CN115616913A - A Model Predictive Leaderless Formation Control Method Based on Distributed Evolutionary Game - Google Patents

Abstract

The invention provides a model prediction leaderless formation control method based on a distributed evolutionary game, which can overcome the defects in a leader-follower formation control algorithm. The invention adopts a leaderless formation control algorithm, namely all agents have the same role and function, and utilizes a model prediction control algorithm to construct a global optimization problem, and realizes the formation purpose by designing a formation error function in a global model prediction cost function. The collision avoidance function is realized by constructing a safe distance set for each intelligent agent by using a Voronoi diagram, converting a formation control problem into an evolution game problem to realize distributed solution, and simultaneously ensuring that each intelligent agent cannot collide in the moving process by using the property of an invariant set in the evolution game. In addition, the invention is also suitable for a time-varying communication network, improves the control performance and the safety performance, reduces the complexity of calculation and reduces the communication burden.

Description

A Model Predictive Leaderless Formation Control Method Based on Distributed Evolutionary Game

technical field

The invention belongs to the technical field of multi-agent formation control, and in particular relates to a model prediction leaderless formation control method based on distributed evolutionary game.

Background technique

In recent years, with the continuous development of multi-agent systems, formation control has become a hot issue in the current multi-agent system research. Formation control means that multiple agents such as unmanned vehicles and unmanned aerial vehicles can keep the desired position with each other while moving towards the target position, and at the same time adapt to environmental constraints (such as avoiding obstacles). It can complete specific and complex tasks without human participation, so it has been widely used in various fields such as military, aerospace, and industry, and has a good development prospect. However, in practical applications, a difficult problem of multi-agent formation control is that all agents must have the ability to avoid collisions with obstacles or other agents, and the communication topology may be time-varying during the movement of agents. In addition, when a formation is formed in a distributed manner, each agent needs to know the state of other agents, but when the communication topology changes, the communication between the agents may not exist.

The leader-follower control method is a method to solve the current formation control problem. Its basic principle is to use one of the agents as the leader to track the reference trajectory, and the other agents as followers to keep a certain distance from the leader to achieve formation control. the goal of. Because of its simple principle, it is widely used in multi-agent formations, but there are two shortcomings in the leader-follower formation problem: 1) The whole system is too dependent on the leader. When the leader cannot track the reference trajectory, the entire multi-agent formation will deviate from Refer to the trajectory; 2) The leader agent does not take into account the formation following of the follower agent, and it may happen that the leader agent moves too fast and the follower agent cannot keep up.

Contents of the invention

In view of this, the present invention provides a distributed model prediction based on distributed evolutionary game leaderless formation control method, all agents have the same role and function, and can achieve under the condition of communication constraints, each Agents only need to obtain the local information of neighbors to form formations without collision.

In order to achieve the above object, a distributed model based on distributed evolutionary game of the present invention predicts a leaderless formation control method, comprising the following steps:

Step 1, establish a multi-agent system, clarify the initial position and target position of the agent, construct the dynamic model of the agent, the obstacle avoidance constraints among the multi-agents, the control constraints of the agents and the optimal control problem of the state constraints ; The optimization problem is that when the final target state is known, the prediction model is used to predict the state of the agent in a period of time in the future, so that the distance between the position of the agent and the target position in a period of time in the future is minimized, and the optimal control input at the current moment is obtained quantity;

Step 2, create a safe distance set for each agent to ensure that each agent will not collide as long as it moves within the specified safe distance set;

In step 3, an evolutionary game of two populations subject to coupling constraints is proposed, and the revised protocol is selected to construct the evolutionary dynamic equation, so that the evolutionary dynamic equation of each population can reach the Nash equilibrium solution of the game through continuous iteration and optimization, and has an invariant set the nature of

Step 4, transform the constructed multi-agent formation problem into a two-group evolutionary game problem subject to coupling constraints, and use the evolutionary dynamics equation of the evolutionary game to solve the multi-agent formation optimization problem.

Wherein, in the step 4, the position of the agent in the formation control is transformed into the population state in the evolutionary game, each agent in the formation control is transformed into a strategy in the evolutionary game, and the cost function and The benefit function of the evolutionary game is combined, and then the optimal control problem in step 1 is solved by using the evolutionary dynamics equation.

