An arc length-based channel-type area coverage control method for multi-agent systems

Abstract

The present invention relates to the field of area coverage control methods, and discloses a channel-type area coverage control method for a multi-agent system based on arc length, including the following steps. Step S1, target area division: Based on the arc length partitioning method, the channel-type target area is divided into multiple sequential sub-areas. Step S2, design of the distributed controller of the virtual leader agent: The distributed controller of the virtual leader agent ensures that the arc length of the coverage area of each group of agents is proportional to the number of agents in that group. Step S3, design of the distributed controller of the individual agent: The distributed controller of the individual agent, combined with the distributed controller of the virtual leader agent, can enable the agents to achieve sequential team coverage control of the area. The distributed controller designed in the present invention enables the agents to adjust their coverage areas in real time according to changes in the actual environment. S The distributed controller designed in the present invention enables the agents to adjust their coverage areas in real time according to changes in the actual environment.

Description

Technical Field

[0001] The present invention relates to the field of area coverage control methods, and specifically to a channel-type area coverage control method for multi-agent systems based on arc length. Background Art

[0002] In the field of multi-agent systems, the coverage control problem is widely applied in many fields such as military surveillance, environmental monitoring, and agricultural management, especially in channel-type areas such as river monitoring and border patrol. These areas usually have non-convex shapes and are narrow and long, with uneven information distribution, which poses relatively high requirements for the deployment and control strategies of agents.

[0003] In the prior art, although many coverage control methods have been proposed, such as Voronoi partitioning, power diagrams, and weighted Voronoi partitioning, etc., these methods have the following several obvious disadvantages and deficiencies:

[0004] 1. Insufficient dynamic adaptation ability: The existing partitioning methods often do not have the ability to dynamically adjust, and cannot flexibly adjust the coverage area according to the change in the number of agents, resulting in an unbalanced load of agents during task execution;

[0005] 2. Slow response to boundary changes: The traditional coverage control methods are not sensitive enough to the dynamic changes of virtual leader agents, and cannot timely adjust the positions of individual agents, thus affecting the overall coverage effect;

[0006] 3. Insufficient processing of information diversity: In channel-type areas where multiple types of information need to be detected, the existing methods usually rely on a single group of agents for coverage, resulting in the inability to effectively meet the detection requirements of different types of information. Even if each agent is considered to be equipped with multiple heterogeneous sensors, due to the difference in the distribution of different information in space, other information may not be fully detected, resulting in an incomplete coverage range and the inability to comprehensively detect the required information.

[0007] Based on this, the present invention proposes a channel-type area coverage control method for multi-agent systems based on arc length. Summary of the Invention

[0008] The purpose of the present invention is to provide a channel-type area coverage control method for multi-agent systems based on arc length to solve the problems raised in the above background art.

[0009] To achieve the above purpose, the present invention provides the following technical solution: A channel-type area coverage control method for multi-agent systems based on arc length, including the following steps:

[0010] Step S1, target area division, based on the arc length partitioning method, divide the channel-type target area into multiple sequential sub-areas;

[0011] Step S2, design of the distributed controller of the virtual leader agent. The distributed controller of the virtual leader agent ensures that the arc length of the coverage area of each group of agents is proportional to the number of agents in that group;

[0012] Step S3, design of the distributed controller of the individual agent. The distributed controller of the individual agent, combined with the distributed controller of the virtual leader agent, enables the agents to achieve sequential team coverage control of area S.

[0013] Preferably: In the process of dividing the target area in step S1, n groups of heterogeneous multi-agent systems are deployed inside a channel-shaped area S. The boundary of this channel-shaped area is defined by two regular curves and where the i-th group of agents contains n i agents, i = 1,..., n. The median line of the channel-shaped area is a regular curve. Define as a regular curve with the abscissa as the parameter, and its parametric equation is denoted as γ(x)=(x, y(x)) Τ . Deploy n + 2 virtual leader agents on the median line of area S. Define as the position of the i-th virtual leader agent, where i = 0, 1,..., n + 1. According to the initial positions of the virtual leader agents, these agents are distributed on in the order of their abscissas, that is l=(l0, l1,..., l n+1 ) represents the set of positions of these virtual leader agents. The coverage area of each group of agents is The coverage area of the entire agent population is where Q = Q1 ∪ Q2 ∪... ∪ Q n . The range of the coverage area Q is determined by the arc length of the curve between l0 and l n+1 , and this arc length is a specified fixed value Define the boundary of the area as and represent the set of indices of the groups adjacent to the i-th group of agents as The range of the coverage area Q i of the i-th group of agents is determined by the curve , and its definition is as follows:

