Multi-group system optimization formation method based on time constraint

Abstract

The invention belongs to the technical field of intelligent algorithms, and particularly relates to a multi-group system optimization formation method based on time constraint, and the method specifically comprises the steps: 1, building a second-order linear time-invariant systematic formula 1 for each main body in a group system; 2, designing a control protocol, calculating a residual state space distance by each agent by using a current state and a target domain boundary, and estimating residual arrival time in combination with dynamic characteristics of the agents, so as to construct a predetermined space-time formation convergence control protocol; and step 3, solving parameters of the control protocol to complete optimization of the performance index formula 2, so that the group system can meet to a specified area within given time, and expected formation is realized under the condition that performance indexes are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent algorithms, and particularly relates to an optimized formation method for multi-group systems based on time constraints. Background Art

[0002] Currently, when group systems distributed in different regions perform unified formation tasks, they often need to reach designated regions within a given time to form an expected formation. For example, when an unmanned aerial vehicle (UAV) cluster located in different warehouses goes to a disaster area to perform communication relay tasks, they need to rendezvous within a specified time so that an effective communication can be established between the rear rescue command post and the vast affected areas in the front; during a large-scale UAV cluster light show, due to site restrictions, the UAV cluster also needs to be dispersed in different regions before the show starts and quickly rendezvous within a given time after the show starts to form an expected formation. However, most of the current cluster formation methods only consider the formation control strategy of a single group system in the same region, lacking algorithms for the formation control of group systems in multiple regions under given time constraints, and there are situations where the queuing path or the calculated output result is not optimal during the formation of multi-clusters in different regions. Summary of the Invention

[0003] The purpose of the present invention is to provide an optimized formation method for multi-group systems based on time constraints to solve the problems mentioned in the background art.

[0004] To achieve the above technical purpose, the technical solution adopted by the present invention is as follows:

[0005] An optimized formation method for multi-group systems based on time constraints, characterized in that the specific steps are as follows:

[0006] Step 1: Establish a dynamic characteristic description for each agent in the group system as a second-order linear time-invariant system, Equation (1):

[0007]

[0008] where k = 1, 2,..., M represents the subgroup sequence, and M is the number of subgroups; i = 1, 2,..., N k , N k represents the number of agents in the k-th subgroup; represents the state vector of agent i in subgroup k, x k,ip (t) ∈ Ρ n is the position state component, x k,iu (t) ∈ Ρ n is the velocity state component, Ρ n represents an n-dimensional real vector space;

[0009] is the system matrix, where α 0 and α 1It can be configured according to the dynamic characteristics of the system;

[0010] is the system input matrix;

[0011] u m (t) ∈ Ρ n is the system control input;

[0012] Step 2: Design the control protocol. Each agent calculates the remaining state space distance using the current state and the target domain boundary, and estimates the remaining arrival time by combining the agent's dynamic characteristics, thereby constructing a predetermined spatio-temporal formation convergence control protocol;

[0013] Step 3: Obtain the parameters of the control protocol to complete the optimal formation control of Equation (1).

[0014] In the above Step 1, it can be specifically seen that the system described by the matrix (A, B) is a controllable canonical form. That is, for any controllable second-order linear time-invariant system represented by a state differential equation, it can be equivalently transformed into Equation (1). In addition, Equation (1) describes a multi-group system, where the subscript k represents the group number, and the subscript i represents the number of each agent within the group.

[0015] Furthermore, for unmanned systems such as unmanned aerial vehicles, ground robots, and unmanned ships, when considering their spatial displacement motion, they can also be modeled as a second-order system like Equation (1). Therefore, the second-order active dynamics modeled by Equation (1) is general. Thus, the time-varying formation vector of the k-th subgroup is defined as The performance index function is designed as Equation (2) below:

[0016]

[0017] In the formula, the parameter t k0 , t k,i , T des , Q k respectively represent the initial time when the k-th subgroup departs, the time to enter the target domain, the expected convergence time, and the performance weight matrix of the formation coordination error within the group; ρ 1 , ρ 2 , ρ 3 are the index weights such as the convergence error, formation coordination error, and time synchronization error; represents the remaining distance error between the state of agent i in the k-th subgroup at time t and the target domain boundary, c is the center of the target area, and C is the radius of the target domain; e k,ij (t) = x k,i (t) - f k,i (t) - x k,j (t) - h k,j (t) is the coordination error between agent i and j;

[0018] The above key parameters and variables make the performance index function J C be constructed as the sum of a finite-time quadratic integral function of the formation convergence control error and the convergence time error, and the optimization objective of the formation convergence control is to minimize the index function J C .

