A collision-free space parameterized formation configuration sequence planning method

Abstract

The application discloses a collision-free space parameterized formation configuration sequence planning method, and belongs to the technical field of intelligent agent / unmanned aerial vehicle / spacecraft cluster motion control, and the method comprises the following steps: according to initial target formation configuration parameters and final target formation configuration parameters, a plurality of intermediate target formation configuration parameters are constructed through linear interpolation; the initial target formation configuration parameters, the intermediate target formation configuration parameters and the final target formation configuration parameters are input into a target formation configuration model, and then the target formation configuration model determines individual target positions at each moment according to the number of cluster individuals; whether the individual target positions at each moment meet constraint conditions is detected in sequence, if the constraint conditions are met, then according to the corresponding intermediate target formation configuration parameters and the target formation configuration model, the intermediate target formation configuration at each moment is directly generated; and according to the directly generated intermediate target formation configuration at each moment, the collision-free space parameterized formation configuration sequence planning is completed. According to the method, related parameters can be adjusted in time according to a complex obstacle environment, and the target formation configuration shape can be flexibly adjusted to avoid obstacles.

Description

Technical Field

[0001] This invention relates to the field of motion control technology for intelligent agents / UAVs / spacecraft swarms, and specifically to a collision-free spatial parameterized formation configuration sequence planning method. Background Technology

[0002] In the study of real-world swarm formation reconfiguration / migration motion control for drones, spacecraft, and other similar applications, a common approach to ensure the safety of swarm movement and effectively avoid obstacles is to plan a separate target trajectory for each individual swarm member to avoid obstacles. However, this method does not fully consider the overall swarm formation configuration, which can easily lead to the swarm temporarily losing its regular formation configuration near obstacles, thus affecting its functional execution. Furthermore, it becomes increasingly computationally difficult as the swarm size increases.

[0003] A more reasonable approach is based on a parametric formation configuration model. By adjusting a few parameters of the target formation configuration, an intermediate target configuration sequence that avoids obstacles is planned for the entire cluster, thereby indirectly determining the trajectory of each individual target. Because the target formation configuration parameters are independent of the number of individuals in the cluster, this method is suitable for the overall reconstruction or migration of large-scale clusters.

[0004] However, existing parametric formation configuration planning mainly targets relatively regular target formation configurations such as spheres and line segments. For complex obstacle environments, it cannot adjust relevant parameters such as size, position, orientation, and shape in a timely manner, cannot provide suitable target formation configuration sequence planning strategies, and cannot flexibly adjust the shape of the target formation configuration to avoid obstacles. Summary of the Invention

[0005] To address the problems in existing parametric formation configuration planning technologies, such as the inability to adjust relevant parameters in a timely manner, the inability to flexibly adjust the target formation configuration shape to avoid obstacles, and the inability to provide a suitable target formation configuration sequence planning strategy, this invention provides a collision-free spatial parametric formation configuration sequence planning method. This method can adjust relevant parameters in a timely manner according to complex obstacle environments and flexibly adjust the target formation configuration shape to avoid obstacles.

[0006] To achieve the above objectives, the present invention provides the following technical solution.

[0007] A collision-free spatial parameterized formation configuration sequence planning method includes:

[0008] Based on the initial target formation configuration parameters and the final target formation configuration parameters, several intermediate target formation configuration parameters are constructed through linear interpolation;

[0009] The initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters are input into the target formation configuration model. Then, the target formation configuration model determines the position of individual targets at each time step based on the number of individuals in the cluster.

[0010] The system sequentially checks whether the individual target positions at each time point meet the constraints. If the constraints are met, the system directly generates the intermediate target formation configuration at each time point based on the corresponding intermediate target formation configuration parameters and the target formation configuration model.

[0011] Based on the directly generated intermediate target formation configurations at each time step, the collision-free spatial parameterized formation configuration sequence planning is completed.

[0012] As a further improvement of the present invention, the target formation configuration model is given by the following spatial Lissajous curve.

