the position of the robot after-sales department is useful in some applications. For example, when an object needs to be moved collaboratively by two or more robots, there is usually a gripper at the hand position of the robot.

[0043] Taking the first derivative and the second derivative of the expression of the hand position of the

[0044]

[0045] Because is not zero, we can get:

[0046] The above equation shows that the system is not single-stage, which means that the control input can effectively affect the position of the robot's hand. The non-zero determinant ensures that the transformation matrix involved in feedback linearization is invertible, which allows the application of output feedback linearization techniques, where the dynamics of the robot can be simplified into a form that makes the system easier to control.

[0047] The relative degree of the system with respect to the output is 2, which means that the applied force and torque affect the second derivative (acceleration) of the robot's hand position, thus providing the necessary control to guide the movement of the robot. The constant relative degree allows the use of output feedback linearization, which achieves the desired hand position by affecting the acceleration of the robot. Therefore, the system with an output can perform output feedback linearization on the robot's hand position, and it can be defined as:

[0048] where is a preset mapping relationship. Since the mapping is a diffeomorphism, we can obtain:

[0049] where is the transformed coordinate, and give the hand position of robot i. The first two components are the actual position of robot i, the third component is the orientation angle of the robot, and the last two components are the linear velocity and angular velocity of robot i; Differentiating the components of , we can obtain:

[0050]

[0051]

[0052] Then, the output linearization control input can be expressed as:

[0053] where is an additional formation controller input. Based on this, we can obtain:

[0054]

[0055] The last equation means that the transformation equation makes the internal dynamics unobservable and uncontrollable. Let , we obtain , the zero - dynamics equation is obtained. Therefore, the zero - dynamics is stable. However, they are not asymptotically stable. When the position of the robotic hand stops moving, the angle stops moving because , represents the velocity of the robotic hand position.

[0056] In summary, the linear - dynamics model of robot i can be obtained:

[0057] where, and represent the position of the robotic hand and the velocity of the robotic - hand position of robot i respectively, and is the controller input.

[0058] S102, intercept the control vector sent from the first robot to the second robot in the target robot formation, and design an attack vector for the control logic of the target robot formation based on the control vector, the non - holonomic dynamics model, and the formation - controller equation.

[0059] In the embodiment of the present invention, the K - tuple pattern of the target robot formation is defined as the set , where , represents the desired hand position in the formation pattern of robot i. When the hand positions of all robots reach , the target robot formation updates the formation pattern from to , and moves towards in . The robot formation has two competing goals: target seeking and formation maintenance. The first goal is to make the robots reach the desired positions in the formation pattern. The second goal is to make the robots maintain the formation during each formation movement. The controller equation of the i - th robot is designed as follows:

[0060] where, , is the displacement information in the formation pattern , , , , are all symmetric positive - definite matrices, is the entry of the adjacency matrix of the associated communication graph. If robot i and robot j are connected to each other, then , otherwise . In the above formula, the first two terms move the i th robot to the desired position. The last two terms maintain a formation with the neighbors of the i th robot. There is no need to consider the change of k in the controller because the analysis of each formation pattern is the same.

[0061] For two adjacent robots, define one robot as robot T and the other as robot R. The attacker exploits and intercepts the displacement information of robot T. Robot R directly receives the attack vector from the attacker, and the state information of robot T and R, such as or .

[0062] In the absence of an attack, the robot will move to the ideal position, which can be reduced to zero. Under the previous displacement attack, the robot deviated from the original trajectory and could not reach the desired position. Due to the unknown system configuration, the robot finally stays at an unknown equilibrium position, and all become unknown values. To improve the attack accuracy, try to ensure that the trajectory deviation can be predefined, and all are as close as possible to q, where q is predefined by the attacker as the attack target vector. Since the purpose of the attack is to change the robot's trajectory, q is not parallel to , where is the attack start time. The attacker can only read information from robot T, so the purpose of the DFD attack can be further simplified to make as close as possible to q because based on the formation maintenance ability, all are almost the same. Define an error function , and then achieving the goal of DFD is equivalent to reducing to 0. A smaller is equivalent to higher attack accuracy.

