A method for self-organizing formation control of polygonal planar formations considering obstacle avoidance

Abstract

This invention discloses a self-organizing formation control method for polygonal planar swarms considering obstacle avoidance, belonging to the field of intelligent agent / UAV / spacecraft swarm motion control technology. The method includes: determining the number of swarm members, the dynamic model, initial state variables, and target configuration parameters; determining whether the vertex coordinates of the target configuration fall within the target configuration plane, and adjusting the final vertex coordinates based on the determination result; determining the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjusting the initial values ​​of temporary target positions; designing control laws using attractive and repulsive potentials; and performing swarm motion simulation based on the number of swarm members, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of temporary target positions, and the control laws. This method enables the swarm to effectively form a target polygonal region configuration with appropriate control variables, meeting the needs of practical tasks in complex obstacle environments.

Description

Technical Field

[0001] This invention relates to the field of motion control technology for intelligent agents / drones / spacecraft swarms, and specifically to a method for self-organizing and forming polygonal planar formations that takes obstacle avoidance into account. Background Technology

[0002] In the study of motion control for real-world swarm formations of drones, spacecraft, and other aircraft, a technique similar to biological swarm movement is the self-organizing formation control of planar formations under a given target formation shape. Its flexibility in adapting to complex conditions and variations in swarm size has garnered increasing attention. However, existing self-organizing control for polygonal planar formations suffers from three shortcomings: first, it generally ignores the presence of obstacles; second, it assumes the swarm is initially distributed within the plane of the target configuration, neglecting the reality of the swarm's movement throughout the entire space outside obstacles; and third, the near-uniform distribution of the swarm relies on significant repulsive forces between individuals, potentially resulting in excessively large control parameters unsuitable for practical tasks.

[0003] For practical missions such as collaborative detection of clusters near large spacecraft, like space stations, it is necessary to restrict the initial position of the cluster and limit the number of obstacles around the space station, otherwise the control input will be too large and unable to meet the actual mission requirements under complex obstacles. Summary of the Invention

[0004] To address the problem that existing technologies impose strict restrictions on the initial position of the swarm, failing to meet the practical needs of tasks in complex obstacle environments, this invention provides a polygonal planar formation self-organizing control method that considers obstacle avoidance. This method enables the swarm to effectively form a target polygonal region configuration with appropriate control parameters, satisfying the practical needs of tasks in complex obstacle environments.

[0005] To achieve the above objectives, the present invention provides the following technical solution.

[0006] A method for controlling the self-organizing formation of polygonal planar formations while considering obstacle avoidance includes the following steps:

[0007] Determine the number of individuals in the cluster, the dynamic model, the initial state variables, and the target configuration parameters;

[0008] Determine whether the vertex coordinates of the target configuration in the target configuration parameters fall within the target configuration plane, and adjust the vertex coordinates of the final target configuration based on the determination result;

[0009] Determine the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjust the initial values ​​of the temporary target positions;

[0010] Construct an attractive potential based on the target configuration plane, construct a repulsive potential based on the boundary equation, and design a control law using the attractive and repulsive potentials.

[0011] Based on the number of individuals in the cluster, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of the temporary target positions, and the control law, a cluster motion simulation is performed.

[0012] As a further improvement of the present invention, the step of determining whether the target configuration vertex coordinates in the target configuration parameters fall within the target configuration plane includes:

[0013] For each target configuration vertex coordinate Use its components in sequence and Replace the formulas respectively Find x, y, and z in the formula, and then check if the equality sign of the formula is satisfied.

[0014] If satisfied, use the vertex coordinates of the target configuration directly;

[0015] If not satisfied, change the vertex coordinates of the target configuration. Replace with its projected coordinates on the target configuration plane.

[0016] in, The number of vertices in the target configuration.

[0017] As a further improvement of the present invention, the target configuration vertex coordinates are... Replace with its projected coordinates on the target configuration plane. Next:

[0018] Check whether the target configuration area intersects with obstacles;

[0019] If the target configuration region intersects with an obstacle, the vertex coordinates of the target configuration are reselected;

[0020] If the target configuration region does not intersect with the obstacle, there is no need to adjust the vertex coordinates of the target configuration.

[0021] As a further improvement of the present invention, determining the boundary equations corresponding to each side of the target configuration in the target configuration plane includes:

[0022] For the j-th edge of the target configuration surface Its boundary surface The equation can be given by the following equation in terms of variables x, y, and z.

[0023]

[0024] And transform it into the following form

[0025]

[0026] in, The direction vector of the target configuration plane; Let J be the coordinates of the j-th target configuration vertex.