[0013]

[0014] in, Let C be the position coordinates of the center C of the target formation configuration, and a = (a x ,a y ,a z ) T Principal semi-axis vector, b = (b x ,b y ,b z ) T The secondary half-axis vector, ω=(ω x ,ω y ,ω z ) T Let u be the angular frequency vector, u∈[0,u] max ) represents the independent variable of the curve, ° represents the Hadamard product symbol, and R b To convert the x-axis unit vector The coordinate transformation matrix for rotating to the unit vector of vector b.

[0015] As a further improvement of the present invention, the R b To convert the x-axis unit vector The coordinate transformation matrix for rotating to the unit vector b, then:

[0016] The calculation is based on the rotation formula as follows:

[0017]

[0018] p is a target formation configuration parameter of the following form.

[0019] p=(x C ,y C ,z C ,a x ,ay ,a z ,b x ,b y ,b z ,ω x ,ω y ,ω z ) T

[0020] For the j-th target formation configuration (j = 1, 2, ..., n) F The specific value of ) is denoted as p(j), and the coordinates of the center position of the target formation configuration corresponding to it are denoted as ξ. C (j) The principal half-axis vector is denoted as a(j), the secondary half-axis vector is denoted as b(j), and the angular frequency vector is denoted as ω(j), i.e.

[0021]

[0022] Initial target formation configuration parameters p0 = p(1), final target formation configuration parameters p f =p(n F All are given in the form of the above formula.

[0023] As a further improvement of the present invention, the step of constructing several intermediate target formation configuration parameters by linear interpolation based on the initial target formation configuration parameters and the final target formation configuration parameters includes:

[0024] The formation configuration parameters for intermediate targets are determined using the following formula:

[0025]

[0026] Where p(k) represents the target formation configuration parameters of the k-th target formation configuration (k = 2, ..., n). F -1).

[0027] As a further improvement of the present invention, the step of inputting the initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters into the target formation configuration model, and then the target formation configuration model determining the individual target positions at each time step based on the number of individuals in the cluster, includes:

[0028] At time j (j = 1, 2, ..., n) F The target position of an individual i (i = 1, 2, ..., n) under the following form is represented as follows:

[0029]

[0030] Where p(j) represents the target formation configuration parameters of the j-th target formation configuration, p(1) = p0, p(n) = p0, p(j ... F ) = pf .

[0031] As a further improvement of the present invention, the individual target position at each time step is sequentially detected to determine whether the constraint conditions are met, including:

[0032] For the k-th target formation configuration (k = 2, 3, ..., n) F -1), the corresponding individual target location (i = 1, 2, ..., n) should satisfy the following constraints:

[0033]

[0034] Make

[0035] And for the (n)th F -1) Target formation configuration Its corresponding individual target location (i = 1, 2, ..., n) should also satisfy the following constraints

[0036] Make

[0037] in, This is an obstacle model.

[0038] As a further improvement of the present invention, the individual target position at each time step is sequentially detected to determine whether the constraint conditions are met, including:

[0039] If the target formation configuration If the position of the corresponding individual target satisfies the constraints, then the corresponding intermediate target formation configuration is directly generated based on the corresponding intermediate target formation configuration parameters and the target formation configuration model.

[0040] As a further improvement of the present invention, the step of sequentially detecting whether the individual target position at each time point satisfies the constraint conditions includes:

[0041] If the constraints are not met, adjust the target formation configuration according to strategy one. (k = 2, ..., n) F -1) the target formation configuration parameter p(k); then continue to check the next target formation configuration. The check is complete once all intermediate target formation configurations meet the constraints, and the intermediate target formation configuration sequence is output.

[0042] As a further improvement of the present invention, the adjustment of the target formation configuration according to strategy one is described. (k = 2, ..., n) F-1) the target formation configuration parameter p(k), where:

[0043] Strategy 1 involves adjusting the target formation configuration parameters, including:

[0044] Determine the optimization variables:

[0045] The optimization variable is taken as

[0046] q=(x C ,y C ,z C ,a x ,a y ,a z ,b x ,b y ,b z ) T

[0047] That is, the vector consisting of the first 9 components of the target formation configuration parameter p;

[0048] Construct n for the parameter optimization problem of the k-th target formation configuration p Initial solutions (i p =1,2,...,n p ), where the i-th p Initial solutions The initial value is taken as

[0049]

[0050] Where q(k) is the target formation configuration The vector consisting of the first 9 components of the target formation configuration parameter p(k); rand(9,1) is a 9x1 random number matrix, with each element uniformly distributed between -1 and 1; ° is the symbol for the Hadamard product;

[0051] Then verify each one in turn. Does it meet the following constraints?

