A preset time enclosure control method for privacy protection under event triggering mechanism

Abstract

The present invention discloses a privacy-preserving preset time enclosure control method under an event-triggered mechanism. First, a multi-robot system comprising multiple leaders and multiple followers is established, and the preset time enclosure control problem under privacy protection constraints is clarified; then, a privacy protector based on an output mask function is designed; further, a preset time privacy protection enclosure controller is constructed, so that all follower robots can enter the convex hull of the leader robots while protecting their own privacy; then, an event trigger function without Zeno behavior is constructed, and a privacy protection preset time enclosure controller based on an event trigger mechanism is designed. The present invention combines the event trigger mechanism with the finite time theory to improve the convergence performance of the privacy protection enclosure control of the multi-robot system and reduce the resource consumption of the algorithm calculation. It further expands the application scenarios of the algorithm by integrating privacy protection, communication bandwidth constraints, and convergence speed.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-robot system collaborative control, and in particular to a preset time enclosure control method for privacy protection under an event triggering mechanism. Background Art

[0002] Multi-robot systems have gained significant attention in various fields due to their wide range of applications, including robotics, self-driving cars, and distributed sensor networks. Cooperative control of multi-robot systems involves designing strategies that enable robots to work together effectively to achieve a common goal. A prominent method in cooperative control is encirclement control, which aims to ensure that one group of robots (follower robots) remains within a specified area or adheres to a specific trajectory, while another group of robots (leader robots) guides their behavior. Encirclement control is particularly important in situations where strict adherence to spatial or operational constraints is required. For example, in formation flying scenarios, encirclement control can ensure that a group of drones maintains a specific formation while another group of drones guides their collective motion. With the further development of technology, although scholars have designed a series of encirclement control methods for multi-robot systems, the existing control strategies still have the following problems:

[0003] First, existing multi-robot pre-timed enclosure control strategies lack privacy protection. However, privacy protection is crucial in enclosure control, and protecting the confidentiality of robot information is crucial. While existing privacy protection methods such as state decomposition, differential privacy, and additive noise have been widely studied, the key issue is how to design a more effective and simple privacy protection mechanism.

[0004] Second, existing multi-robot control strategies for pre-set time encirclement rely on real-time information transmission. However, due to limited communication bandwidth and other factors, real-time information exchange between individuals in a multi-robot system is impossible. Therefore, it is necessary to further design encirclement control strategies based on event-triggered mechanisms to reduce the requirements for communication resources. Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a preset time enclosure control method for privacy protection under an event trigger mechanism. The present invention combines the event trigger mechanism with the finite time theory to improve the convergence performance of the privacy protection enclosure control of the multi-robot system and reduce the resource consumption of the algorithm calculation. It integrates privacy protection, communication bandwidth constraints and convergence speed, and further expands the application scenarios of the algorithm.

[0006] The object of the present invention is achieved through the following technical solution: a preset time enclosure control method for privacy protection under an event trigger mechanism, comprising the following steps:

[0007] S1. Establish a dynamic model of a multi-robot system with multiple leaders and multiple followers, and then clarify the preset time enclosure control problem under privacy protection; including the following sub-steps:

[0008] S11. Construct the communication interaction topology between each robot in the multi-robot system; the communication topology between robots is shown in Figure 1. Indicates that ε and are node sets, edge sets, and adjacency matrices respectively; the system consists of m+n robots, where n is the number of follower robots and m is the number of leader robots. Leader and follower robots are classified into sets and The node set of the entire multi-robot system is The adjacency matrix is ​​represented as If there is an edge from node j to node i in the set ε, then element a ij is positive, otherwise zero; the Laplace matrix of the multi-robot system Defined as D represents the in-degree matrix, which has elements d on the diagonal. i A diagonal matrix, where d i is the sum of the elements in the i-th row of the adjacency matrix, calculated as

[0009] Based on the above definition, the Laplace matrix is ​​constructed as follows:

[0010]

[0011] where the follower-specific sub-Laplacian matrix is ​​expressed as The sub-Laplacian matrix of the interaction between the leader and the follower is expressed as When the index is the same, The elements in are represented as [l ij ], l ij Equal to the node set The adjacency matrix entries a for all p in ip When the index is different, l ij is the corresponding adjacent entry a ij The opposite of ; mathematically expressed as:

[0012]

[0013] S12. Construct dynamic models of follower robots and leader robots;

[0014] The dynamic model of the follower is:

[0015]