[0063] Define the attack vector to be falsified as . When the attacker intercepts the information of robot T and passes to robot R, for robot R, is the error of maintaining the formation with robot T, and the robot controller will try to eliminate to make . However, the controller also has the ability to seek the target, making .

[0064] Consider as a constant vector, and the initial attack time is . In the time period a, the displacement vector moves to the equilibrium position , Reduce to , as Figure 2 shown. Since the attacker does not know the controller parameters and topology, the attacker cannot know in advance the exact value. Therefore, it is difficult to determine whether the equilibrium position can satisfy the attacker based on a constant . The attacker needs to design a varying to counter the target optimization and ensure that can asymptotically approach q, can be decomposed into vectors and . Since the attacker only reads information from robot T, when constructing the attack vector , the attacker needs to utilize instead of . Next, to construct the vector , the attacker needs to select appropriate direction and magnitude. Since the formation maintenance ability always tries to eliminate , so can be selected in the same direction as . Therefore, as decreases, moves towards q. For the magnitude of , due to the lack of knowledge of the controller parameters, the magnitude needs to monotonically increase to compete with the target optimization until . Finally, the attack vector is defined as follows:

[0065]

[0066] where, is the attack vector, is the state information of robot T, q is the control vector, is the error function, is a preset positive constant used to ensure that the denominator is not zero.

[0067] S103, and send the attack vector as a pseudo-control vector to the second robot.

[0068] In the embodiment of the present invention, the attacker uses a man-in-the-middle attack against the existing displacement attack to disrupt the channel between robot j and robot i . The man-in-the-middle attack is a network layer attack that utilizes the vulnerability of the Address Resolution Protocol to intercept the communication channel between two robots, as Figure 3 shown. The attacker intercepts the communication information between robot j and robot i , and at the same time, the attacker reads and carefully forges the communication information of the robotj Regarding the displacement information, the attacker transmits the forged displacement information to the robot. i When the robot i receives the forged displacement information, the robot misidentifies the forged information as the normal displacement information of the robot. j Based on the formation maintenance ability of the controller, the robot adjusts its own position and uses the forged displacement information to maintain the formation. Once the robot i adjusts its position, the neighbors of the robot i also need to adjust their positions due to the formation maintenance ability. Finally, the attack effect spreads, and all robots will deviate towards the attack vector. Therefore, the attacker can deliberately change the movement of the formation of robotic swarms by designing forged displacement information. i The dynamic displacement feedback attack method provided by the present invention intercepts the control vector sent from the first robot to the second robot in the target robot formation by obtaining the linear dynamics model of the target robot formation and the formation controller equation of the target robot formation constructed based on the linear dynamics model, and designs an attack vector based on the control vector, the non-holonomic dynamics model, and the control logic of the formation controller equation of the target robot formation, and sends the attack vector as a pseudo-control vector to the second robot. Without knowing the system parameters, the attacker only destroys one communication channel between two robots, providing a new attack method with high attack accuracy, which is convenient for researchers to study the security of multi-agent systems.

[0069] The present invention also provides a dynamic displacement feedback attack analysis method for analyzing the dynamic displacement feedback attack method described in any of the foregoing embodiments. As

[0070] shown, it includes: Figure 4 S401, obtaining the real-time formation controller equation and error function of the target robot formation after being subjected to the dynamic displacement feedback attack; S402, analyzing the real-time formation controller equation and error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation being subjected to the dynamic displacement feedback attack; S403, determining the degradation characteristics of the dynamic displacement feedback attack based on the attack accuracy. In the implementation of the present invention, the total error function is defined as

[0071] as follows: as follows:

[0072] where , is positive, indicating a connection between robot i and robot j, indicating no connection between robot i and robot j; Since, , and are symmetric positive definite, there is . If can converge to 0, then it is equivalent to and .

[0073] If the robot formation follows the control strategy defined by the formation controller, the error function can converge to . Define , when the attacker intercepts the original displacement information of robot T and sends the DFD attack to robot R, the controller equation of robot R can be expressed as:

[0074] The movement of robot R is affected by the DFD attack. Once the movement of robot R changes, the neighbors of robot R also need to change because they must maintain formation with robot R. Finally, all the robots in the formation are poisoned and deviate from the original trajectory. The trajectory deviation of the robot can be defined as . is not exactly equal to , but maintains the property that the vector magnitude increases with the direction. Therefore, the controller equation under the DFD attack can be expressed as:

[0075] where, , then q can be expressed as , based on this, ; Define , the real-time formation controller equation can be expressed as:

[0076] The first two terms of the above equation represent driving the robot to the desired position, , where is the information pattern defined by the desired robot hand position. There must exist a point to express q as . Therefore, .

