A distributed constraint formation optimal tracking method, device, equipment and medium

Abstract

The application discloses a distributed constraint formation optimal tracking method and device, equipment and medium, and relates to the technical field of formation tracking control of clusters. The method comprises the following steps: establishing a communication topology structure inside a heterogeneous cluster system, establishing a dynamic model of the heterogeneous cluster system, establishing a constraint formation optimal tracking model based on the communication topology structure and the dynamic model, designing a distributed constraint formation optimal tracking control protocol, determining control protocol parameters of the distributed constraint formation optimal tracking control protocol to ensure that a dynamic regret value and a constraint violation value linearly increase over time, solving the constraint formation optimal tracking model based on the distributed constraint formation optimal tracking control protocol and the control protocol parameters, and obtaining an optimal formation tracking result. The application realizes constraint formation optimal tracking.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of formation tracking control of swarms, and particularly relates to a distributed constraint formation optimal tracking method for a heterogeneous swarm system, an apparatus, a device and a medium. BACKGROUND

[0002] In recent years, the formation tracking problem of swarms has attracted increasing attention. For this problem, a leader-follower formation tracking method is proposed by relevant technical personnel. In addition, there are also researches dedicated to various extensions, including multi-leader formation tracking, formation containment control and group formation tracking. These methods mainly focus on the scenario where the leader knows the formation reference trajectory in advance. However, in practical applications, the formation reference trajectory to be implemented may often change significantly over time due to different tasks assigned to followers, rather than being determined solely by the leader. This need is more pronounced when the communication link between the leader and the follower is unstable. The leaderless method based on consensus enables agents to reach consensus through a distributed manner without a leader, but this method lacks consideration in performance optimization. Therefore, it is crucial for a swarm system to maintain formation tracking without a leader while taking into account the performance of each agent.

[0003] To solve this problem, relevant scholars have studied the distributed formation optimal tracking problem characterized by local objective functions and formation configuration requirements. It is assumed that each agent has a time-invariant objective function that is not disclosed to other agents, and the formation configuration requirements are converted into a constraint. In practical scenarios, the objective function may change dramatically with changes in tasks and environments. At the same time, in addition to the formation configuration requirements, there may be multiple constraints coexisting, including the dynamic model limitations of agents, obstacles or threat areas in the environment, and the limited and heterogeneous field of view of agents. Therefore, considering the above actual influencing factors, the formation optimal tracking problem can be converted into a distributed time-varying optimization problem with coupled constraints. For this purpose, some relevant scholars consider the case of coupled inequality constraints, and some relevant scholars solve the problem of heterogeneous linear dynamic systems. Overall, the distributed formation optimal tracking algorithm for heterogeneous linear swarm systems with coupled constraints is still worthy of further study, and there is currently a lack of practical experimental verification. In addition, predictable information has been widely used in various control fields, but there are few research results on the use of predictable information in formation optimal tracking. SUMMARY

[0004] The purpose of the present application is to provide a distributed constraint formation optimal tracking method, apparatus, device and medium, which can realize constraint formation optimal tracking.

[0005] To achieve the above purpose, the present application provides the following solutions:

[0006] In a first aspect, the application provides a distributed constraint formation optimal tracking method, comprising:

[0007] establishing a communication topology structure inside a heterogeneous swarm system; the heterogeneous swarm system comprises a plurality of agents;

[0008] establishing a dynamic model of the heterogeneous swarm system;

[0009] based on the communication topology structure and the dynamic model, a constraint formation optimal tracking model is established; the constraint formation optimal tracking model comprises a global objective function and a constraint condition;

[0010] designing a distributed constraint formation optimal tracking control protocol; the distributed constraint formation optimal tracking control protocol comprises a weighted average consensus mechanism, a predictive tracking controller and an original dual update mechanism; the weighted average consensus mechanism is used for the agent to update the weighted average estimation of the formation center vector and the normalized left eigenvector based on the neighbor information; the predictive tracking controller generates a control input based on the weighted average estimation to track the formation configuration; the original dual update mechanism is used for updating the formation center vector estimation value and the dual vector estimation value;

[0011] determining the control protocol parameters of the distributed constraint formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value increase linearly over time;

[0012] based on the distributed constraint formation optimal tracking control protocol and the control protocol parameters, the constraint formation optimal tracking model is solved to obtain an optimal formation tracking result.

[0013] In a second aspect, the application provides a distributed constraint formation optimal tracking device, comprising:

[0014] a communication topology structure establishing module for establishing a communication topology structure inside a heterogeneous swarm system; the heterogeneous swarm system comprises a plurality of agents;

[0015] a dynamic model establishing module for establishing a dynamic model of the heterogeneous swarm system;

[0016] a constraint formation optimal tracking model establishing module for establishing a constraint formation optimal tracking model based on the communication topology structure and the dynamic model; the constraint formation optimal tracking model comprises a global objective function and a constraint condition;

[0017] The distributed constraint formation optimal tracking control protocol design module is configured to design a distributed constraint formation optimal tracking control protocol, wherein the distributed constraint formation optimal tracking control protocol comprises a weighted average consensus mechanism, a predictive tracking controller and a primal-dual update mechanism; the weighted average consensus mechanism is configured to update a weighted average estimation of a formation center vector and a normalized left eigenvector based on neighbor information of an agent; the predictive tracking controller is configured to generate a control input based on the weighted average estimation to track a formation configuration; and the primal-dual update mechanism is configured to update an estimation value of the formation center vector and an estimation value of a dual vector.