[0027] After all boundary surface equations have been solved, check the orientation of each boundary surface in turn;

[0028] If a certain boundary surface exists The corresponding constraints are as follows

[0029]

[0030] Able to make Middle excluding edges If all points other than the endpoints satisfy the condition, then the boundary surface equation remains unchanged;

[0031] If such a boundary surface does not exist, then each Replace with Then, according to the formula Resolve the equations for each boundary surface;

[0032] in, The number of vertices in the target configuration.

[0033] As a further improvement of the present invention, the adjustment of the initial value of the temporary target position includes:

[0034] For individual i, the initial value of the temporary target position If the formula is satisfied The boundary surfaces of each target configuration shown Constraints, namely In the target configuration plane If the projection within falls within the target configuration region, then No adjustments will be made.

[0035] Where i = 1, 2, ..., n; j = 1, 2, ..., n F .

[0036] As a further improvement of the present invention, the adjustment of the initial value of the temporary target position includes:

[0037] For individual i, the initial value of the temporary target position If there are two or more temporary target location initial values The formula is not satisfied. The boundary surfaces of each target configuration shown The constraints are then measured sequentially. Find the distance to each target configuration vertex. The nearest target configuration vertex Construct the following points

[0038]

[0039] And determine the following points

[0040]

[0041] Whether the boundary surface constraints of each target configuration are satisfied. If some boundary surface constraints are not satisfied, then replace μ with... Then return to the new temporary target position initial value. Calculation steps, until the result is obtained. Continue until the boundary surface constraints of each target configuration are satisfied, then... Replace with

[0042] in, i = 1, 2, ..., n.

[0043] As a further improvement of the present invention, the adjustment of the initial value of the temporary target position includes:

[0044] For individual i, the initial value of the temporary target position If there is only one temporary target location initial value The formula is not satisfied. The boundary surfaces of each target configuration shown The constraints are determined based on the corresponding boundary surfaces. Determine the following points

[0045]

[0046] Whether the boundary surface constraints of each target configuration are satisfied. If some boundary surface constraints are not satisfied, then replace μ with... Then return to the new temporary target position initial value. Calculation steps, until the result is obtained. Continue until the boundary surface constraints of each target configuration are satisfied, then... Replace with in, i = 1, 2, ..., n.

[0047] As a further improvement of the present invention, the step of constructing an attractive potential according to the target configuration plane includes:

[0048] At any point P(x,y,z) in space, the target configuration attraction potential is given. It can be represented in the following form:

[0049]

[0050] in The target configuration attraction coefficient; From point P(x,y,z) to the target configuration plane The distance.

[0051] As a further improvement of the present invention, the construction of the repulsive potential based on the boundary equation includes:

[0052] At any point P(x,y,z) in space, the repulsive potential V of the target configuration boundary is... E (t) can be expressed in the following form:

[0053]

[0054] in, The repulsive potential of the boundary surface of the target configuration.

[0055] As a further improvement of the present invention, the control law is designed using the attraction and repulsion potentials, wherein:

[0056] Repulsion potentials include target configuration boundary repulsion potential, inter-individual repulsion potential, inter-individual temporary target location repulsion potential, inter-individual and obstacle repulsion potential, and inter-individual temporary target location and obstacle repulsion potential.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] This invention provides a polygonal planar formation self-organizing control method considering obstacle avoidance. By defining the number of cluster individuals, the dynamic model, initial state variables, and target configuration parameters, and within a specified target formation configuration region defined by a planar polygon, the method can drive the cluster to self-organize and form that configuration—asymptotically converging to and fully dispersing within that region. This eliminates the requirement that the initial cluster position be within the target configuration plane, thus adapting to the needs of two-dimensional formation self-organizing tasks in a three-dimensional environment. By introducing temporary target positions to guide the movement of individual cluster individuals, the method avoids the direct action of large repulsion terms between temporary target positions on individuals, effectively reducing control variables and allowing planar formation self-organizing control technology to better meet real-world application requirements. Furthermore, obstacles that may exist in three-dimensional space are considered in both the target configuration design and control law design stages, and relevant parameters are adjusted based on cluster motion simulation results to better adapt to the actual formation task requirements. Attached Figure Description

[0059] Figure 1 A flowchart illustrating the obstacle avoidance-inducing polygonal planar formation self-organization control method of the present invention;

[0060] Figure 2The execution flowchart of the polygonal planar formation self-organization control method for obstacle avoidance in this invention is shown below.

[0061] Figure 3 This is a three-dimensional view of the initial positions of each individual in the cluster, the target formation configuration plane, the target formation configuration vertices, and the distribution of obstacles in a specific embodiment.

[0062] Figure 4 This is a front view of the initial positions of each individual member of the cluster, the target formation configuration plane, the target formation configuration vertices, and the distribution of obstacles in a specific embodiment.