Wherein, the optimization problem in the step 1 is:

min _u(k) J(k)

stform＝0,1,...,H _p -1

表示第i个智能体的位置信息，

表示第i个智能体的速度信息，

表示第i个智能体的状态变量，

表示第i个智能体的控制变量，

表示第i个智能体的避碰约束集，

表示多智能体的可移动范围，

表示单个智能体的允许控制输出范围。in:

Indicates the location information of the i-th agent,

Indicates the speed information of the i-th agent,

Represents the state variable of the i-th agent,

Denotes the control variable of the i-th agent,

Represents the collision avoidance constraint set of the i-th agent,

Indicates the movable range of the multi-agent,

Indicates the allowed range of control outputs for a single agent.

Wherein, the definition of the safety distance set in the step 2 is:

是多面体闭集，对于任意

和

满足‖c_i(k)-c_j(k)‖≥R，

表示智能体i的邻居智能体集合，δ_ij(k)、ε_ij(k)以及ω_ij(k)表示用于计算的中间变量。Among them, R is the specified safety distance, set

is a polyhedron closed set, for any

and

Satisfy ‖c _i (k)-c _j (k)‖≥R,

Represents the set of neighbor agents of agent i, δ _ij (k), ε _ij (k) and ω _ij (k) represent intermediate variables for calculation.

Wherein, in the step 2, a distributed evolutionary game of two populations with coupling constraints is adopted, and the specific steps are: solving the optimization problem of the evolutionary game by finding the Nash equilibrium point; substituting the optimization problem for finding the Nash equilibrium point solution into the average Dynamics, to obtain the Smith Dynamics equations for the distribution of two populations with coupled constraints.

Beneficial effect:

1. The present invention extends the average dynamics in the evolutionary game to the coupling constraints between two populations, and proves that the evolutionary dynamics will eventually reach the Nash equilibrium point of the game through continuous iteration and optimization, and is subject to coupling constraints The two-group evolutionary game of has invariant set constraints, that is, in the case of satisfying the initial conditions, the constraints can always be satisfied during the evolution of the evolutionary game. The multi-agent formation control problem is transformed into an evolutionary game problem, so that the centralized optimization problem is split into several sub-problems, and then assigned to each sub-agent to solve. Each self-agent uses its own information, local models and available neighbor information to solve sub-problems, thus greatly reducing the amount of calculation and complexity; in addition, it also makes up for the traditional decentralized control due to insufficient information interaction capabilities. In order to keep the control performance at a high level, the flexibility and scalability of the system are improved; the present invention adopts a leaderless formation control algorithm, and all agents have the same role and function. Therefore, the shortcomings in the leader-follower formation control algorithm can be solved.

2. The present invention utilizes the model predictive control algorithm to construct the global optimization problem, and realizes the goal of formation by designing a formation error function in the global model prediction cost function. By introducing the property of the invariant set, it is guaranteed that each agent will not collide in the process of moving.

3. The present invention is also applicable to time-varying communication networks. While improving the control performance and safety performance, it reduces the complexity of calculation, reduces the communication burden, and solves the problem that some existing formation control algorithms cannot deal with communication constraints or time-varying communication networks.

Description of drawings

Fig. 1 is the transition figure between formation control problem and evolutionary game problem among the present invention;

Fig. 2 is the two-dimensional actual locus diagram of 6 intelligent bodies in the present invention;

Fig. 3 is the positional coordinates-time graph of each intelligent body in the present invention;

Fig. 4 is the safe distance-time curve of each intelligent body in the present invention;

Fig. 5 is the control input-time graph of each agent in the present invention.

detailed description

The present invention will be described in detail below with reference to the accompanying drawings and examples.

The invention introduces an evolutionary game algorithm in the multi-agent formation. As a mathematical tool, the evolutionary game can describe the behavior of a decision maker under the condition of only knowing part of the information of some participants. Through continuous iteration and optimization, the partial behavior of participants can achieve an overall goal. Therefore, evolutionary game is suitable for solving the problem of distributed multi-agent formation control. The present invention provides a distributed model based on distributed evolutionary game prediction leaderless formation control method, comprising the following steps:

The first part, building a multi-agent system, includes the following sub-steps:

Step 11, design of system architecture

个多智能体的编队，取

表示第i个智能体的位置信息，

表示第i个智能体的速度信息，对于任意智能体

其动力学模型表达式为consider a

multi-agent formation, take

Indicates the location information of the i-th agent,

Represents the speed information of the i-th agent, for any agent

Its dynamic model expression is

表示第i个智能体的状态变量，

表示第i个智能体的控制变量。in,

Represents the state variable of the i-th agent,

Denotes the control variable of the i-th agent.

