A cluster formation control method based on dynamic virtual area

Abstract

The application relates to a dynamic virtual area-based cluster formation control method, and belongs to the technical field of unmanned cluster coordinated motion control. The dynamic virtual area-based cluster formation control technology is adopted for the cooperative motion control problem of a large-scale cluster system. Under the coordination of the dynamic virtual area, cluster individuals rely on local communication and interaction to self-organize the coordinated motion. Based on the self-organized cooperative motion of local communication and information interaction, the unmanned cluster converges in a given area, the collision between individuals is avoided, and the control target of maintaining the formation distance is achieved.

Description

Technical Field

[0001] This invention relates to the field of unmanned swarm coordinated motion control technology, specifically to a swarm formation control method based on dynamic virtual regions, and more particularly to a coordinated control method and strategy based on dynamic virtual regions for unmanned swarm formation and transformation tasks. Background Technology

[0002] Currently, one of the key technologies for the emergence of intelligence in unmanned swarm systems is cooperative control. As a core research area of ​​swarm intelligence, it mainly focuses on specific tasks such as swarm formation, collision avoidance, and collision mitigation. Compared to a single intelligent agent, unmanned swarm systems can achieve a "1+1>2" effect due to the emergence of capabilities generated through mutual cooperation. However, because strict topological relationships need to be maintained during swarm design, the computation becomes complex and difficult to implement when the swarm size is large. Therefore, as the swarm size increases, higher demands are placed on the cooperative control of unmanned swarms.

[0003] Currently, formation and maintenance techniques in unmanned swarm systems require the swarm to converge to a stable topology and maintain topological connections between members during movement. Existing formation and maintenance techniques mainly include structured methods and behavior-based methods. Structured methods include leader-follower methods and virtual structure methods. These methods first require identifying the leader or virtual structure, and then followers follow the leader or structures with rigid or relaxed constraints. The main idea of ​​this type of method is to maintain a predefined formation. The leader-follower method is simple to design and implement, and has good formation tracking performance, but it requires the identity and order of individuals in the swarm and is highly dependent on the leader node. The failure of the leader can lead to the failure of the entire swarm's mission, often making it difficult to guide the coordinated movement of large-scale swarms.

[0004] Virtual architecture avoids navigator failure or interference by eliminating the role or hierarchy of the physical navigator in the formation, but it increases the computational and communication burden and is limited in use in large-scale clusters.

[0005] Furthermore, behavior-based methods can be mainly divided into potential field-based methods and consensus-based methods. Compared with other methods, they have lower requirements for communication, but the difficulty lies in how to design the behavior of individual individuals to meet the given group-level norms. They are difficult to model and have low stability. Summary of the Invention

[0006] In view of the above problems, this invention provides a cluster formation control method based on dynamic virtual regions. Addressing the cooperative motion control problem of large-scale unmanned swarm systems, it employs a behavior-based swarm control framework, combined with formation control techniques based on artificial potential fields and the consensus principle. Through coordination within a dynamic virtual region, the cohesion of the swarm is maintained during formation formation and transformation. Individual swarm members rely on local communication and interaction with their neighbors to self-organize and coordinate their movements, enabling the entire swarm system to converge to and maintain movement within the dynamic virtual region. Individual swarm members maintain specific formation distances and avoid collisions.

[0007] This invention provides a cluster formation control method based on dynamic virtual regions, comprising:

[0008] Design a dynamic virtual region for cluster formation and establish a dynamic virtual region shape control component that restricts the cluster formation within the dynamic virtual region.

[0009] Based on the collision avoidance distance between individuals, a local potential energy function for collision avoidance among cluster individuals is designed, and the partial derivative of the local potential energy function is used to obtain the control components for collision avoidance among cluster individuals.

[0010] The cluster formation distance is selected according to the needs of the formation task scenario. Based on the position and velocity vectors of the individual clusters, the formation control components of the individual clusters are constructed based on the artificial potential field method and the consistency principle.

[0011] The navigation control components for each cluster individual are constructed based on the center position and velocity of the dynamic virtual region and the position and velocity of the individual cluster individuals.

[0012] A cluster formation coordination strategy is established based on the formation task scenario. The dynamic virtual area shape control component, the collision avoidance control component between cluster individuals, the formation control component of cluster individuals, and the navigation control component of cluster individuals are input into the cluster formation coordination strategy for weighted combination and output of cluster individual control quantity. The speed and position of cluster individuals are controlled based on the cluster individual control quantity.

[0013] Preferably, at any given time, the dynamic virtual region is a circular or elliptical shape domain.

[0014] Preferably, the expression for the shape control component of the dynamic virtual region is:

[0015]

[0016] Among them, u P,i u is the dynamic virtual region shape control component for the i-th cluster individual. Pc,i Let u be the shape control component of the circular dynamic virtual region of the i-th cluster individual. Pe,iLet i be the shape control component of the elliptical dynamic virtual region of the i-th cluster individual, i = 1, 2, 3, ..., N, where N represents the total number of cluster individuals.

[0017] Furthermore, when the dynamic virtual region is circular, the specific components for establishing a dynamic virtual region shape control component that restricts the cluster formation within the dynamic virtual region include:

[0018] Define the relative positions of cluster individuals in the cluster formation and the center of the circular dynamic virtual region. Construct a shape control objective function for the circular dynamic virtual region based on the relative positions. Obtain the potential energy function for shape control of the circular dynamic virtual region based on the shape control objective function.

[0019] The potential energy function controlling the shape of the circular dynamic virtual region is differentiated with respect to the relative position to obtain the shape control component of the circular dynamic virtual region.

[0020] Furthermore, the expression for the relative position of the cluster individuals in the cluster formation to the center of the circular dynamic virtual region is:

[0021]

[0022] in, x represents the relative position of the i-th cluster individual to the center of the circular dynamic virtual region; i Let x be the position vector of the i-th individual in the cluster, i = 1, 2, 3, ..., N, where N represents the total number of individuals in the cluster. c The coordinates are the center coordinates of the circular dynamic virtual region.

[0023] Furthermore, the objective function expression for shape control of the circular dynamic virtual region is:

[0024]

[0025] Among them, f Gc (·) represents the objective function for shape control of the circular dynamic virtual region; Let R be the relative position of the i-th cluster individual to the center of the circular dynamic virtual region, i = 1, 2, 3, ..., N, where N represents the total number of cluster individuals; R is the radius of the circular dynamic virtual region, R ≥ 0.

[0026] Furthermore, the potential energy function for shape control of the circular dynamic virtual region is expressed as follows:

[0027]

[0028] in, Let k be the potential energy value of the i-th cluster individual relative to the center of the circular dynamic virtual region. cThis is an adjustable parameter for the circular dynamic virtual region, with values ​​that are positive numbers, f. Gc (·) represents the objective function for shape control of the circular dynamic virtual region; Let be the relative position of the i-th cluster individual to the center of the circular dynamic virtual region.