[0063] Figure 5 This is a three-dimensional view of the temporary target location distribution of each individual entity in the cluster in a specific embodiment;

[0064] Figure 6 This is a front view of the temporary target location distribution of each individual entity in the cluster in a specific embodiment;

[0065] Figure 7 This is a schematic diagram of each item in the temporary target position control law in a specific embodiment;

[0066] Figure 8 This is a diagram showing the motion trajectories of each individual member of the cluster in a specific embodiment;

[0067] Figure 9 This is a diagram showing the movement trajectory of the temporary target positions of each individual entity in the cluster in a specific embodiment;

[0068] Figure 10 This is a graph showing the distance from each cluster individual to the target configuration region over time in a specific embodiment;

[0069] Figure 11 This is a graph showing the change of control magnitude values ​​of each individual cluster entity over time in a specific embodiment.

[0070] Figure 12 This is a graph showing the change of the temporary target position control magnitude value of each individual in the cluster over time in a specific embodiment.

[0071] Figure 13 The graph shows the changes over time between the minimum distances between the cluster members and between the cluster members and obstacles in a specific embodiment. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0073] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of this application, including various details to aid understanding. These details should be considered merely exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0074] To address the problem that existing technologies impose strict restrictions on the initial position of the swarm, failing to meet the needs of practical tasks in complex obstacle environments, this invention provides a polygonal planar formation self-organizing control method that considers obstacle avoidance. This overcomes the strict restrictions on the initial position of the swarm in existing technologies and better meets the needs of practical tasks in complex obstacle environments.

[0075] Definitions:

[0076] Earth observation refers to the design of a polygonal formation configuration that is parallel to the local ground plane.

[0077] like Figure 1 As shown, the method includes:

[0078] Determine the number of individuals in the cluster, the dynamic model, the initial state variables, and the target configuration parameters;

[0079] Determine whether the vertex coordinates of the target configuration in the target configuration parameters fall within the target configuration plane, and adjust the vertex coordinates of the final target configuration based on the determination result;

[0080] Determine the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjust the initial values ​​of the temporary target positions;

[0081] Construct an attractive potential based on the target configuration plane, construct a repulsive potential based on the boundary equation, and design a control law using the attractive and repulsive potentials.

[0082] Based on the number of individuals in the cluster, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of the temporary target positions, and the control law, a cluster motion simulation is performed.

[0083] This invention enables the cluster to effectively form the target polygonal region configuration with appropriate control, meeting the actual task needs in complex obstacle environments.

[0084] Reference Figure 2This invention provides a detailed description of a polygonal planar formation self-organization control method considering obstacle avoidance, comprising the following steps:

[0085] S1: Determine the number of individuals in the cluster, the dynamic model of each individual, the dynamic model of the temporary target position of each individual, the initial state variables of each individual, the target configuration parameters, and the obstacle model.

[0086] Each volume dynamics model is a second-order system of the following form:

[0087]

[0088] Where n is the number of individuals in the cluster; ξ i (t)=(x i (t),y i (t),z i (t)) T ∈R 3×1 Let be the position vector of individual i at time t; Let ξ be the velocity vector of individual i at time t; i (0)} and {ξ i (0)} The two vector sets are the initial positions and initial velocities of each object, respectively; f(ξ) i (t),ζ i (t) is a value with a range of R. 3 ×1 The individual open-loop dynamic function; U i (t)∈R 3×1 Let be the control quantity for individual i at time t.

[0089] The dynamic model of the temporary target position of each body is a first-order integrator system of the following form:

[0090]

[0091] in, Let be the temporary target position vector of individual i at time t, and its initial value is... With the initial position ξ of individual i i (0) Same; Let be the control quantity for the temporary target position of individual i at time t.

[0092] Specifically, the target configuration plane The equation is given by the following equation in terms of variables x, y, and z:

[0093]

[0094] Specifically, the vertex coordinates of the target configuration are represented by a set of vectors. Give, For the j-th ( (Number of vertices in the target configuration) Vertex coordinates of the target configuration, j-th edge of the target configuration face. This can be represented by the following line segment.

[0095]

[0096] Its corresponding vector is denoted as

[0097]

[0098] Specifically, the obstacle model should be selected such that any point P(x,y,z) in space is within range of the obstacle. distance All of them can be calculated analytically, and partial derivatives can be obtained with respect to x, y, and z respectively.

[0099] S2: Adjust the vertex coordinates of the target configuration.