[0019] Furthermore, if for any bounded initial state x k,i (0) (i = 1, 2,..., N k , k = 1, 2,..., M), there exists a formation control protocol u k,i (t) such that Equation 3:

[0020]

[0021] holds while the performance index function J obtains the minimum value, then the swarm system is said to be pre-set time optimized formation convergence reachable under the action of the formation control protocol, where x k,ij (t) = x k,i (t) - x k,j (t), f k,ij (t) = f k,i (t) - f k,j (t), i = 1, 2,..., N k , k = 1, 2,..., M, i ≠ j.

[0022] The specific steps of the second step are as follows: construct a predetermined spatio-temporal formation convergence control protocol Equation 4:

[0023]

[0024] In the above formula, i = 1, 2,..., N k , k = 1, 2,..., M; t err = t 0 - t, where t 0 is the starting time, α(t) is a non-linear monotonically increasing function of time, which is an additional time error gain adjustment term and can be used to speed up or slow down the convergence speed of the control system; w k,ij represents the information weight of agent j in subgroup k to agent i, Ν k,i is the neighbor set of agent i in subgroup k, K k is the control gain matrix, β is the adjustment parameter, and the K k term in the control protocol is used for conventional formation convergence control.

[0025] The specific steps of the third step are as follows:

[0026] (1) Obtain the gain matrix. First, construct a linear matrix inequality for each subgroup

[0027]

[0028] wherein, α 0 = x k (0) - f k (0) T , and

[0029]

[0030]

[0031] Solve the matrix R using the LMI toolbox in MATLAB; k for solution;

[0032] (2) Obtain the minimum non - zero eigenvalue λ of the Laplacian matrix corresponding to the communication topology according to the internal communication relationships of each subgroup k,min ;

[0033] (3) The gain matrix K of the k - th subgroup k is designed as

[0034] (4) Adjust the parameter where is the direction vector from the agent i in subgroup k to the center of the target area;

[0035] (5) α(t) is designed as:

[0036]

[0037] (6) Combining the above parameter design methods, under the action of control protocol four, the swarm system one can achieve the optimized formation control of the multi - swarm system based on time constraints.

[0038] The present invention has at least the following advantages compared with the prior art:

[0039] By optimizing the formation method of the multi - swarm system and redesigning the control protocol for each agent, it enables the calculation of the remaining state - space distance using the boundaries between the current state and the target position, thereby generating an estimation result, further optimizing the control of the swarm, improving the overall efficiency of the swarm during arraying, enabling the swarm system to converge to the specified area within a given time, and achieving the desired formation while meeting the performance indicators. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention can be further illustrated by the non - limiting embodiments given in the drawings.

[0041] Figure 1 is the overall flow schematic diagram of the present invention.

[0042] Figure 2 This is a schematic diagram of the specific process of the third step of the present invention. Detailed implementation manner

[0043] In order to enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] As Figure 1-2 shown, a method for optimizing the formation of a multi-group system based on time constraints is as follows:

[0045] Step 1: Establish a dynamic characteristic description for each agent in the group system as a second-order linear time-invariant system formula (1):

[0046]

[0047] where k = 1, 2,..., M represents the subgroup sequence, and M is the number of subgroups; i = 1, 2,..., N k , N k represents the number of agents in the k-th subgroup; represents the state vector of agent i in subgroup k, x k,ip (t) ∈ Ρ n is the position state component, x k,iu (t) ∈ Ρ n is the velocity state component, Ρ n represents an n-dimensional real vector space;

[0048] is the system matrix, where α 0 and α 1 can be configured according to the dynamic characteristics of the system;

[0049] is the system input matrix;

[0050] u m (t) ∈ Ρ n is the system control input;

[0051] In the above Step 1, it can be specifically seen that the system described by the matrix (A, B) is a controllable canonical form, that is, for any controllable second-order linear time-invariant system represented by a state differential equation, it can be equivalently transformed into formula (1). In addition, formula (1) describes a multi-group system, where the subscript k represents the group number, and the subscript i represents the number of each intelligent agent within the group.