[0029] Furthermore, by differentiating the potential energy function for shape control of the circular dynamic virtual region with respect to the relative position, the shape control component of the circular dynamic virtual region is obtained, expressed as:

[0030]

[0031] Among them, u Pc,i Let be the shape control component of the circular dynamic virtual region for the i-th cluster individual. Let be the relative positional potential energy value of the i-th cluster individual and the center of the circular dynamic virtual region. Let R be the relative position of the i-th cluster individual to the center of the circular dynamic virtual region, and R be the radius of the circular dynamic virtual region, where R ≥ 0; k c This is an adjustable parameter for the circular dynamic virtual region, with values ​​that are positive numbers, f. Gc (·) is the objective function for shape control of the circular dynamic virtual region.

[0032] The technical solution of this invention constructs a control objective function and a continuous potential energy function partial derivatives for a continuous dynamic virtual region. When individual members of the cluster are located outside the circular dynamic virtual area (i.e.) ), circular dynamic virtual region shape control component u Pc It functions to cause individual locations to converge toward a given region, and as cluster individuals approach the dynamic virtual region, When cluster members are located within a dynamic virtual region, maintain The shape control component does not function.

[0033] Furthermore, when the dynamic virtual region is elliptical, the specific components for establishing a dynamic virtual region shape control component that restricts the cluster formation within the dynamic virtual region include:

[0034] Define the relative position of cluster individuals in the cluster formation to the center of the elliptical dynamic virtual region, construct the shape control objective function of the elliptical dynamic virtual region based on the relative position, and construct the potential energy function for shape control of the elliptical dynamic virtual region according to the shape control objective function of the elliptical dynamic virtual region.

[0035] The shape control component of the elliptical dynamic virtual region is obtained by differentiating the potential energy function of the shape control of the elliptical dynamic virtual region with respect to the relative position.

[0036] Furthermore, the relative position expression between the cluster individual and the center of the elliptical dynamic virtual region is:

[0037]

[0038] in, x represents the relative position of an individual in the cluster to the center of the elliptical dynamic virtual region. i Let x be the position vector of the i-th individual in the cluster, i = 1, 2, 3, ..., N, where N represents the total number of individuals in the cluster. e The coordinates are the center coordinates of the elliptical dynamic virtual region.

[0039] Furthermore, the expression for the elliptical dynamic virtual region is:

[0040] (xx e ) T M -1 (xx e )≤1

[0041]

[0042] Where x is the coordinate of any point within the elliptical region, x e Let M be the coordinates of the center of the elliptical dynamic virtual region, M be the elliptical characteristic matrix, a be the length of the major axis of the ellipse, b be the length of the minor axis of the ellipse, θ be the angle between the major axis of the ellipse and the positive x-axis, and T be the transpose of the matrix.

[0043] Furthermore, the shape control objective function of the elliptical dynamic virtual region is expressed as:

[0044]

[0045]

[0046]

[0047] Where, f Ge (·) represents the shape control objective function for the elliptical dynamic virtual region; Let be the shape control objective function value of the relative position of the i-th cluster individual with respect to the center of the elliptical dynamic virtual region. Let be the relative position of the i-th cluster individual to the center of the elliptical dynamic virtual region. x e Let x be the center coordinate of the elliptical dynamic virtual region. i1 The x-coordinate represents the x-coordinate of the i-th cluster individual. i2 The ordinate of the i-th cluster individual, x e1 It is the x-coordinate of the center of the elliptical dynamic virtual region. e2y is the ordinate of the center of the elliptical dynamic virtual region; a is the length of the major axis of the ellipse, b is the length of the minor axis of the ellipse, and θ is the angle between the major axis of the ellipse and the positive x-axis. This is the projection of the relative position vector onto the x-axis after rotating it by an angle θ along the x-axis. It is the projection of the relative position vector onto the y-axis after rotating the y-axis by an included angle θ.

[0048] Furthermore, the potential energy function expression for the shape control of the elliptical dynamic virtual region is:

[0049]

[0050] Where, k e This is an adjustable parameter for the elliptical dynamic virtual region, and its value is a positive number. Let be the relative positional potential energy value of the i-th cluster individual and the center of the elliptical dynamic virtual region. Let be the relative position of the i-th cluster individual to the center of the elliptical dynamic virtual region.

[0051] Furthermore, the derivative of the potential energy function controlling the shape of the elliptical dynamic virtual region with respect to the relative position yields the expression for the shape control component of the elliptical dynamic virtual region as follows:

[0052]

[0053] Among them, u Pe,i Let be the shape control component of the elliptical dynamic virtual region for the i-th cluster individual. Let be the relative positional potential energy value of the i-th cluster individual and the center of the elliptical dynamic virtual region. Let be the relative position of the i-th cluster individual to the center of the elliptical dynamic virtual region, where a is the length of the major axis of the ellipse, b is the length of the minor axis of the ellipse, and θ is the angle between the major axis of the ellipse and the positive x-axis. This is the projection of the relative position vector onto the x-axis after rotating it by an angle θ along the x-axis. It is the projection of the relative position vector onto the y-axis after rotating the y-axis by an included angle θ.

[0054] Preferably, the specific steps for obtaining the control components for collision avoidance among individuals in the cluster are as follows:

[0055] A target function for collision avoidance among cluster individuals is established based on the collision avoidance distance between individuals. A local potential energy function for collision avoidance among cluster individuals is designed based on the target function. The partial derivatives of the local potential energy function are obtained and summed to obtain the control components for collision avoidance among cluster individuals.

[0056] Furthermore, the objective function for inter-individual collision avoidance is expressed as:

[0057] fL (x ij )=-ln(||x ij || 2 )+ln(r 2 )≤0

[0058] Among them, f L (x ij Let x be the function value for collision avoidance between the i-th and j-th cluster individuals that are neighbors. ij Let r be the relative position vector between the i-th and j-th cluster individuals that are neighbors, and r be the minimum distance allowed between cluster individuals to avoid collisions, i.e., the collision avoidance distance between the individuals.

[0059] Furthermore, the local potential energy function for collision avoidance among the cluster individuals is expressed as:

[0060]

[0061] Where q(x) ij Let s be the local potential energy values ​​for collision avoidance between the i-th and j-th cluster individuals who are neighbors, i = 1, 2, 3, ..., N, j = 1, 2, 3, ..., N, i ≠ j, and N represent the total number of cluster individuals; ij Let s be the values ​​in the adjacency matrix corresponding to the i-th and j-th cluster individuals that are neighbors. ij The value can be 0 or 1, when ||x i -x j ||≤r c At that time, s ij =1; when ||x i -x j ||>r c At that time, s ij =0, r c x is the communication radius of an individual in the cluster. i Let x be the position of the i-th cluster individual. j f represents the position of the j-th cluster individual; L (x ij ) represents the collision avoidance function between the i-th and j-th cluster individuals that are neighbors.

[0062] Furthermore, the control component for collision avoidance among individuals in the cluster is expressed as:

[0063]

[0064] Among them, u Q,i Let i be the formation control component for the i-th cluster individual. Let u be the set of neighbors of the i-th cluster individual. Q,ij Let q(x) be the collision avoidance control component for the i-th and j-th cluster individuals that are neighbors.ij Let x be the local potential energy value for collision avoidance between the i-th and j-th cluster individuals who are neighbors. ij Let s be the relative position vector between the i-th and j-th cluster individuals who are neighbors. ij Let s be the values ​​in the adjacency matrix corresponding to the i-th and j-th cluster individuals that are neighbors. ij The value can be 0 or 1, when ||x i -x j ||≤r c At that time, s ij =1; when ||x i -x j ||>r c At that time, s ij =0, r c x is the communication radius of an individual in the cluster. i Let x be the position of the i-th cluster individual. j is the position of the j-th cluster individual; r is the minimum distance allowed between cluster individuals to avoid collisions, i.e., the collision avoidance distance between individuals; a neighbor refers to a cluster individual whose distance from the current cluster individual is less than the communication radius, and cluster individuals can interact with neighbors within the communication radius.