[0014]

[0015] where represents the arc length of the curve, n i represents the number of agents in the i-th group, |S i | represents the curve Si Let \(p\) be the length, i,j For the curve \(S\) i and the curve \(S\) j The intersection point satisfies the following relationship:

[0016]

[0017] where Let \(p\) 1,0 \(= l_0\), \(p\) n,n+1 \(= l\) n+1 , is the shared boundary of \(Q\) i and \(Q\) j , which is defined as:

[0018]

[0019] where is a line segment passing through the point \(p\) i,j and perpendicular to the tangent direction of the curve , where is the tangent of the curve at the point \(p\) i,j . \(i = 1,\cdots,n\). \(l_0\) and \(l\) n are located at the back end and the front end of the region \(Q\) respectively.

[0020] Preferably: The coverage area \(Q\) of the \(i\)-th group of agents i is the inner region bounded by and , and its interior is a path-connected region, satisfying where \(i = 1,2,\cdots,n\), Let \(p\) i,m represent the position of the \(m\)-th agent in the \(i\)-th group of agents, where \(i = 1,\cdots,n\), \(m = 1,\cdots,n\) i , define as the position set of the \(i\)-th group of agents, and \(P=(P_1,P_2,\cdots,P n )\) is the position set of this group of agents. For the agents \(p\) i distributed in the region \(Q\) i,m , its coverage area \(Q\) im is defined by the following Voronoi partition:

[0021] \(Q\) im =\(\{q\in Q i \mid ||q - p im || 2 \leq ||q - p is || 2 , s = 1,\cdots,n\i , s ≠ m}, (1.6)

[0022] where n i represents the number of agents in the i-th group, is the boundary of region Q im An agent p im shares part of the regional boundary with its Voronoi partition neighbors, and the index set of the neighbors is where s = 1,..., n i , s ≠ m.

[0023] Preferably: In the design process of the distributed controller for the virtual leader agent in step S2, for the virtual leader agent l i the following first-order distributed controller is designed:

[0024]

[0025] where represents the tangent vector of the curve γ at the point l i ,

[0026]

[0027] and represent the arc length of the curve, i = 1, 2,..., n..

[0028] Preferably: The distributed controller for the individual agent in step S3 is as follows:

[0029]

[0030] where, k im > 0, and respectively represent the mass and centroid of region Q im , and are specifically defined as:

[0031]

[0032] defined by equation (1.11), i = 1, 2,..., n, m = 1, 2,..., n i .

[0033] The beneficial effects of the present invention compared with the prior art are:

[0034] The distributed controller with dynamic adaptive enhancement design of the present invention enables agents to adjust their coverage areas in real time according to changes in the actual environment. When facing changes in the number of agents, each team can reasonably adjust the size of the coverage area according to the number of agents to achieve load balancing. This improvement significantly enhances the adaptability of the system in a dynamic environment;

[0035] The boundary response speed is improved. The controller of each individual agent can quickly respond to boundary changes of the virtual leader agent to ensure optimal local deployment in a dynamic environment;

[0036] Diversified information detection ability. Through the collaborative work of heterogeneous agent teams, the system of the present invention can effectively process different types of information. For example, in a river monitoring scenario, the system can simultaneously detect water quality indicators, temperature, radioactivity, etc. Compared with traditional single-sensor solutions, information collection is more comprehensive. Brief Description of the Drawings

[0037] Figure 1 is the flowchart of the method of the present invention;

[0038] Figure 2 is the schematic diagram of coverage area division in the channel-type area S;

[0039] Figure 3 is the movement trajectory diagram of agents covering in sequence;

[0040] Figure 4 is the graph of the change in the arc length of the coverage area of each group of agents;

[0041] Figure 5 is the overall cost function;

[0042] Figure 6 is the graph of the change in the arc length of the coverage area of each group of agents. Detailed Implementation Manner

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0044] Embodiment

[0045] Please refer to Figure 1 , a method for controlling the coverage of a channel-type area of a multi-agent system based on arc length shown in the figure, includes the following steps:

[0046] Step S1, target area division: Based on the arc - length partitioning method, the channel - type target area is divided into multiple sequential sub - areas;

[0047] Step S2, design of the distributed controller for the virtual - leader agent: The distributed controller of the virtual - leader agent ensures that the arc - length of the coverage area of each group of agents is proportional to the number of agents in that group;

[0048] Step S3, design of the distributed controller for individual agents: The distributed controller of individual agents, combined with the distributed controller of the virtual - leader agent, enables the agents to achieve sequential team coverage control of area S.