[0100] First, check whether each target configuration vertex lies within the target configuration plane. Specifically, for each target configuration vertex coordinate... Use in sequence and Replace x, y, and z in formula (3) respectively, and then check if the equation is satisfied. If it is satisfied, no action is taken; otherwise, the vertex coordinates of the target configuration are changed. Replace with its projected coordinates on the target configuration plane. Where the function (P) H This indicates that any point P(x,y,z) lies in the target configuration plane. The projection points within are calculated using the following formula.

[0101]

[0102] Then check whether the target configuration region intersects with obstacles. Specifically, solve for the following: The optimization problem.

[0103]

[0104] in, From point P in S1 to the obstacle The distance.

[0105] If the optimization results This indicates that the target configuration region intersects with the obstacle. The vertex coordinates of the target configuration should be reselected, for example, by scaling or translating the vertex coordinates of the target configuration as a whole. Then, return to the beginning of S2 and re-execute until the result is obtained by optimization using formula (7). until.

[0106] S3: Determine the boundary surface equations corresponding to each side of the target configuration.

[0107] For the j-th edge of the target configuration surface Its boundary surface The equation can be given by the following equation in terms of variables x, y, and z.

[0108]

[0109] And transform it into the following form

[0110]

[0111] in Let be the direction vector of the target configuration plane, and denote the boundary surface. The direction vector is

[0112] After all boundary surface equations have been solved, check the orientation of each boundary surface in turn. If a certain boundary surface exists... Its corresponding constraint (10) enables Middle excluding edges If all points other than the endpoints satisfy the condition, then the boundary surface equation remains unchanged.

[0113] Among them, the boundary surface The corresponding constraints are as follows:

[0114]

[0115] If it does not exist Middle excluding edges The boundary surface of all points other than the endpoints satisfies formula (10). Then each Replace with Then, the equations of each boundary surface are solved again according to formula (8).

[0116] S4: Adjust the initial values ​​of the temporary target positions for each individual. For each individual i (i = 1, 2, ..., n), the initial values ​​of the temporary target positions are... If it satisfies the boundary surfaces of each target configuration shown in formula (10) Constraints, namely If the projection onto the target configuration plane F falls within the target configuration region, then No adjustments are made; if certain boundary surface constraints are not met, then replace them according to the following rules. Among them, each is judged When constrained, the initial value of μ is taken as D. rO D rO>0 represents the avoidance detection distance between the temporary target location and the obstacle:

[0117] Case 1: If there are two or more unsatisfied boundary surface constraints, then measure them sequentially. Find the distance to each target configuration vertex. The nearest target configuration vertex Construct the following points

[0118]

[0119] And determine the following points

[0120]

[0121] Whether the boundary surface constraints of each target configuration are satisfied. If some boundary surface constraints are not satisfied, then replace μ with... Then return to Calculation steps, until the result is obtained. Continue until the boundary surface constraints of each target configuration are satisfied. Then... Replace with

[0122] Case 2: If there is only one unsatisfied boundary surface constraint, then it depends on the corresponding boundary surface. Determine the following points

[0123]

[0124] Whether the boundary surface constraints of each target configuration are satisfied. This indicates that any point P(x,y,z) lies on the boundary surface. The projection points within the area are calculated using a formula similar to formula (6), only requiring the following steps: and Replace with and If certain boundary surface constraints are not satisfied, then μ is replaced with Then return to Calculation steps, until the result is obtained. Continue until the boundary surface constraints of each target configuration are satisfied. Then... Replace with

[0125] S5: Construct the target configuration attraction potential, the target configuration boundary repulsion potential, the inter-individual repulsion potential, the inter-individual temporary target position repulsion potential, the inter-individual and obstacle repulsion potential, and the inter-individual temporary target position and obstacle repulsion potential respectively.

[0126] Specifically, at any point P(x,y,z) in space, the target configuration attraction potential is expressed in the following form:

[0127]

[0128] in For the target configuration attraction coefficient, From point P(x,y,z) to the target configuration plane The distance can be expressed in the following form:

[0129]

[0130] At any point P(x,y,z) in space, the repulsive potential of the target configuration boundary can be expressed in the following form:

[0131]

[0132] in The repulsive potential of the boundary surface of the target configuration can be expressed in the following form.

[0133]

[0134] in Let P(x,y,z) be the boundary surface of the target configuration. The distance, based on formula (15), will be... and Replace them with the formula (9) respectively and Get c E >0 represents the boundary surface avoidance coefficient for the target configuration, D E >0 represents the target configuration boundary surface avoidance detection distance.

[0135] The inter-individual repulsion potential can be expressed in the following form:

[0136]

[0137] Where, ξ i (t) and ξ h (t) represents the position coordinates of cluster individuals i and h (i, h = 1, 2, ..., n, i ≠ h) at time t, and c C >0 represents the inter-individual avoidance coefficient, D C >0 represents the inter-individual detection avoidance distance. D C A value that is not too large should be chosen so that the inter-individual repulsion potential between each pair of individuals is 0 at the initial moment.