其时变通信拓扑为

这里节点集

对应的是智能体集

顶点集

代表着可以交互信息的智能体对，A(k)＝[a_ij(k)]_M×M表示邻接矩阵，其中当智能体i和智能体j可以交互信息时，a_ij(k)＝1，否则a_ij(k)＝0。令

表示智能体i的期望状态，对于任意智能体i和智能体j，需要满足：Step 12, determine the communication topology and target of each agent. The communication range of each multi-agent is

Its time-varying communication topology is

Here node set

Corresponding to the agent set

vertex set

Represents the agent pair that can exchange information, A(k)=[a _ij (k)] _M×M represents the adjacency matrix, where when agent i and agent j can exchange information, a _ij (k)=1 , otherwise a _ij (k)=0. make

Indicates the desired state of agent i, for any agent i and agent j, it needs to satisfy:

(1) Control objectives:

(2) Obstacle avoidance constraints: d _ij (k)=|| _{ci (k)-c j (} k)||≥R, where the minimum safe distance

其中

是智能体允许到达的区域；(3) Position constraints:

in

is the area that the agent is allowed to reach;

其中

是控制输入允许的范围；(4) Input constraints:

in

is the range allowed by the control input;

for all

即不同智能体之间期待的目标位置距离大于安全距离；

表示智能体i的邻居智能体集合。(5) Expected state requirements:

for all

That is, the expected target position distance between different agents is greater than the safe distance;

Represents the set of neighbor agents of agent i.

Step 13, design a safe distance set for each agent. At each moment k, the positions c _i (k) and c _j (k) of the agent i and all its neighbors j are obtained, and the constraint set is reconstructed using the Voronoi diagram as

in

是多面体闭集，即无碰撞集，并且对于任意

和

都会满足‖c_i(k)-c_j(k)‖≥R。Among them, δ _ij (k), ε _ij (k) and ω _ij (k) represent the intermediate variables used for calculation, and the set

is a polyhedral closed set, that is, a collision-free set, and for any

and

will satisfy ‖c _i (k)-c _j (k)‖≥R.

代表智能体i的位置偏差，定义代价函数为：Step 14, building a model to predict the optimization problem. In order to achieve the control objective, the

Represents the position deviation of agent i, and defines the cost function as:

和

都是对称正定矩阵，H_p为预测时域，无人机编队的最优控制问题描述为：in,

and

Both are symmetric positive definite matrices, H _p is the prediction time domain, the optimal control problem of UAV formation is described as:

min _u(k) J(k) (8a)

stform=0,1,...,H _p -1 (8b)

When the optimization problem (8) has a feasible solution, the optimal control input for a period of time in the future will be obtained. Considering the model mismatch and interference in the actual application, it is not the optimal control sequence that is solved. All are applied to the system one by one, but the first element in the optimal control sequence is used in the actual system. At the next moment k+1, re-sample the current state of the system, reconstruct the optimization problem (8) and solve it, and continue to repeat the preceding steps. However, the optimization problem constructed at this time is still a centralized optimization problem. In the following steps, the above-mentioned optimization problem will be solved in a distributed manner through the distributed evolutionary game method.

Since the collision avoidance constraint is non-convex in nature, it can lead to a non-convex optimization problem. In order to solve this calculation problem, the idea of Voronoi diagram is introduced to create a safe distance set for each agent. It is guaranteed that each agent will not collide as long as it moves in a concentrated safe distance.

取种群p中接受策略i的比例为ρ_p,i＝m_p,i/m_p≥0，并且可以得到p_p＝[ρ_p,1,ρ_p,2,…,ρ_p,n]^T和π_p＝∑_i∈Sρ_p,i＝1。同时，令种群p的适度函数为F_p(p_p)＝[f_p,1(p_p),f_p,2(p_p),…,f_p,n(p_p)]^T。这里，统一定义x_i:＝ρ_1,i，y_i:＝ρ_2,i，x:＝p₁，y:＝p₂，f_i ^x:＝f_1,i(p₁)，f_i ^y:＝f_2,i(p₂)，

和

The second part is the evolutionary game of two populations subject to coupling constraints. There are two populations p∈(1,2), each of which has a large number of limited participants, and has the same strategy set S in both populations. Let s _i ∈ S denote the i-th strategy, denote the strategy set, which contains n strategies, let m _p,i denote the number of individuals receiving strategy i in population p, and