[0049] In the present invention, the symbol represents one - dimensional Euclidean space, represents non - negative real numbers, the symbol and respectively represent n - dimensional Euclidean space and its corresponding n×n matrix space. For any real number its absolute value is defined as |x|. For the vector its Euclidean norm is denoted as ||x||, where x=(x1,x2,...,x n ) Τ >>0 means x i >0, i = 1,2,...,n. Define as a matrix, and its transpose is denoted as A Τ , while row(A) i represents the row vector formed by the elements of the i - th row of matrix A. If all the eigenvalues of matrix A have negative real parts, then A is called a Hurwitz matrix; if the non - diagonal elements of A are all non - negative, then A is called a Metzler matrix. Define as a two - dimensional region. If for any there exists a continuous mapping τ:[0,1]→X such that τ(0)=a and τ(1)=b, then the region X is called path - connected.

[0050] In the two - dimensional space consider a regular curve γ parameterized by the abscissa: where the coordinates of the curve satisfy a certain functional relationship y = y(x). Therefore, the regular curve can be expressed as

[0051] γ(x)=(x,y(x)) Τ .(1.1)

[0052] On the curve γ, the tangent vector at the point p=(x,y(x)) is expressed as γ′(x)=(1,y′(x)), and its direction points to the positive direction of the curve. Define the starting point a=(x a ,y(xa )) to point b = (x b , y(x b )) is the arc length,

[0053]

[0054] The curvature κ(p) of the curve γ at the point p = (x, y(x)) is defined as,

[0055]

[0056] The present invention is defined as deploying n groups of heterogeneous multi-agent systems inside a channel-shaped region S, the boundary of which is defined by two regular curves and where the i-th group of agents contains n i agents, i = 1,..., n, and the median line of the channel-shaped region is also a regular curve, defined as a regular curve with the abscissa as the parameter, and its parametric equation is denoted as γ(x) = (x, y(x)) Τ , in order to delimit the coverage areas between different groups of agents, n + 2 virtual leader agents are deployed on the median line of the region S, defined as the position of the i-th virtual leader agent, where i = 0, 1,..., n + 1. According to the initial positions of the virtual leader agents, these agents are distributed in order of their abscissas on , that is l = (l0, l1,..., l n+1 ) represents the set of positions of these virtual leader agents. The coverage area of each group of agents is The coverage area of the entire agent population is where Q = Q1 ∪ Q2 ∪... ∪ Q n , and the range of the coverage area Q is determined by the arc length of the curve between l0 and l n+1 and this arc length is a prescribed fixed value Define the boundary of the region as and denote the set of indices of the adjacent groups to the i-th group of agents as The coverage area Q i of the i-th group of agents is determined by the curve and is defined as follows:

[0057]

[0058] where represents the arc length of the curve, n i represents the number of agents in the i-th group, |S i|Denote the length of curve S i , let p i,j be the intersection point of curve S i and curve S j , satisfying the following relationship:

[0059]

[0060] where In particular, let p 1,0 = l0, p n,n+1 = l n+1 . is the shared boundary of Q i and Q j , and its definition is:

[0061]

[0062] where is the line segment passing through point p i,j and perpendicular to the tangent direction of the curve , where is the tangent line of the curve at point p i,j , i = 1, …, n., l0 and l n are located at the rear end and the front end of region Q respectively. At this time, no agent is deployed in the group, that is, n0 = n n+1 = 0, is a line segment passing through point p 1,0 and perpendicular to the direction. Accordingly, also satisfies similar conditions.

[0063] Next, the present invention gives the definition of the coverage area Q i of the i-th group of agents.

[0064] Definition 1: The coverage area Q i of the i-th group of agents is the inner area bounded by and , and its interior is a region that is path-connected and satisfies where i = 1, 2, ..., n,

[0065] Let p i,m represent the position of the m-th agent in the i-th group of agents, where i = 1, ..., n, m = 1, ..., n i , define as the position set of the i-th group of agents, and P = (P1, P2, …, P n ) as the position set of this group of agents. For the distribution in region Qi the agent p in i,m , whose coverage area Q im is defined by the following Voronoi partition:

[0066] Q im ={q ∈ Q i | ||q - p im || 2 ≤ ||q - p is || 2 , s = 1,..., n i , s ≠ m}, (1.6)

[0067] where n i represents the number of agents in the i-th group, is the boundary of the area Q im , and the agent p im shares part of the area boundary with its Voronoi partition neighbors, and the index set of the neighbors is where s = 1,..., n i , s ≠ m.