[0065] Preferably, the formation control component of the cluster individual is expressed as:

[0066]

[0067]

[0068] Among them, u n,i Let i be the formation control component for the i-th cluster individual. Weight parameters for maintaining distance between individual neighbors in a cluster. Weight parameters for maintaining speed alignment among individual neighbors in the cluster; Let φ be the set of neighbors of the i-th cluster individual. α The action function for maintaining the grouping distance between individual neighbors in the cluster, x i Let x be the position of the i-th cluster individual. j Let be the position of the j-th cluster individual, σ be the norm that measures the length of the vector space, and n be the position of the j-th cluster individual. ij Let a be the normalized relative position between the i-th cluster individual and the j-th cluster individual, which are neighbors. ij (x) represents the element of the spatial adjacency matrix between the i-th and j-th cluster individuals who are neighbors, where x is the position vector of the cluster individual, and v i Let v be the velocity of the i-th individual in the cluster. jLet ψ be the speed of the j-th individual in the cluster, i = 1, 2, 3, ..., N, j = 1, 2, 3, ..., N, i ≠ j, and N represent the total number of individuals in the cluster; ε (·) is the normalization function that measures the length of the vector space, and ε is the parameter that measures the norm of the vector space.

[0069] Furthermore, the expression for the elements of the spatial adjacency matrix between the i-th and j-th cluster individuals that are neighbors is:

[0070]

[0071] Among them, a ij (x) represents the elements of the spatial adjacency matrix between the i-th and j-th cluster individuals who are neighbors, ρ h Let x be the impulse function (a function that smoothly changes from 0 to 1). i Let x be the position of the i-th cluster individual. j Let be the position of the j-th cluster individual, where i = 1, 2, 3, ..., N, j = 1, 2, 3, ..., N, i ≠ j, and N represents the total number of cluster individuals; σ is the norm that measures the length of the vector space, r c This refers to the communication radius of an individual member in the cluster.

[0072] Furthermore, the expression for the impact function is:

[0073]

[0074] Where, ρ h (·) represents the impulse function, h represents the parameter of the impulse function, h∈(0,1), and z represents the independent variable of the impulse function.

[0075] Furthermore, the norm, which measures the length of a vector space, is expressed as:

[0076]

[0077] Where s is a vector of arbitrary dimensions, σ is the norm that measures the length of the vector space, and ε is a parameter that measures the norm of the length of the vector space.

[0078] Furthermore, the action function for maintaining the formation distance between individual neighbors in the cluster is expressed as follows:

[0079]

[0080]

[0081] Where, φ α ρ is the action function value for maintaining the formation distance between individual neighbors in the cluster. hLet r be the impulse function (a function that smoothly changes from 0 to 1). β It is the communication radius r c The norm of the vector space, i.e., r, is a measure of the length of the vector space. β =||r c || σ f is the independent variable of the action function, ω1(·) is a smooth function, and its form satisfies d β It is the norm of the vector space length that measures the formation distance d, i.e., d β =|d| σ φ(·) is a non-uniform sigmoid function, where a, b, and c are the three parameters of the function φ(·), and satisfy 0. <a≤b, This is to ensure that φ(0) = 0.

[0082] Preferably, the expression for constructing the cluster individual navigation control component is:

[0083]

[0084] Among them, u g1,i Let i be the navigation control component for the i-th cluster individual. The control objective is for the cluster individual to track the center position of the dynamic virtual region and maintain the same speed as the movement of the dynamic virtual region. At that time, u g1,i Degenerate into u g2,i u g2,i The control objective is to keep the movement speed of individual cluster members consistent with that of the dynamic virtual region; To control the weights of individual cluster members tracking the center position of the dynamic virtual region, To control the weights that ensure the movement speed of individual cluster members remains consistent with that of the dynamic virtual region, x i Let x be the position of the i-th cluster individual. o x is the center position of the dynamic virtual region (if the dynamic virtual region is elliptical). o =x e If the dynamic virtual region is circular, x o =x c ), v i Let v be the velocity of the i-th cluster individual. o The center velocity of the dynamic virtual region.

[0085] In the technical solution of this invention, navigation control components are designed for individual clusters to play a navigation role, causing the positions of the individual clusters to converge toward the center of a given dynamic virtual region and making the speed of the individual clusters consistent with the speed of the given dynamic virtual region.

[0086] Preferably, the formation mission scenarios include: energy-saving scenarios and complex obstacle adaptation scenarios, wherein the complex obstacle scenarios are narrow passages and curves.

[0087] The cluster formation coordination strategy includes a "center-first" strategy and an "edge-first" strategy. The "center-first" strategy involves cluster members first filling the center of a dynamic virtual region during movement, then occupying the edge positions, ensuring the unmanned cluster maintains full connectivity while coordinating its movement to the dynamic virtual region. Figure 1 As shown;

[0088] The described "edge-first" formation coordination strategy involves cluster members first filling the edge positions of a dynamically virtual region, with the edges filled first and the center filled later. This strategy has a faster convergence speed and saves energy, but it cannot guarantee connectivity. Figure 3 As shown.

[0089] Preferably, the specific steps for inputting the dynamic virtual region shape control component, the collision avoidance control component between cluster individuals, the formation control component of cluster individuals, and the navigation control component of cluster individuals into the cluster formation coordination strategy for weighted combination and output of cluster individual control quantity are as follows:

[0090] When formation missions require adaptation to complex obstacle scenarios;

[0091] The control components for the shape of the dynamic virtual region, collision avoidance between cluster individuals, formation, and navigation are input into the "center priority" strategy to determine whether the cluster individuals are located within the dynamic virtual region.

[0092] When a cluster member has no neighbors (a neighbor is defined as a member whose distance from the current cluster member is less than the communication radius r) c When the individual (other cluster individuals) is located outside the dynamic virtual region, the control strategy requires the cluster individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the dynamic virtual region, and outputs the control quantity of the cluster individual.

[0093] When a cluster individual has neighbors and its position is outside the dynamic virtual region, the control strategy requires the individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the center of the dynamic virtual region, and also considering collision avoidance between cluster individuals, and outputting the cluster individual control quantity.

[0094] When individuals within a cluster are located within a dynamic virtual region, the control strategy requires them to maintain formation distance and speed alignment with their neighbors while moving towards and navigating to the center of the dynamic virtual region, outputting the cluster's control variables; such as Figure 2 ;

[0095] When formation mission scenarios require adaptation to energy-saving scenarios;

[0096] The control components for the shape of the dynamic virtual region, collision avoidance between cluster individuals, formation, and navigation are input into the "edge-first" strategy to determine whether cluster individuals are located within the dynamic virtual region.

[0097] When a cluster individual has no neighbors and its position is outside the dynamic virtual region, the control strategy requires the cluster individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the dynamic virtual region, and outputting the cluster individual control quantity.

