Preset time encircling control method for privacy protection under event trigger mechanism

Abstract

The invention discloses a preset time encircling control method for privacy protection under an event trigger mechanism. The method comprises the following steps: firstly, establishing a multi-robot system comprising a plurality of leaders and a plurality of followers, and defining a preset time encircling control problem under privacy protection constraints; designing a privacy protector based on an output mask function; a preset time privacy protection surrounding controller is further constructed, so that all the follower robots can enter the convex hulls of the leader robots on the premise of protecting the privacy of the follower robots; then, constructing an event trigger function without a sesame behavior, and designing a privacy protection preset time encircling controller based on an event trigger mechanism; according to the method, an event triggering mechanism and a finite time theory are combined, the convergence performance of privacy protection surrounding control of the multi-robot system is improved, resource consumption of algorithm calculation is reduced, privacy protection, communication broadband constraint and convergence speed are integrated, and the application scene of the algorithm is further expanded.

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 great 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 in 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, the existing multi-robot preset time enclosure control strategy does not have privacy protection performance. However, privacy protection is crucial in enclosure control, and protecting the confidentiality of robot information is crucial. Although existing privacy protection methods such as state decomposition, differential privacy, and additive noise have been widely studied, how to design a more effective and simple privacy protection mechanism is more critical.

[0004] Second, the existing multi-robot preset time enclosure control strategy relies on real-time transmission of information. However, due to poor communication factors such as communication bandwidth, real-time information exchange between individuals in the multi-robot system cannot be achieved. Therefore, it is necessary to further design an enclosure control strategy based on an event-triggered mechanism 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 prior art and provide a preset time enclosure control method for privacy protection under an event trigger mechanism. The present invention combines the event trigger mechanism and 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, and comprehensively considers privacy protection, communication bandwidth constraints and convergence speed, further expanding the application scenarios of the algorithm.

[0006] The object of the present invention is to achieve 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 multi-robot system dynamics model including 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 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 d elements 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 Laplacian 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 indexes are the same, The elements in are represented as [l ij ],l ij Equal to the node set The adjacency matrix entries a of 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 the dynamic model of the follower robot and the leader robot;

[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, For x i The first derivative of (t);

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

[0018]

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

[0020] S13. The realization of preset time enclosure 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 needs to 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 beneficial effects of the present invention are: providing a preset time enclosure control method for privacy protection under an event trigger mechanism, combining the event trigger mechanism and the finite time theory, improving the convergence performance of the privacy protection enclosure control of the multi-robot system and reducing the resource consumption of the algorithm calculation, and integrating privacy protection, communication bandwidth constraints and convergence speed, further expanding the application scenarios of the algorithm. Compared with the prior art, the innovation of the present invention is reflected in the following three aspects:

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

[0029] (2) The control scheme proposed in the present invention guarantees convergence within a preset time, which has obvious advantages over finite time and fixed time methods. Unlike these traditional methods whose convergence time is usually affected by initial conditions and system parameters, preset time control ensures that the desired state is reached within a preset time, thereby enhancing the predictability and reliability of the system.

[0030] (3) In addition, the present invention designs a privacy-preserving enclosure control scheme that protects the confidentiality of robot information by masking the robot's output while maintaining accurate control. Compared with alternative privacy-preserving methods 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 It is a flow chart of the preset time enclosure control method for privacy protection under the event trigger mechanism of the present invention;

[0032] Figure 2 This is the communication topology diagram of twelve robots;

[0033] Figure 3 is the 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] The present invention studies a preset time enclosure control method for privacy protection under an event-triggered mechanism. A decentralized finite-time transformation function is designed as a privacy mask, and the event-triggered mechanism and the predefined time theory are combined to enhance the performance of the multi-robot system. Then, a enclosure controller that comprehensively considers privacy protection, communication bandwidth constraints and convergence speed is proposed. The scheme combines privacy protection with the event-triggered mechanism, optimizes network efficiency by minimizing unnecessary data transmission, and ensures robust enclosure control within a preset time range. The proposed control scheme ensures the confidentiality of robot information through the output mask while maintaining privacy and control accuracy. In addition, compared with traditional finite-time and fixed-time control methods, it provides obvious advantages by ensuring convergence to the desired state within a preset time regardless of the initial conditions. The present invention focuses on the issues of privacy protection, communication bandwidth constraints and convergence speed in multi-robot systems, designs an effective enclosure controller, and improves the performance of multi-robot systems.