[0068] Figure 2 shows the deployment of three groups of agents in the channel-type area S. The green curve represents the boundary of area S and the gray dashed line represents the median line of area S The blue solid dots represent the positions of the virtual leader agents, the blue dashed lines represent the boundaries between different groups, the red solid dots represent the positions of the agents in the third group, the red dashed lines represent the shared boundaries between the agents in the same group, the brown arrows represent the unit outer normal vectors at the boundaries, and the area Q moves from left to right along area S under the drive of the virtual leader. During this process, the length of the area remains unchanged.

[0069] Among them, the coverage area Q of each group of agents i is a connected area, and the range of area Q is not necessarily limited to and . If intersects with , then at this time Q i is a simply connected area containing the curve S i , and there is a partially shared area Q i-1 and Q i+1 Q i-1 ∩ Q i+1 , which may lead to collisions between the agents in the (i - 1)-th group and the agents in the (i + 1)-th group. Therefore, the present invention requires that the agents between different groups have an obstacle avoidance mechanism, such as methods based on potential fields or control barrier functions, etc.

[0070] To describe the coverage effect of this group of multi-agent systems on region Q, first define the coverage region Q of the i-th group of agents i of the cost function:

[0071]

[0072] where α i > 0 represents the gain coefficient of the i-th group of agents, represents the density function value of the agent detection point q, i = 1, 2,..., n. At this time, the cost functions of the n groups of agents can be expressed as:

[0073]

[0074] where represents the coverage cost function of the i-th group of agents. Since the sensors equipped by different groups of agents are different, they can only identify specific targets in the coverage area, which leads to different contents detected by different groups of agents. This optimization problem involves two levels of region division. First, each group of agents divides its coverage area according to the position of the virtual leader. On this basis, each group of agents is deployed to the local optimal position of its coverage area to make (1.7) reach the local minimum value.

[0075] The above coverage control problem in the channel-type region can be defined as follows.

[0076] Definition 2: Sequential coverage control. Deploy n groups of heterogeneous multi-agent systems inside a channel-type region S. The coverage regions Q of these agents move along the positive direction of the region and remain unchanged. The division of the coverage regions between different groups is given by Definition 1, while the coverage regions of the agents within the same group are divided using Voronoi partitioning (1.6). The dynamics of the virtual leader agent and each agent are described by the following first-order integrator:

[0077]

[0078]

[0079] where s = 0, 1,..., n + 1, i = 1, 2,..., n, m = 1, 2,..., n i , to achieve sequential coverage control of region S, the designed controller needs to satisfy the following conditions:

[0080] (i)

[0081]

[0082] (ii) Minimize the cost function (1.7).

[0083] The present invention considers the region Q to be a dynamic situation, and at this time, it is required to satisfy where v > 0, the virtual leader agent l0 and l n+1 move along the positive direction of the curve γ at the same rate, which ensures that the curve of the coverage area of the agents maintains a constant length.

[0084] For the virtual leader agent l i , the present invention designs the following first-order distributed controller:

[0085]

[0086] where represents the tangent vector of the curve γ at the point l i ,

[0087]

[0088] and represent the arc length of the curve, i = 1, 2,..., n.

[0089] Before presenting the first theoretical result, the following lemma regarding positive systems is first given.

[0090] Lemma 1: Let be a Metzler matrix. Then, A is Hurwitz if and only if there exists a vector θ >> 0 such that Aθ << 0.

[0091] Lemma 2: When the region Q is in a stationary situation, under the drive of the controller (1.11), the arc length corresponding to the coverage area Q of each group of agents i satisfies (1.10).

[0092] Furthermore, the controller (1.11) of the virtual leader ensures that the arc length of the coverage area of each group of agents is proportional to the number of agents in that group. At the same time, the controller designed by the present invention realizes the flexible deployment of agents. When a new agent is added to a group or an agent fails and needs to withdraw, the controller can dynamically adjust the size of the coverage area of that group to ensure the load balance of this group of agents.

