Multi-bionic robotic fish system formation control method and device

Abstract

The present application discloses a formation control method and device for a multi-bionic robotic fish system. The method includes: determining the triggering error of any bionic robotic fish at the current moment, and determining the event triggering function value of any bionic robotic fish at the current moment based on the triggering error; when the event triggering function value meets a preset condition, taking the current moment as the triggering moment, and determining the consensus formation control law of any bionic robotic fish at the triggering moment based on the state information of any bionic robotic fish and its corresponding neighboring bionic robotic fish at the triggering moment, as well as the state information of the leader at the triggering moment; and controlling any bionic robotic fish based on the consensus formation control law of any bionic robotic fish at the triggering moment. The method and device provided by the present application can reduce the communication energy consumption between bionic robotic fish and increase the endurance time of each bionic robotic fish.

Description

Technical Field

[0001] The present application relates to the technical field of underwater robot control, and more specifically, to a formation control method and device for a multi-bionic fish system. Background Art

[0002] Through long-term natural evolution, fish have developed extraordinary underwater survival abilities. Relying on excellent locomotor performance, they have well adapted to the underwater environment and evolved into a wide variety of species. Scientists have also tried to find inspiration from various fish to provide reference for the design of underwater vehicles. Bionic fish, from the perspective of bionics, simulate the shape and swimming mode of real fish to obtain better performance than traditional underwater vehicles. For example, they have high maneuverability, high efficiency, high stealth, and good underwater adaptability, and have good application prospects in complex and changeable marine environments.

[0003] However, the limited internal space of bionic fish restricts the selection of the battery capacity and sensors they carry, which also becomes an urgent problem to be solved for further improving the underwater endurance time and underwater control performance of bionic fish. By exploring the highly maneuverable and energy-efficient collective motion behaviors of bird flocks, fish schools, and ant colonies in nature, multi-agent technology has gradually developed and matured and has been widely applied in the field of robotics. Building a multi-agent control system for underwater bionic fish can, to a certain extent, make up for the problems of low sensor accuracy carried by a single bionic fish and limited underwater operation ability. Different agents can efficiently achieve cooperative perception, cooperative motion, and cooperative control through communication, enabling bionic fish to complete complex operation tasks only relying on limited perception ability and locomotor performance. This working mode of information interaction and cooperative cooperation among multi-agents greatly improves the intelligence level of the underwater bionic fish platform and is an important development direction for future intelligent underwater operations of bionic fish.

[0004] During the process of multi-robot systems exploring unknown environments, it is usually necessary to regulate the state information such as the position and speed of some individuals in the system, which is also called the multi-robot system scheduling problem. In the multi-robot system scheduling task, formation control is usually used to complete environmental exploration and monitoring tasks. At this time, individuals occupy certain predetermined positions in the multi-robot system, making the whole system present a certain specific shape from a global perspective, which can not only increase the exploration range but also adapt to different detection environments through simple adjustment.

[0005] Since the body size of fish robots is small and they cannot carry large-scale batteries, communication energy consumption greatly affects the underwater operation endurance time during the underwater formation control process of multi-bionic fish systems.

[0006] Therefore, how to reduce communication energy consumption while ensuring the formation control of multi-bionic robotic fish has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0007] In a first aspect, the present application provides a method for formation control of a multi-bionic robotic fish system, including:

[0008] Perform state observation on the multi-bionic robotic fish system to determine the estimated value of the state information of any bionic robotic fish at the current moment;

[0009] Based on the estimated value of the state information of any bionic robotic fish at the current moment, determine the triggering error of any bionic robotic fish at the current moment, and based on the triggering error, determine the event trigger function value of any bionic robotic fish at the current moment;

[0010] When the event trigger function value meets the preset condition, use the current moment as the trigger moment, and based on the state information of any bionic robotic fish and its corresponding neighboring bionic robotic fish at the trigger moment, and the state information of the leader at the trigger moment, determine the consensus formation control law of any bionic robotic fish at the trigger moment;

[0011] Control any bionic robotic fish based on the consensus formation control law of any bionic robotic fish at the trigger moment.

[0012] In some embodiments, the performing state observation on the multi-bionic robotic fish system to determine the estimated value of the state information of any bionic robotic fish at the current moment includes:

[0013] Perform unscented transformation on the estimated value of the state information of any bionic robotic fish at the previous moment to obtain multiple sampling points corresponding to any bionic robotic fish at the previous moment;

[0014] Based on the constant turn rate and velocity model, estimate the state values of the multiple sampling points at the current moment to obtain the predicted state mean and the predicted state covariance matrix corresponding to any bionic robotic fish at the current moment;

[0015] Predict the measured values of the multiple sampling points at the current moment to obtain the predicted measurement mean and the predicted measurement covariance matrix corresponding to any bionic robotic fish at the current moment;

[0016] Based on the predicted state values and the predicted state mean of the multiple sampling points at the current moment, and the predicted measurement values and the predicted measurement mean of the multiple sampling points at the current moment, determine the cross-correlation matrix, and based on the cross-correlation matrix and the predicted state covariance matrix, determine the Kalman gain;

[0017] Based on the predicted state mean, the Kalman gain, the predicted measurement values of the multiple sampling points at the previous moment, and the predicted measurement values of the multiple sampling points at the current moment, determine the estimated value of the state information of any bionic fish at the current moment.

[0018] In some embodiments, the determining the triggering error of any bionic fish at the current moment based on the estimated value of the state information of any bionic fish at the current moment, and determining the event triggering function value of any bionic fish at the current moment based on the triggering error includes:

[0019] Based on the communication relationships between the bionic fish and the communication relationships between each bionic fish and the leader, determine the adjacency matrix, degree matrix, and Laplacian matrix corresponding to the multi-bionic fish system, and the communication matrix between the leader and each bionic fish;

[0020] Take the estimated value of the state information of any bionic fish at the current moment as the state information of any bionic fish at the previous triggering moment, and based on the state information of any bionic fish at the previous triggering moment and the state information of any bionic fish at the current moment, determine the triggering error of any bionic fish at the current moment;

[0021] Based on the adjacency matrix, degree matrix, Laplacian matrix, communication matrix, and the triggering error of any bionic fish at the current moment, determine the event triggering function value of any bionic fish at the current moment.