[0052] Furthermore, for unmanned systems such as unmanned aerial vehicles, ground robots, and unmanned ships, when considering their spatial displacement motion, they can also be modeled as a second-order system as shown in Equation (1). Therefore, the second-order active dynamics modeled by Equation (1) is general. The time-varying formation vector of the k-th subgroup is defined as The performance index function is designed as Equation (2) below:

[0053]

[0054] where the parameter t k0 , t k,i , T des , Q k represent the initial time when subgroup k departs, the time when it enters the target domain, the expected convergence time, and the performance weight matrix of the formation coordination error within the group, respectively; ρ 1 , ρ 2 , ρ 3 are the weights of indicators such as the convergence error, formation coordination error, and time synchronization error; represents the remaining distance error between the state of agent i in subgroup k at time t and the boundary of the target domain, c is the center of the target area, and C is the radius of the target domain; e k,ij (t) = x k,i (t) - f k,i (t) - x k,j (t) - h k,j (t) is the coordination error between agent i and j;

[0055] The above key parameters and variables construct the performance index function J C as the sum of the finite-time quadratic integral function of the formation convergence control error and the convergence time error. The optimization goal of the formation convergence control is to minimize the index function J C .

[0056] Furthermore, if for any bounded initial state x k,i (0) (i = 1, 2,..., N k , k = 1, 2,..., M), there exists a formation control protocol u k,i (t) such that Equation (3):

[0057]

[0058] holds and at the same time the performance index function J obtains the minimum value, then the group system is said to be pre-set time optimized formation convergence reachable under the action of the formation control protocol, where x k,ij (t) = x k,i (t) - x k,j (t), f k,ij (t) = f k,i (t) - f k,j(t), i = 1, 2, ..., N k , k = 1, 2, ..., M, i ≠ j。

[0059] Step 2: Design the control protocol. Each agent calculates the remaining state space distance using the current state and the target domain boundary, and estimates the remaining time to arrival in combination with the agent dynamics characteristics, so as to construct a predetermined spatio-temporal formation convergence control protocol;

[0060] The specific steps of the above Step 2 are to construct the predetermined spatio-temporal formation convergence control protocol formula four:

[0061]

[0062] In the above formula, i = 1, 2, ..., N k , k = 1, 2, ..., M; t err = t 0 - t, where t 0 is the starting time, α(t) is a non-linear monotonically increasing function of time, and is an additional time error gain adjustment term, which can be used to speed up or slow down the convergence speed of the control system; w k,ij represents the information weight of agent j in subgroup k to agent i, Ν k,i is the neighbor set of agent i in subgroup k, K k is the control gain matrix, β is the adjustment parameter, and in the control protocol, the K k term is used for conventional formation convergence control.

[0063] Step 3: Obtain the parameters of the control protocol to complete the optimal formation control of formula one.

[0064] The specific steps of the above Step 3 are:

[0065] (1) Obtain the gain matrix. First, construct a linear matrix inequality for each subgroup

[0066]

[0067] where, α 0 = x k (0) - f k (0) T , and

[0068]

[0069]

[0070] Use the LMI toolbox in MATLAB to solve the matrix R k ;

[0071] (2) Calculate the minimum non-zero eigenvalue λ of the Laplacian matrix corresponding to the communication topology according to the internal communication relationships within each subgroup. k,min ;

[0072] (3) The gain matrix K of the k-th subgroup k is designed as

[0073] (4) Adjustment parameters where is the direction vector from the agent i in subgroup k to the center of the target area;

[0074] (5) α(t) is designed as:

[0075]

[0076] (6) Combining the above parameter design methods, under the action of Control Protocol IV, the multi-group system in Equation I can achieve time-constrained multi-group system optimal formation control.