[0093] Then, a controller is designed for each agent to minimize the cost function (1.7). Before designing the controller, it is necessary to analyze the influence of the virtual leader agent and each agent on the value of the cost function (1.7).

[0094] First, consider the influence of the virtual leader agent on the value of the cost function (1.7). Take the partial derivative of equation (1.7) with respect to l i to obtain:

[0095]

[0096] where represents the number of agents in the i-th group of agents located at the boundary of the region Q i , and these agents share part of the boundary of the region with . These agents are called the boundary group of the i-th group of agents; similarly, represents the number of agents in the i-th group of agents located inside the region Q i , and these agents do not share the boundary of the region with . These agents are called the internal group of the i-th group of agents. Here, i = 1, 2,..., n, and N ij represents the unit outer normal vector of the boundary . It should be noted that N ij and N ji are two unit vectors with opposite directions, that is, N ij = -N ji . represents the unit outer normal vector of the boundary of the region S, where b = 1, 2. For it holds. The boundaries of the coverage regions of different groups of agents are determined by equation (1.5). Therefore, the partial derivative with respect to needs to be calculated according to the equation. The following lemma gives the calculation result of this partial derivative.

[0097] Lemma 3: For the partial derivative of q with respect to l i is

[0098]

[0099] where

[0100]

[0101]

[0102] κ(p i,j ) represents the curvature of the curve γ at the point p i,j , and λ satisfies i = 1, 2,..., n.

[0103] Next, consider the agent p imThe local optimal position, taking the partial derivative of the cost function (1.7) with respect to p im gives:

[0104]

[0105] where, denotes the unit outer normal vector at the boundary and N im,s denotes the unit outer normal vector at the shared boundary for the i-th group of agents.

[0106] where, according to the Voronoi partition definition (1.6), for any ||q - p im || 2 = ||q - p is || 2 holds, N im,s and N is,m are unit vectors in opposite directions, i.e., N im,s = -N is,m , so the third line of formula (1.14) can be eliminated, and for any holds.

[0107] Considering that the movement of the virtual leader l i will cause the boundary i of the region Q to change. When the region of the agent p im has a shared boundary with Q i , the agent also needs to consider the dynamic change problem of the boundary. Therefore, when designing the controller for the agent p im , the influence of the dynamic boundary on the cost function (1.7) needs to be considered. According to the above analysis, the present invention designs the following controller for the agent p im :

[0108]

[0109] where, k im > 0, and respectively represent the mass and centroid of the region Q im , and are specifically defined as:

[0110]

[0111] Defined by Lemma 3, Defined by equation (1.11), i = 1, 2,..., n, m = 1, 2,..., n i .

[0112] Further, the controller (1.15) of the agent is a distributed controller. The first part of the controller needs to use the information of the Voronoi - segmented neighbors of p im and the η im term is related to the dynamic boundary of the region. Therefore, the influence of l and l i on the region boundary j needs to be considered. The agents located in the boundary group can obtain the dynamic state information of the virtual - leader agents in their adjacent groups, and this information can be obtained through the agents in the adjacent boundary groups.

[0113] Meanwhile, in Equation (1.16), when i = 1 and j = 0, is fixed. At this time, since there are no agents in the group where the virtual - leader agent l0 is located, when i = n and j = n + 1, similar results can be obtained.

[0114] Therefore, when deploying n groups of heterogeneous multi - agents in the channel - type region S, when the region Q is in a dynamic situation, given the initial positions of the virtual - leader agents and each group of agents l(0)=(l0(0), l1(0),..., l n+1 (0)) and P(0)=(P1(0), P2(0),..., P n (0)), under the drive of the controllers (1.11) and (1.15), this group of agents can achieve sequential team coverage control of the region S.

[0115] The specific implementation manners of the present invention aim to elaborate in detail the innovative methods and control strategies proposed in the content of the present invention, so as to perform effective coverage control in practical applications. In order to demonstrate the effectiveness of the coverage control strategy proposed by the invention, the effectiveness of the present invention will be illustrated below through mathematical proof and numerical simulation respectively.