[0052]

[0053] Where ω(k) is the target formation configuration The specific value of the corresponding angular frequency vector;

[0054] When verifying each one in turn If all the above constraints are met, then a global optimization algorithm such as a genetic algorithm is used, and the obtained result is used. Given the set of initial solutions, solve the following optimization problem with respect to variable q.

[0055]

[0056] Obtain the optimal solution

[0057] Then temporarily replace p(k) with Under the given conditions, determine the following constraints

[0058] Constraint 1: Make

[0059] Constraint 2: Make

[0060] Does it meet the requirements?

[0061] If not satisfied, then the above optimization problem with respect to variable q is solved again until the above constraints are satisfied;

[0062] After satisfying the constraints, let

[0063]

[0064] As the adjusted kth target formation configuration The target formation configuration parameters.

[0065] As a further improvement to the present invention, the sequential verification of each Does it meet the following constraints?

[0066]

[0067] in:

[0068] If the conditions are not met, then perform the following replacement.

[0069]

[0070] Get new in and They are respectively The corresponding principal and secondary half-axis vectors; then return to the above constraint check process, repeating this process until... Continue until the constraints are met.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] This invention provides a collision-free spatial parameterized formation configuration sequence planning method. First, based on the initial and final target formation configuration parameters that satisfy constraints, linear interpolation is used to initially establish an intermediate target formation configuration parameter sequence that smoothly transitions from the initial target formation configuration to the final target formation configuration. Then, a two-step optimization strategy of optimization followed by verification is employed to adjust the intermediate target formation configuration parameters. This avoids the impact of computationally intensive occlusion constraints on the solution progress of the optimization problem, while leveraging the multiple solutions of the global optimization algorithm to find solutions that satisfy the occlusion constraints more quickly. The target formation configuration parameters of this invention have clear meanings, facilitating the flexible adjustment of different parameters to change the position, size, orientation, and shape of the target formation configuration. Therefore, it is applicable to the reconstruction or migration between a large class of different formation configurations and enhances adaptability to complex obstacle environments and task requirements. Due to the constant number of target formation configuration parameters, this method is suitable for the reconstruction or migration of large-scale clusters. By planning intermediate target formation configurations with a smooth transition, this method can guide the swarm to avoid obstacles while ensuring the continuity of the formation configuration shape, so that the swarm can better perform its target mission during formation movement. Attached Figure Description

[0073] Figure 1 This is a flowchart of a collision-free spatial parameterized formation configuration sequence planning method according to the present invention;

[0074] Figure 2 This is a flowchart illustrating a collision-free spatial parameterized formation configuration sequence planning method according to the present invention.

[0075] Figure 3 This refers to the initial target formation configuration, final target formation configuration, and obstacle distribution map in embodiment S1 of the present invention.

[0076] Figure 4 This is a diagram showing the intermediate target formation configuration and the corresponding individual target position distribution at various times in embodiment S2 of the present invention.

[0077] Figure 5 This is a diagram showing the adjusted intermediate target formation configuration and the corresponding individual target position distribution at each time point in embodiment S3 of the present invention.

[0078] Figure 6 This is a three-dimensional view showing the adjusted target positions of each body at adjacent time points in embodiment S3 of the present invention.

[0079] Figure 7 This is a front view showing the adjusted target positions of each body at adjacent time points in embodiment S3 of the present invention.

[0080] Figure 8 This is a right view showing the lines connecting the target positions of each body at adjacent moments in embodiment S3 of the present invention;

[0081] Figure 9 This is a top view showing the adjusted target positions of each body at adjacent times in embodiment S3 of the present invention. Detailed Implementation

[0082] 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.

[0083] The following detailed description is 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.