[0018] The control protocol parameter determination module is configured to determine a control protocol parameter of the distributed constraint formation optimal tracking control protocol to ensure that a dynamic regret value and a constraint violation value increase linearly over time.

[0019] The constraint formation optimal tracking model solving module is configured to solve the constraint formation optimal tracking model based on the distributed constraint formation optimal tracking control protocol and the control protocol parameter to obtain an optimal formation tracking result.

[0020] In a third aspect, the present application provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned distributed constraint formation optimal tracking method.

[0021] In a fourth aspect, the present application provides a computer readable storage medium having a computer program stored thereon, wherein the computer program is executable by a processor to implement the above-mentioned distributed constraint formation optimal tracking method.

[0022] According to the embodiments provided in the present application, the following technical effects are achieved:

[0023] The application provides a distributed constraint formation optimal tracking method, device, equipment and medium, proposes a distributed constraint formation optimal tracking control protocol, the distributed constraint formation optimal tracking control protocol utilizes an original dual mechanism to cope with challenges brought by time-varying optimization tasks and various coupled constraints for a trajectory estimation layer, and introduces a prediction optimal tracking control technology to process problems brought by heterogeneous linear dynamics and rapidly changing trajectory estimation values for a tracking control layer, through designing control inputs for a heterogeneous cluster system, so that each intelligent agent can solve a constraint formation optimal tracking model in a distributed manner online under the condition that local information (including self-set constraints, a sub-gradient of a local target function, and a sub-gradient of a local inequality constraint function) of a current time is known, and part of information (including neighbor formation center vector update estimation and normalized left eigenvector estimation) of neighbors is obtained through a communication topology, so that dynamic regret values and constraint violation values are linearly increased over time, thereby realizing constraint formation optimal tracking. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0025] Figure 1 An application environment diagram of a distributed constraint formation optimal tracking method in an embodiment of the present application;

[0026] Figure 2 A flowchart of a distributed constraint formation optimal tracking method provided by an embodiment of the present application;

[0027] Figure 3 A specific process diagram of a distributed constraint formation optimal tracking method provided by an embodiment of the present application;

[0028] Figure 4 A distributed constraint formation optimal tracking control protocol block diagram provided by an embodiment of the present application;

[0029] Figure 5 A communication topology diagram provided by an embodiment of the present application;

[0030] Figure 6 A dynamic regret value curve diagram provided by an embodiment of the present application;

[0031] Figure 7 A cumulative violation value curve diagram about formation constraints provided by an embodiment of the present application;

[0032] Figure 8 A cumulative violation value graph about inequality constraints provided for an embodiment of the present application;

[0033] Figure 9 A trajectory curve result schematic diagram provided for an embodiment of the present application;

[0034] Figure 10 A function module schematic diagram of a distributed constraint formation optimal tracking device provided for an embodiment of the present application;

[0035] Figure 11 A structure schematic diagram of a computer device provided for an embodiment of the present application. DETAILED DESCRIPTION

[0036] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0037] The above purposes, features and advantages of the present application can be more obvious and easy to understand. The present application will be further described in detail below with reference to the drawings and specific embodiments.

[0038] The distributed constraint formation optimal tracking method provided by the embodiments of the present application can be applied to, for example Figure 1The application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data required by the server 104 to process. The data storage system can be set up separately, or integrated on the server 104, or placed on the cloud or other servers. The terminal 102 can send a tracking control request to the server 104. After receiving the tracking control request, the server 104 establishes a communication topology structure within the heterogeneous cluster system for the tracking control request, establishes a dynamic model of the heterogeneous cluster system, establishes a constrained formation optimal tracking model based on the communication topology structure and the dynamic model, designs a distributed constrained formation optimal tracking control protocol, determines the control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value grow linearly with time, and solves the constrained formation optimal tracking model based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters. The server 104 can feed back the video tags obtained for the video to the terminal 102. In addition, in some embodiments, the distributed constrained formation optimal tracking method can also be implemented by the server 104 or the terminal 102 alone, such as the terminal 102 directly processing the video tags for the tracking control request, or the server 104 obtaining the tracking control request from the data storage system and processing the video tags for the tracking control request.

[0039] Among them, the terminal 102 can be, but not limited to, various desktop computers, notebook computers, smart phones, tablet computers, Internet of Things devices and portable wearable devices. The Internet of Things device can be a smart speaker, a smart TV, a smart air conditioner, a smart vehicle device, etc. The portable wearable device can be a smart watch, a smart bracelet, a head-mounted device, etc. The server 104 can be implemented by an independent server or a server cluster composed of multiple servers, and can also be a cloud server.

[0040] In an exemplary embodiment, as Figure 2 shown, a distributed constrained formation optimal tracking method is provided, which is executed by a computer device, specifically by a terminal or a server, etc. Computer device alone, or by a terminal and a server together, in the embodiment of the application, take the server 104 in the Figure 1 application environment as an example for illustration, including the following steps 201 to 206. Among them:

[0041] Step 201, a communication topology structure within the heterogeneous cluster system is established; the heterogeneous cluster system includes a plurality of intelligent agents.