[0116] Mathematical proof: Substitute the cost function (1.7) as the Lyapunov function:

[0117]

[0118] Obviously, V(t)≥0 holds. Take the derivative of the function V(t) with respect to time t, and we can get:

[0119]

[0120] where λ im and η im ​Defined by Equation (1.16), the first term on the right side of Equation (1.18) is only related to the region boundary while is related to the agents in the boundary group of each group. Therefore, this term can be rewritten as:

[0121]

[0122] The first integral on the right side of Equation (1.19) represents the influence of the movement of the i-th virtual leader on the cost function of the boundary group in the i-th group of agents. Therefore, this term is related to The second integral on the right side represents the influence of the movement of the virtual leader l j adjacent to the i-th group on the cost function of the boundary group in the i-th group of agents. Therefore, this term is related to where It can be seen that the cost function of the boundary group is affected by the virtual leader that determines this shared boundary, which can be obtained through Definition (1.5).

[0123] For the last term on the right side of Equation (1.18), substituting the values of λ im η im gives:

[0124]

[0125] The last term in the middle equation of (1.20) is an integral at the region boundary Therefore, this term is only related to the agents in the boundary group.

[0126] Substituting (1.19) and (1.20) into Equation (1.18) gives:

[0127]

[0128] Since k im > 0, therefore According to the LaSalle invariance principle, each agent p im will converge to the centroid of its coverage area while minimizing the cost function (1.7). Therefore, it can be concluded that the controllers (1.11) and (1.15) designed in the present invention can achieve sequential team coverage control of the region S.

[0129] Among them, since the region S is a non-convex region, the coverage area of the agent p im in the boundary group may be a non-convex region, where i = 1, 2,..., n, If the centroid of the coverage area Q im of the boundary group agents Outside the area Q im , and if the agent still has a tendency to move outside the area, it is required that the agent move along its projection direction on the boundary or tangent to ensure that the agents in the boundary group remain within the area Q im .

[0130] Numerical simulation is carried out to verify the correctness of the theory proposed in the present invention through numerical simulation. Simulation 1 is used to verify the applicability of the sequential coverage control theory in the river area; Simulation 2 is used to test the robustness of the virtual leader agent controller to the change in the number of agents in each group.

[0131] Simulation 1

[0132] As Figure 3 shown, a section of the Yellow River area in Inner Mongolia Autonomous Region is selected for verification. This river section is located at 111.4359°E, 39.9018°N Figure 3 , which shows the movement trajectories of the agents driven by the virtual leader agent. The movement speed of the virtual leader agent is limited to 2 m / s, and the movement speed of each group of agents is limited to 3 m / s. In the figure, the solid dots represent the initial positions of the agents, the asterisks represent the final positions, the cyan curve represents the movement trajectory of the first group of agents, the blue curve represents the second group of agents, and the magenta curve represents the third group of agents.

[0133] In Simulation 1, each group of agents adopts a Gaussian density function in the following form:

[0134]

[0135] where i = 1, 2, 3. For the first group of agents, the density function is defined as Let [x1 x2 x3] = [150 350 560], [y1 y2 y3] = [50 200 300], σ1 = σ2 = σ3 = 150. Let the density function of the second group of agents be a uniform density function For the density function of the third group of agents Let [x1 x2] = [200 300], [y1 y2] = [200 300], σ1 = σ2 = 150.

[0136] The initial positions of the virtual leader agents are respectively l0(0) = [50 145] Τ , l1(0) = [90 131] Τ , l2(0) = [153 152] Τ , l3(0) = [250 181] Τ, l4(0) = [300 219] Τ , the initial positions of the first group of agents are p 11 = [75 160] Τ , p 12 = [60 120] Τ , p 13 = [58 141] Τ , p 14 = [100 110] Τ , p 15 = [100 140] Τ , the initial positions of the second group of agents are p 21 = [170 160] Τ , p 22 = [180 140] Τ , p 23 = [170 100] Τ , the initial positions of the third group of agents are p 31 = [220 180] Τ , p 32 = [250 130] Τ , p 33 = [260 130] Τ , p 34 = [270 170] Τ , let the gain coefficients of each group of agents be [α1 α2 α3] = [1 2 3].

[0137] Figure 4 Records the change in the arc length of the coverage area of each group of agents. It can be seen from Figure 4 that the arc length of the coverage area of each group of agents is proportional to the number of agents in that group. Figure 5 Shows the change in the cost function of this group of agents, indicating that when the leader agents l0 and l4 stop moving, that is, when the dynamic area Q no longer moves, the cost function converges to a local minimum.