[0098] When a cluster individual has neighbors and its position is outside the dynamic virtual region, the control strategy requires the individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the center of the dynamic virtual region, and also considering collision avoidance between cluster individuals, and outputting the cluster individual control quantity.

[0099] When a cluster individual is located within a dynamic virtual region, the node degree of the cluster individual is determined based on its communication radius and relative positional relationship; the node degree is the number of neighbors of the cluster individual; when the node degree = 0, the cluster individual maintains the same movement speed as the dynamic virtual region, and the cluster individual control quantity is output.

[0100] When the node degree is 1 or 2, determine whether the cluster individual has any neighboring individuals outside the dynamic virtual region. If so, the control strategy requires the individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while maintaining the formation distance and speed alignment with the surrounding neighboring individuals. If not, the cluster individual keeps the movement speed consistent with the dynamic virtual region, while maintaining the formation distance and speed alignment with the surrounding neighboring individuals, and outputs the cluster individual control quantity.

[0101] When the node degree is ≥3, determine if any cluster individual has neighboring individuals outside the dynamic virtual region. If so, the control strategy requires the individual to move towards and navigate to the center of the dynamic virtual region, while maintaining formation distance and speed alignment with its neighboring individuals. If not, the cluster individual maintains the same movement speed as the dynamic virtual region, while maintaining formation distance and speed alignment with its neighboring individuals, and outputs the cluster individual's control variable, such as... Figure 4 .

[0102] The reference for setting the node degree boundary in this invention is the spatial occupancy around the cluster individuals. When the node degree is above 3, the coordination effect of the cluster individuals towards the regional center in order to maintain the formation distance decreases.

[0103] Preferably, the specific steps for outputting the cluster individual control quantity are as follows:

[0104] a. Obtain the control parameters and initial position and velocity of each individual in the cluster formation. Obtain the position and velocity of each individual in the cluster formation at time t. Let T be the upper limit of the execution time, and t = 1, 2, 3...T, representing the total number of time points T. The control parameters are the cluster control parameters and the dynamic virtual region control parameters. The cluster control parameters are the cluster size, the communication radius of each individual, the maximum movement speed, the maximum acceleration, and the formation distance. The dynamic virtual region control parameters are the major axis length, the minor axis length, the pointing angle, and the center coordinates.

[0105] b. Based on the position and velocity of the cluster individuals at time t, obtain the dynamic virtual region shape control component, the collision avoidance control component between cluster individuals, the formation control component and the navigation control component of the cluster individuals respectively.

[0106] c. Input the above four control components into the cluster formation coordination strategy, obtain the control quantity of the individual clusters through weighted combination, obtain the position and velocity of the individual clusters at time t+1, save the position and velocity data of the individual clusters, and draw the real-time motion trajectory of the cluster formation.

[0107] d. Update the control parameters, position, and velocity of the individual cluster members, and iterate. If t≤T, the iteration continues and returns to step a. If t>T or the target point is reached, output the final position and velocity of the individual cluster members and terminate the iteration.

[0108] Compared with the prior art, the present invention has at least the following beneficial effects:

[0109] (1) The control method of the present invention coordinates the movement of the cluster through a dynamic virtual region. Under the constraints of the dynamic virtual region, individuals in the cluster self-organize and coordinate their movements based on local communication and information interaction, thereby achieving the control objective of unmanned cluster convergence and maintaining within a given area, avoiding collisions between individuals and maintaining formation distance.

[0110] (2) The control method of the present invention only constrains the distance between individuals in the cluster without imposing strict geometric restrictions on the topology of the cluster, thus making it easier to extend to the formation coordination control of larger clusters.

[0111] (3) The control method of the present invention ensures the cohesion and connectivity of the cluster during coordinated movement due to the constraints of the dynamic virtual region, and is also easier to extend to larger clusters.

[0112] (4) The control method of the present invention addresses the needs of coordinated motion control of large-scale clusters and the limitations of existing collaborative methods in large-scale cluster applications. The proposed cluster formation control method has the potential to be applied to large-scale clusters, and the effectiveness of the control method under different changing scenarios in dynamic virtual regions has been tested through numerical simulation. Attached Figure Description

[0113] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0114] Figure 1 This is a schematic diagram of the "center-first" strategy of the present invention;

[0115] Figure 2 This is a schematic diagram of the "center-first" strategy calculation control input flowchart of the present invention;

[0116] Figure 3 This is a schematic diagram of the "edge-first" strategy of the present invention;

[0117] Figure 4 This is a schematic diagram of the calculation control input flowchart for the "edge-first" strategy of this invention;

[0118] Figure 5 This is a schematic diagram of the simulation results of the dynamic virtual region deformation scene based on the "center priority" strategy of this invention.

[0119] Figure 6 This is a schematic diagram of the simulation results of the dynamic virtual region rotation scene based on the "center priority" strategy of this invention;

[0120] Figure 7 This is a schematic diagram of the simulation results of the dynamic virtual region deformation scene of the "edge-first" strategy of the present invention. Detailed Implementation

[0121] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0122] A specific embodiment of the present invention, such as Figure 1-7 This invention discloses a cluster formation control method based on dynamic virtual regions. To illustrate the effectiveness of the proposed method, a specific embodiment is provided below for detailed explanation of the above technical solution. The specific implementation steps are as follows:

[0123] Design a dynamic virtual region for cluster formation and establish a dynamic virtual region shape control component that restricts the cluster formation within the dynamic virtual region.

[0124] Based on the collision avoidance distance between individuals, a local potential energy function for collision avoidance among cluster individuals is designed, and the partial derivative of the local potential energy function is used to obtain the control components for collision avoidance among cluster individuals.

[0125] The cluster formation distance is selected according to the needs of the formation task scenario. Based on the position and velocity vectors of the individual clusters, the formation control components of the individual clusters are constructed based on the artificial potential field method and the consistency principle.

[0126] The navigation control components for each cluster individual are constructed based on the center position and velocity of the dynamic virtual region and the position and velocity of the individual cluster individuals.

[0127] A cluster formation coordination strategy is established based on the formation task scenario. The dynamic virtual area shape control component, the collision avoidance control component between cluster individuals, the formation control component of cluster individuals, and the navigation control component of cluster individuals are input into the cluster formation coordination strategy for weighted combination and output of cluster individual control quantity. The speed and position of cluster individuals are controlled based on the cluster individual control quantity.

[0128] Preferably, at any given time, the dynamic virtual region is a circular or elliptical shape domain.

[0129] Preferably, the expression for the shape control component of the dynamic virtual region is:

[0130]

[0131] Among them, u P,i u is the dynamic virtual region shape control component for the i-th cluster individual. Pc,i Let u be the shape control component of the circular dynamic virtual region of the i-th cluster individual. Pe,i Let i be the shape control component of the elliptical dynamic virtual region of the i-th cluster individual, i = 1, 2, 3, ..., N, where N represents the total number of cluster individuals.

[0132] Furthermore, when the dynamic virtual region is circular, the specific components for establishing a dynamic virtual region shape control component that restricts the cluster formation within the dynamic virtual region include:

[0133] Define the relative positions of cluster individuals in the cluster formation and the center of the circular dynamic virtual region. Construct a shape control objective function for the circular dynamic virtual region based on the relative positions. Obtain the potential energy function for shape control of the circular dynamic virtual region based on the shape control objective function.