[0022] In some embodiments, the determining the event triggering function value of any bionic fish at the current moment based on the adjacency matrix, degree matrix, Laplacian matrix, communication matrix, and the triggering error of any bionic fish at the current moment includes:

[0023] Γ i (t) = (‖σL + σ l W‖‖Φ‖ + β(‖D‖ + ‖W‖))||e ηi (t) + e vi (t)|| + Δ f

[0024]

[0025] where, Γ i (t) is the event triggering function of any bionic fish i at the current moment t, σ is the first positive coefficient, σ lis the second positive coefficient, l is the label of the leader, L is the Laplacian matrix, W is the communication matrix, Φ is the normalization matrix, β is the third positive coefficient, and D is the degree matrix;

[0026] The triggering error includes a position triggering error and a velocity triggering error, e ηi (t) is the position triggering error of any bionic fish i at the current time t, e vi (t) is the velocity triggering error of any bionic fish i at the current time t, is the estimated value of the position information of any bionic fish i at the current time t, η i (t) is the position information of any bionic fish i at the current time t, is the estimated value of the velocity information of any bionic fish i at the current time t, υ i (t) is the velocity information of any bionic fish i at the current time t;

[0027] Δ f is the motion limit parameter of the leader, λ i is the positive threshold coefficient, λ i ≤ 1, j is the label of any neighboring bionic fish corresponding to the bionic fish i, V is the set of points corresponding to the multi-bionic fish system, a ij is used to represent the communication relationship between the bionic fish i and any neighboring bionic fish j, is the position information of any bionic fish at the triggering moment is the position information of the leader at the triggering moment il is the expected position difference between any bionic fish i and the leader l, is the velocity information of any bionic fish i at the triggering moment is the velocity information of the leader l at the triggering moment

[0028] In some embodiments, when the event trigger function of any bionic fish satisfies a preset condition, the current time is used as the triggering moment, and based on the state information of any bionic fish and the neighboring bionic fish corresponding to any bionic fish at the triggering moment, and the state information of the leader at the triggering moment, the consensus formation control law of any bionic fish at the triggering moment is determined, including:

[0029] ​​​​

[0030] Among them, τ i (t) is the consensus formation control law of any one of the bionic robotic fish i at the current moment t, is the position information of any one of the neighboring bionic robotic fish j at the triggering moment of, is the position information of any one of the neighboring bionic robotic fish j at the triggering moment of, w i is used to represent the communication relationship between any one of the bionic robotic fish i and the leader l, δ li is the expected position difference between the leader l and the bionic robotic fish i.

[0031] In some embodiments, the method further includes:

[0032] Based on the dynamic model of any one of the bionic robotic fish at the current moment and the consensus formation control law of any one of the bionic robotic fish at the current moment, determine the error dynamic model of any one of the bionic robotic fish at the current moment;

[0033] Based on the error dynamic models of each bionic robotic fish at the current moment, determine the error dynamic model corresponding to the multi-bionic robotic fish system;

[0034] Based on the error dynamic model corresponding to the multi-bionic robotic fish system, determine the system state error corresponding to the multi-bionic robotic fish system;

[0035] Based on the system state error corresponding to the multi-bionic robotic fish system, construct a Lyapunov function model;

[0036] Based on the Lyapunov function model, perform stability analysis on the multi-bionic robotic fish system to determine the third positive coefficient in the event trigger function.

[0037] In some embodiments, the error dynamic model of the bionic robotic fish at the current moment is:

[0038]

[0039] Among them, is the position information error value of any one of the bionic robotic fish i at the triggering moment t, is the speed information error value of any one of the bionic robotic fish i at the triggering moment t, η l (t) is the position information of the leader l at the current moment t, v l (t) is the speed information of the leader l at the current moment t, M i is the inertia matrix of any one of the bionic robotic fish i, lij is an element in the Laplacian matrix, is the position information error value of any one of the neighboring biomimetic robotic fish j at the current moment t, is the velocity information error value of any one of the neighboring biomimetic robotic fish j at the current moment t, and e ηl (t) is the position triggering error of the leader l at the current moment t, and e υl (t) is the velocity triggering error of the leader l at the current moment t, and f i (t) is the force function of any one of the biomimetic robotic fish i except for the control force, and f l (t) is the force function of the leader l.

[0040] In a second aspect, the present application provides a formation control device for a multi-bionic robotic fish system, including:

[0041] A state estimation unit for observing the state of the multi-bionic robotic fish system and determining the estimated value of the state information of any one of the bionic robotic fish at the current moment;

[0042] An event triggering unit for determining the triggering error of any one of the bionic robotic fish at the current moment based on the estimated value of the state information of any one of the bionic robotic fish at the current moment, and determining the event triggering function value of any one of the bionic robotic fish at the current moment based on the triggering error;

[0043] A control strategy unit for, when the event triggering function of any one of the bionic robotic fish meets a preset condition, taking the current moment as the triggering moment, and determining the consensus formation control law of any one of the bionic robotic fish at the triggering moment based on the state information of any one of the bionic robotic fish and the corresponding neighboring bionic robotic fish at the triggering moment, and the state information of the leader at the triggering moment;

[0044] A formation control unit for controlling any one of the bionic robotic fish based on the consensus formation control law of any one of the bionic robotic fish at the triggering moment.

[0045] In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the method described in any one of the above is implemented.

[0046] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method described in any one of the above is implemented.

[0047] The formation control method and device for a multi-bionic fish system provided by the embodiments of the present application can determine the estimated value of the state information of any bionic fish in the multi-bionic fish system at the current moment by observing the state of the multi-bionic fish system; through the estimated value of the state information of any bionic fish at the current moment, the triggering error and the event triggering function value of any bionic fish at the current moment can be determined. Whether the current moment is used as the triggering moment can be judged through the event triggering function value, that is, it can be determined whether any bionic fish communicates with the corresponding neighboring bionic fish. Only when the event triggering function value meets the preset conditions, the current moment is used as the triggering moment to trigger any bionic fish to communicate with the corresponding neighboring bionic fish. While realizing formation control, the number of communications can be reduced, the communication energy consumption can be reduced, and the endurance time of the multi-bionic fish system for underwater operations can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present application and used together with the specification to explain the principles of the present application.

[0049] In order to more clearly illustrate the technical solutions in the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0050] Figure 1 It is a schematic flowchart of the formation control method for a multi-bionic fish system provided by an embodiment of the present application;

[0051] Figure 2 It is a schematic flowchart of the formation control method for a multi-bionic fish system provided by another embodiment of the present application;

[0052] Figure 3 It is a schematic structural diagram of the formation control device for a multi-bionic fish system provided by an embodiment of the present application;

[0053] Figure 4 It is a schematic structural diagram of an electronic device provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] To enable those skilled in the art to better understand the solution of this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this application.

[0055] It should be noted that the terms "first", "second", etc. in this application are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances so that the embodiments of this application described here can be implemented in an order other than those illustrated or described here. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units does not have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0056] Figure 1 is a schematic flowchart of a formation control method for a multi-bionic robotic fish system provided by an embodiment of this application. As Figure 1 shown, the method includes step 110, step 120, step 130, and step 140. The process steps of this method are only a possible implementation manner of this application.