[0016] where x i (t) and u i (t) represent the position and control input of the i-th follower robot, is x i The first derivative of (t);

[0017] The leader's dynamic model is represented by the following equation:

[0018]

[0019] Where x i (t) represents the position of the i-th leader robot;

[0020] S13. The implementation of preset time encirclement control requires that the position state of the follower robot converges to the convex hull formed by the leader robot within the preset time T. Specifically, for any given initial condition, the following set of equations must be satisfied:

[0021]

[0022] in If the above conditions are met, the designed controller can achieve preset time enclosure control of the multi-robot system;

[0023] S2. Design a privacy-preserving information masker to ensure the security of information transmission and interaction in multi-robot systems;

[0024] S3. Design a preset time encirclement controller so that all follower robots can enter the convex hull formed by the leader robots within a preset time T;

[0025] S4. Construct an event-triggered function without Zeno behavior and design a privacy-preserving preset time enclosure controller under the event-triggered mechanism;

[0026] S5. Complete the encirclement control of the multi-robot system.

[0027] The present invention provides a privacy-preserving, preset-time enclosure control method under an event-triggered mechanism. By combining the event-triggered mechanism with finite-time theory, the method improves the convergence performance of privacy-preserving enclosure control for multi-robot systems and reduces the resource consumption of algorithm calculations. By integrating privacy protection, communication bandwidth constraints, and convergence speed, the algorithm's application scenarios are further expanded. Compared to existing technologies, the present invention is innovative in the following three aspects:

[0028] (1) A novel event-triggered, preset-time enclosure control scheme was developed to optimize network efficiency while ensuring robust enclosure performance within a preset time range. By employing event-triggered control, this scheme significantly reduces unnecessary data transmission, ensuring that robots communicate only when necessary. This approach effectively balances communication efficiency and system performance.

[0029] (2) The proposed control scheme guarantees convergence within a preset time, offering significant advantages over finite-time and fixed-time methods. Unlike these traditional methods, where convergence time is often affected by initial conditions and system parameters, preset-time control ensures that the desired state is reached within a preset time, thereby enhancing system predictability and reliability.

[0030] (3) Furthermore, we design a privacy-preserving encirclement control scheme that protects the confidentiality of robot information by masking the robot's output while maintaining accurate control. Compared to alternative privacy-preserving approaches such as differential privacy or state decomposition, this scheme provides a simpler and more efficient solution. It ensures privacy and communication efficiency without compromising overall system performance, making it particularly suitable for applications with strict privacy and bandwidth requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Flowchart of the preset time enclosure control method for privacy protection under the event trigger mechanism of the present invention;

[0032] Figure 2 The communication topology diagram of twelve robots;

[0033] Figure 3 Control input for the follower robot;

[0034] Figure 4 is the trajectory of the state measurement error and boundary threshold;

[0035] Figure 5 are the trajectories of all robots in the two-dimensional plane. DETAILED DESCRIPTION

[0036] This paper studies a privacy-preserving, preset-time enclosure control method under an event-triggered mechanism. A decentralized finite-time transformation function is designed as a privacy mask, and the event-triggered mechanism and predefined-time theory are combined to enhance the performance of multi-robot systems. Furthermore, a enclosure controller is proposed that comprehensively considers privacy protection, communication bandwidth constraints, and convergence speed. This scheme combines privacy protection with an event-triggered mechanism to optimize network efficiency by minimizing unnecessary data transmission, while ensuring robust enclosure control within a preset time range. The proposed control scheme ensures the confidentiality of robot information through output masks while maintaining privacy and control accuracy. Furthermore, compared with traditional finite-time and fixed-time control methods, it offers significant advantages by ensuring convergence to the desired state within a preset time, regardless of initial conditions. This paper focuses on the issues of privacy protection, communication bandwidth constraints, and convergence speed in multi-robot systems, designing an effective enclosure controller that improves the performance of multi-robot systems.

[0037] The technical solution of the present invention is further described below with reference to the accompanying drawings.