[0134] The potential energy function controlling the shape of the circular dynamic virtual region is differentiated with respect to the relative position to obtain the shape control component of the circular dynamic virtual region.

[0135] Furthermore, the expression for the relative position of the cluster individuals in the cluster formation to the center of the circular dynamic virtual region is:

[0136]

[0137] in, x represents the relative position of the i-th cluster individual to the center of the circular dynamic virtual region; i Let x be the position vector of the i-th individual in the cluster, i = 1, 2, 3, ..., N, where N represents the total number of individuals in the cluster. c The coordinates are the center coordinates of the circular dynamic virtual region.

[0138] Furthermore, the objective function expression for shape control of the circular dynamic virtual region is:

[0139]

[0140] Among them, f Gc (·) represents the objective function for shape control of the circular dynamic virtual region; R represents the relative position of the i-th cluster individual to the center of the circular dynamic virtual region; R is the radius of the circular dynamic virtual region, R≥0.

[0141] Furthermore, the potential energy function for shape control of the circular dynamic virtual region is expressed as follows:

[0142]

[0143] in, Let k be the potential energy value of the i-th cluster individual relative to the center of the circular dynamic virtual region. c This is an adjustable parameter for the circular dynamic virtual region, with values ​​that are positive numbers, f. Gc (·) represents the objective function for shape control of the circular dynamic virtual region; Let be the relative position of the i-th cluster individual to the center of the circular dynamic virtual region.

[0144] Furthermore, by differentiating the potential energy function for shape control of the circular dynamic virtual region with respect to the relative position, the shape control component of the circular dynamic virtual region is obtained, expressed as:

[0145]

[0146] Among them, u Pc,i Let be the shape control component of the circular dynamic virtual region for the i-th cluster individual. Let be the relative positional potential energy value of the i-th cluster individual and the center of the circular dynamic virtual region. Let R be the relative position of the i-th cluster individual to the center of the circular dynamic virtual region, and R be the radius of the circular dynamic virtual region, where R ≥ 0; kc This is an adjustable parameter for the circular dynamic virtual region, with values ​​that are positive numbers, f. Gc (·) is the objective function for shape control of the circular dynamic virtual region.

[0147] The technical solution of this invention constructs a control objective function and a continuous potential energy function partial derivatives for a continuous dynamic virtual region. When individual members of the cluster are located outside the circular dynamic virtual area (i.e.) ), circular dynamic virtual region shape control component u Pc It functions to cause individual locations to converge toward a given region, and as cluster individuals approach the dynamic virtual region, When cluster members are located within a dynamic virtual region, maintain The shape control component does not function.

[0148] Furthermore, when the dynamic virtual region is elliptical, the specific components for establishing a dynamic virtual region shape control component that restricts the cluster formation within the dynamic virtual region include:

[0149] Define the relative position of cluster individuals in the cluster formation to the center of the elliptical dynamic virtual region, construct the shape control objective function of the elliptical dynamic virtual region based on the relative position, and construct the potential energy function for shape control of the elliptical dynamic virtual region according to the shape control objective function of the elliptical dynamic virtual region.

[0150] The shape control component of the elliptical dynamic virtual region is obtained by differentiating the potential energy function of the shape control of the elliptical dynamic virtual region with respect to the relative position.

[0151] Furthermore, the relative position expression between the cluster individual and the center of the elliptical dynamic virtual region is:

[0152]

[0153] in, x represents the relative position of an individual in the cluster to the center of the elliptical dynamic virtual region. i Let x be the position vector of the i-th individual in the cluster, i = 1, 2, 3, ..., N, where N represents the total number of individuals in the cluster. e The coordinates are the center coordinates of the elliptical dynamic virtual region.

[0154] Furthermore, the expression for the elliptical dynamic virtual region is:

[0155] (xx e ) T M -1 (xx e )≤1

[0156]

[0157] Where x is the coordinate of any point within the elliptical region, x e Let M be the coordinates of the center of the elliptical dynamic virtual region, M be the elliptical characteristic matrix, a be the length of the major axis of the ellipse, b be the length of the minor axis of the ellipse, θ be the angle between the major axis of the ellipse and the positive x-axis, and T be the transpose of the matrix.

[0158] Furthermore, the shape control objective function of the elliptical dynamic virtual region is expressed as:

[0159]

[0160]

[0161]

[0162] Among them, f Gc (·) represents the objective function for shape control of the circular dynamic virtual region. Let be the relative position of the i-th cluster individual to the center of the elliptical dynamic virtual region. x e Let x be the center coordinate of the elliptical dynamic virtual region. i1 x represents the x-coordinate of the i-th cluster individual. i2 The ordinate of the i-th cluster individual, x e1 It is the x-coordinate of the center of the elliptical dynamic virtual region. e2 y is the ordinate of the center of the elliptical dynamic virtual region; a is the length of the major axis of the ellipse, b is the length of the minor axis of the ellipse, and θ is the angle between the major axis of the ellipse and the positive x-axis. This is the projection of the relative position vector onto the x-axis after rotating it by an angle θ along the x-axis. It is the projection of the relative position vector onto the y-axis after rotating the y-axis by an included angle θ.

[0163] Furthermore, the potential energy function expression for the shape control of the elliptical dynamic virtual region is:

[0164]

[0165] Where, k e This is an adjustable parameter for the elliptical dynamic virtual region, and its value is a positive number. Let be the relative positional potential energy value of the i-th cluster individual and the center of the elliptical dynamic virtual region. Let be the relative position of the i-th cluster individual to the center of the elliptical dynamic virtual region.

[0166] Furthermore, the derivative of the potential energy function controlling the shape of the elliptical dynamic virtual region with respect to the relative position yields the expression for the shape control component of the elliptical dynamic virtual region as follows:

[0167]

[0168] Among them, u Pe,i Let be the shape control component of the elliptical dynamic virtual region for the i-th cluster individual. Let be the relative positional potential energy value of the i-th cluster individual and the center of the elliptical dynamic virtual region. Let be the relative position of the i-th cluster individual to the center of the elliptical dynamic virtual region, where a is the length of the major axis of the ellipse, b is the length of the minor axis of the ellipse, and θ is the angle between the major axis of the ellipse and the positive x-axis. This is the projection of the relative position vector onto the x-axis after rotating it by an angle θ along the x-axis. It is the projection of the relative position vector onto the y-axis after rotating the y-axis by an included angle θ.

[0169] Preferably, the specific steps for obtaining the control components for collision avoidance among individuals in the cluster are as follows:

[0170] An objective function for collision avoidance among cluster individuals is established based on the collision avoidance distance between individuals. A local potential energy function for collision avoidance among cluster individuals is designed based on the objective function. The partial derivatives of the local potential energy function are obtained and summed to obtain the control components for collision avoidance among cluster individuals.

[0171] Furthermore, the objective function for inter-individual collision avoidance is expressed as:

[0172] f L (x ij )=-ln(||x ij || 2 )+ln(r 2 )≤0

[0173] Among them, f L (x ij Let x be the function value for collision avoidance between the i-th and j-th cluster individuals that are neighbors. ij Let r be the relative position vector between the i-th and j-th cluster individuals that are neighbors, and r be the minimum distance allowed between cluster individuals to avoid collisions, i.e., the collision avoidance distance between the individuals.