[0057] Step 110: Perform state observation on the multi-bionic robotic fish system to determine the estimated value of the state information of any bionic robotic fish at the current moment.

[0058] Specifically, the formation control method for the multi-bionic robotic fish system provided by the embodiments of this application is applicable to a terminal device, which can be various electronic devices, including but not limited to smartphones, tablets, laptop computers, desktop computers, and servers.

[0059] The execution subject of the formation control method for the multi-bionic robotic fish system provided by the embodiments of this application is a formation control device for the multi-bionic robotic fish system. This device can be a hardware device set in the terminal device or a software program running in the terminal device.

[0060] The multi-bionic robotic fish system consists of multiple bionic robotic fish. The state information of the bionic robotic fish includes position information and speed information.

[0061] For example, the state information of bionic robotic fish i includes position information η i =[x i ,yi , ψ i T and speed information where p i = [x i , y i T is the two - dimensional coordinate of the bionic robotic fish i in the world coordinate system, and ψ i is the yaw angle of the bionic robotic fish i, and respectively represent the derivatives of x i , y i and ψ i . The estimated value of the state information is the estimated numerical value of the position and speed of the bionic robotic fish at the current moment.

[0062] The formation control device of the multi - bionic robotic fish system performs state observation on the multi - bionic robotic fish system by constructing a state observer, and calculates the estimated value of the state information of each bionic robotic fish in the multi - bionic robotic fish system at the current moment.

[0063] Step 120: Based on the estimated value of the state information of any bionic robotic fish at the current moment, determine the triggering error of any bionic robotic fish at the current moment, and determine the event - triggering function value of any bionic robotic fish at the current moment based on the triggering error.

[0064] Specifically, the triggering error is the state deviation between the previous triggering moment and the current moment, including the position deviation and the speed deviation. Among them, the position deviation of the bionic robotic fish i at time t Speed deviation where is the speed information of the bionic robotic fish i at the triggering moment , and k i represents the k - th time the bionic robotic fish i receives the triggering information.

[0065] The event - triggering function is used to determine whether to control the movement of this bionic robotic fish, that is, to determine whether the bionic robotic fish communicates with the neighboring bionic robotic fish and the leader.

[0066] Through the estimated value of the state information of any bionic robotic fish at the current moment, the triggering error of any bionic robotic fish at the current moment can be calculated. According to the triggering error, the event - triggering function value of any bionic robotic fish at the current moment can be calculated. According to the event - triggering function value, it can be determined whether to control the movement of this bionic robotic fish.

[0067] ​​Step 130: When the value of the event trigger function meets the preset condition, use the current moment as the trigger moment. Based on the state information of any bionic fish and its corresponding neighboring bionic fish at the trigger moment, as well as the state information of the leader at the trigger moment, determine the consensus formation control law of any bionic fish at the trigger moment.

[0068] Specifically, the trigger moment is the moment when the bionic fish that triggers sends its current state information to the neighboring bionic fish and the leader. The neighboring bionic fish are other bionic fish around the bionic fish.

[0069] The leader is used to guide the formation composed of multiple bionic fish to move along a predetermined trajectory, so as to achieve dynamic formation control. Among them, the leader can be at the center of the formation. The leader does not belong to any bionic fish and can be real or virtual.

[0070] The consensus formation control law is an algorithm for the consensus formation control instructions formed to restrict the movement of each bionic fish.

[0071] If the value of the event trigger function meets the preset condition, use the current moment as the trigger moment. At this time, the bionic fish sends its own state information to the corresponding neighboring bionic fish and the leader, and receives the state information of the neighboring bionic fish and the leader at the current moment. According to the state information of the bionic fish, the neighboring bionic fish and the leader at the current moment, the consensus formation control law of the bionic fish at the current moment can be obtained, that is, the consensus formation control law of the bionic fish at the trigger moment can be obtained.

[0072] Step 140: Control any bionic fish based on the consensus formation control law of any bionic fish at the trigger moment.

[0073] Specifically, control the movement of the bionic fish according to the consensus formation control law of the bionic fish at the trigger moment.

[0074] The formation control method for the multi-bionic fish system provided by the embodiments of the present application can determine the estimated value of the state information of any bionic fish in the multi-bionic fish system at the current moment through state observation of the multi-bionic fish system; through the estimated value of the state information of any bionic fish at the current moment, the triggering error and the event triggering function value of any bionic fish at the current moment can be determined. Whether the current moment is used as the triggering moment can be judged through the event triggering function value, that is, it can be determined whether any bionic fish communicates with the corresponding neighboring bionic fish. Only when the event triggering function value meets the preset conditions, the current moment is used as the triggering moment to trigger any bionic fish to communicate with the corresponding neighboring bionic fish. While realizing formation control, the number of communications can be reduced, the communication energy consumption can be reduced, and the endurance time of the multi-bionic fish system for underwater operations can be improved.

[0075] It should be noted that each embodiment of the present application can be freely combined, the order can be swapped, or each can be executed independently, and does not need to rely on or depend on a fixed execution order.

[0076] In some embodiments, step 110 includes:

[0077] Perform unscented transformation on the estimated value of the state information of any bionic fish at the previous moment to obtain multiple sampling points corresponding to any bionic fish at the previous moment;

[0078] Based on the constant turn rate and speed model, estimate the state values of multiple sampling points at the current moment to obtain the predicted state mean value and the predicted state covariance matrix corresponding to any bionic fish at the current moment;

[0079] Predict the measured values of multiple sampling points at the current moment to obtain the predicted measurement mean value and the predicted measurement covariance matrix corresponding to any bionic fish at the current moment;

[0080] Based on the predicted state values and the predicted state mean value of multiple sampling points at the current moment, as well as the predicted measurement values and the predicted measurement mean value of multiple sampling points at the current moment, determine the cross-correlation matrix, and based on the cross-correlation matrix and the predicted state covariance matrix, determine the Kalman gain;

[0081] Based on the predicted state mean value, the Kalman gain, the predicted measurement values of multiple sampling points at the previous moment, and the predicted measurement values of multiple sampling points at the current moment, determine the estimated value of the state information of any bionic fish at the current moment.

[0082] Specifically, the embodiments of the present application construct a state observer according to the Unscented Kalman Filter (UKF). The state space of bionic fish i at the k-th moment is represented by which, where and is the two-dimensional position estimate of the bionic robotic fish i, is the estimated forward velocity of the bionic robotic fish i, is the estimated heading angle of the bionic robotic fish i, is the estimated heading angular velocity of the bionic robotic fish i.