[0084] To address the shortcomings of current parametric formation planning methods, such as the inability to adjust relevant parameters in a timely manner, the inability to flexibly adjust the target formation shape to avoid obstacles, and the inability to provide suitable target formation sequence planning strategies, this invention provides a collision-free spatial parametric formation sequence planning method. Figure 1 As shown, the method includes:

[0085] Based on the initial target formation configuration parameters and the final target formation configuration parameters, several intermediate target formation configuration parameters are constructed through linear interpolation;

[0086] The initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters are input into the target formation configuration model. Then, the target formation configuration model determines the position of individual targets at each time step based on the number of individuals in the cluster.

[0087] The system sequentially checks whether the individual target positions at each time point meet the constraints. If the constraints are met, the system directly generates the intermediate target formation configuration at each time point based on the corresponding intermediate target formation configuration parameters and the target formation configuration model.

[0088] Based on the directly generated intermediate target formation configurations at each time step, the collision-free spatial parameterized formation configuration sequence planning is completed.

[0089] The present invention will now be described in detail with reference to the accompanying drawings:

[0090] like Figure 2 As shown, a collision-free spatial parameterized formation configuration sequence planning method includes the following steps:

[0091] S1: Provide the target formation configuration model, the number of cluster individuals n, and the number of target formations n. FInitial target formation configuration parameters p0, final target formation configuration parameters p f Obstacle Model Obstacle avoidance detection distance D O .

[0092] Specifically, the target formation configuration model is given by the following spatial Lissajous curve.

[0093]

[0094] in, The position coordinates of the target formation configuration center C determine the target formation position; a = (a x ,a y ,a z ) T The principal semi-axis vector determines the size and shape of the target formation; b = (b x ,b y ,b z ) T The secondary half-axis vector determines the size, shape, and orientation of the target formation; ω = (ω x ,ω y ,ω z ) T The angular frequency vector determines the shape of the target formation; u∈[0,u max ) is the independent variable of the curve ( Let be the maximum value of the independent variable of the curve; max(·) is the function to find the maximum value; This is the symbol for the Hadamard product (the element-wise multiplication of matrices of the same size).

[0095] When ω=(1,1,1) T When the target formation configuration degenerates into an ellipse, a is the major semi-axis vector of the ellipse and b is the minor semi-axis vector of the ellipse.

[0096] R b To convert the x-axis unit vector The coordinate transformation matrix for rotating to the unit vector b can be calculated using Rodrigues' rotation formula as follows (I3 represents the 3rd order identity matrix).

[0097]

[0098] p is a target formation configuration parameter of the following form.

[0099] p=(x C ,y C ,z C ,a x ,a y ,a z ,bx ,b y ,b z ,ω x ,ω y ,ω z ) T (3)

[0100] For the j-th target formation configuration (j = 1, 2, ..., n) F The specific value of ) is denoted as p(j), and its corresponding target formation configuration center position coordinates, principal half-axis vector, secondary half-axis vector, and angular frequency vector are denoted as ξ, respectively. C (j), a(j), b(j), ω(j), that is

[0101]

[0102] Initial target formation configuration parameters p0 = p(1), final target formation configuration parameters p f =p(n F All are given in the form of formula (3).

[0103] Specifically, obstacle model We need to find an analytical expression for the distance from its surface to any point P(x,y,z) in space.

[0104] Specifically, the initial and final target formation configurations should not only avoid intersecting with obstacles, but also maintain a sufficient distance from them, ensuring that the following two inequalities hold true.

[0105]

[0106]

[0107] If formula (5) does not hold, then adjust the initial target formation configuration parameter p0;

[0108] If formula (6) does not hold, then adjust the final target formation configuration parameter p. f .

[0109] S2: Based on the initial target formation configuration parameters and the final target formation configuration parameters, construct (n) through linear interpolation. F -2) intermediate target formation configuration parameters, and determine the position of individual targets at each time step.

[0110] Specifically, the formation configuration of the k-th target (k = 2, ..., n) F The target formation configuration parameter p(k) can be expressed in the following form:

[0111]

[0112] And p(1) = p0, p(n) F ) = p f .

[0113] Specifically, at the j-th time (j = 1, 2, ..., n) F The target position of an individual i (i = 1, 2, ..., n) under the following conditions can be represented as follows:

[0114]

[0115] S3: Sequentially check whether the configuration parameters of each intermediate target formation meet the constraints. If they do not meet the constraints, adjust the corresponding intermediate target formation configuration parameters, and then combine them with the target formation configuration model to regenerate the intermediate target formation configuration.