[0038] like Figure 1 As shown, a preset time enclosure control method for privacy protection under an event trigger mechanism of the present invention includes the following steps:

[0039] S1. Establish a dynamic model of a multi-robot system with multiple leaders and multiple followers, and then clarify the preset time enclosure control problem under privacy protection; including the following sub-steps:

[0040] S11. Construct the communication interaction topology between each robot in the multi-robot system; the communication topology between robots is shown in Figure 1. Indicates that ε and are node sets, edge sets, and adjacency matrices respectively; the system consists of m+n robots, where n is the number of follower robots and m is the number of leader robots. Leader and follower robots are classified into sets and The node set of the entire multi-robot system is According to the definition of node set, the adjacency matrix is ​​expressed as represents the field of real numbers. If there is an edge from node j to node i in the set ε, then element a ij is positive (the specific value can be set by the user, usually set to 1), otherwise it is zero; the Laplace matrix of the multi-robot system Defined as D represents the in-degree matrix, which has elements d on the diagonal. i A diagonal matrix, where di is the sum of the elements in the i-th row of the adjacency matrix, calculated as

[0041] Based on the above definition, the Laplace matrix is ​​constructed as follows:

[0042]

[0043] where the follower-specific sub-Laplacian matrix is ​​expressed as The sub-Laplacian matrix of the interaction between the leader and the follower is expressed as When the index is the same, The elements in are represented as [l ij ], l ij Equal to the node set The adjacency matrix entries a for all p in ip When the index is different, l ij is the corresponding adjacent entry a ij The opposite of ; mathematically expressed as:

[0044]

[0045] S12. Construct dynamic models of follower robots and leader robots;

[0046] The dynamic model of the follower is:

[0047]

[0048] where x i (t) and u i (t) represent the position and control input of the i-th follower robot, is x i The first derivative of (t); The robots in this embodiment refer to ground mobile robots (ground unmanned vehicles) used for collaborative logistics. The leader is an unmanned vehicle carrying high-value sensors, and the followers are unmanned vehicles without high-value sensors. The leader can perceive the external environment and thus determine the safe range. The followers enter the safe range to ensure safe transportation. Position x i (t)=(x i ,y i ) can be measured by the position sensor and inertial measurement unit carried by the ground mobile robot itself, and the control input u i (t) is the speed set for the robot.

[0049] The leader's dynamic model is represented by the following equation:

[0050]

[0051] Where x i (t) represents the position of the i-th leader robot;

[0052] S13. Consider a single-integrator robot system consisting of m leader robots and n follower robots. The implementation of preset time enclosure control requires that the position states of the follower robots converge to the convex hull formed by the leader robot within a preset time T. Specifically, for any given initial condition, the following set of equations must be satisfied:

[0053]

[0054] in If the above conditions are met, the designed controller can achieve preset time enclosure control of the multi-robot system.

[0055] S2. Design a privacy-preserving information masker to ensure the security of information transmission and interaction in the multi-robot system; this includes the following sub-steps:

[0056] S21. During the information exchange process between robots, independent mask functions are designed to protect the security of the robot's initial state information; the mask function is:

[0057]

[0058] According to the privacy protection requirements of the mask function, robot i The information broadcast to neighbors is designed to be:

[0059]

[0060] where Ω i Satisfies the following equation:

[0061]

[0062] in, Each robot has its own unique encoding key, denoted as m i ={a i ,b i ,c i}, the encoding key of each robot is not disclosed to other robots.

[0063] S3. Design a preset time encirclement controller so that all follower robots can enter the convex hull formed by the leader robots within a preset time T; including the following sub-steps:

[0064] S31. Based on the mask function and the mask information obtained from the adjacent robots, the preset time encirclement controller of the i-th robot is expressed as follows:

[0065]

[0066] Where ρ>0 represents the control gain; δ is a positive control parameter, δ>0; μ represents the time-varying proportional function, which is in the form of:

[0067]

[0068] Here, the real number h satisfies the condition h>2.

[0069] S4. Construct an event-triggered function without Zeno behavior and design a privacy-preserving preset time enclosure controller under the event-triggered mechanism; this includes the following sub-steps:

[0070] S41. When the event trigger mechanism is used, it is assumed that each robot has the ability to actively monitor its status information in real time. In addition, the robot is designed to perform relevant status updates only when the designed event trigger conditions are met. In order to ensure synchronization between all robots, the trigger sequence is constructed as {t1, t2, ..., t k This sequential arrangement ensures that all robots update their control rates simultaneously at the same trigger time; therefore, the controller (9) can be reformulated as:

[0071]

[0072] S42. For each robot, the state measurement error between the trigger and the true state is:

[0073]

[0074] Substituting the state measurement error and control law into the robot's dynamic model, we obtain:

[0075]

[0076] in Its corresponding compact form is expressed as:

[0077]

[0078] in: They are follower transmission information, leader transmission information, leader state measurement error, and follower state measurement error respectively; Indicates taking x i The i-th to n+m-th columns of (t) are arranged to form a vector; in addition, let

[0079] S43. Further, a closed-loop error system is constructed as follows:

[0080]

[0081] in

[0082]

[0083] e m (t) indicates and A collection of It means that the m1,…,m1…m (m+n)-1 Set the elements to 0, Indicates that the m1,…,m1…m (m+n)-1 elements are set to 0; according to the setting of the privacy protection function, each robot will converge to the true value in different time periods. After converging to the true value, the corresponding a i and b i To become 0, the elements corresponding to vectors A and B need to be modified to 0 in turn, and iterate step by step, so that the output of the mask function is consistent with the actual state.