[0083] According to the unscented transform, generate n σ = 2n a + 1 sigma point set, where n a is the dimension of X k The generated multiple sigma points are the multiple sampling points corresponding to any bionic robotic fish at the previous moment.

[0084] According to the constant turn rate and velocity model (CTRV) f p (·), the sigma points at the estimated current moment (time k + 1) can be obtained:

[0085] χ k+1|k,m = f p (χ k,i , v k,i )

[0086] where v k,i is the process noise, χ k,i is the state of the bionic robotic fish i at time k, and χ k+1|k,m is the state of the m-th sigma point estimated from time k to time k + 1. At this time, the predicted state mean μ k+1|k and the predicted state covariance matrix P k+1|k can be updated as:

[0087]

[0088]

[0089] where ω σ,m is the weighting coefficient. The predicted state mean and predicted state covariance matrix of the sigma points at time k + 1 are the predicted state mean and predicted state covariance matrix corresponding to any bionic robotic fish at the current moment. According to the measurement values of multiple sensors on the bionic robotic fish, the measurement sigma point vector Z k+1|k,m and the measurement error covariance matrix R k+1 are obtained, so as to obtain the predicted measurement mean z k+1|k and the predicted measurement covariance matrix S k+1|k as follows:

[0090]

[0091]

[0092] At this time, the cross-correlation matrix T k+1|k and the Kalman gain K k+1|k can be expressed as:

[0093]

[0094]

[0095] Based on the predicted state mean, the Kalman gain, the predicted measurement values of multiple sampling points at the previous moment, and the predicted measurement values of multiple sampling points at the current moment, determine the estimated value of the state information of any bionic fish at the current moment.

[0096] Update the estimated state vector and the covariance matrix, and transform them into system state information, to obtain:

[0097] X k+1 = μ k+1|k + K k+1|k (z k+1 - z k+1|k )

[0098]

[0099] According to the state space X k+1 of the bionic fish i at the k+1 moment, the estimated value of the state information of the bionic fish i at the k+1 moment can be obtained.

[0100] The multi-bionic fish system formation control method provided by the embodiments of the present application performs state observation on the multi-bionic fish system through unscented Kalman filtering, and determines the estimated value of the state information of any bionic fish in the multi-bionic fish system at the current moment, which can improve the calculation accuracy of the triggering error, and further improve the calculation accuracy of the event triggering function value of any bionic fish at the current moment.

[0101] In some embodiments, step 120 includes:

[0102] Based on the communication relationships between the bionic fish and the communication relationships between each bionic fish and the leader, determine the adjacency matrix, degree matrix, and Laplacian matrix corresponding to the multi-bionic fish system, and the communication matrix between the leader and each bionic fish;

[0103] Estimate the state information value of any bionic fish at the current moment as the state information of any bionic fish at the previous trigger moment, and determine the trigger error of any bionic fish at the current moment based on the state information of any bionic fish at the previous trigger moment and the state information of any bionic fish at the current moment.

[0104] Based on the adjoint matrix, degree matrix, Laplacian matrix, communication matrix, and the trigger error of any bionic fish at the current moment, determine the event trigger function value of any bionic fish at the current moment.

[0105] Specifically, for example, the multi-bionic fish system contains N bionic fish, where N is a positive integer. The communication topology relationship of each bionic fish in the multi-bionic fish system is represented by an undirected graph G=(V, E), including the point set V={1, 2, …, N} and the edge set Each point in the point set represents a bionic fish, and each edge in the edge set represents the communication relationship between two bionic fish.

[0106] The adjoint matrix A = [a ij N×N , (i, j) ∈ E, where a ij = 1 indicates that bionic fish i and the corresponding neighboring bionic fish j can communicate with each other. The degree matrix D = diag{d1, d2, …, d N}, where The Laplacian matrix

[0107] Through the communication relationships between each bionic fish, each bionic fish can communicate with neighboring bionic fish and share state information.

[0108] In addition, the embodiment of the present application decomposes the formation control task into two stages, including the formation stage and the formation maintenance stage. In the formation stage: N bionic fish in the multi-bionic fish system quickly gather to form a reliable communication relationship and present a predetermined formation; in the formation maintenance stage: a dynamic leader is set, and the formation can be guided to move along a predetermined trajectory with the leader as the center, so as to achieve the dynamic formation control task.

[0109] Use W = diag{w1, w2, …, w N} to represent the connection situation between the leader and N bionic fish in the multi-bionic fish system. The formation in the formation control process is represented by Δ = [δ ij , where δ ij = δ i - δ j ​Represents the estimated relative position information between the bionic robotic fish i and the corresponding neighboring bionic robotic fish j. The state information of the leader is represented by the position information η l =[x l , y l , ψ l T and the speed information to represent, δ l is the center of the formation. To maintain the formation, the motion of each bionic robotic fish can be controlled by the following formula:

[0110]

[0111]

[0112] In the formula, 0 n is the n-order zero vector.

[0113] By the estimated state information and replace the triggering state information at the previous moment and to obtain the triggering error at the current moment.

[0114] According to the adjoint matrix, degree matrix, Laplacian matrix, communication matrix, and the triggering error of any bionic robotic fish at the current moment, the triggering function value of any bionic robotic fish at the current moment can be calculated.

[0115] The multi-bionic robotic fish system formation control method provided by the embodiments of the present application can more accurately obtain the triggering error of any bionic robotic fish at the current moment by using the estimated value of the state information of any bionic robotic fish at the current moment as the state information of any bionic robotic fish at the previous triggering moment. Furthermore, the accuracy of the calculated triggering function value is higher, and the communication times between each bionic robotic fish can be reduced more accurately.

[0116] In some embodiments, determining the triggering function value of any bionic robotic fish at the current moment based on the adjoint matrix, degree matrix, Laplacian matrix, communication matrix, and the triggering error of any bionic robotic fish at the current moment includes:

[0117]

[0118] Where, Γ i (t) is the triggering function of any bionic robotic fish i at the current moment t, σ is the first positive coefficient, σ l is the second positive coefficient, l is the label of the leader, L is the Laplacian matrix, W is the communication matrix, Φ is the normalization matrix, β is the third positive coefficient, D is the degree matrix, and λ is the fourth positive coefficient.​

[0119] The triggering error includes position triggering error and speed triggering error, where e ηi (t) is the position triggering error of any bionic robotic fish i at the current moment t, and e vi (t) is the speed triggering error of any bionic robotic fish i at the current moment t, η is the estimated value of the position information of any bionic robotic fish i at the current moment t, i (t) is the position information of any bionic robotic fish i at the current moment t, υ is the estimated value of the speed information of any bionic robotic fish i at the current moment t, i (t) is the speed information of any bionic robotic fish i at the current moment t;

[0120] Δ f λ is the motion limit parameter of the leader, i λ is the positive threshold coefficient, i ≤ 1, j is the label of any neighboring bionic robotic fish corresponding to bionic robotic fish i, V is the set of points corresponding to the multi-bionic robotic fish system, and a ij is used to represent the communication relationship between bionic robotic fish i and any neighboring bionic robotic fish j, is the position information of any bionic robotic fish i at the triggering moment , is the position information of the leader at the triggering moment , and δ il is the expected position difference between any bionic robotic fish i and the leader l, is the speed information of any bionic robotic fish i at the triggering moment , is the speed information of the leader l at the triggering moment .