[0042] Step 202, a dynamic model of the heterogeneous cluster system is established.

[0043] Step 203, based on the communication topology and the dynamic model, a constrained formation optimal tracking model is established; the constrained formation optimal tracking model includes a global objective function and a constraint condition.

[0044] Step 204, a distributed constrained formation optimal tracking control protocol is designed; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller and a primal-dual update mechanism; the weighted average consensus mechanism is used for an agent to update a weighted average estimation of a formation center vector and a normalized left eigenvector based on neighbor information; the predictive tracking controller generates a control input based on the weighted average estimation to track a formation configuration; and the primal-dual update mechanism is used for updating an estimated value of the formation center vector and an estimated value of a dual vector.

[0045] Step 205, control protocol parameters of the distributed constrained formation optimal tracking control protocol are determined to ensure that a dynamic regret value and a constraint violation value linearly grow over time.

[0046] Step 206, based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, the constrained formation optimal tracking model is solved to obtain an optimal formation tracking result.

[0047] The steps 201 to 206 are implemented to propose a distributed constrained formation optimal tracking control protocol, which uses a primal-dual mechanism to cope with challenges brought by time-varying optimization tasks and multiple coupling constraints to a trajectory estimation layer, and introduces a predictive optimal tracking control technology to deal with problems brought by heterogeneous linear dynamics and rapidly changing trajectory estimation values to a tracking control layer, and by designing control inputs for a heterogeneous cluster system, each agent can solve the constrained formation optimal tracking model in a distributed manner online under the condition that local information (including its own set constraints, a subgradient of a local objective function, and a subgradient of a local inequality constraint function) at a current time is known, and part of neighbor information (including neighbor formation center vector update estimation and normalized left eigenvector estimation) is obtained through a communication topology, so that the dynamic regret value and the constraint violation value linearly grow over time. In addition, the application can use online convex optimization theory and discrete-time Lyapunov theory to provide a parameter determination method, which can ensure that an upper bound of related errors of the distributed constrained formation optimal tracking control protocol has a linear convergence speed, that is, the optimal solution can be approximated with a bounded error in a sufficiently large time domain, so as to realize the constrained formation optimal tracking.

[0048] As Figure 3As shown, first, the communication topology within the heterogeneous swarm system is described; second, the dynamic model of each agent in the heterogeneous swarm system is established; then, based on the above description of the communication topology and the dynamic model, the constrained formation optimal tracking problem in this application is defined clearly, thereby laying a foundation for the subsequent protocol design; next, the specific expression form of the constrained formation optimal tracking control protocol is given; finally, the control protocol parameters to be designed in the distributed constrained formation optimal tracking control protocol are determined to ensure that the heterogeneous swarm system can achieve the above constrained formation optimal tracking under the proposed distributed constrained formation optimal tracking control protocol.

[0049] In another exemplary embodiment of the present application, the above step 201 specifically includes: representing the structure within the heterogeneous swarm system based on graph theory to obtain a directed graph; the directed graph is used to define the communication topology within the heterogeneous swarm system; the directed graph is composed of a node set and an edge set; the node set includes a plurality of nodes; one node corresponds to one agent; the edge set is composed of a plurality of edges; the agents corresponding to the two nodes connected by the edge can obtain each other's information.

[0050] The communication topology can be a directed graph , where, and represent the node set and the edge set, respectively; N is a positive integer, representing the number of agents; (i,j) represents an edge with the nodes corresponding to agent i and agent j as endpoints. If agent i can obtain the information of agent j through the communication topology, then (i,j) ∈ E; otherwise If there is a path from agent i to agent j for any agent , then the directed graph is connected. In addition, represents the neighbor set of agent i; represents the in-degree of agent i, i.e., the cardinality of the neighbor set of agent i.

[0051] It should be noted that the agent in this application can be a type of unmanned vehicle, unmanned aerial vehicle, etc., and the heterogeneous swarm system is a swarm system composed of at least two different types of agents.

[0052] Let be a weight matrix associated with the directed graph that satisfies the line stochastic property, i.e., for any agent , represents a set of N×N real-valued matrices, w ij represents the weight factor of agent i to agent j. For any , if (i,j) ∈ E, then wij > 0, otherwise w ij = 0, i.e. the edge between the nodes corresponding to agent i and agent j belongs to the edge set E, the weight factor w ij > 0, otherwise the weight factor w ij = 0. Let be the normalized left eigenvector of the weight matrix W, i.e. T W = π T and π T 1 = 1, denote a set of a-dimensional real-valued vectors, (·) T denotes the transpose. It is noted that the weight matrix W is usually artificially set in advance according to the connectivity of the directed graph .

[0053] In step 202, for any time where K is a positive integer, the dynamic model of the heterogeneous swarm system is:

[0054]

[0055] where, is the state of agent i at time k, is the output of agent i at time k, is the input of agent i at time k, A i , B i , C i is the system matrix, p i , m, r i are positive integers, representing the state dimension, the output dimension, and the input dimension, respectively.

[0056] Based on the above description of the communication topology structure and the dynamic model, the constraint formation optimal tracking problem mainly concerned by the present application is defined, i.e. the constraint formation optimal tracking problem is described.

