Safe cooperative control method for multiple autonomous underwater robot systems under asynchronous DoS attacks

Abstract

The invention discloses a safe cooperative control method for a multi-autonomous underwater robot system under asynchronous DoS attacks, comprising: establishing a kinematic model and a dynamic model of a fully-driven multi-autonomous underwater robot system; assuming that there are N autonomous underwater robots AUVs, the communication between the autonomous underwater robots AUVs is represented by a communication graph, thereby establishing topological communication of the N autonomous underwater robots AUVs, and constructing cooperative control targets of the N autonomous underwater robots AUVs according to the topological relationship; analyzing the asynchronous denial of service attacks that the multi-autonomous underwater robot system may suffer, designing a controller combined with a trigger rate, so that the multi-autonomous underwater robot system can still complete the system control target under the corresponding network attack; the invention enables the multi-autonomous underwater unmanned robot linkage system to resist DoS asynchronous attacks.

Description

Technical Field

[0001] The invention relates to the technical field of unmanned autonomous underwater robots, and in particular to a safe collaborative control method for a multi-autonomous underwater robot system under asynchronous DoS attacks. Background Art

[0002] With the deepening of marine geoscience research, the application of autonomous underwater robots is becoming more and more extensive. The cooperative control of underwater robots is the key to their successful underwater operations and is one of the important technologies of underwater robots. However, with the continuous improvement of engineering requirements and the increasing complexity of engineering, it is difficult for a single autonomous underwater robot to complete underwater operation tasks. Therefore, the research on the consistent formation tracking control of a group of autonomous underwater robots has gradually received attention.

[0003] In recent years, the formation tracking research of multi-autonomous underwater robot systems has achieved many meaningful results. In a complex underwater environment, the information exchange between underwater robots will be affected. It should be noted that multi-autonomous underwater robot systems are vulnerable to malicious network attacks, such as DoS attacks, replay attacks, etc. Therefore, it is necessary to design a multi-autonomous underwater robot system with strong robustness under network attacks in the control field. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a safe collaborative control method for a multi-autonomous underwater robot system under asynchronous DoS attacks. The present invention enables the multi-autonomous underwater robot linkage system to resist asynchronous DoS attacks.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a safe collaborative control method for a multi-autonomous underwater robot system under asynchronous DoS attack, comprising the following steps:

[0006] Step 1: Establish the kinematic model and dynamic model of the fully-driven multi-autonomous underwater robot system;

[0007] Step 2: Assuming that there are N autonomous underwater robots AUV, the communication between the autonomous underwater robots AUV is represented by a communication graph, so as to establish the topological communication of the N autonomous underwater robots AUV, and construct the collaborative control target of the N autonomous underwater robots AUV according to the topological relationship;

[0008] Step 3: Analyze the asynchronous denial of service attacks that the multi-autonomous underwater robot system may suffer, and design a controller combined with the trigger rate so that the multi-autonomous underwater robot system can still achieve the system control goals under the corresponding network attacks.

[0009] As a further improvement of the present invention, the step 1 is specifically as follows:

[0010] Assume η i =[x i ,y i ,z i ] T is the position vector in the inertial reference coordinate system; Θ i =[θ i ,φ i ,ψ i ] T is the direction vector in the inertial reference coordinate system; ν i =[u i ,q i ,w i ] T is the linear velocity in the inertial reference frame;

[0011] The origin of the Earth-fixed coordinate system is O E Choose any point on the sea level, X E The Y axis points to due north. E The axis points due east, Z E Axis perpendicular to plane O E X E Y E Points to the surface of the Earth; the origin of the inertial reference coordinate system is O b Select the center of mass of the AUV, X b The Y axis points to the bow direction along the centerline of the AUV. b The axis is perpendicular to the centerline of the AUV and points to the starboard side. b Axis perpendicular to plane O b X b Y b Point to the bottom of the AUV

[0012] Among them, x i ,y i ,z i They are respectively represented as the surge position, sway position, and heave position of the i-th autonomous underwater robot in the inertial reference coordinate system; u i ,q i ,w i They are respectively expressed as the surge velocity, sway velocity, and heave velocity of the AUV in the body coordinate system;