[0174] Furthermore, the local potential energy function for collision avoidance among the cluster individuals is expressed as:

[0175]

[0176] Where q(x) ij Let s be the local potential energy values ​​for collision avoidance between the i-th and j-th cluster individuals who are neighbors, i = 1, 2, 3, ..., N, j = 1, 2, 3, ..., N, i ≠ j, and N represent the total number of cluster individuals; ijLet s be the values ​​in the adjacency matrix corresponding to the i-th and j-th cluster individuals that are neighbors. ij The value can be 0 or 1, when ||x i -x j ||≤r c At that time, s ij =1; when ||x i -x j ||>r c At that time, s ij =0, r c x is the communication radius of an individual in the cluster. i Let x be the position of the i-th cluster individual. j f represents the position of the j-th cluster individual; L (x ij ) represents the collision avoidance function between the i-th and j-th cluster individuals that are neighbors.

[0177] Furthermore, the control component for collision avoidance among the cluster individuals is expressed as follows:

[0178]

[0179] Among them, u Q,i Let i be the formation control component for the i-th cluster individual. Let u be the set of neighbors of the i-th cluster individual. Q,ij For the formation control components of the i-th and j-th cluster individuals that are neighbors, q(x ij Let x be the local potential energy value for collision avoidance between the i-th and j-th cluster individuals who are neighbors. ij Let s be the relative position vector between the i-th and j-th cluster individuals who are neighbors. ij Let s be the values ​​in the adjacency matrix corresponding to the i-th and j-th cluster individuals that are neighbors. ij The value can be 0 or 1, when ||x i -x j ||≤r c At that time, s ij =1; when ||x i -x j ||>r c At that time, s ij =0, r c x is the communication radius of an individual in the cluster. i Let x be the position of the i-th cluster individual. j is the position of the j-th cluster individual; r is the minimum distance allowed between cluster individuals to avoid collisions, i.e., the collision avoidance distance between individuals; a neighbor refers to a cluster individual whose distance from the current cluster individual is less than the communication radius, and cluster individuals can interact with neighbors within the communication radius.

[0180] Preferably, the formation control component of the cluster individual is expressed as:

[0181]

[0182]

[0183] Among them, u n,i Let i be the formation control component for the i-th cluster individual. Weight parameters for maintaining distance between individual neighbors in a cluster. Weight parameters for maintaining speed alignment among individual neighbors in the cluster; Let φ be the set of neighbors of the i-th cluster individual. α The action function for maintaining the grouping distance between individual neighbors in the cluster, x i Let x be the position of the i-th cluster individual. j Let be the position of the j-th cluster individual, σ be the norm that measures the length of the vector space, and n be the position of the j-th cluster individual. ij Let a be the normalized relative position between the i-th cluster individual and the j-th cluster individual, which are neighbors. ij (x) represents the element of the spatial adjacency matrix between the i-th and j-th cluster individuals who are neighbors, where x is the position vector of the cluster individual, and v i Let v be the velocity of the i-th cluster individual. j Let ψ be the speed of the j-th individual in the cluster, i = 1, 2, 3, ..., N, j = 1, 2, 3, ..., N, i ≠ j, and N represent the total number of individuals in the cluster; ε (·) is the normalization function that measures the length of the vector space, and ε is the parameter that measures the norm of the vector space.

[0184] Furthermore, the a ij (x) is the expression for the elements of the spatial adjacency matrix between the i-th and j-th cluster individuals who are neighbors:

[0185]

[0186] Among them, a ij (x) represents the elements of the spatial adjacency matrix between the i-th and j-th cluster individuals who are neighbors, ρ h Let x be the impulse function (a function that smoothly changes from 0 to 1). i Let x be the position of the i-th cluster individual. j Let be the position of the j-th cluster individual, where i = 1, 2, 3, ..., N, j = 1, 2, 3, ..., N, i ≠ j, and N represents the total number of cluster individuals; σ is the norm that measures the length of the vector space, r c This refers to the communication radius of an individual member in the cluster.

[0187] Furthermore, the expression for the impact function is:

[0188]

[0189] Where, ρ h (·) represents the impulse function, h represents the parameter of the impulse function, h∈(0,1), and z represents the independent variable of the impulse function.

[0190] Furthermore, the norm, which measures the length of a vector space, is expressed as:

[0191]

[0192] Where s is a vector of arbitrary dimensions, σ is the norm that measures the length of the vector space, and ε is a parameter that measures the norm of the length of the vector space.

[0193] Furthermore, the action function for maintaining the formation distance between individual neighbors in the cluster is expressed as follows:

[0194]

[0195]

[0196] Where, φ α The action function ρ is used to maintain the grouping distance between individual neighbors in the cluster. h Let r be the impulse function (a function that smoothly changes from 0 to 1). β It is the communication radius r c The measure of the length of a vector space, i.e., r β =||r c || σ f is the independent variable of the action function, ω1(·) is a smooth function, and its form satisfies d β The formation distance d is a measure of the length of the vector space, i.e., d β =|d| σ φ(·) is a non-uniform sigmoid function, where a, b, and c are the three parameters of the function φ(·), and satisfy 0. <a≤b, This is to ensure that φ(0) = 0.

[0197] Preferably, the expression for constructing the cluster individual navigation control component is:

[0198]

[0199] Among them, u g1,i Let i be the navigation control component for the i-th cluster individual. The control objective is for the cluster individual to track the center position of the dynamic virtual region and maintain the same speed as the movement of the dynamic virtual region. At that time, u g1,iDegenerate into u g2,i u g2,i The control objective is to keep the movement speed of individual cluster members consistent with that of the dynamic virtual region; To control the weights of individual cluster members tracking the center position of the dynamic virtual region, To control the weights that ensure the movement speed of individual cluster members remains consistent with that of the dynamic virtual region, x i Let x be the position of the i-th cluster individual. o x is the center position of the dynamic virtual region (if the dynamic virtual region is elliptical, x o =x e If the dynamic virtual region is circular, x o =x c ), v i Let v be the velocity of the i-th individual in the cluster. o The center velocity of the dynamic virtual region.

[0200] In the technical solution of this invention, navigation control components are designed for individual clusters to play a navigation role, causing the positions of the individual clusters to converge toward the center of a given dynamic virtual region and making the speed of the individual clusters consistent with the speed of the given dynamic virtual region.

[0201] Preferably, the formation mission scenarios include: energy-saving scenarios and complex obstacle adaptation scenarios, wherein the complex obstacle scenarios are narrow passages and curves.

[0202] The cluster formation coordination strategy includes a "center-first" strategy and an "edge-first" strategy. The "center-first" strategy involves cluster members first filling the center of a dynamic virtual region during movement, then occupying the edge positions, ensuring the unmanned cluster maintains full connectivity while coordinating its movement to the dynamic virtual region. Figure 1 As shown;

[0203] The described "edge-first" formation coordination strategy involves cluster members first filling the edge positions of a dynamically virtual region, with the edges filled first and the center filled later. This strategy has a faster convergence speed and saves energy, but it cannot guarantee connectivity. Figure 3 As shown.