[0057] Firstly, the formation constraint is defined. Given the desired formation configuration for any has is the formation constraint set, which is composed of all possible formation configuration affine transformations, where diag denotes a diagonal matrix, I m denotes an m-dimensional identity matrix, and a i denotes the formation configuration affine transformation of agent i.

[0058] Secondly, the constraint formation optimal tracking problem is defined. For any time , any agent is given the local set constraint Local objective function f i,k : Local inequality constraint function g i,k : denotes a set of real-valued scalars. Based on this, the constrained formation optimal tracking problem is to design the control input for the heterogeneous swarm system such that the following holds, i.e., the constrained formation optimal tracking model is given by

[0059]

[0060] where min denotes minimization; s.t. is the abbreviation of subject to, denoting the constraint condition; is the global set constraint, which is stacked by the local set constraints of all agents; denotes the set of agents; y k+1 is the global output vector, which is stacked by the output vectors of all agents; f k : is the global objective function, which is the summation of the cumulative local objective functions of all agents; f i,c (y i,k+1 ) is the local objective function of agent i at time k+1; y i,k+1 ) is the output vector of agent i at time k+1; is the formation constraint; g k : is the global inequality constraint function, which is stacked by the cumulative local inequality constraint functions of all agents.

[0061] Further, the constrained formation optimal tracking problem is equivalently converted to facilitate the design of the subsequent distributed constrained formation optimal tracking control protocol. The constrained formation optimal tracking model shown in equation (2) can be equivalently converted to the following.

[0062]

[0063] where, is the formation center vector; is the local set constraint of agent i with respect to the formation center vector, satisfying is the global set constraint with respect to the formation center vector, which is the intersection of the local set constraints of all agents with respect to the formation center vector; h′ is the augmented formation configuration matrix, satisfying where horz and vert denote horizontal connection and vertical connection, respectively, and 1 denotes a 1 vector with appropriate dimension. i is the augmented formation vector of agent i, i.e., the i-th row of h′.

[0064] Finally, we define whether the distributed constraint formation optimal tracking control protocol can achieve the above-mentioned constraint formation optimal tracking problem, that is, we give the performance evaluation conditions of the distributed constraint formation optimal tracking control protocol.

[0065] Definition 1: Given the output {y} of a heterogeneous cluster system i,c The values ​​of c = 1, 2, ..., k+1 and the estimated values ​​of the formation center vector. The dynamic regret value and constraint violation value of formula (3) are shown in the following formula.

[0066]

[0067] in, This is the dynamic regret value, used to represent the cumulative error between the actual output and the optimal value; Let i be the local cumulative violation value of agent i with respect to the inequality constraints; It refers to the cumulative violation value of formation constraints; y c* =h'q c* Let q be the optimal value of the global output vector at time c; c* Let be the optimal value of the formation center vector at time c; Let ρ be the weighted average of the formation center vector estimates of all agents at time c, where ρ is a row random vector, [·]. i This represents the i-th element of the random vector in that row; Π + This represents the projection onto the non-negative quadrant. If the upper bounds of the dynamic regret value and constraint violation value increase linearly with time, i.e. in If k represents the same order as k, then the heterogeneous cluster system is said to approximate the optimal solution with bounded error over a sufficiently large time domain, thus achieving constrained formation optimal tracking.

[0068] In summary, the objective of this application is to design control inputs for heterogeneous cluster systems, such that each agent, knowing its local information at the current time (including its own set constraints, the subgradient of the local objective function, and the subgradient of the local inequality constraint function), and through the communication topology... With partial information about the neighbors (including the update estimate of the neighbor's formation center vector and the estimate of the normalized left eigenvector), formula (2) (or formula (3)) can be solved online in a distributed manner, so that the dynamic regret value and constraint violation value in formula (4) both increase linearly with time, thereby achieving optimal constrained formation tracking. Next, step 204 will design a distributed constrained formation optimal tracking control protocol for this objective to determine the control input.

[0069] like Figure 4 As shown, in step 204, for any given time... each agent The distributed constraint formation optimal tracking control protocol of each agent mainly based on the following flow, including the following steps 301-303.

[0070] Step 301: First, based on the updated estimation in step 303 at the last time (i.e. the updated estimation of the formation center vector estimation value and the updated estimation of the dual vector estimation value) and the neighbor information obtained by using the communication topology, a weighted average consensus mechanism is designed to obtain the weighted average estimation at the current time to ensure that the estimation of the heterogeneous cluster system can reach a consensus as a whole; the neighbor information includes the updated estimation of the neighbor (neighbor agent).

[0071] Specifically: the weighted average consensus mechanism. Agent i calculates the weighted average estimation of the formation center vector and the weighted average estimation of the normalized left eigenvector through communication with neighbor agents, and the calculation formula of the weighted average consensus mechanism is:

[0072]

[0073] wherein, denotes the weighted average estimation of the formation center vector of agent i at time k for the time k+v-1; N is the number of agents, w ij denotes the weight factor of agent i to agent j; q j,k+v-1 denotes the updated estimation of the formation center vector of agent j at time k-1 for the time k+v-1; κ i,k+v denotes the weighted average estimation (or updated estimation) of the normalized left eigenvector of agent i at time k for the time k+v; κ j,k+v-1 denotes the weighted average estimation (or updated estimation) of the normalized left eigenvector of agent j at time k-1 for the time k+v-1, q j,k+v-1 and κ j,k+v-1 are obtained through the communication between agent i and agent j. The initial value is selected as q i,l =0, κ i,l =e i , l=1,...,v, wherein 0 denotes a 0 vector or a 0 matrix with appropriate dimensions, e i denotes a vector with appropriate dimensions, the i-th element is 1, and the rest of the elements are all 0.