[0138] Repulsive potential between temporary target locations of individuals Simply add ξ to formula (18) i (t), ξ h (t), cC D C The coordinates of the temporary target positions of cluster individuals i (i = 1, 2, ..., n) are respectively replaced. Temporary target position coordinates of cluster individual h (j = 1, 2, ..., n, h ≠ i) Individual temporary target location avoidance coefficient c rC >0. Detection distance D between individual temporary target locations rC D is obtained by obtaining >0. rC The choices are all subject to high requirements.

[0139] The repulsive potential between an individual and an obstacle can be expressed in the following form:

[0140]

[0141] in, Let represent the cluster individuals i (i = 1, 2, ..., n) and obstacles at time t. The distance between, c O >0 represents the individual's avoidance coefficient between the individual and the obstacle, D O >0 represents the avoidance detection distance between the individual and the obstacle. D O A value that is not too large should be chosen so that the inter-individual repulsion potential between each pair of individuals is 0 at the initial moment.

[0142] Repulsive potential between the temporary target location and the obstacle Simply add ξ to formula (19) i (t), c C D C The coordinates of the temporary target positions of cluster individuals i (i = 1, 2, ..., n) are respectively replaced. Individual temporary target location and obstacle avoidance coefficient c rO Individual temporary target location and obstacle avoidance detection distance D rO We obtain D here by getting >0. rO with D in S4 rO Consistent. Let represent the cluster individuals i (i = 1, 2, ..., n) and obstacles at time t. The distance between them.

[0143] S6: Design a temporary target position control law so that the temporary target positions of each individual asymptotically converge to the target configuration region and spread out sufficiently within that region.

[0144] Specifically, based on the artificial potential field method and according to the various potential functions constructed above, a control law of the following form can be designed for the temporary target position of each individual i (i = 1, 2, ..., n) in the cluster:

[0145]

[0146] in The target configuration attraction term, target configuration boundary repulsion term, temporary target position repulsion term, and temporary target position and obstacle repulsion term of the temporary target position control law for individual i are designed as follows:

[0147]

[0148] (a) τ This indicates that any vector a is perpendicular to... The directional component can be represented as follows:

[0149]

[0150] The terms in the above control law are as follows: Figure 7 As shown.

[0151] S7: Design a real control law for each individual in the cluster so that each individual in the cluster i (i = 1, 2, ..., n) can effectively track the temporary target position, thereby self-organizing to form a target polygonal planar formation configuration.

[0152] Specifically, based on the artificial potential field method, and according to formula (1) and the various potential functions constructed above, a real control law of the following form can be designed for each individual i (i = 1, 2, ..., n) in the cluster:

[0153]

[0154] in The dynamic feedforward compensation term, target configuration attraction term, damping term, inter-individual repulsion term, and inter-individual and obstacle repulsion term of the real control law for individual i are designed in the following forms:

[0155]

[0156] k A >0 and k D >0 are called the position feedback coefficient and velocity feedback coefficient, respectively.

[0157] S8: Based on the dynamic models of each body and its temporary target position in S1, the initial state variables of each body, the vertex coordinates of the target configuration determined in S2, the initial values ​​of the temporary target position determined in S4, and the control laws designed in S5 and S6, perform cluster motion simulation. Determine if the simulation results meet the user's requirements. If not, try adjusting k in S5 respectively. F Various avoidance coefficients, various avoidance detection distances, and k in S6 A and k D This continues until the simulation results satisfy the user.

[0158] The present invention will be further described below.

[0159] Example

[0160] The following description uses the hexagonal formation configuration of a spacecraft cluster for Earth observation.

[0161] Within the LVLH coordinate system of the reference spacecraft under consideration, it should be perpendicular to the x-axis.

[0162] S1: Determine the number of individuals in the cluster, the dynamic model of each individual, the dynamic model of the temporary target position of each individual, the initial state variables of each individual, the target configuration parameters, and the obstacle model.

[0163] The individual initial state parameters include initial position and initial velocity; the target configuration parameters include the target configuration plane equation and the target configuration vertex coordinates.

[0164] Specifically, the number of individuals in the cluster is n = 10, and the dynamic model of each individual can be expressed in the reference spacecraft LVLH coordinate system according to the CW equations of relative motion of the spacecraft as follows:

[0165]

[0166] in, ω is the angular velocity of the reference spacecraft's orbit around the Earth, which is taken as 1.131 × 10⁻⁶ m at an orbital altitude of 400 m. -3 rad / s, U i (t) represents the required control variable. The initial positions of each body are randomly distributed within the interval [-60m, 60m] × [-60m, 60m] × [-60m, 60m], and the initial velocity of each body is 0.