[0116] Specifically, for the k-th target formation configuration (k = 2, 3, ..., n) F -1), the corresponding individual target location The following two sets of constraints should be satisfied:

[0117] Obstacle avoidance constraints:

[0118] Occlusion constraint 1: Make

[0119] Formula (9) means avoiding obstacles, and formula (10) means there is no obstruction between the formation and the previous formation.

[0120] And for the (n)th F -1) Target formation configuration Its corresponding individual target location (i = 1, 2, ..., n) should also satisfy the following constraint, which means that there is no obstruction between it and the next formation.

[0121] Occlusion constraint 2: Make

[0122]

[0123] If the target formation configuration Corresponding individual target location If the constraints are satisfied for (i = 1, 2, ..., n), no action is taken; otherwise, the target formation configuration is adjusted according to strategy one. (k = 2, ..., n) F -1) the target formation configuration parameter p(k). Then continue to check the next target formation configuration. Until all intermediate target formation configurations have been checked.

[0124] Strategy 1: Adjusting the target formation configuration parameters

[0125] SS1: Determine the optimization variables.

[0126] Specifically, the optimization variable is taken as

[0127] q=(x C ,y C ,z C ,a x ,a y ,a z ,b x ,b y ,b z ) T (12)

[0128] That is, the vector consisting of the first 9 components of the target formation configuration parameter p.

[0129] SS2: Construct n for the optimization problem of formation configuration parameters for the k-th target p Initial solutions (i p =1,2,...,n p ). Where the i-th p Initial solutions The initial value is taken as

[0130]

[0131] Where q(k) is the target formation configuration The vector consisting of the first 9 components of the target formation configuration parameter p(k); rand(9,1) is a 9-row, 1-column random number matrix, with each element uniformly distributed between -1 and 1;

[0132] This is the symbol for the Hadamard product. And... The corresponding target formation configuration center position coordinates, principal half-axis vector, and secondary half-axis vector are denoted as follows: and Right now

[0133]

[0134] Then verify each one in turn. Does it meet the following constraints?

[0135]

[0136] Where ω(k) is the target formation configuration. The specific value of the corresponding angular frequency vector. If satisfied, no adjustment is made; otherwise, the following replacement is performed.

[0137]

[0138] Get new Then return to the checking process of formula (15) above, and repeat this process until... Until formula (15) is satisfied.

[0139] SS3: Utilizes global optimization algorithms such as genetic algorithms, and takes the results obtained in SS2 as an example. Given the set of initial solutions, solve the following optimization problem with respect to variable q.

[0140]

[0141] Obtain the optimal solution Then temporarily replace p(k) with Under the condition of [condition], check whether formula (10) in occlusion constraint 1 and formula (11) in occlusion constraint 2 are satisfied. If not, resolve formula (17) until formula (10) in occlusion constraint 1 and formula (11) in occlusion constraint 2 are satisfied. Finally, let [condition].

[0142]

[0143] As the adjusted kth target formation configuration The target formation configuration parameters.

[0144] S4: Output the intermediate target formation configuration sequence.

[0145] Specifically, according to the target formation configuration model formula (1), the intermediate target formation configuration (k = 2, 3, ..., n) F The parametric equation for -1) can be expressed as c(u; p(k)), where u∈[0,u max ).

[0146] The present invention will be further described below with reference to the embodiments.

[0147] Example

[0148] S1: Provide the target formation configuration model, the number of cluster individuals n, and the number of target formations n. F Initial target formation configuration parameters p0, final target formation configuration parameters p f Obstacle Model Obstacle avoidance detection distance D O .