[0013] The kinematic model of the autonomous underwater robot is expressed as:

[0014]

[0015] in is the derivative of the position vector with respect to time; J i is the motion transformation matrix of the system, which is related to the linear velocity vector v iThe product of is used to reflect the time derivative of the motion displacement of the i-th AUV;

[0016]

[0017] J i (Θ i ) is given by the posture vector Θ i =[θ i ,φ i ,ψ i ] is used to convert the linear velocity v and the position vector η i Derivative relationships;

[0018] The following equation is used to describe the relationship between system input and AUV motion dynamics:

[0019]

[0020] in, C i are the Coriolis matrix and centripetal force matrix of the ith AUV, M i is the inertia matrix, D i is the hydrodynamic drag matrix, gi is the vector of the restoring force, τ i is the input to the system.

[0021] As a further improvement of the present invention, in step 2, the established topological communication of N autonomous underwater robots AUV is represented by a directed graph, and the relevant graph theory is as follows:

[0022] Assume that the system consisting of N AUVs is represented by a graph G(V,E,A), where V is the node set of the system, represents the set of communication edges of the system, A=[a ij ]∈R N×N Represents the adjacency matrix of the topological graph G; if AUV i can receive information from its neighbor AUVj, the corresponding a ij =1, otherwise a ij = 0, the neighbor j that can send messages to i becomes the inner neighbor j, and i is called the outer neighbor of j accordingly; the graph structure of the system is strongly connected, the Laplace matrix L = DA, and its structure can be expressed as:

[0023]

[0024] As a further improvement of the present invention, in step 2, the collaborative control objectives of N autonomous underwater robots AUV are constructed according to the topological relationship as follows:

[0025] First, we make an assumption about the duration of the DoS attack. The attack model is expressed as:

[0026]

[0027] in and They are all constants greater than 0, used to describe the duration of the communication channel being attacked by DoS;

[0028] The frequency and number of DoS attacks on edge ij are described as follows:

[0029]

[0030] Where n ij (t0,t) represents the number of times edge ij receives DoS attacks in the time period (t0,t), f ij (t0,t) represents the frequency of receiving DoS attacks;

[0031] Defining time intervals Used to describe the duration of a system being affected by a DoS attack:

[0032]

[0033] According to the AUV kinematic model, its properties include:

[0034] Property (1): There exists a finite constant such that λ min <λ max <∞,λ min I n×n ≤M i ≤λ max I n×n ;

[0035] Property (2): There exists a matrix It has oblique symmetry;

[0036] Property (3): k i ,k c >0,K d >0,k g >0,||C i (v i )||≤k c ||v i ||,||D i (v i )||≤k d ||v i ||,‖g i ||≤k g ;

[0037] Assuming that the linear velocity and its derivatives of the AUV system are bounded,

[0038] The coordinated control objectives that need to be achieved when the multi-AUV system is subjected to asynchronous DoS attacks are:

[0039]

[0040] As a further improvement of the present invention, the step 3 is specifically as follows:

[0041] Design auxiliary variables for the controller:

[0042]

[0043]

[0044] It means that during this period, edge ij is in the DoS sleep period; is the time period when edge ij is attacked by DoS, Indicates the last state information transmitted by the AUV before being attacked by DoS. Indicates the current location status information during the DoS sleep period. Indicates that the i-th AUV is at the triggering time The uploaded location information. The following formula can be obtained from the designed auxiliary variables:

[0045] θ i =v i -s i

[0046]

[0047]

[0048] To achieve the cooperative control goal, the controller is set as follows:

[0049] τ i =-k i s i +B i

[0050] Through the designed auxiliary variables and the properties of the system, we can get:

[0051]

[0052]

[0053] The communication of the system adopts event-triggered control. Event-triggered control is to design a trigger function for the system. When the state of the system meets the conditions of the trigger function, the system adjusts the multi-unmanned autonomous underwater robot system through sensors and controllers.