[0074] Step 302: Based on the weighted average estimation of the formation center vector obtained in step 301 and the first local information, a prediction tracking controller is formulated, which enables the output of the agent to track the estimation information at the next time; the first local information includes the state, output and formation configuration vector of itself.

[0075] Specifically, the predicted tracking control protocol. The agent i estimates the weighted average of the formation center vector, and calculates the control input at the k+1 time at the k time. The control input of the predicted tracking controller is as follows:

[0076]

[0077] Where, Δu i,k = u i,k+1 - u i,k represents the control input difference of agent i at k time, u i,k+1 represents the control input of agent i at k+1 time, u i,k represents the control input of agent i at k time, represents the optimal control gain, represents the augmented state of agent i at k time, represents the augmented error, represents the tracking error, Δx i,k = x i,k+1 - x i,k represents the state difference, x i,k+1 represents the state of agent i at k+1 time, x i,k represents the state of agent i at k time, represents the augmented predicted state estimate, T represents transposition.

[0078] Specifically, the evolution equation of the augmented state is as follows:

[0079]

[0080] Where, X i,k+1 represents the augmented state of agent i at k+1 time, and represents a system matrix with appropriate dimensions, and the formula is as follows:

[0081]

[0082] In the formula, G i ' ,q , A i ', G i =, G i,q represents an intermediate variable matrix; A i , B i , C i is a system matrix 0, which represents a 0 vector or 0 matrix with appropriate dimensions; I represents a unit matrix with appropriate dimensions.

[0083] The optimal control gain calculation formula is as follows:

[0084]

[0085] where argmin denotes the argument that minimizes the function, K i denotes the control gain of agent i, J i,k denotes a quadratic objective function for evaluating the optimal control gain, which is formulated as follows:

[0086]

[0087] where X i,c denotes the augmented state of agent i at time c, denotes an augmented evaluation matrix with respect to the augmented state, Q i denotes an evaluation matrix with respect to the state, R i denotes an evaluation matrix with respect to the control input difference.

[0088] Step 303: Based on the weighted average estimate in step 301 and the second local information, an original dual-based updating mechanism is designed to update the weighted average estimate in step 301 as the input of 1) at the next time. The second local information includes the sub-gradient of the local objective function, the sub-gradient of the local inequality constraint function, the local set constraint and the formation configuration vector.

[0089] It should be noted that each agent can predict the information of the local objective function and the local inequality constraint function in v steps in advance, where v is a positive integer, representing the prediction time step.

[0090] Specifically, the original dual-based updating mechanism. Agent i updates the formation center vector estimate value at the k+v time and the dual vector estimate value for processing constraints based on the weighted average estimate of the formation center vector and the weighted average estimate of the normalized left eigenvector, respectively. The original dual updating mechanism includes the update of the formation center vector estimate value and the update of the dual vector estimate value, which are represented as follows:

[0091]

[0092] where q i,k+v denotes the formation center vector update estimate of agent i at the k time for the k+v time, Π M denotes the projection on M, denotes the weighted average estimate of the formation center vector of agent i at the k time for the k+v-1 time, α k and δ k are control protocol parameters, h' is an augmented formation configuration matrix, λ i,k+v denotes the dual vector update estimate of agent i at the k time for the k+v time, Π +denotes the projection on the non-negative quadrant, λ i,k+v-1 denotes the dual vector update estimation of agent i at time k-1 for time k+v-1, and denote the subgradient of the Lagrangian function with respect to the formation center vector and the subgradient of the Lagrangian function with respect to the dual vector, respectively, and are calculated as follows.

[0093]

[0094] where the initial value is selected as λ i,l = 0, l = 1,..., v, and i,k and i,k denote the subgradient of the local inequality constraint function and the local objective function with respect to the formation center vector, respectively, and are given as the own information.

[0095] In step 205, the control protocol parameters are determined by using the online convex optimization theory and the discrete-time Lyapunov theory, and the specific process is as follows: the control protocol parameters include the evaluation matrix, the optimal control gain and the step length; based on the definition 1 in step 203, in order to ensure that the distributed constraint formation optimal tracking control protocol in step 204 can realize formula (2) (or formula (3)), that is, to ensure that the dynamic regret value and the constraint violation value is linearly increasing, for any time each agent in the distributed constraint formation optimal tracking control protocol can be designed as follows:

[0096] 1) the evaluation matrix Q i with respect to the state and the evaluation matrix R i with respect to the control input difference are selected as symmetric positive definite matrices, and is detectable;

[0097] 2) the optimal control gain satisfies where is the unique positive definite solution of the Riccati equation as follows:

[0098]

[0099] 3) the step length is set as k = k -0.5 , and k = k -0.2 .