Take the proportion of acceptance strategy i in population p as ρ _p,i =m _p,i /m _p ≥0, and we can get p _p =[ρ _p,1 ,ρ _p,2 ,…,ρ _p,n ] ^T and π _p =∑ _i∈S ρ _p,i =1. Meanwhile, let the fitness function of the population p be F _p (p _p )=[f _p,1 (p _p ),f _p,2 (p _p ),…,f _p,n (p _p )] ^T . Here, uniformly define x _i :=ρ _1,i , y _i :=ρ _2,i , x:=p ₁ , y:=p ₂ , f _i ^x :=f _1,i (p ₁ ), f _i ^y := f _2,i (p ₂ ),

and

来表示，其中节点集

代表所有的策略集，顶点集

代表着种群x中个体可以采取不同的策略，A(k)＝[a_ij(k)]_M×M表示邻接矩阵，其中当个体采取策略i，并且也可以采取策略j时，a_ij(k)＝1，否则a_ij(k)＝0。同理，对于第二个种群，各个个体之间的策略交互可以用无向图

来表示。Step 21, setting the communication topology map in the evolutionary game. For two populations (x,y), in order to maintain a certain balance, it is necessary to satisfy the set Ξ={(x,y)∣Ax+By≤C}, where A=diag{a ₁ ,a ₂ ,…,a _n } , B=diag{b ₁ ,b ₂ ,...,b _n } and C=[c ₁ c ₂ . . . c _n ] ^T . In the process of evolution, the set Λ:={(x,y)∣∑ _i∈S x _i =π ₁ ,∑ _i∈S y _i =π ₂ , _xi ≥0,y _i ≥0} contains the all possible states. For the first population, the strategy interaction between individuals can be used as an undirected graph

to represent, where the node set

Represents all strategy sets, vertex sets

Represents that individuals in population x can adopt different strategies, A(k)=[a _ij (k)] _M×M represents the adjacency matrix, where when an individual adopts strategy i and can also adopt strategy j, a _ij (k )=1, otherwise a _ij (k)=0. In the same way, for the second population, the strategy interaction between individuals can use the undirected graph

To represent.

The optimization problem of the evolutionary game is solved by finding the Nash equilibrium point, and can be described as:

max _x,y W(x,y) (9a)

s.t.Ax+By≤C (9b)

x _i ≥ 0 (9e)

y _i ≥ 0 (9f)

Among them, the cost function W(x, y) is a strictly continuous and differentiable concave function, and ( _xi , y _i ) is the state of the population.

The evolution process of the proportional change of strategy i in population x and population y can be described by distributed evolution dynamics, and its expression is:

This kinetics is also known as mean kinetics. In addition, the revised protocol φ _ij takes the current payoff and aggregation behavior as input, and outputs the switching frequency, that is, the frequency at which an individual adopts strategy i and switches to adopting strategy j according to the current overall state and payoff.

表示一组三元数，并对任意q∈S，满足

则

是关于矢量C-(Ax+By)最小元素对应的系数。因此，对于种群p的修正协议可以设计为：Step 21, setting of the communication protocol. For any given x and y, use

Represents a set of ternary numbers, and for any q∈S, satisfies

but

is the coefficient corresponding to the smallest element of the vector C-(Ax+By). Therefore, the modified protocol for population p can be designed as:

Substituting (12) into (10) and (11), we can get

This is Distributed Smith Dynamics of Two Populations with Coupling Constraints (DSD2PC), and an evolutionary game with such dynamics is called a Distributed Evolutionary Game of Two Populations with Coupling Constraints (DEG2PC).

则(13)和(14)重新表达为：make

Then (13) and (14) are re-expressed as:

Express the evolutionary dynamics as a compact form, the expression is

和

分别是关于图

和

的拉普拉斯矩阵。in,

and

are about graph

and

The Laplace matrix of .

得到

并且令

得到S10. Prove that the evolutionary game constrained by two groups has the property of an invariant set. Given (x,y)∈Ξ∩Λ, by

get

and make

get

可以表示为：Therefore, r ^x (i, j)=r ^x (j, i)≧0. adjacency matrix

It can be expressed as:

可以得到By the relation of Laplacian matrix

can get

是半正定的。同理可证

是半正定的且

According to the non-negativity of r ^x (i,j), the Laplacian matrix

is positive semi-definite. The same reason can be proved

is positive semidefinite and

和

可以得到

和

也就是说

和

是常数。另外，当x_i＝0或y_i＝0时，根据(13)和(14)，得到S11. According to Lemma 1

and

can get

and

That is to say

and

is a constant. In addition, when x _i =0 or y _i =0, according to (13) and (14), we get

Thus for x _i ≥ 0 and y _i ≥ 0, (x(t), y(t))∈Λ.