[0121] Specifically, taking bionic robotic fish i as an example, when it is determined that the current moment is the triggering moment, bionic robotic fish i sends its state information and to neighboring bionic robotic fish and the leader, thus completing the interaction between bionic robotic fish i and neighboring bionic robotic fish and the leader. At this time, the triggering moments of each bionic robotic fish can be expressed as in the following form:

[0122]

[0123] When the triggering function Γ iWhen the value of (t) is greater than or equal to 0, the bionic fish i will communicate with the neighboring bionic fish and the leader to share the status information. The current moment when the trigger function value is greater than or equal to 0 is the trigger moment.

[0124] For the multi-bionic fish system formation control method provided by the embodiments of the present application, by setting an event trigger function, only when the trigger function value is greater than or equal to 0, the bionic fish will communicate with the neighboring bionic fish and the leader to share the status information, which can reduce the communication times between the bionic fish and improve the endurance time of the multi-bionic fish system underwater operation.

[0125] In some embodiments, step 130 includes:

[0126]

[0127] Among them, τ i (t) is the consensus formation control law of any bionic fish i at the current moment t, is the position information of any neighboring bionic fish j at the trigger moment , is the velocity information of any neighboring bionic fish j at the trigger moment , w i is used to represent the communication relationship between any bionic fish i and the leader l, and δ li is the expected position difference between the leader l and the bionic fish i.

[0128] For the multi-bionic fish system formation control method provided by the embodiments of the present application, by calculating the consensus formation control law of any bionic fish at the trigger moment, the movement of any bionic fish can be effectively controlled.

[0129] In some embodiments, the method further includes:

[0130] Based on the dynamic model of any bionic fish at the current moment and the consensus formation control law of any bionic fish at the current moment, determine the error dynamic model of any bionic fish at the current moment;

[0131] Based on the error dynamic models of each bionic fish at the current moment, determine the error dynamic model corresponding to the multi-bionic fish system;

[0132] Based on the error dynamic model corresponding to the multi-bionic fish system, determine the system state error corresponding to the multi-bionic fish system;

[0133] Based on the system state error corresponding to the multi-bionic fish system, construct a Lyapunov function model;

[0134] Perform a stability analysis on the multi-bionic fish system based on the Lyapunov function model to determine the third positive coefficient in the event-triggered function.

[0135] Specifically, by analyzing the motion mode of the bionic fish, the dynamic models of the bionic fish and the leader are constructed as follows:

[0136]

[0137] Among them, M i and M l represent the inertia matrices of the bionic fish i and the leader respectively, and τ i represents the control input of the bionic fish i. To expand the application scenario of the control framework, the dynamic model of the leader is represented by an autonomous system, and the motion of the leader can be restricted by

[0138] According to the dynamic model of any bionic fish at the current moment and the consensus formation control law of any bionic fish at the current moment, the error dynamic model of any bionic fish at the current moment is determined.

[0139] According to the error dynamic models of each bionic fish at the current moment, the error dynamic model corresponding to the multi-bionic fish system can be determined;

[0140] The error dynamic model of any bionic fish at the current moment is:

[0141]

[0142] Among them, is the position information error value of any bionic fish i at the trigger moment t, is the velocity information error value of any bionic fish i at the trigger moment t, η l (t) is the position information of the leader l at the current moment t, υ l (t) is the velocity information of the leader l at the current moment t, M i is the inertia matrix of any bionic fish, l ij is the element in the Laplacian matrix, is the position information error value of any neighboring bionic fish j at the current moment t, is the velocity information error value of any neighboring bionic fish j at the current moment t, e ηl (t) is the position trigger error of the leader l at the current moment t, e υl (t) is the velocity trigger error of the leader l at the current moment t, f i (t) is the force function of any bionic fish i other than the control force, f​l (t) is the force function of the leader l.

[0143] For the multi-bionic fish system, The error dynamics model of the multi-bionic fish system can be expressed as:

[0144]

[0145] where M is the inertia matrix of the multi-bionic fish system, I Nn is an N*n identity matrix (a matrix full of 1s), O Nn is an N*n zero matrix (a matrix full of 0s), K, J, N, and H can be expressed as:

[0146]

[0147]

[0148]

[0149] According to the error dynamics model corresponding to the multi-bionic fish system, the system state error corresponding to the multi-bionic fish system can be determined.

[0150] To verify the stability of the error dynamics model, a Lyapunov function V ξ is constructed as follows:

[0151]

[0152] where the positive definite matrix P can be expressed as:

[0153]

[0154] The derivative of the Lyapunov function is obtained as follows:

[0155]

[0156] where Q can be expressed as:

[0157]

[0158] In the above error dynamics model, and are used to measure the error of formation control. The bionic fish i may not be able to obtain these state information at any time. Therefore, An event-triggering function Γ i (t) of any bionic fish at time t is set:

[0159] Among them, the event trigger function Γ l (t) of the leader at time t can be expressed as:

[0160]

[0161] where β is a positive coefficient, and λ l is a positive threshold coefficient, and λ l ≤ 1.

[0162] The derivative of the Lyapunov function can be further derived as follows:

[0163]

[0164] λ min is the minimum eigenvalue of the matrix. When , the stability of the multi-bionic fish system can be guaranteed. The range of β at this time is obtained as follows:

[0165]

[0166] The formation control method of the multi-bionic fish system provided by the embodiment of the present application constructs a Lyapunov function model, performs stability analysis on the multi-bionic fish system according to the Lyapunov function model, and can determine the third positive coefficient in the event trigger function, improving the stability of the multi-bionic fish system.

[0167] Figure 2 is a schematic flowchart of the formation control method of the multi-bionic fish system provided by another embodiment of the present application. As Figure 2 shown, the method includes:

[0168] Step 1: Set the communication topology structure of the multi-bionic fish system, and construct the dynamic models of each bionic fish and the multi-bionic fish system.

[0169] Step 2: According to the consensus formation control law by setting an event trigger mechanism, make the multi-bionic fish converge to a preset formation.