[0077] The above embodiments are only used to exemplarily illustrate the principles and effects of the present invention, rather than to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes completed by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A multi-group system optimization formation method based on time constraints, characterized by: The specific steps are as follows: Step 1: Establish the dynamic characteristics of each subject in the group system as a second-order linear time-invariant system formula 1: Where k = 1, 2, ..., M represents the subgroup sequence, M is the number of subgroups; i = 1, 2, ..., N k , N k represents the number of entities in the kth subgroup; represents the state vector of agent i in subgroup k, x k,ip (t)∈Ρ n is the position state component, x k,iu (t)∈Ρ n is the velocity state component, P n represents an n-dimensional real vector space; is the system matrix, where α0 and α1 can be configured according to the dynamic characteristics of the system; is the system input matrix; u m (t)∈Ρ n is the system control input; Step 2: Design a control protocol. Each agent uses the current state and the boundary of the target domain to calculate the remaining state space distance. At the same time, the remaining arrival time is estimated based on the dynamic characteristics of the agent, thereby constructing a predetermined spatiotemporal formation convergence control protocol. Step 3: Obtain the parameters of the control protocol to complete the optimized formation control of equation 1.

2. The method for optimizing formation of a multi-group system based on time constraints according to claim 1, characterized in that: In the step 1, it can be specifically seen that the system described by the matrix (A, B) is a controllable standard form, that is, for any controllable second-order linear time-invariant system represented by a state differential equation, it can be equivalently transformed into Formula 1. In addition, Formula 1 describes a multi-group system, the subscript k represents the group number, and the subscript i represents the number of each intelligent agent in the group.

3. The method for optimizing formation of a multi-group system based on time constraints according to claim 2, characterized in that: Furthermore, for unmanned systems such as drones, ground robots, and unmanned ships, when considering their spatial displacement motion, they can also be modeled as a second-order system as in Equation 1. Therefore, the second-order active dynamics modeled by Equation 1 is general. The time-varying formation vector of the kth subgroup is defined as The performance index function is designed as follows: The parameter t k0 ,t k,i ,T des ,Q k They represent the initial departure time, target domain entry time, expected convergence time, and the performance weight matrix of formation coordination error within the group respectively; ρ1, ρ2, ρ3 are the weights of indicators such as convergence error, formation coordination error, and time synchronization error; represents the residual distance error between the state of agent i in subgroup k at time t and the boundary of the target domain, c is the center of the target area, and C is the radius of the target domain; e k,ij (t) = x k,i (t)-f k,i (t)-x k,j (t)-h k,j (t) is the collaborative error between agents i and j; The above key parameters and variables will be the performance index function J C It is constructed as the sum of the finite-time quadratic integral function of the formation convergence control error and the convergence time error. The optimization objective of the formation convergence control is to minimize the index function J C .

4. The method for optimizing formation of a multi-group system based on time constraints according to claim 3 is characterized in that: Furthermore, if for any bounded initial state x k,i (0)(i=1,2,...,N k ,k=1,2,...,M), there exists a formation control protocol u k,i (t) makes equation 3: When the performance index function J reaches the minimum value, the group system is said to be reachable by optimizing the formation convergence at the preset time under the formation control protocol, where x k,ij (t) = x k,i (t)-x k,j (t), f k,ij (t) = f k,i (t)-f k,j (t), i=1,2,...,N k ,k=1,2,...,M,i≠j.

5. The method for optimizing formation of a multi-group system based on time constraints according to claim 4, characterized in that: The specific steps of step 2 are to construct a predetermined spatiotemporal formation convergence control protocol formula 4: In the above formula, i=1,2,...,N k ,k=1,2,...,M;t err =t0-t, where t0 is the starting time, α(t) is a nonlinear monotonically increasing function of time, and is an additional time error gain adjustment term that can be used to speed up or slow down the convergence speed of the control system; w k,ij represents the information weight of agent j to agent i in subgroup k, Ν k,i is the set of neighbors of agent i in subgroup k, K k is the control gain matrix, β is the adjustment parameter, and K in the control protocol k Item is used for conventional formation convergence control.

6. The method for optimizing formation of a multi-group system based on time constraints according to claim 5, characterized in that: The specific steps of step three are: (1) To obtain the gain matrix, first construct a linear matrix inequality for each subgroup. Where α0 = x k (0)-f k (0) T , and Using the LMI toolbox in MATLAB, the matrix R k To solve; (2) According to the internal communication relationship of each subgroup, the minimum non-zero eigenvalue λ of the Laplacian matrix corresponding to the communication topology is obtained k,min ; (3) The gain matrix K of the kth subgroup k Designed for (4) Adjustment parameters in is the direction vector from agent i in subgroup k to the center of the target area; (5)α(t) is designed as: (6) Combined with the above parameter design method, under the action of control protocol formula four, group system formula one can realize the optimal formation control of multi-group system based on time constraints.

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