[0149] Specifically, the target formation configuration model is given in formula (1), where the number of cluster individuals n = 10 and the number of target formations n F =4 (meaning two intermediate formation configurations need to be planned), obstacle avoidance detection distance D O =8m, initial target formation configuration parameters p0 and final target formation configuration parameters p f The following are respectively:

[0150] p0=(40m,-40m,0,20m,20m,20m,-20m,20m,0m,1,1,1) T (19)

[0151] p f =(0m,0m,0m,20m,20m,20m,-20m,20m,0m,1,1,2) T (20)

[0152] obstacle model Let P be a sphere with its center coinciding with the origin and a radius of 20m. Therefore, the expression for the distance from its surface to any point P(x,y,z) in space is... It can be represented as

[0153]

[0154] The distance from the initial target formation configuration to the obstacle can be calculated using formulas (5) and (6). The final target is the distance from the formation configuration to the obstacle. Both formulas (5) and (6) are satisfied.

[0155] To visually illustrate the initial target formation configuration, the final target formation configuration, and the relative positions of obstacles, we have plotted them in the same diagram, as shown below. Figure 3 The ellipse, Lissajous curve and sphere are shown in the figure. The solid square and pentagram are the initial and final target positions of each body determined by the initial and final target formation configuration and formula (8), respectively.

[0156] S2: Construct (n) based on the initial and target formation configuration parameters using linear interpolation. F -2) Parameters of the intermediate target formation configuration, and determine the position of individual targets at each time step.

[0157] Specifically, the parameters of each intermediate target formation configuration are shown in Table 1.

[0158] Table 1 Parameters of intermediate target formation configuration

[0159]

[0160]

[0161] The target formation configuration parameter vector p(k) of the intermediate target formation configuration can be constructed according to formula (4). The shapes of these formation configurations are as follows: Figure 4 The finer open curve is shown in the figure. The individual target position at each time point can be constructed according to formula (8), or as shown in the figure. Figure 4 The solid squares (corresponding to the initial time / initial target formation configuration), hollow circles (corresponding to the intermediate time / intermediate target formation configuration), and pentagrams (corresponding to the final time / final target formation configuration) are shown in the diagram.

[0162] Depend on Figure 4 It can be observed that both intermediate target formation configuration curves intersect with obstacles, and correspondingly, some individual target positions are located inside the obstacles. Therefore, the original target formation configuration sequence cannot be used directly and needs to be adjusted.

[0163] S3: Sequentially check whether each intermediate target formation configuration meets the constraints. If not, adjust the corresponding formation configuration parameters, and then combine the target formation configuration model to generate the intermediate target formation configuration.

[0164] Specifically, it is checked sequentially whether the formation configuration of each intermediate target satisfies formulas (9) and (10) in constraint condition 1. Figure 4 It is evident that since some individual targets in both intermediate target formation configurations are located inside obstacles, neither configuration satisfies the constraints and their parameters need to be adjusted according to Strategy 1. The adjusted parameters for each intermediate target formation configuration are shown in Table 2.

[0165] Table 2 Parameters of the Adjusted Intermediate Target Formation Configuration

[0166] serial number Center position coordinates / m Principal half-axis vector / m Secondary half-axis vector / m Angular frequency vector 2 <![CDATA[(26.8258,-26.8992,0) T ]]> <![CDATA[(20.9578,20.1143,20.3069) T ]]> <![CDATA[(-6.6494,14.5329,0) T ]]> <![CDATA[(1,1,1.33) T ]]> 3 (13.2700,-10.4132,-6.8 <![CDATA[(20.9925,25.0907,24.3482) T ]]> <![CDATA[(-14.3667,23.5121,0) T ]]> <![CDATA[(1,1,1.67) T ]]>

[0167] The corresponding intermediate target formation configuration is as follows: Figure 5 As shown by the finer open curves, it can be observed that the adjusted intermediate target formation configuration effectively avoids obstacles.

[0168] To visually demonstrate the unobstructed effect of adjacent target formations, we connect the target positions of each object within the adjacent target formation with straight line segments. The 3D view, front view, right view, and top view are shown below. Figure 6 , Figure 7 , Figure 8 , Figure 9 As shown, the optimized target formation configuration does indeed avoid occlusion of target positions at adjacent time points.

[0169] S4: Output the intermediate target formation configuration sequence.

[0170] Specifically, the adjusted intermediate target formation configuration has been represented as follows: Figure 5 The parameters of the finer open curves are shown in Table 2. Their parametric equations can be obtained by replacing the target formation configuration parameter p in formula (1) with its specific value p(k) for the k-th target formation configuration (k=2,...,n). F -1) Constructed.