[0170] Step 3: Perform stability analysis on the error dynamic model by constructing a Lyapunov function, and set an event trigger function to ensure the stability of the formation control.

[0171] Step 4: Estimate the state of the bionic fish through UKF, and construct an event trigger mechanism to reduce the communication energy consumption of the formation control.

[0172] The formation control method for a multi-bionic fish system provided by an embodiment of the present application constructs a communication topology structure of the multi-bionic fish system and sets an event trigger function to determine the trigger moment during the formation process. By constructing a Lyapunov function, the robustness of the control framework is ensured. The state information of the bionic fish, its neighboring bionic fish, and the leader obtained at the trigger moment is used to perform distributed estimation of the motion state of the bionic fish through the unscented Kalman filter algorithm. At the same time, according to the event trigger mechanism, unnecessary waste of communication resources can be further avoided, effectively improving the operation efficiency of the bionic fish during underwater formation, reducing operation energy consumption, and effectively increasing the endurance time of the underwater operation of the vehicle.

[0173] The formation control device for a multi-bionic fish system provided by an embodiment of the present application will be described below. The formation control device for a multi-bionic fish system described below can be mutually corresponding and referred to the formation control method for a multi-bionic fish system described above.

[0174] Figure 3 is a schematic structural diagram of a formation control device for a multi-bionic fish system provided by an embodiment of the present application, as Figure 3 shown. The formation control device for a multi-bionic fish system is applied to a distributed data management system. The device includes a state estimation unit 310, an event trigger unit 320, a control strategy unit 330, and a formation control unit 340.

[0175] The state estimation unit is used to perform state observation on the multi-bionic fish system to determine the estimated value of the state information of any bionic fish at the current moment;

[0176] The event trigger unit is used to determine the trigger error of any bionic fish at the current moment based on the estimated value of the state information of any bionic fish at the current moment, and determine the event trigger function value of any bionic fish at the current moment based on the trigger error;

[0177] The control strategy unit is used to use the current moment as the trigger moment when the event trigger function of any bionic fish meets the preset conditions, and determine the consensus formation control law of any bionic fish at the trigger moment based on the state information of any bionic fish and the corresponding neighboring bionic fish of any bionic fish at the trigger moment, and the state information of the leader at the trigger moment;

[0178] The formation control unit is used to control any bionic fish based on the consensus formation control law of any bionic fish at the trigger moment.

[0179] Specifically, according to the embodiments of the present application, any plurality of units among the state estimation unit, the event triggering unit, the control strategy unit, and the formation control unit may be combined and implemented in one unit, or any one of them may be split into multiple units.

[0180] Alternatively, at least part of the functions of one or more of these units may be combined with at least part of the functions of other units and implemented in one unit.

[0181] According to the embodiments of the present application, at least one of the state estimation unit, the event triggering unit, the control strategy unit, and the formation control unit may be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on chip, a system on substrate, a system on package, an application specific integrated circuit (ASIC), or any other reasonable way of integrating or packaging circuits, etc., implemented by hardware or firmware, or implemented in any one of the three implementation manners of software, hardware, and firmware, or in any appropriate combination of several of them.

[0182] Alternatively, at least one of the state estimation unit, the event triggering unit, the control strategy unit, and the formation control unit may be at least partially implemented as a computer program unit, which can execute the corresponding functions when the computer program unit is run.

[0183] The formation control device for a multi-bionic fish system provided by the embodiments of the present application can determine the estimated value of the state information of any bionic fish in the multi-bionic fish system at the current moment by observing the state of the multi-bionic fish system; through the estimated value of the state information of any bionic fish at the current moment, the triggering error and the event triggering function value of any bionic fish at the current moment can be determined. Whether the current moment is used as the triggering moment can be judged through the event triggering function value, that is, it can be determined whether any bionic fish communicates with the corresponding neighboring bionic fish. Only when the event triggering function value meets the preset conditions, the current moment is used as the triggering moment to trigger any bionic fish to communicate with the corresponding neighboring bionic fish. While realizing formation control, the number of communications can be reduced, the communication energy consumption can be reduced, and the endurance time of the multi-bionic fish system for underwater operations can be improved.

[0184] In some embodiments, the state estimation unit is specifically used for:

[0185] Performing an unscented transformation on the estimated value of the state information of any bionic fish at the previous moment to obtain a plurality of sampling points corresponding to any bionic fish at the previous moment;

[0186] Based on the constant turn rate and speed model, estimate the state values of multiple sampling points at the current moment, and obtain the predicted state mean and the predicted state covariance matrix corresponding to any bionic fish at the current moment;

[0187] Predict the measurement values of multiple sampling points at the current moment, and obtain the predicted measurement mean and the predicted measurement covariance matrix corresponding to any bionic fish at the current moment;

[0188] Based on the predicted state values and the predicted state mean of multiple sampling points at the current moment, as well as the predicted measurement values and the predicted measurement mean of multiple sampling points at the current moment, determine the cross-correlation matrix, and based on the cross-correlation matrix and the predicted state covariance matrix, determine the Kalman gain;

[0189] Based on the predicted state mean, the Kalman gain, the predicted measurement values of multiple sampling points at the previous moment, and the predicted measurement values of multiple sampling points at the current moment, determine the estimated value of the state information of any bionic fish at the current moment.

[0190] In some embodiments, the event trigger unit is specifically configured to:

[0191] Based on the communication relationships among the bionic fish and the communication relationships between each bionic fish and the leader, determine the adjacency matrix, degree matrix, and Laplacian matrix corresponding to the multi-bionic fish system, as well as the communication matrix between the leader and each bionic fish;

[0192] Take the estimated value of the state information of any bionic fish at the current moment as the state information of any bionic fish at the previous trigger moment, and based on the state information of any bionic fish at the previous trigger moment and the state information of any bionic fish at the current moment, determine the trigger error of any bionic fish at the current moment;

[0193] Based on the adjacency matrix, degree matrix, Laplacian matrix, communication matrix, and the trigger error of any bionic fish at the current moment, determine the event trigger function value of any bionic fish at the current moment.