并且

将a_i和b_i代入(13)和(14)，得到When (x(0), y(0))∈Ξ, once the trajectory (x(t), y(t)) reaches the boundary of the set Ξ, for i∈S, a _i x _i +b _i y _i = c _i . According to Theorem 1,

and

Substituting a _i and b _i into (13) and (14), we get

和

Discuss in the following four situations

and

若a_i>0,b_i>0

If a _i >0, b _i >0

若a_i>0,b_i≤0

If a _i >0, b _i ≤0

若a_i≤0,b_i>0

If a _i ≤0, b _i >0

若a_i≤0,b_i≤0

If a _i ≤ 0, b _i ≤ 0

和非增长性a_ix_i+b_iy_i≤c_i。由于轨迹(x,y)的连续性，得出在后续的所有时间步长中(x(t),y(t))∈Λ。因此，集合Ξ∩Λ是不变集。then always satisfies the non-negativity

and non-increasing a _i x _i +b _i y _i ≤ c _i . Due to the continuity of the trajectory (x, y), it follows that (x(t), y(t)) ∈ Λ in all subsequent time steps. Therefore, the set Ξ∩Λ is an invariant set.

S12, select E(x, y):=W(x ^* , y ^* )-W(x, y) as the Lyapunov function, and E(x, y)≥0, its derivative can be expressed as

Therefore, when the initial value (x(0), y(0)) ∈ Ξ evolves along (13) and (14), DEG2PC approaches the Nash equilibrium point, and the Nash equilibrium point is locally asymptotically stable.

The third part, the distributed model predictive control algorithm based on DEG2PC theory:

相关联，关系式为Step 31, the transition diagram between the formation control problem and the evolutionary game problem in the present invention is shown in Figure 1, using the method of evolutionary game theory, the population state ( _xi , y _i ) in the DEG2PC theory and the optimal control problem positional components in

related, the relationship is

According to the kinetic model in (6), u _i (k+m|k) and v _i (k+m+1|k) can be re-expressed as:

u _i (k+m|k)＝c _i (k+m+1|k)-2c _i (k+m|k)+c _i (k+m-1|k) (19)

v _i (k+m+1|k)＝ _ci (k+m+1|k)-ci ( _k +m|k) (20)

的形式，与问题(9)中的约束(9b)相对应。And substitute (19) and (20) into the optimization problem (8). Since problem (8) is to minimize the cost function J(k), and problem (9) is to maximize the concave function W(x,y), the fitness function for each strategy can be described as f ^x =- _x J and f ^y =- _y J . Furthermore, constraints (8d), (8e) and (8f) in problem (8) can be transformed into

of the form, corresponding to constraint (9b) in problem (9).

Step 32, for the populations x and y, choose the modified protocol as in (12), and use the dynamic evolution of (15) and (16), the population result will tend to the Nash equilibrium point. After that, the optimal position trajectory (x ^* (k), y ^* (k)) and the optimal control input sequence u ^* (k) can be obtained at time k. Therefore, the formation control problem (9) is solved in a distributed manner by DEG2PC.

预测时域H_p、安全距离R、交流范围θ、权重矩阵Q_i、P_i和R_i。需求输出：(x^*(k),y^*(k))和u_i ^*(k|k)In summary, the distributed model based on distributed evolutionary game predicts the leaderless formation control method can be described as: given input: expected position

Prediction time domain H _p , safety distance R, communication range θ, weight matrix Q _i , _Pi and R _i . Demand output: (x ^* (k), y ^* (k)) and u _i ^* (k|k)

(1) Given sample z _i (k) and communication topology at time k

设计修正协议(12)；(2) Structural formation control problem (8); select

Design Amendment Agreement (12);

(3) For each strategy f ^x and f ^y , obtain a fitness function;

(4) Through (13) and (14), solve the optimal position trajectory (x ^* (k), y ^* (k)) and the optimal control input sequence u ^* (k);

(5) Substitute u _i ^* (k|k) into each agent, and repeat the above operation.