[0167] Specifically, the dynamic model of the temporary target position of each body is a first-order integrator system of the following form:

[0168]

[0169] Wherein, the initial value of the temporary target position of individual i With the initial position ξ of individual i i (0) Same.

[0170] Specifically, the target configuration plane The equation for is given by the following equation:

[0171] x-40m=0 (26)

[0172] And determine the direction vector of the target configuration plane.

[0173] Specifically, the vertex coordinates of the target configuration are designed as follows:

[0174]

[0175] Then, according to formulas (4) and (5), each edge of the target configuration surface and its corresponding vector can be constructed. The vectors of each edge of the target configuration surface are shown in the table below.

[0176]

[0177] Specifically, the obstacle model is simplified to an obstacle whose center coincides with the origin of the LVLH coordinate system of the reference spacecraft, and whose radius is... The sphere is such that any point P(x,y,z) in space is at a distance from the obstacle. The distance can be expressed by the following formula.

[0178]

[0179] To visually demonstrate the initial positions of each individual element in the cluster, the target formation configuration plane, the target formation configuration vertices, the distribution of obstacles, and their relative positions, we plotted them in the same 3D image, as shown below. Figure 3 The hollow circle, transparent hexagon, square dot, and sphere are shown in the image. Its front view is shown below. Figure 4 As shown. The vertices of the target configuration are labeled with subscript numbers.

[0180] S2: Adjust the vertex coordinates of the target configuration.

[0181] First, check whether each target configuration vertex falls within the target configuration plane. Substituting the coordinates of each target configuration vertex shown in formula (27) into formula (26) shows that they all satisfy the condition. Therefore, each target configuration vertex falls within the target configuration plane and its position does not need to be adjusted.

[0182] Then check whether the target configuration region intersects with obstacles. By solving the optimization problem shown in equation (7), the optimized result can be obtained. Therefore, since the target configuration region does not intersect with the obstacle, there is still no need to adjust the position of the target configuration vertex.

[0183] S3: Determine the boundary surface equations corresponding to each side of the target configuration.

[0184] Specifically, the boundary surface is calculated according to formula (8). The equation is

[0185]

[0186] And transform it into the following form

[0187]

[0188] The boundary surface The direction vector is

[0189] Then, the orientation of each boundary surface was checked sequentially, and each boundary surface was found to be... The corresponding constraint (10) can all make Middle excluding edges All points other than the endpoints satisfy the condition, thus keeping the boundary surface equations shown in formulas (30) and (31) unchanged.

[0190] S4: Adjust the initial values ​​of the temporary target positions for each entity.

[0191] pass Figure 4 It can be observed that the projection of the initial position of some individuals onto the target configuration plane F falls outside the target configuration region, therefore the initial values ​​of the temporary target positions need to be adjusted. The adjusted initial values ​​of the temporary target positions according to formulas (12) and (13) are as follows: Figure 5 and Figure 6 The hollow pentagram in the image indicates that its label corresponds to the individual's number.

[0192] S5: Construct the target configuration attraction potential, the target configuration boundary repulsion potential, the inter-individual repulsion potential, the inter-individual temporary target position repulsion potential, the inter-individual and obstacle repulsion potential, and the inter-individual temporary target position and obstacle repulsion potential respectively.

[0193] Specifically, these potential functions can be constructed according to formulas (14) to (19) in the invention content S5, and the corresponding coefficients are shown in Table 1.

[0194] Table 1. Parameter settings for various potential functions

[0195] Target configuration attraction coefficient <![CDATA[k F ]]> <![CDATA[0.001s -2 ]]> Target configuration boundary surface avoidance coefficient <![CDATA[c E ]]> <![CDATA[1m 4 / s 2 ]]> Inter-individual avoidance coefficient <![CDATA[c C ]]> <![CDATA[1m 4 / s 2 ]]> Individual-to-obstacle avoidance coefficient <![CDATA[c O ]]> <![CDATA[1m 4 / s 2 ]]> Individual temporary target location avoidance coefficient <![CDATA[c rC ]]> <![CDATA[1000m 4 / s 2 ]]> Individual temporary target location and obstacle avoidance coefficient <![CDATA[c rO ]]> <![CDATA[1m 4 / s 2 ]]> Target configuration boundary surface avoidance detection distance <![CDATA[D E ]]> +∞ Inter-individual avoidance of detection distance <![CDATA[D C ]]> 10m Detection distance between individuals and obstacles <![CDATA[D O ]]> 10m Detection avoidance distance between individual temporary target locations <![CDATA[D rC ]]> +∞ Individual temporary target location and obstacle avoidance detection distance <![CDATA[D rO ]]> 10m

[0196] S6: Design a temporary target position control law so that the temporary target positions of each individual asymptotically converge to the target configuration region and spread out sufficiently within that region.