[0194] Among them, determining the event trigger function value of any bionic fish at the current moment based on the adjacency matrix, degree matrix, Laplacian matrix, communication matrix, and the trigger error of any bionic fish at the current moment includes:

[0195]

[0196] Among them, Γ i (t) is the event trigger function of any bionic fish i at the current moment t, σ is the first positive coefficient, σ lis the second positive coefficient, l is the label of the leader, L is the Laplacian matrix, W is the communication matrix, Φ is the normalization matrix, β is the third positive coefficient, and D is the degree matrix;

[0197] The triggering error includes the position triggering error and the speed triggering error, e ηi (t) is the position triggering error of any bionic fish i at the current time t, e vi (t) is the speed triggering error of any bionic fish i at the current time t, is the estimated value of the position information of any bionic fish i at the current time t, η i (t) is the position information of any bionic fish i at the current time t, is the estimated value of the speed information of any bionic fish i at the current time t, v i (t) is the speed information of any bionic fish i at the current time t;

[0198] Δ f is the motion limit parameter of the leader, λ i is the positive threshold coefficient, λ i ≤1, j is the label of any neighboring bionic fish corresponding to bionic fish i, V is the set of points corresponding to the multi-bionic fish system, a ij is used to represent the communication relationship between bionic fish i and any neighboring bionic fish j, is the position information of any bionic fish at the triggering moment is the position information of the leader at the triggering moment il is the expected position difference between any bionic fish i and the leader l, is the speed information of any bionic fish i at the triggering moment is the speed information of the leader l at the triggering moment

[0199] In some embodiments,

[0200]

[0201] where, τ i (t) is the consensus formation control law of any bionic fish i at the current time t, is the position information of any neighboring bionic fish j at the triggering moment is the speed information of any neighboring bionic fish j at the triggering moment iUsed to represent the communication relationship between any bionic robotic fish i and the leader l, δ li is the expected position difference between the leader l and the bionic robotic fish i.

[0202] In some embodiments, the formation control device of the multi-bionic robotic fish system further includes a stability analysis unit for:

[0203] Based on the dynamic model of any bionic robotic fish at the current moment and the consensus formation control law of any bionic robotic fish at the current moment, determine the error dynamic model of any bionic robotic fish at the current moment;

[0204] Based on the error dynamic models of each bionic robotic fish at the current moment, determine the error dynamic model corresponding to the multi-bionic robotic fish system;

[0205] Based on the error dynamic model corresponding to the multi-bionic robotic fish system, determine the system state error corresponding to the multi-bionic robotic fish system;

[0206] Based on the system state error corresponding to the multi-bionic robotic fish system, construct a Lyapunov function model;

[0207] Based on the Lyapunov function model, perform stability analysis on the multi-bionic robotic fish system to determine the third positive coefficient in the event trigger function.

[0208] Among them, the error dynamic model of the bionic robotic fish at the current moment is:

[0209]

[0210] Among them, is the position information error value of any bionic robotic fish i at the trigger moment t, is the velocity information error value of any bionic robotic fish i at the trigger moment t, η l (t) is the position information of the leader l at the current moment t, υ l (t) is the velocity information of the leader l at the current moment t, M i is the inertia matrix of any bionic robotic fish, l ij is the element in the Laplacian matrix, is the position information error value of any neighboring bionic robotic fish j at the current moment t, is the velocity information error value of any neighboring bionic robotic fish j at the current moment t, e ηl (t) is the position trigger error of the leader l at the current moment t, e υl (t) is the velocity trigger error of the leader l at the current moment t, f i (t) is the force function of any bionic robotic fish i other than the control force, f l(t) is the force function of the leader l.

[0211] It should be noted here that the formation control device of the multi-bionic fish system provided in the embodiment of the present application can implement all the method steps implemented by the above-mentioned formation control method embodiment of the multi-bionic fish system, and can achieve the same technical effects. The same parts and beneficial effects as those in the method embodiment will not be specifically described in this embodiment.

[0212] Figure 4 It is a schematic structural diagram of an electronic device provided in an embodiment of the present application. As Figure 4 shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440. Among them, the processor 410, the communication interface 420, and the memory 430 complete mutual communication through the communication bus 440. The processor 410 can call the logical operations in the memory 430 to execute the formation control method of the multi-bionic fish system, and the method includes:

[0213] Perform state observation on the multi-bionic fish system to determine the estimated value of the state information of any bionic fish at the current moment;

[0214] Based on the estimated value of the state information of any bionic fish at the current moment, determine the triggering error of any bionic fish at the current moment, and determine the event trigger function value of any bionic fish at the current moment based on the triggering error;

[0215] When the event trigger function value meets the preset conditions, use the current moment as the trigger moment, and based on the state information of any bionic fish and its corresponding neighboring bionic fish at the trigger moment, and the state information of the leader at the trigger moment, determine the consensus formation control law of any bionic fish at the trigger moment;

[0216] Control any bionic fish based on the consensus formation control law of any bionic fish at the trigger moment.

[0217] In addition, when the logical operations in the above-mentioned memory can be implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several operations for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical discs that can store program codes.

[0218] The processor in the electronic device provided in the embodiments of this application can call the logical instructions in the memory to implement the above method. The specific implementation manner is the same as that of the foregoing method implementation manner and can achieve the same beneficial effects, which will not be elaborated herein.

[0219] The embodiments of this application also provide a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is configured to execute the methods provided in the above various embodiments.

[0220] The specific implementation manner is the same as that of the foregoing method implementation manner and can achieve the same beneficial effects, which will not be elaborated herein.

[0221] The embodiments of this application provide a computer program product, including a computer program. When the computer program is executed by a processor, it implements the method as described above.

[0222] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without creative efforts.

[0223] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0224] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A formation control method for a multi-bionic robotic fish system, characterized in that Including: Performing state observation on the multi-bionic fish system to determine the estimated value of the state information of any bionic fish at the current moment; Based on the estimated value of the state information of any bionic fish at the current moment, determining the triggering error of any bionic fish at the current moment, and determining the event triggering function value of any bionic fish at the current moment based on the triggering error; When the event triggering function value meets the preset condition, taking the current moment as the triggering moment, and determining the consensus formation control law of any bionic fish at the triggering moment based on the state information of any bionic fish and its corresponding neighboring bionic fish at the triggering moment, and the state information of the leader at the triggering moment; Controlling any bionic fish based on the consensus formation control law of any bionic fish at the triggering moment.

2. The formation control method of the multi-bionic robotic fish system according to claim 1, characterized in that The performing state observation on the multi-bionic fish system to determine the estimated value of the state information of any bionic fish at the current moment includes: Performing unscented transformation on the estimated value of the state information of any bionic fish at the previous moment to obtain multiple sampling points corresponding to any bionic fish at the previous moment; Based on the constant turn rate and speed model, estimating the state values of the multiple sampling points at the current moment to obtain the predicted state mean and the predicted state covariance matrix corresponding to any bionic fish at the current moment; Predicting the measurement values of the multiple sampling points at the current moment to obtain the predicted measurement mean and the predicted measurement covariance matrix corresponding to any bionic fish at the current moment; Based on the predicted state values and the predicted state mean of the multiple sampling points at the current moment, and the predicted measurement values and the predicted measurement mean of the multiple sampling points at the current moment, determining the cross-correlation matrix, and determining the Kalman gain based on the cross-correlation matrix and the predicted state covariance matrix; Based on the predicted state mean, the Kalman gain, the predicted measurement values of the multiple sampling points at the previous moment, and the predicted measurement values of the multiple sampling points at the current moment, determining the estimated value of the state information of any bionic fish at the current moment.