[0077] Furthermore, there is another competing goal for the controller equation. The controller equation attempts to drive , while also trying to drive . equal The parameters in the formula are and right and The relative importance of is an increasing function, so Compare More importantly, the real-time formation controller equation and error function can be rewritten in stacked form as follows:

[0078] in, , , , ,

[0079] Where L is an undirected graph G and The Laplace function of .

[0080] Choose the following Lyapunov function:

[0081] Taking the derivative of V, we get:

[0082] Based on this, we can get:

[0083] because , , we can get:

[0084] in, , According to q and The size relationship of the angle between them determines the attack accuracy of each robot in the target robot formation when it is attacked by the DFD.

[0085] Specifically, if q and If the angle between is acute or right, then is negative definite. Therefore, we need to The relationship between the vector directions is discussed.

[0086] like Figure 5 - 6 As shown, For q and The included angle between is q and The included angle between. According to the controller equation, there are two velocity components: Drive , Drive . Among them is composed of and combined.

[0087] There are two cases. For the first case, if the included angle between q and is obtuse or right, as Figure 5 shown, due to and , so there is . For the second case, as Figure 6 shown, if The included angle with q is acute, then in this case Can be acute, right or obtuse. Since Is an increasing function, as time goes by, Is more important than . Moreover, as mentioned above, the two velocity components and Drive respectively and . Therefore, when , . If , Is acute. When the time t increases, Will be less than 0. If , Can converge to , because the attack message Stops increasing at . When V converges, the attack accuracy will increase.

[0088] The value of V cannot be converted to zero, and the attack accuracy of each robot is not equal. Since the attacker only reads information from robot T, the attack message Can only guarantee . In order to make , robot R needs to provide a suitable For robot T. Therefore, . And, when the robot is in the equilibrium position, except for robot R, the neighbors of robot T all receive the displacement information From robot T. According to the previous discussion, due to the competition between the target seeking ability and the formation maintaining ability, the neighbor robots finally reach the equilibrium position, all not equal to q.

[0089] Furthermore, the phenomenon of unequal attack precision is defined as the degradation characteristic of the DFD attack, and is defined as the attack precision of robot i. A larger corresponds to a higher attack precision and also corresponds to a smaller , and vice versa. By comparing all in the topology, we can study the details of the degradation characteristics. The factors affecting are divided into positive factor P and negative factor N, and positive or negative depends on whether these factors can make , and the subscript of the factor indicates the source of the factor. For each robot, the factor source can be divided into two categories: a) Due to the formation-maintenance ability, the source comes from another robot; b) Due to its goal-seeking ability, the source comes from the robot itself. When a robot tries to maintain formation with another robot i, the factor can be expressed as or . Since the attacker tries to change, the movement and goal-seeking ability of the robot drive the robot to reach the desired position. Therefore, from the perspective of the source of the goal-seeking ability, the factor is negative and can be expressed as . For example, if robot i is only connected to robot j, then the of robot i is affected by the formation maintenance from robot j and the goal-seeking ability from itself. can be expressed as .

[0090] Since robot R is directly affected by the attack, while all other robots are indirectly affected, robot R is marked separately, and the other robots are numbered and marked in the subsequent analysis.

[0091] First, we analyze the radial topology. The radial topology is defined as follows: Robot R is an endpoint, and there is only one path from other robots to robot R, and a path is a sequence of edges connecting two different robots.

[0092] Figure 7 is a simple example where three robots are affected by robot R and its goal-seeking ability. represents that the robot tries to maintain formation with robot R and makes , . represents that the robot tries to move to the original desired position. Therefore, the attack precision of the three robots can be expressed as , .