[0204] Preferably, the specific steps for inputting the dynamic virtual region shape control component, the collision avoidance control component between cluster individuals, the formation control component of cluster individuals, and the navigation control component of cluster individuals into the cluster formation coordination strategy for weighted combination and output of cluster individual control quantity are as follows:

[0205] When formation missions require adaptation to complex obstacle scenarios;

[0206] The control components for the shape of the dynamic virtual region, collision avoidance, formation, and navigation among cluster individuals are input into the "center priority" strategy to determine whether cluster individuals are located within the dynamic virtual region.

[0207] When a cluster member has no neighbors (a neighbor is defined as a member whose distance from the current cluster member is less than the communication radius r) c When the individual (other cluster individuals) is located outside the dynamic virtual region, the control strategy requires the cluster individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the dynamic virtual region, and outputs the control quantity of the cluster individual.

[0208] When a cluster individual has neighbors and its position is outside the dynamic virtual region, the control strategy requires the individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the center of the dynamic virtual region, and also considering collision avoidance between cluster individuals, and outputting the cluster individual control quantity.

[0209] When individuals within a cluster are located within a dynamic virtual region, the control strategy requires them to maintain formation distance and speed alignment with their neighbors while moving towards and navigating to the center of the dynamic virtual region, outputting the cluster's control variables; such as Figure 2 ;

[0210] When formation mission scenarios require adaptation to energy-saving scenarios;

[0211] The control components for the shape of the dynamic virtual region, collision avoidance, formation, and navigation among cluster individuals are input into the "edge-first" strategy to determine whether cluster individuals are located within the dynamic virtual region.

[0212] When a cluster individual has no neighbors and its position is outside the dynamic virtual region, the control strategy requires the cluster individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the dynamic virtual region, and outputting the cluster individual's control quantity.

[0213] When a cluster individual has neighbors and its position is outside the dynamic virtual region, the control strategy requires the individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while ensuring that the movement speed is aligned with the speed of the center of the dynamic virtual region, and also considering collision avoidance between cluster individuals, and outputting the cluster individual control quantity.

[0214] When a cluster individual is located within a dynamic virtual region, the node degree of the cluster individual is determined based on its communication radius and relative positional relationship; the node degree is the number of neighbors of the cluster individual; when the node degree = 0, the cluster individual maintains the same movement speed as the dynamic virtual region, and the cluster individual control quantity is output.

[0215] When the node degree is 1 or 2, determine whether the cluster individual has any neighboring individuals outside the dynamic virtual region. If so, the control strategy requires the individual to move towards the center of the dynamic virtual region and navigate to the center of the dynamic virtual region, while maintaining the formation distance and speed alignment with the surrounding neighboring individuals. If not, the cluster individual keeps the movement speed consistent with the dynamic virtual region, while maintaining the formation distance and speed alignment with the surrounding neighboring individuals, and outputs the cluster individual control quantity.

[0216] When the node degree is ≥3, determine if any cluster individual has neighboring individuals outside the dynamic virtual region. If so, the control strategy requires the individual to move towards and navigate to the center of the dynamic virtual region, while maintaining formation distance and speed alignment with its neighboring individuals. If not, the cluster individual maintains the same movement speed as the dynamic virtual region, while maintaining formation distance and speed alignment with its neighboring individuals, and outputs the cluster individual's control variable, such as... Figure 4 .

[0217] The reference for setting the node degree boundary in this invention is the spatial occupancy around the cluster individuals. When the node degree is above 3, the coordination effect of the cluster individuals towards the regional center in order to maintain the formation distance decreases.

[0218] Preferably, the specific steps for outputting the individual control quantity of the cluster are as follows:

[0219] a. Obtain the control parameters and initial position and velocity of individual cluster members. Obtain the position and velocity of each individual cluster member in the cluster formation at time t. Let T be the upper limit of the execution time, and t = 1, 2, 3...T, representing the total number of time points T. The control parameters are cluster control parameters and dynamic virtual region control parameters. The cluster control parameters are the cluster size, communication radius of individual cluster members, maximum movement speed, maximum acceleration, and formation distance. The dynamic virtual region control parameters are the major axis length, minor axis length, pointing angle, and center coordinates. b. Based on the position and velocity of the individual cluster members at time t, obtain the dynamic virtual region shape control components, collision avoidance control components between individual cluster members, formation control components, and navigation control components of the individual cluster members.

[0220] c. Input the above four control components into the cluster formation coordination strategy, obtain the control quantity of the individual clusters through weighted combination, obtain the position and velocity of the individual clusters at time t+1, save the position and velocity data of the individual clusters, and draw the real-time motion trajectory of the cluster formation.

[0221] d. Update the control parameters, position, and velocity of the individual cluster members, and iterate. If t≤T, the iteration continues and returns to step a. If t>T or the target point is reached, output the final position and velocity of the individual cluster members and terminate the iteration.

[0222] Example 1

[0223] 1. Select a swarm of ground robots and perform mathematical modeling of its motion and communication.

[0224] The intelligent individuals in the cluster are selected as ground robots, and their kinematic model is chosen as a typical vehicle kinematic model under nonholonomic constraints, namely:

[0225]

[0226] Where [x] g,i ,y g,i ] is the Cartesian coordinate of the center of the i-th robot, θ g,i It is the i-th robot turning, v g,i It is linear velocity, ω g,i It is angular velocity, m g,i It's the quality of the robot, J g,i It is the robot's moment of inertia, f g,i and τ g,i These are the forces and torques acting on the robot. Using the input-output feedback linearization method, the kinematic model of the ground robot can be simplified to a second-order integrator model, i.e.:

[0227]

[0228] Where, x i Let v be the position of the i-th robot. i Let u be the velocity of the i-th robot. i Let N be the control input for the i-th robot, and N be the number of robots in the cluster.

[0229] The communication area of ​​the ground robot is circular, defined by the communication radius r. c The representation, specifically the mathematical description, is as follows:

[0230]

[0231] Where, x i and x j Let r be the position of the i-th and j-th robots. c V represents the communication radius, and V represents the ID number of the robot cluster other than i (i.e., j = 1, 2, ..., N, j ≠ i, N is the number of robots in the cluster).

[0232] 2. Simulation initial conditions and simulation parameter settings

[0233] For ground robots, the cluster size is set to 36 robots, and their communication radius is set to r. c The length is 8.4m, and the maximum speed of the ground robot is 4m / s (i.e., ||v||). iThe maximum acceleration of the ground robot is 4 m / s² (i.e., ||u||≤4). i ‖≤4), the expected formation distance d between ground robots is 7m. The initial position distribution center coordinates of the ground robots are [0,0], the distribution radius is 30m, and the coordinates of the endpoint of the moving target are [150,0]. The parameter values ​​in the formation control component are... ε = 0.1, f = 0.5. The relevant parameters in the navigation control components are set to... The total simulation duration is 50 seconds, and the simulation step size is T. p The value was set to 0.1s.

[0234] The simulation scenarios involved dynamic virtual regions undergoing deformation and rotation, and simulation tests were conducted for both the "center-first" and "edge-first" strategies. The parameter settings for different simulation scenarios are shown in Tables 1 and 2.