[0054] The measurement error of the system is set as:

[0055]

[0056] time Indicates the triggering of the event trigger function, the sampling time of the system edge ij; according to the set sampling error, the trigger function of the system is obtained:

[0057]

[0058] The beneficial effects of the present invention are:

[0059] Cooperative control of autonomous underwater vehicles (AUVs) is becoming increasingly important in marine exploration and underwater operations. One of the important issues is defending against malicious network attacks in multi-node networks. DoS attacks, as a common network attack, are easy to initiate and have poor communication destruction effects. The effect of the present invention is to enable a multi-underwater autonomous robot system to achieve the goal of cooperative control while encountering asynchronous DoS attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 A communication topology diagram of multiple underwater autonomous robots in an embodiment of the present invention;

[0061] Figure 2 A schematic diagram of an asynchronous DoS attack suffered by a system in an embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram of an asynchronous DoS attack sequence in an embodiment of the present invention;

[0063] Figure 4 Schematic diagram of coordinated position control in three directions of X, Y, and Z in an embodiment of the present invention;

[0064] Figure 5 Schematic diagram of controller input in three directions of X, Y, and Z in an embodiment of the present invention;

[0065] Figure 6 Schematic diagram of the triggering time of each communication edge in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0067] Example

[0068] A safe cooperative control method for a multi-autonomous underwater robot system under asynchronous DoS attacks. This embodiment first gives a kinematic model and a dynamic model of a fully driven underwater robot, and then gives a problem statement of cooperative control of the multi-autonomous underwater robots; specifically includes:

[0069] A. AUV model:

[0070] Assume η i =[x i ,y i ,z i ] T is the position vector in the inertial reference coordinate system; Θ i =[θ i ,φ i ,ψ i ] T is the direction vector in the inertial reference coordinate system; ν i =[u i ,q i ,w i ] T is the linear velocity in the inertial reference frame;

[0071] The origin of the Earth-fixed coordinate system is O E Choose any point on the sea level, X E The Y axis points to due north. E The axis points due east, Z E Axis perpendicular to plane O E X E Y E Points to the surface of the Earth; the origin of the inertial reference coordinate system is O b Select the center of mass of the AUV, X b The Y axis points to the bow direction along the centerline of the AUV. b The axis is perpendicular to the centerline of the AUV and points to the starboard side. b Axis perpendicular to plane O b X b Y b Point to the bottom of the AUV

[0072] Among them, x i ,y i ,z i They are respectively represented as the surge position, sway position, and heave position of the i-th autonomous underwater robot in the inertial reference coordinate system; u i ,q i ,w i They are respectively expressed as the surge velocity, sway velocity, and heave velocity of the AUV in the body coordinate system;

[0073] The kinematic model of the autonomous underwater robot is expressed as:

[0074]

[0075] in is the derivative of the position vector with respect to time. i is the motion transformation matrix of the system, which is related to the linear velocity vector v i The product of can reflect the time derivative of the motion displacement of the i-th AUV.

[0076]

[0077] J i (Θ i ) is given by the posture vector Θ i =[θ i ,φ i ,ψ i ] is used to convert the linear velocity v and the position vector η i The following formula is used to describe the relationship between the system input and the AUV motion dynamics:

[0078]

[0079]

[0080] C i are the Coriolis matrix and centripetal force matrix of the ith AUV.

[0081]

[0082]

[0083]

[0084] Among them, M i is the inertia matrix, D i is the hydrodynamic drag matrix, g i is the vector of the restoring force, τ i It is the input of the system. Based on these variables, the relationship between the kinematics of the AUV system and the system input is described.