[0084] S44. Design the event triggering conditions of the multi-robot system and complete the preset time privacy protection encirclement control under the event triggering mechanism, that is,

[0085]

[0086] in, is the Laplace matrix The second smallest eigenvalue of ; parameter ε∈(0,1); inf() represents the lower bound of a quantity; |||| represents the two norm; Indicates that it includes tracking error. When a trigger event occurs, all robots discard their previous states and continue to sample their current states to update their control inputs; they then send the newly sampled states to their neighboring robots; during the event trigger interval, the robot's control input remains unchanged until the next event trigger condition is met.

[0087] S5, completing the encirclement control of the multi-robot system; including the following sub-steps:

[0088] S51. Under the event triggering condition (17) and the control input (11), the preset time privacy protection enclosure control of the multi-robot system described by Figure G can be realized.

[0089] S52. Privacy performance analysis of preset time enclosure control for multi-robot systems. Consider a scenario where the dynamics f(·) of all robots are public and each robot can access the hidden output states of its neighboring robots. The real state xi (t) and the encoding key {a i ,b i ,c i} is considered as the private information of each robot. For an honest but curious robot, the accessible information includes the unsigned graph G, the collective states of the neighboring robots, and the hidden states of their neighboring robots. After applying a finite time-varying transformation to hide the initial state of robot i, the hidden output is With the true initial value x i (t) has no similarity. Therefore, any set of information obtained by the honest but curious robot is futile in determining the true initial state of robot i. Moreover, the integration of the masked output trajectory and the robot dynamics f(·) is not sufficient to recover x i (0), so the robot’s initial conditions are undecipherable from the known information. Importantly, even an external eavesdropper cannot obtain the true initial state, as demonstrated by the process mentioned above. Therefore, it is clear that the integrity of the initial state remains elusive to all parties involved, which confirms the claim that it is unattainable by external eavesdroppers.

[0090] S53. Based on the above steps, the preset time enclosure control design of privacy protection under the event trigger mechanism is completed.

[0091] The multi-agent communication topology diagram in this embodiment is as follows Figure 2 As shown in Figure 1, there are 12 independent robots, including 6 follower robots and 6 leader robots. Each robot can be regarded as a communication node. The initial state of the system is:

[0092] x 1 (0) = [-10, 0, 10, 10, 0, -10, -30, -5, 20, 30, 5, -15] T ,

[0093] x 2 (0) = [5,5,5,-5,-5,-5,5,20,25,-10,-15,-20] T .

[0094] Furthermore, the parameter ε is selected as 0.5, and the preset time is T=1.5s.

[0095] The encoding key selection is:

[0096] A=[-5,-9,-5,8,-3,6,-4,5,6,-4,5,-3] T ,

[0097] B=[2,4,3,-4,1,-3,2,-1,-3,2,-1,1] T,

[0098] C=[3,4,1,-3,2,-2,1,-3,-2,1,-3,2] T

[0099] The numerical simulation results are as follows Figure 3-5 shown. Figure 3 The control input trajectories of all follower robots are shown, where the sudden changes in the trajectories are attributed to the event-triggered mechanism. Figure 4 The trajectory of the state measurement error and boundary threshold shows that when the event triggering conditions are met and the designed boundary threshold is exceeded, the robot state is sampled and updated. Figure 5 are the trajectories of all robots in the two-dimensional plane. The square markers represent the follower robots and the circular markers represent the leader robot. The leader robot forms a rectangular convex hull. Figure 5 We demonstrate that all follower robots successfully move from their initial positions into the convex hull formed by a fixed leader, achieving privacy-preserving preset-time enclosure control under an event-triggered mechanism for a multi-robot system.