[0100] The effect of the routine of the distributed constraint formation optimal tracking method provided in the application is as follows:

[0101] Consider a heterogeneous swarm system including two types of agents, i.e., UAVs and UGVs, which specifically includes 1 UAV and 4 UGVs. Based on the inner-outer loop control framework, the dynamics of UAVs and UGVs can be approximated by Equation (1). Note that the flight altitude of UAVs is assumed to be constant, thus the altitude is not considered in this routine, and the following routine is implemented in a two-dimensional plane, i.e., m = 2 in Equation (1). Specifically, the parameters of UAV (i = 1) are:

[0102]

[0103] The parameters of UGV (i = 2, 3, 4, 5) are:

[0104] A i = I2, B i = I2Δt, C i = I2 (17).

[0105] where Δt = 0.02s is the sampling interval.

[0106] The communication topology of the above heterogeneous swarm system is shown in Figure 5 , where the hexagon represents a UAV, the circle represents a UGV, and the number represents the agent index; the solid line represents the communication edge, and the arrow represents the information transmission direction.

[0107] The constrained formation optimal tracking task is defined by Equation (2), specifically, f i,k (y i,k+1 ) = 0.5||a i,k + b i,k 0.05kΔt + c i,k h i - y i,k+1 || 2 , where a i,k , b i,k , c i,k are randomly generated, and h is set to a regular pentagon. The above task can be understood as: in a fixed rectangular region , there are two threat regions with strong and weak threats, and each agent expects to complete the dynamic task described by f i,k with good global performance in the non-threat region of the rectangular region while maintaining the regular pentagon formation configuration. In addition, each agent can only obtain partial information about the task at any time, and has a limited and different field of view when observing the threat region, which is described by g i,k .

[0108] Figure 6 、 Figure 7 and Figure 8The heterogeneous swarm system obtains the curve results of the dynamic regret value, the cumulative violation value of the formation constraint, and the cumulative violation value of the inequality constraint under the distributed constraint formation optimal tracking control protocol of the application. In the legend, "total" represents the component related to the agent 1, 2, 3, 4, and 5 in the formula (4), "agent 1, 2, 3, 4, 5 (threat zone 1, threat zone 2)" represents the component related to the agent 1, 2, 3, 4, and 5 in the formula (4) and the threat zone 1 and the threat zone 2. and "Agent 1, 2, 3, 4, 5" represents the component related to the agent 1, 2, 3, 4, and 5 in the formula (4). and "Agent 1, 2, 3, 4, 5 (threat zone 1, threat zone 2)" represents the component related to the agent 1, 2, 3, 4, and 5 in the formula (4) and the threat zone 1 and the threat zone 2. and Figure 6 In (a) of FIG. 13, (a) is the evolution curve of the dynamic regret value at all times, Figure 6 (b) is the partial evolution curve of the dynamic regret value under the equidistant scale. Figure 7 In (a) of FIG. 14, (a) is the evolution curve of the cumulative violation value of the formation constraint at all times, Figure 7 (b) is the partial evolution curve of the cumulative violation value of the formation constraint under the equidistant scale.

[0109] As can be seen from Figure 6 , Figure 7 and Figure 8 , the dynamic regret value and the formation constraint violation value can achieve linear growth, and the inequality constraint violation value can achieve sub-linear growth better than linear growth. Therefore, the distributed constraint formation optimal tracking control protocol proposed in the application can enable the heterogeneous swarm system to achieve constraint formation optimal tracking.

[0110] In addition, in order to more intuitively give the implementation process of the constraint formation optimal tracking, Figure 9 the trajectory curve results obtained by the heterogeneous swarm system under the distributed constraint formation optimal tracking control protocol of the application are shown. Figure 9 In the figure, the rhombus represents the initial position of the agent, the pentagram represents the end position of the agent, the line represents the trajectory curve of the agent, the horizontal coordinate represents the state component along the X-axis, and the vertical coordinate represents the state component along the Y-axis. The formation configuration of all agents at time k = 100, 200, 300, 400, 500, 600, 700, 800, 900, and 1000 is shown, and the gray area represents the threat zone. As can be seen from Figure 9 , all agents can always satisfy the formation constraint of the regular pentagon and can avoid the threat zone. Therefore, the constraint formation optimal tracking can be achieved.

[0111] The application also provides an application scenario of the distributed constraint formation optimal tracking method. Specifically, the distributed constraint formation optimal tracking method provided in the embodiment can be applied in a formation optimal tracking scenario. The formation optimal tracking scenario includes a request generation link, a formation optimal tracking processing link, and a formation control link. A tracking control request enters the formation optimal tracking link from the request generation link, obtains corresponding content features through human-computer cooperation, and enters the downstream formation control link. The distributed constraint formation optimal tracking method provided in the embodiment belongs to the formation optimal tracking link. Specifically, in the process of the formation optimal tracking link for the tracking control request, a communication topology structure inside a heterogeneous cluster system can be established, a dynamic model of the heterogeneous cluster system can be established, a constraint formation optimal tracking model can be established based on the communication topology structure and the dynamic model, a distributed constraint formation optimal tracking control protocol can be designed, control protocol parameters of the distributed constraint formation optimal tracking control protocol can be determined to ensure that a dynamic regret value and a constraint violation value linearly increase over time, the constraint formation optimal tracking model can be solved based on the distributed constraint formation optimal tracking control protocol and the control protocol parameters, and an optimal formation tracking result can be obtained.