[0085] B. Graph Theory:

[0086] In the autonomous underwater robot collaborative control method, the topological communication of the multi-AUV system can be represented by a directed graph, and the relevant graph theory is as follows:

[0087] Assume that the system consisting of five AUVs can be represented by a graph G(V,E,A), where V is the node set of the system, represents the set of communication edges of the system, A=[a ij ]∈R N×NRepresents the adjacency matrix of the topological graph G. If AUV i Can receive neighboring AUV j information, the corresponding ij =1, otherwise a ij = 0, the communication topology of this embodiment is directed, so the fact that i can receive j's message does not mean that j can definitely receive i's message. In the system designed in this embodiment, the neighbor j that can send a message to i is called an inner neighbor j, and i is correspondingly called an outer neighbor of j. The graph structure of the system is strongly connected, and the Laplace matrix L = DA, and its structure can be expressed as:

[0088]

[0089] C. Control objectives:

[0090] Denial of service attack (DoS) is a common malicious network attack against network communication systems. The attacker blocks the communication channel by sending a large amount of useless information to the system, interrupting the communication between the nodes of the system and making it impossible to obtain the location, speed and other information of each node. This type of attack often causes multi-node system disorder, such as collisions between multiple drones, multiple robots, and multiple unmanned vehicles. It is easy to initiate and has a great impact, so it is a malicious attack that multi-node systems often suffer.

[0091] Different from the common saturation DoS attack, this embodiment studies the asynchronous denial of service attack. The attack model is divided into different time periods, and different channels are subjected to different attacks. Compared with the common saturation DoS attack, such a hypothetical attack model is more difficult to predict and the attack mode is more diverse. The system designed for this type of attack has stronger robustness. The following introduces the model of asynchronous DoS attack that the system may suffer.

[0092] When the multi-AUV system is attacked by asynchronous DoS, the attacked channel will be blocked. The topological relationship of the multi-AUV system in this embodiment is a connected directed graph. Because the DoS attack will destroy the connectivity of the system, the control target cannot be achieved. Here, a DoS attack model is given, assuming that each side of the multi-AUV system has an independent communication channel.

[0093] First, we make an assumption about the duration of the DoS attack. The attack model can be expressed as:

[0094]

[0095] in and They are all constants greater than 0, used to describe the duration of the communication channel being attacked by DoS.

[0096] The frequency and number of DoS attacks on edge ij can be described as:

[0097]

[0098] Where n ij (t0,t) represents the number of times edge ij is attacked by DoS in the time period (t0,t), and f ij (t0,t) represents the frequency of DoS attacks.

[0099] Since it takes a short time for edge ij to recover communication after receiving DoS attack, a shorter time interval is defined here. Used to describe the duration of a system being affected by a DoS attack:

[0100]

[0101] The above assumptions about the DoS attacks that the system may suffer are based on the characteristics of DoS attacks, which are easy to initiate, limited energy, and limited frequency, and are consistent with the characteristics of DoS attacks.

[0102] First, the properties of AUV are analyzed based on its kinematic model:

[0103] Property (1): There exists a finite constant such that λ min <λ max <∞,λ min I n×n ≤M i ≤λ max I n×n ;

[0104] Property (2): There exists a matrix It has oblique symmetry;

[0105] Property (3): k i ,k c >0,K d >0,k g >0,||C i (v i )‖≤k c ‖v i ‖,‖D i (v i )||≤k d ‖v i ‖,‖g i ||≤k g ;

[0106] Assumption (1): The linear velocity and its derivatives of the AUV system are bounded.

[0107] The coordinated control objectives that need to be achieved when the multi-AUV system is subjected to asynchronous DoS attacks are:

[0108]

[0109] The multi-autonomous unmanned submersible system achieves collaborative control while being attacked by DoS. In order to facilitate the design of the controller, necessary auxiliary variables are designed:

[0110]

[0111]

[0112] It means that during this period, edge ij is in the DoS sleep period; is the time period when edge ij is attacked by DoS, Indicates the last state information transmitted by the AUV before being attacked by DoS. Indicates the current location status information during the DoS sleep period. Indicates that the i-th AUV is at the triggering time The uploaded location information. The following formula can be obtained from the designed auxiliary variables:

[0113] θ i =v i -s i

[0114]

[0115]

[0116] To achieve the cooperative control goal, the controller is set as follows:

[0117] τ i =-k i s i +B i

[0118] Through the designed auxiliary variables and the properties of the system, we can get:

[0119]

[0120]

[0121] In order to save communication resources in the system to cope with the complex marine environment and resist DoS attacks, the system's communication adopts event-triggered control.