[0093] In the second case, as Figure 8As shown, we discuss three robots in pairs. For robot 2, the attack accuracy of robot 2 is , and the only positive factor is caused by robot 1 because robot 2 maintains formation with robot 1, making . Therefore, no matter how large it is, always holds. Additionally, since is larger than , when the attack is fully spread, . For robot 1, maintaining formation with robot 2 can increase . For robot 1, the influence from robot 2 is negative, denoted as . The attack accuracy of robot 1 is . For robot 3, has the same positive factor as robot 1, but robot 1 has an additional negative factor from robot 2. Therefore, is larger than , and in this case, the comparison of attack accuracy can be summarized as .

[0094] In the third case, as Figure 9 shown, the analysis is the same as that of the pair of robots 1 and 2 in the second case. The comparison of attack accuracy in the third case is summarized as .

[0095] Further comparing Figure 8 and 10 for the attack accuracy among robots 1 - 6, for robots 2 and 5, if robot 6 does not exist, robots 2 and 5 have the same attack accuracy. Therefore, when robot 6 provides a negative factor to robot 5, . Based on the analysis of the first and second cases, we can obtain . Additionally, since , the negative factor received by robot 4 is worse than that received by robot 1. Therefore, we can obtain .

[0096] Based on this, two conclusions can be drawn: Based on and , we can conclude that the farther a robot is from robot R, the lower its attack accuracy; Based on and , we can conclude that for robots at the same hop count from robot R, the attack accuracy of a robot depends on the total number of robots on the line from robot R to the end robot. If robots are at the same hop count from R, the more robots there are on the line, the lower the attack accuracy of the robot.

[0097] Furthermore, we analyze the ring topology. The ring topology is defined as each robot being connected to two robots, and all robots being connected like a circle.

[0098] The ring topology can be divided into an odd-robot ring and an even-robot ring, as shown respectively in Figure 10 and 11 For the ring of odd robots, as shown in Figure 10 , if robots 2 and 3 are not connected, they have the same attack accuracy. Therefore, formation maintenance does not change their displacements when they are connected because they already have the same displacements. The comparison of attack accuracies can be summarized as .

[0099] For the ring with an even number of robots, there must be a robot that jumps the most from robot R, and this robot is defined as . In our example, robot 3 is the robot shown in Figure 11 . The impacts of robots 2 and 4 on robot 3 are the same. The attack accuracy of robot 3 can be expressed as . The two positive factors are both or . Although there are two positive factors, we can get . The reason is as follows: If holds, then there is no and , and there is only one to drive the robot to reach the desired formation goal. Due to formation maintenance, it is impossible to have only one , and the comparison of attack accuracies can be generalized as .

[0100] From the above discussion on the ring topology, we can obtain three conclusions: For the ring of odd robots, except for robot R, the robots on both sides of robot R can be symmetrically divided into two groups. The attack accuracies of the two groups are symmetrically equal, and their changes are similar to the conclusions in the radical topology. If two robots have the same attack accuracy before topological connection, their attack accuracies remain unchanged after topological connection. For the ring of even robots, except for robot , the change in attack accuracy is the same as that of the ring of odd robots, and robot has the lowest attack accuracy in the topological graph.

[0101] Moreover, for a pair of adjacent robots i and i + 1, we can summarize two general rules for analyzing the attack accuracy: If robot i has a positive impact on another robot i + 1, then robot i + 1 will definitely have a negative impact on robot i; if robot i can have a positive impact on robot i+1, then , and vice versa.

[0102] Analyzing the hybrid topology, which refers to a topology that contains both radial and loop topologies, such as Figure 12 shown. For robots 1 - 4, they construct three loops A, B, and C. If robots 2 and 4 are disconnected, then robots 1 and 4 are symmetric, holds. When robot 2 is connected to robot 4, robot 4 receives a negative impact . Then, robots 1 and 4 have the same positive factor and the same negative factor and . Because robot 4 has an additional negative factor , so is larger than . Then and hold. Similarly, if robots 2 and 3 are disconnected, they have the same positive factor and the same negative factor . Since robot 2 has an additional positive factor , so when robot 2 is connected to robot 3, is greater than . Then we can get and , and the comparison of the attack accuracy can be summarized as .