[0112] Based on the same inventive concept, the embodiment of the application further provides a distributed constraint formation optimal tracking device for implementing the distributed constraint formation optimal tracking method described above. The implementation scheme for solving problems provided by the device is similar to the implementation scheme described in the above method, and therefore the specific limitations in one or more distributed constraint formation optimal tracking device embodiments provided below can be referred to the limitations of the distributed constraint formation optimal tracking method described above, which will not be repeated here.

[0113] In one exemplary embodiment, as shown in Figure 10 a distributed constraint formation optimal tracking device is provided, which includes the following modules:

[0114] A communication topology structure establishment module T1 is configured to establish a communication topology structure inside a heterogeneous cluster system; the heterogeneous cluster system includes a plurality of intelligent agents;

[0115] A dynamic model establishment module T2 is configured to establish a dynamic model of the heterogeneous cluster system;

[0116] A constraint formation optimal tracking model establishment module T3 is configured to establish a constraint formation optimal tracking model based on the communication topology structure and the dynamic model; the constraint formation optimal tracking model includes a global objective function and a constraint condition;

[0117] The distributed constraint formation optimal tracking control protocol design module T4 is configured to design a distributed constraint formation optimal tracking control protocol. The distributed constraint formation optimal tracking control protocol comprises a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism. The weighted average consensus mechanism is configured to update a weighted average estimate of a formation center vector and a normalized left eigenvector based on neighbor information of an agent. The predictive tracking controller is configured to generate a control input based on the weighted average estimate to track a formation configuration. The primal-dual update mechanism is configured to update an estimate of the formation center vector and an estimate of a dual vector.

[0118] The control protocol parameter determination module T5 is configured to determine a control protocol parameter of the distributed constraint formation optimal tracking control protocol to ensure that a dynamic regret value and a constraint violation value increase linearly over time.

[0119] The constraint formation optimal tracking model solving module T6 is configured to solve the constraint formation optimal tracking model based on the distributed constraint formation optimal tracking control protocol and the control protocol parameter to obtain an optimal formation tracking result.

[0120] In an exemplary embodiment, a computer device can be provided, which can be a server or a terminal. An internal structure diagram of the computer device can be as shown in Figure 11 The computer device comprises a processor, a memory, an input / output interface (I / O), and a communication interface. The processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for running the operating system and the computer program in the non-volatile storage medium. The database of the computer device is configured to store distributed constraint formation optimal tracking processing data. The input / output interface of the computer device is configured to exchange information between the processor and external devices. The communication interface of the computer device is configured to communicate with external terminals through a network connection. The computer program is executed by the processor to implement a distributed constraint formation optimal tracking method.

[0121] Those skilled in the art can understand that Figure 11 The structure shown in the above embodiment is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. Specifically, the computer device can comprise more or fewer components than those shown in the figure, or some components can be combined, or have a different arrangement of components.

[0122] In an example embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, and the processor implementing the steps in the above method embodiments when executing the computer program.

[0123] In an example embodiment, a computer readable storage medium is provided, storing a computer program, and the computer program implements the steps in the above method embodiments when executed by a processor.

[0124] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties, and the collection, use and processing of related data need to comply with relevant regulations.

[0125] It can be understood by those skilled in the art that all or part of the processes in the above embodiments can be completed by a computer program instructing related hardware, and the computer program can be stored in a non-volatile computer readable storage medium. When the computer program is executed, it can include the processes of the above embodiments. Any reference to memory, database or other medium used in the embodiments provided by the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0126] The database involved in each of the embodiments provided in the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a blockchain, and the like, without being limited thereto. The processor involved in each of the embodiments provided in the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, and the like, without being limited thereto.

[0127] The technical features of the above embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, but it should be considered that any combination of the technical features is within the scope of the present disclosure, as long as there is no contradiction.

[0128] The principles and implementation manners of the present application are described by using specific examples herein, and the above embodiments are only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation manners and application ranges can be changed according to the idea of the present application. In summary, the content of the present description should not be understood as a limitation of the present application.

Claims

1. A distributed constrained formation optimal tracking method, characterized in that, The distributed constrained formation optimal tracking method includes: Establish the communication topology within the heterogeneous cluster system; the heterogeneous cluster system includes several intelligent agents; Establish a dynamic model for the heterogeneous cluster system; Based on the communication topology and the dynamic model, a constrained formation optimal tracking model is established; the constrained formation optimal tracking model includes a global objective function and constraints. Design a distributed constrained formation optimal tracking control protocol; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism; the weighted average consensus mechanism is used by the agent to update the weighted average estimate of the formation center vector and the normalized left eigenvector based on neighbor information; the predictive tracking controller generates control input based on the weighted average estimate to track the formation configuration; the primal-dual update mechanism is used to update the estimated values ​​of the formation center vector and the dual vector; the primal-dual update mechanism includes updating the estimated values ​​of the formation center vector and the dual vector, respectively represented as follows: Where, q i,k+v Π represents the update estimate of the formation center vector of agent i at time k to that at time k+v. M This represents the projection onto M. α represents the weighted average estimate of the formation center vector at time k by agent i at time k+v-1. k and δ k To control protocol parameters, and Let represent the subgradients of the Lagrange function with respect to the formation center vector and the dual vector, respectively; h′ is the augmented formation configuration matrix; λ i,k+v Π represents the update estimate of the dual vector at time k+v by agent i at time k. + λ represents the projection onto the non-negative quadrant. i,k+v-1 This represents the update estimate of the dual vector at time k+v-1 by agent i at time k-1; Determine the control protocol parameters of the optimal tracking control protocol for the distributed constraint formation to ensure that the dynamic regret value and constraint violation value increase linearly with time. Based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, the constrained formation optimal tracking model is solved to obtain the optimal formation tracking result.