3. The multi-bionic robotic fish system formation control method according to claim 1, characterized in that: The based on the estimated value of the state information of any bionic fish at the current moment, determining the triggering error of any bionic fish at the current moment, and determining the event triggering function value of any bionic fish at the current moment based on the triggering error includes: Based on the communication relationships between each bionic fish and the communication relationships between each bionic fish and the leader, determining the adjacency matrix, degree matrix and Laplacian matrix corresponding to the multi-bionic fish system, and the communication matrix between the leader and each bionic fish; Take the estimated value of the state information of any one of the bionic robotic fish at the current moment as the state information of any one of the bionic robotic fish at the previous trigger moment, and based on the state information of any one of the bionic robotic fish at the previous trigger moment and the state information of any one of the bionic robotic fish at the current moment, determine the trigger error of any one of the bionic robotic fish at the current moment; Based on the adjoint matrix, degree matrix, Laplacian matrix, communication matrix, and the trigger error of any one of the bionic robotic fish at the current moment, determine the event-triggering function value of any one of the bionic robotic fish at the current moment.

4. The formation control method for the multi-bionic robotic fish system according to claim 3, characterized in that The determining the event-triggering function value of any one of the bionic robotic fish at the current moment based on the adjoint matrix, degree matrix, Laplacian matrix, communication matrix, and the trigger error of any one of the bionic robotic fish at the current moment includes: Among them, Γ i (t) is the event trigger function of any one of the bionic robotic fish i at the current moment t, σ is the first positive coefficient, σ l is the second positive coefficient, l is the label of the leader, L is the Laplacian matrix, W is the communication matrix, Φ is the normalization matrix, β is the third positive coefficient, and D is the degree matrix; The triggering error includes a position triggering error and a speed triggering error, e ηi (t) is the position triggering error of any one of the bionic fish i at the current time t, e vi (t) is the speed triggering error of any one of the bionic fish i at the current time t, is the estimated value of the position information of any one of the bionic fish i at the current time t, η i (t) is the position information of any one of the bionic fish i at the current time t, is the estimated value of the speed information of any one of the bionic fish i at the current time t, υ i (t) is the speed information of any one of the bionic fish i at the current time t; Δ f is the motion limit parameter of the leader, λ i is the positive threshold coefficient, λ i ≤ 1, j is the label of any neighboring bionic fish corresponding to the bionic fish i, V is the point set corresponding to the multi-bionic fish system, a ij is used to represent the communication relationship between the bionic fish i and any neighboring bionic fish j is the position information of any bionic fish i at the trigger moment is the position information of the leader at the trigger moment δ il is the expected position difference between any bionic fish i and the leader l is the velocity information of any bionic fish i at the trigger moment is the velocity information of the leader l at the trigger moment ​​​ 5. The multi-bionic robotic fish system formation control method according to claim 4, characterized in that: When the event-triggering function of any one of the bionic robotic fish meets the preset conditions, take the current moment as the trigger moment, and based on the state information of any one of the bionic robotic fish and the corresponding neighboring bionic robotic fish of any one of the bionic robotic fish at the trigger moment, and the state information of the leader at the trigger moment, determine the consensus formation control law of any one of the bionic robotic fish at the trigger moment, including: where τ i (t) is the consensus formation control law of any one of the bionic robotic fish i at the current moment t, is the position information of any one of the neighboring bionic robotic fish j at the trigger moment , is the velocity information of any one of the neighboring bionic robotic fish j at the trigger moment , w i is used to represent the communication relationship between any one of the bionic robotic fish i and the leader l, and δ li is the expected position difference between the leader l and the bionic robotic fish i.

6. The formation control method of the multi-bionic robotic fish system according to claim 5, characterized in that, The method further includes: Based on the dynamic model of any one of the bionic robotic fish at the current moment and the consensus formation control law of any one of the bionic robotic fish at the current moment, determine the error dynamic model of any one of the bionic robotic fish at the current moment; Based on the error dynamic models of each bionic robotic fish at the current moment, determine the error dynamic model corresponding to the multi-bionic robotic fish system; Based on the error dynamic model corresponding to the multi-bionic robotic fish system, determine the system state error corresponding to the multi-bionic robotic fish system; Based on the system state error corresponding to the multi-bionic robotic fish system, construct a Lyapunov function model; Based on the Lyapunov function model, conduct a stability analysis on the multi-bionic robotic fish system to determine the third positive coefficient in the event-triggering function.

7. The formation control method for the multi-bionic robotic fish system according to claim 6, characterized in that The error dynamic model of the bionic robotic fish at the current moment is: Among them, is the position information error value of any one of the bionic fish i at the trigger time t, is the speed information error value of any one of the bionic fish i at the trigger time t, η l (t) is the position information of the leader l at the current time t, v l (t) is the speed information of the leader l at the current time t, M i is the inertia matrix of any one of the bionic fish i, l ij is an element in the Laplacian matrix, is the position information error value of any neighboring bionic fish j at the current time t, is the speed information error value of any neighboring bionic fish j at the current time t, e ηl (t) is the position trigger error of the leader l at the current time t, e vl (t) is the speed trigger error of the leader l at the current time t, f i (t) is the force function of any one of the bionic fish i except for the control force, f l (t) is the force function of the leader l.

8. A formation control device for a multi-bionic robotic fish system, characterized in that, including: A state estimation unit for performing state observation on the multi-bionic robotic fish system to determine the estimated value of the state information of any one of the bionic robotic fish at the current moment; An event-triggering unit for determining the trigger error of any one of the bionic robotic fish at the current moment based on the estimated value of the state information of any one of the bionic robotic fish at the current moment, and determining the event-triggering function value of any one of the bionic robotic fish at the current moment based on the trigger error; A control strategy unit for taking the current moment as the trigger moment when the event-triggering function of any one of the bionic robotic fish meets the preset conditions, and determining the consensus formation control law of any one of the bionic robotic fish at the trigger moment based on the state information of any one of the bionic robotic fish and the corresponding neighboring bionic robotic fish of any one of the bionic robotic fish at the trigger moment, and the state information of the leader at the trigger moment; The formation control unit is used to control any one of the bionic fish based on the consistency formation control law of any one of the bionic fish at the trigger moment.

9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the formation control method of the multi-bionic fish system according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the formation control method of the multi-bionic fish system according to any one of claims 1 to 7.

Images