[0138] Simulation Two

[0139] In this part of the simulation, consider the change in the arc length of the coverage area of each group of agents when an agent in a certain group leaves the team or a new agent joins. This simulation uses the same task area, density function, initial positions of the agents, and initial positions of the leader agents as in Simulation One. When t = 200s, the agent p 15 in the first group leaves the team, and a new agent p 35 , Figure 6The change in the arc length of the coverage area of each group of agents is recorded. It can be seen from this that when the number of agents in each group changes, the controller (1.11) designed in the present invention can adjust the range of the coverage area of this group in real time to ensure that the arc length of the coverage area of each group of agents is proportional to the number of agents in this group.

[0140] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0141] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A channel - type area coverage control method for multi - agent systems based on arc length, characterized in that, It includes the following steps: Step S1, target area division. Based on the arc length partitioning method, the channel-type target area is divided into multiple sequential sub-areas; Step S2, design of the distributed controller of the virtual leader agent. The distributed controller of the virtual leader agent ensures that the arc length of the coverage area of each group of agents is proportional to the number of agents in that group; Step S3, design of the distributed controller of the individual agent. The distributed controller of the individual agent, combined with the distributed controller of the virtual leader agent, enables the agents to achieve sequential team coverage control of area S; The process of dividing the target area in step S1 is as follows: deploy n groups of heterogeneous multi-agent systems inside a channel-shaped area S, and the boundary of this channel-shaped area is composed of two regular curves and defined, where the i-th group of agents contains n i agents, i = 1,..., n, and the median line of the channel-shaped area is a regular curve, defined as a regular curve with the abscissa as the parameter, and its parametric equation is denoted as γ(x) = (x, y(x)) Τ , deploy n + 2 virtual leader agents on the median line of area S, define as the position of the e-th virtual leader agent, where e = 0, 1,..., n + 1. According to the initial positions of the virtual leader agents, these agents are distributed on in the order of their abscissas, that is l = (l0, l1,..., l n+1 ) represents the set of positions of these virtual leader agents. The coverage area of each group of agents is The coverage area of the entire agent population is where Q = Q1 ∪ Q2 ∪... ∪ Q n , and the range of the coverage area Q is determined by the arc length of the curve between l0 and l n+1 , and this arc length is a specified fixed value Define the boundary of the area as and represent the set of indices of the groups adjacent to the i-th group of agents as The range of the coverage area Q i of the i-th group of agents is determined by the curve as defined below: where s li,q represents the arc length of the curve, and n i represents the number of agents in the i-th group, and |S i | represents the length of the curve S i Let p i,j be the intersection point of the curve S i and the curve S j satisfying the following relationship: Among them Let p 1,0 = l0, p n,n+1 = l n+1 , be Q i and the shared boundary of Q j , which is defined as: where is the line segment passing through point p i,j and perpendicular to the tangent direction of curve γ′(xp i,j ), where γ′(xp i,j ) is the tangent line of curve at point p i,j , i = 1,..., n, l0 and l n+1 are respectively located at the rear end and the front end of region Q.

2. The method for channel-type area coverage control of a multi-agent system based on arc length according to claim 1, wherein: The coverage area Q of the i-th group of agents i is the inner area bounded by and , and its interior is a region that is connected by roads, satisfying where i = 1, 2,..., n, Let p i,m represent the position of the m-th agent in the i-th group of agents, where i = 1,..., n, m = 1,..., n i , and define as the set of positions of the i-th group of agents, and P = (P1, P2,..., P n ) as the set of positions of this group of agents. For the agent p i distributed in the region Q i,m , its coverage area Q im is defined by the following Voronoi partition: where n i represents the number of agents in the i-th group, is the boundary of region Q im and agent p im shares part of the regional boundary with its Voronoi partition neighbors, and the set of neighbor indices is where s = 1,..., n i , s ≠ m.

3. A method for channel-type area coverage control of a multi-agent system based on arc length according to claim 2, characterized in that: The design process of the virtual leader agent distributed controller in step S2, for the virtual leader agent l i designed the following first-order distributed controller: where γ′(x li ) represents the tangent vector of the curve γ at the point l i , and represents the arc length of the curve, where \(i = 1, 2, \cdots, n\).

4. A method for channel - type area coverage control of a multi - agent system based on arc length according to claim 3, characterized in that: The distributed controller of the individual agent in step S3 is as follows: where k im > 0, and represent the mass and the centroid of region Q im respectively, and are specifically defined as: Defined by Equation (1.11), where \(i = 1, 2, \cdots, n\) and \(m = 1, 2, \cdots, n\). i .

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