[0122] Event-triggered control is to design a trigger function for the system. When the state of the system meets the conditions of the trigger function, the system adjusts the multi-unmanned autonomous robot system through sensors, controllers, etc.

[0123] The measurement error of the system is set as:

[0124]

[0125] time It represents the sampling time of the system edge ij when the event trigger function is triggered. According to the set measurement error, the trigger function of the system is obtained:

[0126]

[0127]

[0128]

[0129]

[0130] Obviously, the trigger rate of the system is different when the system is under DoS attack than when it is idle. This design is to improve the robustness of the system by enabling the controller to be controlled even when the system is under DoS attack.

[0131] In the above formula, q, ε ij are all numbers greater than 0. ij Updated by:

[0132]

[0133]

[0134]

[0135]

[0136] The Lyapunov function is used to analyze the stability of the system. Taking the derivative of V1 we get:

[0137]

[0138] It can be obtained that the Lyapunov function is convergent, and according to the Cauchy theorem:

[0139]

[0140] You can get i , are all bounded, and through Barbalaat's lemma and its corollary we can get: Next, we use the Lyapunov function Define the matrix O as: O = LA T +D out , where D out is the out-degree matrix of the system. Obviously, the matrix O is a symmetric matrix. Taking the derivative along time we get:

[0141]

[0142] According to the auxiliary variables set by the system, the measurement error, so the time derivative of the position can be written in this form:

[0143]

[0144] Taking the derivative of the Lyapunov function V2, we get:

[0145]

[0146]

[0147] It can be seen that during the dormant period of DoS attack, the Lyapunov function converges exponentially. Next, it is proved that the system will not have Zeno behavior under the framework of dual-terminal event trigger control. Since there is a fixed trigger interval when under DoS attack, only the dormant period of DoS attack is analyzed here.

[0148] Since the time derivative of the system velocity must have upper and lower bounds, the following equation holds:

[0149]

[0150] According to the designed trigger function, we can get:

[0151]

[0152]

[0153] because get The system will not exhibit Zeno behavior.

[0154] Now consider that the DoS attack satisfies the following conditions, and the system is stable under asynchronous DoS attack.

[0155]

[0156] After the system is attacked by DoS, the derivative of the Lyapunov function is as follows:

[0157]

[0158]

[0159]

[0160] Combine the DoS idle time and the DoS attack launch time to analyze the Lyapunov function:

[0161]

[0162] From the above formula, we can see that the DoS network attack suffered by the system meets The system can have strong robustness when subjected to DoS attacks and achieve the goal of collaborative control.

[0163] The following is a further explanation of this embodiment through simulation: The topological relationship of the autonomous underwater robot is as follows: Figure 1 As shown, the DoS attack is shown as follows Figure 2 As shown; the gain k of the designed controller i Set to 15, N m 4 =1000,

[0164] Assume that there are 5 AUVs in the system, and the initial position ω ij (0)=10.

[0165] To facilitate the adjustment of the trigger frequency, ij The parameter is set to 0.005. The DoS attack sequence encountered by the system has been demonstrated after the attack to achieve the collaborative control goal. Figure 3-Figure 6 shown.