[0171] In summary, this method is applicable to the formation reconfiguration or migration of large-scale clusters. By planning intermediate formation configurations with a smooth transition, it is possible to guide the cluster to avoid obstacles while ensuring the continuity of the formation configuration shape, thus enabling the cluster to better perform its target mission during formation movement.

[0172] The second objective of this invention is to propose a collision-free spatial parameterized formation configuration sequence planning system, comprising:

[0173] Construction Parameters Module: Used to construct several intermediate target formation configuration parameters through linear interpolation based on the initial target formation configuration parameters and the final target formation configuration parameters;

[0174] The location determination module is used to input the initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters into the target formation configuration model. Then, the target formation configuration model determines the individual target positions at each time step based on the number of individuals in the cluster.

[0175] The detection constraint module is used to sequentially detect whether the position of individual targets at each time step meets the constraint conditions. If the constraint conditions are met, the intermediate target formation configuration at each time step is directly generated based on the corresponding intermediate target formation configuration parameters and target formation configuration model.

[0176] The planning module is used to complete the planning of collision-free spatial parameterized formation configuration sequences based on the intermediate target formation configurations generated at each time step.

[0177] A third objective of this invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the collision-free spatial parameterized formation configuration sequence planning method.

[0178] The collision-free spatial parameterized formation configuration sequence planning method includes:

[0179] Based on the initial target formation configuration parameters and the final target formation configuration parameters, several intermediate target formation configuration parameters are constructed through linear interpolation;

[0180] The initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters are input into the target formation configuration model. Then, the target formation configuration model determines the position of individual targets at each time step based on the number of individuals in the cluster.

[0181] The system sequentially checks whether the individual target positions at each time point meet the constraints. If the constraints are met, the system directly generates the intermediate target formation configuration at each time point based on the corresponding intermediate target formation configuration parameters and the target formation configuration model.

[0182] Based on the directly generated intermediate target formation configurations at each time step, the collision-free spatial parameterized formation configuration sequence planning is completed.

[0183] 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 collision-free spatial parameterized formation configuration sequence planning method.

[0184] The collision-free spatial parameterized formation configuration sequence planning method includes:

[0185] Based on the initial target formation configuration parameters and the final target formation configuration parameters, several intermediate target formation configuration parameters are constructed through linear interpolation;

[0186] The initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters are input into the target formation configuration model. Then, the target formation configuration model determines the position of individual targets at each time step based on the number of individuals in the cluster.

[0187] The system sequentially checks whether the individual target positions at each time point meet the constraints. If the constraints are met, the system directly generates the intermediate target formation configuration at each time point based on the corresponding intermediate target formation configuration parameters and the target formation configuration model.

[0188] Based on the directly generated intermediate target formation configurations at each time step, the collision-free spatial parameterized formation configuration sequence planning is completed.

[0189] 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.

[0190] 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.

[0191] 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.

[0192] 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.

[0193] 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 collision-free space parameterized formation configuration sequence planning method, characterized in that, include: Based on the initial target formation configuration parameters and the final target formation configuration parameters, several intermediate target formation configuration parameters are constructed through linear interpolation; The initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters are input into the target formation configuration model. Then, the target formation configuration model determines the position of individual targets at each time step based on the number of individuals in the cluster. The system sequentially checks whether the individual target positions at each time point meet the constraints. If the constraints are met, the system directly generates the intermediate target formation configuration at each time point based on the corresponding intermediate target formation configuration parameters and the target formation configuration model. Based on the directly generated intermediate target formation configurations at each time step, the collision-free spatial parameterized formation configuration sequence planning is completed. The step of constructing several intermediate target formation configuration parameters through linear interpolation based on the initial target formation configuration parameters and the final target formation configuration parameters includes: The formation configuration parameters for intermediate targets are determined using the following formula: in, Indicates the first Target formation configuration parameters for each target formation configuration ; These are the initial target formation configuration parameters; The target number of squadrons; For the final target formation configuration parameters; The system sequentially checks whether the individual target positions at each time step satisfy the constraints, including: For the Target formation configuration , The corresponding individual target location , The following constraints must be met: ， , making And for the first Target formation configuration The corresponding individual target location , The following constraints should also be satisfied. , making in, This is an obstacle model.