系统模型为The fourth part is theoretical simulation. Choose a multi-agent system with six agents, for each agent

The system model is

交流范围θ＝2.3，安全距离R＝0.5，预测时域H_p＝20，权重矩阵Q_i＝R_i＝P_i＝I_4×4，每个智能体的初始速度和期待速度都设置为0，初始位置为Input constraints for each agent

Communication range θ=2.3, safety distance R=0.5, prediction time domain H _p =20, weight matrix Q _i ＝R _i ＝P _i ＝I _4×4 , the initial speed and expected speed of each agent are set to 0 , the initial position is

c ₁ (0)=[3 3] ^T , c ₂ (0)=[1 4] ^T , c ₃ (0)=[2 0] ^T

c ₄ (0)=[4 1] ^T , c ₅ (0)=[0 2] ^T , c ₆ (0)=[3 5] ^T

To form a formation formation, the desired position of each agent is:

Use ICLOCS and PDToolbox solving tool on MATLAB to carry out emulation experiment, the result is as shown in the accompanying drawing description, and Fig. 2 is the two-dimensional actual locus figure of 6 intelligent bodies in the present invention, and Fig. 3 is the position of each intelligent body in the present invention Coordinate-time graph, Fig. 4 is the safety distance-time curve of each agent pair in the present invention, and Fig. 5 is the control input-time graph of each agent in the present invention. The simulation results in Figure 2 show that under the control of the algorithm, each agent can finally reach the designated target point. Figure 3 shows the position of each agent during the movement. Each sub-graph in Figure 4 shows the relative positions of the agents respectively. It can be seen that the relative positions of the agents are always greater than the safety distance of 0.5, that is, the agents have the effect of avoiding collisions. The results in Fig. 4 show that the agent can guarantee the satisfaction of the input constraints in the process of moving.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (5)

1. A distributed model prediction leaderless formation control method based on a distributed evolutionary game is characterized by comprising the following steps of:

step 1, establishing a multi-agent system, determining an initial position and a target position of an agent, and constructing a dynamic model of the agent, and an optimal control problem of obstacle avoidance constraint, agent control constraint and state constraint among the agents; the optimization problem is that under the condition that the final target state is known, the state of the intelligent agent in a future period of time is predicted through a prediction model, so that the distance between the position of the intelligent agent and the target position in the future period of time is minimum, and the optimal control input quantity at the current moment is obtained;

step 2, a safe distance set is established for each intelligent agent, and each intelligent agent is guaranteed not to collide as long as the intelligent agent moves in the specified safe distance set;

step 3, two group evolution games constrained by coupling are provided, and a correction protocol is selected to construct an evolution kinetic equation, so that the evolution kinetic equation of each group can reach Nash equilibrium solution of the games through continuous iteration and optimization and has the property of invariant set;

and 4, converting the constructed multi-agent formation problem into two group evolutionary game problems which are constrained by coupling, and solving the multi-agent formation optimization problem by using an evolutionary kinetic equation of the evolutionary game.

2. The method according to claim 1, wherein in step 4, the positions of the agents in the formation control are converted into the population states in the evolutionary game, each agent in the formation control is converted into a strategy in the evolutionary game, the cost function in the formation control problem is combined with the benefit function in the evolutionary game, and then the optimal control problem in step 1 is solved by using an evolutionary dynamic equation.

3. The method according to claim 1 or 2, characterized in that the optimization problem in step 1 is:

min _u(k) J(k)

s.t.for m＝0,1,…,H _p -1

wherein:

indicating the location information of the ith agent,

indicating the speed information of the ith agent,

a state variable representing the ith agent,

a control variable representing the ith agent,

representing the set of collision avoidance constraints for the ith agent,

representing the range of mobility of the multi-agent,

representing the allowable control output range of a single agent.

4. The method according to claim 3, wherein the safe distance set in step 2 is defined as:

wherein R is a prescribed safe distance, set

Is a closed set of polyhedrons, for arbitrary

And

satisfy | c _i (k)-c _j (k)‖≥R，

Set of neighbor agents, δ, representing agent i _ij (k)、ε _ij (k) And ω _ij (k) Representing intermediate variables for the calculation.

5. The method according to claim 1,2 or 4, wherein the step 2 adopts a distributed evolutionary game with two populations having coupling constraints, and comprises the following specific steps: solving the optimization problem of the evolutionary game by searching Nash balance points; substituting the optimization problem solved by searching for the Nash equilibrium point into the average dynamics to obtain the distributed Smith kinetic equation of the two populations with coupling constraint.

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