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

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

[0039] S1. Establish a multi-robot system dynamics model including 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 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 d elements 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 Laplacian 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 indexes are the same, The elements in are represented as [l ij ],l ij Equal to the node set The adjacency matrix entries a of 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 the dynamic model of the follower robot and the leader robot;

[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, For x i The first derivative of (t); The robot in this embodiment refers to a ground mobile robot (ground unmanned vehicle) used for collaborative logistics. The leader is an unmanned vehicle carrying high-value sensors, and the follower is an unmanned vehicle without high-value sensors. The leader can perceive the external environment and 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] In the formula, x i (t) represents the position of the i-th leader robot;

[0052] S13. Considering a single integrator robot system including m leader robots and n follower robots, the realization of preset time enclosure 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 needs to 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; including the following sub-steps:

[0056] S21. In the process of information exchange 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, designing a preset time enclosure controller so that all follower robots can enter the convex hull formed by the leader robots within a preset time T; comprising the following sub-steps:

[0064] S31, based on the mask function and the mask information obtained from the adjacent robots, the preset time enclosure 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 trigger function without Zeno behavior and design a privacy protection preset time enclosure controller under the event trigger mechanism; including the following sub-steps:

[0070] S41. When the event trigger mechanism is adopted, 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 among 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) is 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 get:

[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:

[0080]

[0081] in

[0082]

[0083] e m (t) means and A collection of It means that the m1,…,m1…m (m+n)-1 elements are set to 0, It means 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, 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 enclosure 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 infimum of a quantity; |||| represents the binorm; 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; subsequently, they 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 implemented.

[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 With the true initial value x i (t). 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 condition is 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 an external eavesdropper.

[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, there are 12 independent robots, including 6 follower robots and 6 leader robots, each of which 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 trajectories are attributed to the event-triggered mechanism. Figure 4 The trajectory of the state measurement error and boundary threshold shows that the robot state is sampled and updated when the event triggering condition is met and exceeds the designed boundary threshold. Figure 5 are the trajectories of all robots in the two-dimensional plane, square markers represent follower robots, and circular markers represent leader robots. The leader robot forms a rectangular convex hull. Figure 5 It is demonstrated that all follower robots successfully move from their initial positions into the convex hull formed by a fixed leader, achieving the preset time enclosure control with privacy preservation under the event-triggered mechanism of the 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 should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope 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 multi-robot system dynamics model with multiple leaders and multiple followers, and then clarify the preset time enclosure control problem under privacy protection; It includes the following sub-steps: S11. Construct the communication interaction topology between each robot in the multi-robot system; the communication topology between robots is shown in Figure 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 d elements 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 Laplacian 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 indexes are the same, The elements in are represented as [l ij ],l ij Equal to the node set The adjacency matrix entries a of 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 the dynamic model of the follower robot and the leader robot; 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, For x i The first derivative of (t); The leader's dynamic model is represented by the following equation: In the formula, x i (t) represents the position of the i-th leader robot; S13. The realization of preset time enclosure 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 needs to 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 preset time enclosure control method for privacy protection under an event trigger mechanism according to claim 1 is characterized in that: The step S2 comprises the following sub-steps: S21. In the process of information exchange 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: 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 preset time enclosure control method for privacy protection under an event trigger mechanism according to claim 2 is characterized in that: The step S3 comprises the following sub-steps: S31, based on the mask function and the mask information obtained from the adjacent robots, the preset time enclosure 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 preset time enclosure control method for privacy protection under an event trigger mechanism according to claim 3 is characterized in that: The step S4 comprises the following sub-steps: S41, construct a trigger sequence of {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 get: 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; S43. Further, a closed-loop error system is constructed as: in e m (t) means and A collection of It means that the m1,…,m1…m (m+n)-1 elements are set to 0, It means 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 enclosure control under the event triggering mechanism, that is, in, is the Laplace matrix The second smallest eigenvalue of ; parameter ε∈(0,1); || || represents the bi-norm; Indicates that it contains 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; subsequently, they 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.

Images