2. The collision-free spatial parameterized formation configuration sequence planning method according to claim 1, characterized in that, The target formation configuration model is given by the following spatial Lissajous curve. in, For the target formation configuration center Location coordinates, Principal semi-axis vector, It is the secondary half-axis vector. It is the angular frequency vector. Let be the independent variable of the curve. The symbol for the Hadamarda complex. To be Axis unit vector Rotate to The coordinate transformation matrix of a unit vector.

3. The collision-free spatial parameterized formation configuration sequence planning method according to claim 2, characterized in that, The To be Axis unit vector Rotate to The coordinate transformation matrix of the unit vector, then: The calculation is based on the rotation formula as follows: For target formation configuration parameters in the following form Its for the first , The specific value of the target formation configuration is denoted as The coordinates of the center position of the corresponding target formation configuration are marked. The principal half-axis vector is denoted as The secondary half-axis vector is denoted as Angular frequency vector is denoted as ,Right now Initial target formation configuration parameters Final target formation configuration parameters All are given in the form of the above formula.

4. The collision-free spatial parameterized formation configuration sequence planning method according to claim 1, characterized in that, The process involves inputting the initial target formation configuration parameters, intermediate target formation configuration parameters, and final target formation configuration parameters into the target formation configuration model. The target formation configuration model then determines the individual target positions at each time step based on the number of individuals in the cluster, including: No. An individual at a given moment , Target location Represented in the following form in, Indicates the first Target formation configuration parameters for each target formation configuration , .

5. The collision-free spatial parameterized formation configuration sequence planning method according to claim 1, characterized in that, The system sequentially checks whether the individual target positions at each time step satisfy the constraints, including: If the target formation configuration If the position of the corresponding individual target satisfies the constraints, then the corresponding intermediate target formation configuration is directly generated based on the corresponding intermediate target formation configuration parameters and the target formation configuration model.

6. The collision-free spatial parameterized formation configuration sequence planning method according to claim 1, characterized in that, The step of sequentially detecting whether the individual target position at each time step meets the constraint conditions includes: If the constraints are not met, adjust the target formation configuration according to strategy one. , Target formation configuration parameters Then proceed to check the next target formation configuration. The check is complete once all intermediate target formation configurations meet the constraints, and the intermediate target formation configuration sequence is output.

7. The collision-free spatial parameterized formation configuration sequence planning method according to claim 6, characterized in that, The adjustment of the target formation configuration according to strategy one , Target formation configuration parameters ,in: Strategy 1 involves adjusting the target formation configuration parameters, including: Determine the optimization variables: The optimization variable is taken as That is, the target formation configuration parameters The vector formed by the first 9 components; For the first Constructing a parameter optimization problem for a single target formation configuration Initial solutions , , of which Initial solutions The initial value is taken as in, For target formation configuration Target formation configuration parameters The vector formed by the first 9 components; It is a 9-row, 1-column random number matrix, where each element is uniformly distributed between -1 and 1; The symbol for the Hadamarda complex; Then verify each one in turn. Does it meet the following constraints? ， in, Target formation configuration The specific value of the corresponding angular frequency vector; When verifying each one in turn If all the above constraints are met, then a global optimization algorithm such as a genetic algorithm is used, and the obtained result is used. As the initial set of solutions, solve the following about the variables. optimization problem Obtain the optimal solution ; Then in Temporarily replaced with Under the given conditions, determine the following constraints Constraint 1: , making Constraint 2: , making Does it meet the requirements? If not satisfied, then resolve the above problem regarding the variables. The optimization problem continues until the above constraints are satisfied; After satisfying the constraints, let As the adjusted number Target formation configuration The target formation configuration parameters.

8. The collision-free spatial parameterized formation configuration sequence planning method according to claim 7, characterized in that, The sequential verification of each Does it meet the following constraints? ， in: If the conditions are not met, then perform the following replacement. Get new ,in and They are respectively The corresponding principal and secondary half-axis vectors; then return to the above constraint check process, repeating this process until... Continue until the constraints are met.

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