[0100] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A preset time enclosure control method for privacy protection under an event trigger mechanism, characterized in that: The following steps are involved: S1. Establish a dynamic model of a multi-robot system with multiple leaders and multiple followers, and then clarify the preset time enclosure control problem under privacy protection; The following sub-steps are included: S11. Construct the communication interaction topology between each robot in the multi-robot system; the communication topology between robots is shown in Figure 1. Indicates that ε and are node sets, edge sets, and adjacency matrices respectively; the system consists of m+n robots, where n is the number of follower robots and m is the number of leader robots. Leader and follower robots are classified into sets and The node set of the entire multi-robot system is The adjacency matrix is ​​represented as If there is an edge from node j to node i in the set ε, then element a ij is positive, otherwise zero; the Laplace matrix of the multi-robot system Defined as D represents the in-degree matrix, which has elements d on the diagonal. i A diagonal matrix, where d i is the sum of the elements in the i-th row of the adjacency matrix, calculated as Based on the above definition, the Laplace matrix is ​​constructed as follows: where the follower-specific sub-Laplacian matrix is ​​expressed as The sub-Laplacian matrix of the interaction between the leader and the follower is expressed as When the index is the same, The elements in are represented as [l ij ], l ij Equal to the node set The adjacency matrix entries a for all p in ip When the index is different, l ij is the corresponding adjacent entry a ij The opposite of ; mathematically expressed as: S12. Construct dynamic models of follower robots and leader robots; The dynamic model of the follower is: where x i (t) and u i (t) represent the position and control input of the i-th follower robot, is x i The first derivative of (t); The leader's dynamic model is represented by the following equation: Where x i (t) represents the position of the i-th leader robot; S13. The implementation of preset time encirclement control requires that the position state of the follower robot converges to the convex hull formed by the leader robot within the preset time T. Specifically, for any given initial condition, the following set of equations must be satisfied: in If the above conditions are met, the designed controller can achieve preset time enclosure control of the multi-robot system; S2. Design a privacy-preserving information masker to ensure the security of information transmission and interaction in multi-robot systems; S3. Design a preset time encirclement controller so that all follower robots can enter the convex hull formed by the leader robots within a preset time T; S4. Construct an event-triggered function without Zeno behavior and design a privacy-preserving preset time enclosure controller under the event-triggered mechanism; S5. Complete the encirclement control of the multi-robot system.

2. The method for controlling the preset time enclosure of privacy protection under an event triggering mechanism according to claim 1, characterized in that: The step S2 includes the following sub-steps: S21. During the information exchange process between robots, independent mask functions are designed to protect the security of the robot's initial state information; the mask function is: According to the privacy protection requirements of the mask function, the information broadcast by robot i to its neighbors is designed as follows: where Ω i Satisfies the following equation: in, Each robot has its own unique encoding key, denoted as m i ={a i ,b i ,c i }, the encoding key of each robot is not disclosed to other robots.

3. The method for controlling the preset time enclosure of privacy protection under an event triggering mechanism according to claim 2, characterized in that: The step S3 includes the following sub-steps: S31. Based on the mask function and the mask information obtained from the adjacent robots, the preset time encirclement controller of the i-th robot is expressed as follows: Where ρ>0 represents the control gain; δ is a positive control parameter; μ represents the time-varying proportional function, which is in the form of: Here, the real number h satisfies the condition h>2.

4. The method for controlling the preset time enclosure of privacy protection under an event triggering mechanism according to claim 3, characterized in that: The step S4 includes the following sub-steps: S41, construct a trigger sequence {t1, t2, ..., t k }, the controller (9) is reformulated as: S42. For each robot, the state measurement error between the trigger and the true state is: Substituting the state measurement error and control law into the robot's dynamic model, we obtain: in Its corresponding compact form is expressed as: are the follower transmission information, the leader transmission information, the leader state measurement error, and the follower state measurement error respectively; let S43. Further, a closed-loop error system is constructed as follows: in e m (t) indicates and A collection of It means that the m1,…,m1…m (m+n)-1 Set the elements to 0, Indicates that the m1,…,m1…m (m+n)-1 Set the elements to 0; S44. Design the event triggering conditions of the multi-robot system and complete the preset time privacy protection encirclement control under the event triggering mechanism, that is, in, is the Laplace matrix The second smallest eigenvalue of ; parameter ε∈(0,1); |||| represents the two norm; Indicates that tracking error is included; When a trigger event occurs, all robots discard their previous states and continue to sample their current states to update their control inputs; they then send the newly sampled states to their neighboring robots; during the event trigger interval, the robot's control input remains unchanged until the next event trigger condition is met.

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