[0197] Specifically, the temporary target position control law can be designed according to formula (20).

[0198] S7: Design a real control law for each individual in the cluster so that each individual in the cluster i (i = 1, 2, ..., n) can effectively track the temporary target position, thereby self-organizing to form a target polygonal planar formation configuration.

[0199] Specifically, the temporary target position control law can be designed according to formula (23). Where the position feedback coefficient k is taken as... A =2.5e-5 s -2 Speed ​​feedback coefficient k D =0.01 s -1 .

[0200] S8: Based on the dynamic models of each body and its temporary target position in S1, the initial state variables of each body, the vertex coordinates of the target configuration determined in S2, the initial values ​​of the temporary target position determined in S4, and the control laws designed in S5 and S6, perform cluster motion simulation. Then determine whether the simulation results meet the user's requirements. Specifically, in... Figure 8 In the trajectories of the spacecraft cluster shown, the initial and final positions of each object are represented by hollow and solid dots, respectively. Figure 9 In the motion trajectory of the temporary target positions of each individual spacecraft in the spacecraft cluster shown, the initial and final values ​​of the temporary target positions of each individual spacecraft are shown as hollow pentagrams and solid pentagrams, respectively.

[0201] Depend on Figures 8 to 13 The simulation results show that the spacecraft swarm can converge well to a hexagonal target formation configuration with appropriate accuracy and control, and maintain sufficient distance between individual spacecraft and between spacecraft and obstacles. In contrast, [the following is a separate, unrelated sentence:] Figure 12 It can be seen that the control amount of the temporary target position of each individual in the cluster is very large. Directly applying it to the individual will result in an excessive actual control amount, thus verifying the effectiveness of this method in reducing the control amount.

[0202] Therefore, the task requirements are considered met. The implementation example has been completed.

[0203] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0204] Obviously, the described embodiments are only some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0205] The second objective of this invention is to provide a system for a polygonal planar formation self-organizing formation control method that considers obstacle avoidance, comprising:

[0206] Determine the module: determine the number of individuals in the cluster, the dynamic model, the initial state variables, and the target configuration parameters;

[0207] Judgment module: Determines whether the vertex coordinates of the target configuration in the target configuration parameters fall within the target configuration plane, and adjusts the vertex coordinates of the final target configuration based on the judgment result;

[0208] Adjustment module: Determines the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjusts the initial values ​​of the temporary target positions;

[0209] Design module: Construct an attractive potential based on the target configuration plane, construct a repulsive potential based on the boundary equations, and design the control law using the attractive and repulsive potentials;

[0210] Simulation module: Based on the number of individuals in the cluster, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of the temporary target positions, and the control law, the cluster motion simulation is performed.

[0211] A third objective of this invention is to provide an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor performing the steps of the aforementioned method for controlling the self-organizing formation of polygonal planar formations with obstacle avoidance in mind.

[0212] The aforementioned method for controlling the self-organizing formation of polygonal planar formations that considers obstacle avoidance includes the following steps:

[0213] Determine the number of individuals in the cluster, the dynamic model, the initial state variables, and the target configuration parameters;

[0214] Determine whether the vertex coordinates of the target configuration in the target configuration parameters fall within the target configuration plane, and adjust the vertex coordinates of the final target configuration based on the determination result;

[0215] Determine the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjust the initial values ​​of the temporary target positions;

[0216] Construct an attractive potential based on the target configuration plane, construct a repulsive potential based on the boundary equation, and design a control law using the attractive and repulsive potentials.

[0217] Based on the number of individuals in the cluster, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of the temporary target positions, and the control law, a cluster motion simulation is performed.

[0218] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the aforementioned method for controlling the self-organizing formation of polygonal planar formations with obstacle avoidance considerations.

[0219] The aforementioned method for controlling the self-organizing formation of polygonal planar formations that considers obstacle avoidance includes the following steps:

[0220] Determine the number of individuals in the cluster, the dynamic model, the initial state variables, and the target configuration parameters;

[0221] Determine whether the vertex coordinates of the target configuration in the target configuration parameters fall within the target configuration plane, and adjust the vertex coordinates of the final target configuration based on the determination result;

[0222] Determine the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjust the initial values ​​of the temporary target positions;

[0223] Construct an attractive potential based on the target configuration plane, construct a repulsive potential based on the boundary equation, and design a control law using the attractive and repulsive potentials.

[0224] Based on the number of individuals in the cluster, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of the temporary target positions, and the control law, a cluster motion simulation is performed.