2. The distributed constrained formation optimal tracking method according to claim 1, characterized in that, Establishing the communication topology within the heterogeneous cluster system specifically includes: Based on graph theory, the internal structure of a heterogeneous cluster system is represented to obtain a directed graph. The directed graph is used to define the communication topology within the heterogeneous cluster system. The directed graph consists of a set of nodes and a set of edges. The set of nodes includes several nodes, and each node corresponds to an agent. The set of edges consists of several edges, and the agents corresponding to the two nodes connected by the edges can obtain each other's information.

3. The distributed constrained formation optimal tracking method according to claim 1, characterized in that, The dynamic model is as follows: Where, x i,k Let y be the state of agent i at time k. i,k Let u be the output of agent i at time k. i,k Let A be the input of agent i at time k. i B i C i This is the system matrix.

4. The distributed constrained formation optimal tracking method according to claim 1, characterized in that, The constrained formation optimal tracking model is represented as follows: Where min represents minimization; st represents the constraint condition; The global set constraints are composed of a stack of local set constraints from all agents. Represents a set of intelligent agents; y k+1 The global output vector is a stack of the output vectors of all agents; f k The global objective function is f. i,c (y i,k+1 Let y be the local objective function of agent i at time k+1; i,k+1 Let be the output vector of agent i at time k+1; For formation constraints; g k It is a global inequality constraint function, which is composed of a stack of cumulative local inequality constraint functions of all agents.

5. The distributed constrained formation optimal tracking method according to claim 1, characterized in that, The calculation formula for the weighted average consensus mechanism is as follows: in, This represents the weighted average estimate of the formation center vector at time k by agent i at time k+v-1; N is the number of agents, w ij q represents the weight factor of agent i to agent j; j,k+v-1 This represents the update estimate of the formation center vector of agent j at time k-1 to that at time k+v-1; κ i,k+v κ represents the normalized left eigenvector weighted average estimate of agent i at time k to time k+v; j,k+v-1 This represents the weighted average estimate of the normalized left eigenvector at time k+v-1 by agent j at time k-1.

6. The distributed constrained formation optimal tracking method according to claim 1, characterized in that, The control input for the predictive tracking controller is: Where, Δu i,k =u i,k+1 -u i,k U represents the control input difference of agent i at time k. i,k+1 U represents the control input of agent i at time k+1. i,k This represents the control input of agent i at time k. X represents the optimal control gain. i,k It indicates an augmented state.

7. A distributed constrained formation optimal tracking device, characterized in that, The distributed constrained formation optimal tracking device includes: A communication topology establishment module is used to establish the communication topology within a heterogeneous cluster system; the heterogeneous cluster system includes several intelligent agents. The dynamics model building module is used to build the dynamics model of the heterogeneous cluster system. A constrained formation optimal tracking model establishment module is used to establish a constrained formation optimal tracking model based on the communication topology and the dynamic model; the constrained formation optimal tracking model includes a global objective function and constraints; A distributed constrained formation optimal tracking control protocol design module is used to design a distributed constrained formation optimal tracking control protocol. The distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism. The weighted average consensus mechanism is used by the agent to update the weighted average estimate of the formation center vector and the normalized left eigenvector based on neighbor information. The predictive tracking controller generates control input based on the weighted average estimate to track the formation configuration. The primal-dual update mechanism is used to update the estimated values ​​of the formation center vector and the dual vector. The primal-dual update mechanism includes updating the estimated values ​​of the formation center vector and the dual vector, respectively represented as follows: Where, q i,k+v Π represents the update estimate of the formation center vector of agent i at time k to that at time k+v. M This represents the projection onto M. α represents the weighted average estimate of the formation center vector at time k by agent i at time k+v-1. k and δ k To control protocol parameters, and Let represent the subgradients of the Lagrange function with respect to the formation center vector and the dual vector, respectively; h′ is the augmented formation configuration matrix; λ i,k+v Π represents the update estimate of the dual vector at time k+v by agent i at time k. + λ represents the projection onto the non-negative quadrant. i,k+v-1 This represents the update estimate of the dual vector at time k+v-1 by agent i at time k-1; The control protocol parameter determination module is used to determine the control protocol parameters of the optimal tracking control protocol for the distributed constraint formation to ensure that the dynamic regret value and constraint violation value increase linearly over time. The constrained formation optimal tracking model solution module is used to solve the constrained formation optimal tracking model based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, so as to obtain the optimal formation tracking result.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the distributed constrained formation optimal tracking method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the distributed constrained formation optimal tracking method as described in any one of claims 1-6.

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