[0103] For robots 5 - 0, they construct a straight line with a loop D. According to the previous conclusion, we can quickly get , , . If robots 8 and 9 are disconnected, the 6 - 7 - 8 line and the 6 - 9 - 0 line are symmetric, holds. When robot 8 is connected to robot 9, robot 9 receives a negative impact . Robots 9 and 7 have the same unique positive factor and the same negative factor and . Moreover, since robot 9 has an additional negative factor , so is larger than Thus, it can be obtained that , , . The comparison of the attack accuracy can be summarized as .

[0104] The dynamic displacement feedback attack analysis method provided by the present invention combines the real-time formation controller equation and the error function obtained after the target robot formation is subjected to the dynamic displacement feedback attack, and analyzes the real-time formation controller equation and the error function by combining the Lyapunov function to determine the attack accuracy of each robot in the target robot formation suffering from the dynamic displacement feedback attack; based on the attack accuracy, the degradation characteristics of the dynamic displacement feedback attack are determined, which can accurately judge the attack accuracy of each robot in the target robot formation under the dynamic displacement feedback attack, facilitating the subsequent security research of the multi-agent system.

[0105] In order to better implement the dynamic displacement feedback attack and analysis method in the embodiments of the present invention, on the basis of the dynamic displacement feedback attack and analysis, correspondingly, as Figure 13 shown, the embodiments of the present invention further provide a dynamic displacement feedback attack device. The dynamic displacement feedback attack device 1300 includes: A model construction module 1301, configured to obtain the linear dynamics model of the target robot formation and the formation controller equation of the target robot formation constructed based on the linear dynamics model; An attack vector design module 1302, configured to intercept the control vector sent by the first robot to the second robot in the target robot formation, and design an attack vector for the control logic of the target robot formation based on the control vector, the non-holonomic dynamics model, and the formation controller equation; An attack module 1303, configured to send the attack vector as a pseudo control vector to the second robot.

[0106] Corresponding to the dynamic displacement feedback attack analysis method, the present invention also provides a dynamic displacement feedback attack analysis device for attacking the dynamic displacement feedback attack method described in any of the foregoing embodiments, as Figure 14 shown, including: A function construction module 1401, configured to obtain the real-time formation controller equation and the error function of the target robot formation after being subjected to the dynamic displacement feedback attack; An attack accuracy determination module 1402, configured to analyze the real-time formation controller equation and the error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation suffering from the dynamic displacement feedback attack; A degradation characteristic analysis module 1403, configured to determine the degradation characteristics of the dynamic displacement feedback attack based on the attack accuracy.

[0107] The dynamic displacement feedback attack and analysis device provided by the above embodiments can implement the technical solutions described in the above embodiments of the dynamic displacement feedback attack and analysis method. The specific implementation principles of the above modules or units can be referred to the corresponding content in the above embodiments of the magnetic resonance image optimization method, which will not be elaborated here.

[0108] Correspondingly, an embodiment of the present application further provides a computer-readable storage medium, which is used to store computer-readable programs or instructions. When the programs or instructions are executed by a processor, the steps or functions in the magnetic resonance image optimization method provided by the above method embodiments can be implemented.

[0109] Those skilled in the art can understand that all or part of the processes of implementing the above method embodiments can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.

[0110] The above 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 thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A dynamic displacement feedback attack method, characterized in that: include: Acquire a linear dynamics model of a target robot formation and a formation controller equation of the target robot formation constructed based on the linear dynamics model; intercepting a control vector sent by a first robot to a second robot in the target robot formation, and designing an attack vector for the control logic of the target robot formation based on the control vector, the linear dynamics model and the formation controller equation; And the attack vector is sent to the second robot as a pseudo control vector.

2. The dynamic displacement feedback attack method according to claim 1, characterized in that: The step of obtaining the linear dynamics model of the target robot formation includes: The nonholonomic dynamics model of the i-th robot in the target robot formation composed of n non-complete differentially driven robots is constructed as follows: in, For the i The inertial position of the robot in the Cartesian coordinate system, subscript xi and yi Respectively represent i The horizontal and vertical coordinates of the robot, For the i The linear speed of the robot, For the i The angular velocity of the robot, For the i The robot's orientation angle, is the moment of inertia, is the applied force, is the applied torque; Based on the nonholonomic kinetic model, it can be determined that i The hand positions of the robots are: in, For the i The position of the robot's hands, For point With point The length of the straight line between Not zero; Based on the hand position of the ith robot, the linear dynamic model of the ith robot can be determined as: in, and Respectively represent robots i The robot position and the speed of the robot position are Controller input.