[0225] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0226] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0227] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0228] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0229] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A control method for polygonal planar formation self-organization formation considering obstacle avoidance, characterized in that, Includes the following steps: Determine the number of individuals in the cluster, the dynamic model, the initial state variables, and the target configuration parameters; Determine whether the vertex coordinates of the target configuration in the target configuration parameters fall within the target configuration plane, and adjust the vertex coordinates of the final target configuration based on the determination result; Determine the boundary equations corresponding to each side of the target configuration in the target configuration plane, and adjust the initial values ​​of the temporary target positions; Construct an attractive potential based on the target configuration plane, construct a repulsive potential based on the boundary equation, and design a control law using the attractive and repulsive potentials. Based on the number of individuals in the cluster, the dynamic model, the initial state variables, the vertex coordinates of the target configuration, the initial values ​​of the temporary target positions, and the control law, a cluster motion simulation is performed. The determination of whether the target configuration vertex coordinates in the target configuration parameters fall within the target configuration plane includes: For each target configuration vertex coordinate Use its components in sequence , and Replace the formulas respectively In , and Then check if the equation satisfies the equality condition. If satisfied, then use the vertex coordinates of the target configuration directly; If the conditions are not met, then the vertex coordinates of the target configuration will be... Replace with its projected coordinates on the target configuration plane. ; wherein , Ntarget is the number of target configuration vertices; The determination of the boundary equations corresponding to each side of the target configuration in the target configuration plane includes: For the target configuration surface, the first Strip edge Its boundary surface The equation can be expressed as follows with respect to the variables: , and The equation gives And transform it into the following form in, The direction vector of the target configuration plane; For the first The coordinates of the vertex of the target configuration; After all boundary surface equations have been solved, check the orientation of each boundary surface in turn; If there is a certain boundary surface which corresponds to the following constraint condition can be made all points other than the endpoints of the edge satisfy the boundary surface equation remains unchanged; If such boundary surfaces do not exist, then the respective , , are replaced by and the respective boundary surface equations are then solved anew according to the formula ​ wherein , Ntarget is the number of target configuration vertices; The adjustment of the initial value of the temporary target position includes: For individuals Initial value of temporary target position If there are two or more temporary target location initial values The formula is not satisfied. The boundary surfaces of each target configuration shown The constraints are then measured sequentially. Find the distance to each target configuration vertex. The nearest target configuration vertex Construct the following points And determine the following points Whether the boundary surface constraints of each target configuration are satisfied; if some boundary surface constraints are not satisfied, then... Replace with Then return to the new temporary target position initial value. Calculation steps, until the result is obtained. Continue until the boundary surface constraints of each target configuration are satisfied, then... Replace with ; wherein ; .

2. The method of claim 1, wherein, said target configuration vertex coordinates replaced by their projection coordinates on the target configuration plane Next: Check whether the target configuration area intersects with obstacles; If the target configuration region intersects with an obstacle, the vertex coordinates of the target configuration are reselected; If the target configuration region does not intersect with the obstacle, there is no need to adjust the vertex coordinates of the target configuration. 3.The method of claim 1, wherein, The adjustment of the initial value of the temporary target position includes: For individuals Initial value of temporary target position If the formula is satisfied The boundary surfaces of each target configuration shown Constraints, namely In the target configuration plane If the projection within falls within the target configuration region, then No adjustments will be made. wherein ; .

4. The method of claim 1, wherein, The adjustment of the initial value of the temporary target position includes: For individuals Initial value of temporary target position If there is only one temporary target position initial value The formula is not satisfied. The boundary surfaces of each target configuration shown The constraints are determined based on the corresponding boundary surfaces. Determine the following points Whether the boundary surface constraints of each target configuration are satisfied; if some boundary surface constraints are not satisfied, then... Replace with Then return to the new temporary target position initial value. Calculation steps, until the result is obtained. Continue until the boundary surface constraints of each target configuration are satisfied, then... Replace with ; wherein ; .

5. The method of claim 1, wherein, The process of constructing an attractive potential based on the target configuration plane includes: At any point in space whose target configuration attractive potential is expressed in the form: wherein is the target configuration attraction coefficient; is the point distance to the target configuration plane .

6. The method of claim 1, wherein, The construction of the repulsive potential based on the boundary equation includes: At any point in space whose target configuration boundary repulsive potential may be expressed in the form: wherein is the repulsive potential of the target configuration interface.

7. The method of claim 1, wherein, The control law is designed using the attraction and repulsion potentials, wherein: Repulsion potentials include target configuration boundary repulsion potential, inter-individual repulsion potential, inter-individual temporary target location repulsion potential, inter-individual and obstacle repulsion potential, and inter-individual temporary target location and obstacle repulsion potential.

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