[0166] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A safe collaborative control method for a multi-autonomous underwater robot system under asynchronous DoS attack, characterized in that: The following steps are involved: Step 1: Establish the kinematic model and dynamic model of the fully-driven multi-autonomous underwater robot system; Step 2: Assuming that there are N autonomous underwater robots AUV, the communication between the autonomous underwater robots AUV is represented by a communication graph, so as to establish the topological communication of the N autonomous underwater robots AUV, and construct the collaborative control target of the N autonomous underwater robots AUV according to the topological relationship; Step 3: Analyze the asynchronous denial of service (DoS) attacks that the multi-autonomous underwater robot system may suffer, and design a controller combined with the trigger rate so that the multi-autonomous underwater robot system can still achieve the system control goal under the corresponding network attack; The step 1 is specifically as follows: set up is the position vector in the inertial reference coordinate system; is the direction vector in the inertial reference coordinate system; is the linear velocity in the inertial reference frame; The origin of the Earth-fixed coordinate system is O E Choose any point on the sea level, X E The Y axis points to due north. E The axis points due east, Z E Axis perpendicular to plane O E X E Y E Points to the surface of the Earth; the origin of the inertial reference coordinate system is O b Select the center of mass of the AUV, X b The Y axis points to the bow direction along the centerline of the AUV. b The axis is perpendicular to the centerline of the AUV and points to the starboard side. b Axis perpendicular to plane O b X b Y b Point to the bottom of the AUV; Among them, x i ,y i ,z i They are respectively represented as the surge position, sway position, and heave position of the i-th autonomous underwater robot in the inertial reference coordinate system; u i ,q i ,w i They are respectively expressed as the surge velocity, sway velocity, and heave velocity of the AUV in the body coordinate system; The kinematic model of the autonomous underwater robot is expressed as: in is the derivative of the position vector with respect to time; J i is the motion transformation matrix of the system, which is related to the linear velocity vector v i The product of is used to reflect the time derivative of the motion displacement of the i-th AUV; J i (Θ i ) is given by the direction vector Θ i =[θ i ,φ i ,ψ i ] is used to convert the linear velocity v i With the position vector η i Derivative relationships; The following equation is used to describe the relationship between system input and AUV motion dynamics: in, C i are the Coriolis matrix and centripetal force matrix of the ith AUV, M i is the inertia matrix, D i is the hydrodynamic drag matrix, g i is the vector of the restoring force, τ i is the input to the system; In step 2, the established topological communication of N autonomous underwater robots AUV is represented by a directed graph, and the relevant graph theory is as follows: Assume that the system consisting of N AUVs is represented by a graph G(V,E,A), where V is the node set of the system, represents the set of communication edges of the system, A=[a ij ]∈R N×N Represents the adjacency matrix of the topological graph G; if AUV i can receive information from its neighbor AUVj, the corresponding a ij =1, otherwise a ij = 0, the neighbor j that can send a message to i becomes an inner neighbor j, and correspondingly i is called an outer neighbor of j; the Laplace matrix L = DA, and its structure can be expressed as: In step 2, the collaborative control objectives of N autonomous underwater robots AUV are constructed according to the topological relationship as follows: First, we make an assumption about the duration of the DoS attack. The attack model is expressed as: in and They are all constants greater than 0, used to describe the duration of the communication channel ij being subjected to DoS attack; The frequency and number of DoS attacks on edge ij are described as follows: Where n ij (t0,t) represents the number of times edge ij receives DoS attacks in the time period (t0,t), f ij (t0,t) represents the frequency of DoS attack; Defining time intervals Used to describe the duration of a system being affected by a DoS attack: According to the AUV kinematic model, its properties include: Property (1): There exists a finite constant such that λ min <λ max <∞,λ min I n×n ≤M i ≤λ max I n×n ; Property (2): There exists a matrix It has oblique symmetry; Properties (3): Assuming that the linear velocity and its derivatives of the AUV system are bounded, The coordinated control objectives that need to be achieved when the multi-AUV system is subjected to asynchronous DoS attacks are: The step 3 is as follows: Design auxiliary variables for the controller: It means that during this period, edge ij is in the DoS sleep period; is the time period when edge ij is attacked by DoS. Indicates the last state information transmitted by the AUV before being attacked by DoS. Indicates the current location status information during the DoS sleep period. Indicates the i-th AUV at the triggering time The uploaded location information; the following formula can be obtained from the designed auxiliary variables: i i =v i -s i To achieve the cooperative control goal, the controller is set as follows: t i =-k i s i +B i Through the designed auxiliary variables and the properties of the system, we can get: The communication of the system adopts event-triggered control. Event-triggered control is to design a trigger function for the system. When the state of the system meets the conditions of the trigger function, the system adjusts the multi-autonomous underwater robot system through sensors and controllers. The measurement error of the system is set as: time Indicates the triggering of the event trigger function, the sampling time of the system edge ij; according to the set measurement error, the trigger function of the system is obtained: By combining the controller designed above with the trigger rate method, the multi-underwater autonomous robot system can achieve the goal of collaborative control under asynchronous DoS attacks.

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