3. The dynamic displacement feedback attack method according to claim 2, characterized in that: The formation controller equation of the target robot formation is: in, , is the displacement information in the formation pattern, , , , , are all symmetric positive definite matrices, Represents a robot i Formation mode The desired hand position in indicates that robots i and j are connected to each other, Indicates that there is no connection between robot i and robot j.

4. The dynamic displacement feedback attack method according to claim 3, characterized in that: The attack vectors are: in, is the attack vector, is the state information of robot T, q is the control vector, is the error function, It is a preset positive constant used to ensure that the denominator is not zero.

5. A dynamic displacement feedback attack analysis method, characterized in that: Used to analyze the dynamic displacement feedback attack method described in any one of claims 1 to 4, comprising: Obtain the real-time formation controller equation and error function of the target robot formation after being attacked by dynamic displacement feedback; Analyzing the real-time formation controller equation and the error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation when subjected to the dynamic displacement feedback attack; A degradation feature of the dynamic displacement feedback attack is determined based on the attack accuracy, and the degradation feature is used to indicate the relationship between the attack accuracy of each robot in the target robot formation subjected to the dynamic displacement feedback attack and the position of each robot in the target robot formation.

6. The dynamic displacement feedback attack analysis method according to claim 5, characterized in that: The step of obtaining a real-time formation controller equation and an error function of the target robot formation after being attacked by dynamic displacement feedback includes: Define the total error function as follows: in, , is positive, indicates that robots i and j are connected to each other, It means that there is no connection between robot i and robot j; Then the controller equation of robot R can be expressed as: in, ; According to the controller equation of the robot R, the real-time formation controller equation of the target robot formation after being attacked by dynamic displacement feedback is determined as follows: in, , , ; The real-time formation controller equation and error function are rewritten in stacked form as follows: in, , , , , Where L is the undirected graph G of the target robot formation and The Laplace function of .

7. The dynamic displacement feedback attack analysis method according to claim 6, characterized in that: The analyzing the real-time formation controller equation and the error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation subjected to the dynamic displacement feedback attack includes: Choose the following Lyapunov function: Taking the derivative of V, we get: Combining the real-time formation controller equation and the error function, we can get: because , , we can get: in, , According to the The calculation results determine q and The size of the angle between q and The size relationship of the angle between them determines the attack accuracy of each robot in the target robot formation when it is attacked by the dynamic displacement feedback attack.

8. The dynamic displacement feedback attack analysis method according to claim 7, characterized in that: The determining of the degradation characteristics of the dynamic displacement feedback attack based on the attack accuracy includes: Sorting the robots in the target robot formation according to the attack accuracy of the dynamic displacement feedback attack; The ranking results of the attack accuracies and the positions of the robots in the target robot formation are combined to determine the degradation characteristics of the dynamic displacement feedback attack.

9. A dynamic displacement feedback attack device, characterized in that: include: A model building module, used to obtain a linear dynamics model of a target robot formation and a formation controller equation of the target robot formation built based on the linear dynamics model; an attack vector design module, used to intercept a control vector sent by a first robot to a second robot in the target robot formation, and to design an attack vector for the control logic of the target robot formation based on the control vector, the nonholonomic dynamics model and the formation controller equation; The attack module is used to send the attack vector as a pseudo control vector to the second robot.

10. A dynamic displacement feedback attack analysis device, characterized in that: Used to analyze the dynamic displacement feedback attack method described in any one of claims 1 to 4, comprising: A function building module is used to obtain the real-time formation controller equation and error function of the target robot formation after being attacked by dynamic displacement feedback; An attack accuracy determination module, used for analyzing the real-time formation controller equation and the error function based on the Lyapunov function to determine the attack accuracy of each robot in the target robot formation when it is attacked by the dynamic displacement feedback attack; A degradation feature analysis module is used to determine the degradation feature of the dynamic displacement feedback attack based on the attack accuracy, and the degradation feature is used to indicate the relationship between the attack accuracy of each robot in the target robot formation subjected to the dynamic displacement feedback attack and the position of each robot in the target robot formation.

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