[0235] Table 1. Dynamic Virtual Region Deformation Simulation Scene Settings

[0236]

[0237]

[0238] Table 2 Dynamic Virtual Region Rotation Simulation Scene Settings

[0239]

[0240] 3. Based on the technical solution in the invention, the program is designed using the MATLAB platform. The execution flow of the proposed cluster formation control method based on dynamic virtual regions is as follows:

[0241]

[0242]

[0243] 4. Output and analyze simulation results

[0244] Figures 5-7 The figures show the simulation results of coordinated movement of ground robot swarms under three different initial simulation conditions. Figure 5 This corresponds to the simulation scenario of dynamic virtual region deformation under the "center-first" strategy. Figure 6 This corresponds to a simulation scenario of dynamic virtual region rotation under the "center-first" strategy. Figure 7 This corresponds to a simulation scenario of dynamic virtual region deformation under the "edge-first" strategy.

[0245] Specifically, in the simulation diagrams, the first image in each group reflects the location distribution of the cluster at a specific moment, the second image reflects the location of the cluster relative to the center of the dynamic virtual region, the third image reflects the shortest distance between individual members of the cluster, and the fourth image reflects the energy consumption of the cluster's coordinated movement process.

[0246] Figure 5 The simulation results reflect the formation control effect of the cluster when the area of ​​the dynamic virtual region remains constant and the major and minor axes change accordingly. The simulation results show that when the virtual region is deformed, the robot cluster can maintain itself within the virtual region through self-organization and coordination, and ensure that it does not collide with each other.

[0247] Figure 6 The simulation results reflect the cluster formation control in a dynamic virtual area rotation scenario. The results show that the coordination algorithm and strategy can keep the robot cluster within the area as much as possible and avoid collisions between individuals when the virtual area rotates, but it places higher demands on the motion capability (maximum acceleration) of the ground robot.

[0248] Figure 7 Simulation results reflecting the deformation of the dynamic virtual region under the "edge-first" strategy demonstrate the effectiveness of the swarm motion coordination algorithm and strategy. Compared to the "center-first" strategy, the "edge-first" strategy has poorer coordination ability in converging to the dynamic virtual region, while prioritizing motion coordination among individual robots. These simulation results verify that the swarm formation control method based on dynamic virtual regions proposed in this invention is applicable to the coordinated control of large-scale ground robot swarms and still meets the expected control objectives even when the virtual region undergoes deformation, rotation, or other changes.

[0249] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A cluster formation control method based on dynamic virtual regions, characterized in that, include: Design a dynamic virtual region for the cluster formation, and establish a virtual region shape control component that restricts the cluster formation within the dynamic virtual region. The expression is as follows: in, For the first The dynamic virtual region shape control component for each cluster individual. For the first The circular dynamic virtual region shape control component for each cluster individual. For the first The shape control component of the elliptical dynamic virtual region of each cluster individual. This represents the total number of individuals in the cluster. A local potential energy function for collision avoidance among cluster individuals is designed based on the collision avoidance distance between individuals, and the control components for collision avoidance among cluster individuals are obtained based on the local potential energy function. Select the cluster formation distance, obtain the position and velocity of individual cluster members, and construct the formation control components of the individual cluster members based on the position, velocity and formation distance; Based on the center location of the dynamic virtual region, the position and velocity of the cluster individuals, the navigation control components of the cluster individuals are constructed, and the expression is: in, For the first Navigation control components for each individual cluster; To control the weights of individual cluster members tracking the center position of the dynamic virtual region, To control the weights that ensure the movement speed of individual cluster members remains consistent with that of the dynamic virtual region, For the first The location of each individual in the cluster. The center of the dynamic virtual region. For the first The speed of each individual in the cluster The center velocity of the dynamic virtual region; Establish a cluster formation coordination strategy, and input the virtual region shape control component, the collision avoidance control component between cluster individuals, the formation control component, and the navigation control component into the cluster formation coordination strategy to output the cluster individual control quantity. The speed and position of the cluster individuals are controlled based on the cluster individual control variables.

2. The cluster formation control method according to claim 1, characterized in that, The specific steps for obtaining the control components for collision avoidance among individuals in the cluster are as follows: A target function for collision avoidance among cluster individuals is established based on the collision avoidance distance between individuals. A local potential energy function for collision avoidance among cluster individuals is designed based on the target function. The partial derivatives of the local potential energy function are obtained and summed to obtain the control components for collision avoidance among cluster individuals.

3. The cluster formation control method according to claim 1, characterized in that, The control component for collision avoidance among individuals in the cluster is expressed as follows: in, For the first The formation control component for each individual cluster member For the first The set of neighbors of an individual in a cluster. For the neighboring countries The and the first The relative position vectors between individuals in the cluster For the neighboring countries The and the first The values ​​in the adjacency matrix corresponding to each cluster individual; This is the minimum distance allowed between individuals in the cluster to avoid collisions. , This represents the total number of individuals in the cluster.

4. The cluster formation control method according to claim 1, characterized in that, The formation control component of the cluster individual is expressed as follows: in, For the first The formation control component for each individual cluster member Weight parameters for maintaining distance between individual neighbors in a cluster. Weight parameters for maintaining speed alignment among individual neighbors in the cluster; For the first The set of neighbors of an individual in a cluster. Represents the individual neighbors in the cluster. An action function for maintaining the grouping distance between individual neighbors in the cluster. For the first The location of each individual in the cluster. For the first The location of each individual in the cluster. The norm is used to measure the length of a vector space. For the normalized neighboring units The cluster individual and the first The distance between individual members in a cluster For the neighboring countries The and the first The spatial adjacency matrix corresponds to the elements of each individual in the cluster. For each individual in the cluster, For the first The speed of each individual in the cluster For the first The speed of each individual in the cluster , This represents the total number of individuals in the cluster.

5. The cluster formation control method according to claim 1, characterized in that, The specific steps for outputting the individual control quantity of the cluster are as follows: a. Obtain the control parameters, initial position, and initial velocity of each individual in the cluster; obtain the position and velocity of each individual in the cluster formation at time t; let T be the upper limit of the execution time, and t = 1, 2, 3…T, representing the total number of times T. b. Based on the position and velocity of the cluster individuals at time t, obtain the dynamic virtual region shape control component, the collision avoidance control component between cluster individuals, the formation control component and the navigation control component of the cluster individuals respectively. c. Input the above four control components into the cluster formation coordination strategy, obtain the control quantity of the individual clusters through weighted combination, obtain the position and velocity of the individual clusters at time t+1, save the position and velocity data of the individual clusters, and draw the real-time motion trajectory of the cluster formation. d. Update the control parameters, position, and velocity of the individual cluster members, and iterate. If t≤T, the iteration continues and returns to step a. If t>T or the target point is reached, output the final position and velocity of the individual cluster members and terminate the iteration.

6. The cluster formation control method according to claim 1, characterized in that, The formation coordination strategy model includes a center-first strategy and / or an edge-first strategy.

7. The cluster formation control method according to claim 6, characterized in that, The center-priority formation coordination strategy is that during the movement of cluster individuals, the center position of the dynamic virtual region is filled first, and then the edge position of the dynamic virtual region is occupied.

8. The cluster formation control method according to claim 7, characterized in that, The edge-first formation coordination strategy involves cluster individuals first filling the edge positions of the dynamic virtual region during movement, and then occupying the center position of the dynamic virtual region.

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