Multi-robot pattern formation method based on multi-parameter assignment model

Abstract

The application discloses a multi-robot pattern formation method based on a multi-parameter distribution model, and aims at minimizing the square sum of the distance from a robot to a target point under the constraint condition of an obstacle environment, introduces a scale parameter, a translation parameter and a rotation parameter of an expected graph, constructs a matching model of a target point of the expected graph and the robot, converts the matching model into a relaxation problem by using a space branch and bound algorithm, solves an optimal solution of the matching model, determines an optimal distribution matrix between the robot and the target point according to the optimal solution of the matching model, and plans a collision-free motion path of the robot by using a biological heuristic neural network algorithm. The application has the advantages that the scale parameter, the translation parameter and the rotation parameter of the expected graph are introduced when solving the optimal expected pattern of the multi-robot in the obstacle environment, the biological heuristic neural network algorithm is used to plan the path of the robot, the real-time performance is good, and the robot can simultaneously avoid obstacles and escape from a dead zone.

Description

Technical Field

[0001] This invention relates to the field of robot applications, and in particular to a method for constructing multi-robot patterns based on a multi-parameter allocation model. Background Technology

[0002] With the development of wireless communication technology, embedded technology, artificial intelligence, computer technology and materials science and many other fields, the manufacturing cost of robots is getting lower and lower. Compared with manufacturing a single robot with complex functions, manufacturing multiple simpler robots is cheaper and has better robustness and stability. They can better adapt to various complex working environments. Multi-robot systems have been widely used in many fields such as industrial manufacturing, transportation, medical rehabilitation, aerospace and defense, which has promoted the research of multi-robot systems to a certain extent.

[0003] Current research on multi-robot systems faces many challenges, such as aggregation, pattern formation, and self-scheduling. Pattern formation involves changing the position of each robot in a group according to predefined rules to form a specific shape. Pattern formation and coordinated movement are of significant research importance and can be applied to many complex scenarios. They have crucial applications in pathfinding, area coverage, and target search in aerospace, military, disaster relief, and other fields, and can also be used in commercial performances, drone shows, and multi-robot dances, becoming highlights in many major events.

[0004] However, most current multi-robot pattern formation methods are based on ideal, obstacle-free environments, which cannot effectively address issues such as optimizing desired patterns in obstacle-prone environments, real-time collision avoidance, and the inability to effectively identify desired patterns when their positions are poor. Patent publication number CN111766784A proposes an iterative optimization method for multi-robot pattern formation in obstacle-prone environments, but this method only fails to effectively identify desired patterns when their positions are poor, and its consideration of translation and scaling parameters alone cannot minimize the robot's path to the target point. Furthermore, the obstacle avoidance algorithm used cannot effectively avoid obstacles in scenarios where multiple robots may collide, causing robot shaking. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing multi-robot patterns based on a multi-parameter allocation model, which can optimize the target pattern according to the robot's initial position and the desired pattern position.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The multi-robot pattern construction method based on a multi-parameter allocation model described in this invention aims to minimize the sum of squared distances from the robot to the target point under the constraints of an obstacle environment. It introduces scaling parameters, translation parameters, and rotation parameters of the initial desired graphic to construct a matching model between the target point and the robot. A spatial branch and bound algorithm is used to transform the matching model into a relaxation problem, and the optimal solution is obtained. Based on the optimal solution, the optimal allocation matrix between the robot and the target point is determined. Finally, a bio-inspired neural network algorithm is used to plan a collision-free motion path for the robot.

[0008] Furthermore, the matching model is

[0009] ,

[0010] in, For proportional parameters, For translation parameters, For rotation parameters, for The assignment matrix; n is the number of robots or target points; This represents the position of the i-th robot; Represents the j-th target point Location;

[0011] The ;

[0012] The .

[0013] Furthermore, the rotation parameters The The angle difference between the desired shape after rotation and the initial desired shape.

[0014] Furthermore, the matching model is transformed into the optimal solution of the relaxation problem using a spatial branch and bound algorithm. Specifically, this includes: when the optimal solution of the relaxation problem of the matching model satisfies the constraints of the obstacle environment, the optimal solution of the relaxation problem is the optimal solution of the matching model; otherwise, the optimal solution of the relaxation problem is used as the upper bound of the matching model solution, and the entire feasible solution space of the matching model is repeatedly divided into several subsets. The minimum value of the matching model in each subset is used as the lower bound of the matching model solution. This process is repeated iteratively to continuously reduce the upper bound and the lower bound of the matching model solution until the minimum value of the matching model in all subsets is greater than the lower bound of the matching model solution, thus obtaining the optimal solution of the matching model.

[0015] Furthermore, planning collision-free motion paths for robots using bio-inspired neural network algorithms includes: establishing a grid map and dividing the robot's movement area into... For each of the three grid cells with the same area, the neuron activity value of each cell is calculated and propagated in the grid map. An activation function is constructed based on the neuron activity value of the cell at the robot's current position and the robot's previous position. The cell with the largest activation function is taken as the robot's next position. This process is repeated iteratively until all robots reach the target point.

[0016] The advantages of this invention are that, in obstacle-prone environments, when solving for the optimal desired pattern of multiple robots, it introduces the scaling parameters, translation parameters, and rotation parameters of the desired pattern, and uses a bio-inspired neural network algorithm to perform path planning for the robots, which has good real-time performance and can simultaneously avoid obstacles and escape dead zones. Attached Figure Description

[0017] Figure 1 This is a flowchart of the process for finding the optimal solution of the matching model as described in this invention.

[0018] Figure 2 This is a flowchart of the collision-free motion path planning for the robot described in this invention. Detailed Implementation

[0019] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] like Figure 1 and Figure 2 As shown, the multi-robot pattern construction method based on a multi-parameter allocation model of the present invention, under the constraint of an obstacle environment, aims to minimize the sum of squared distances from the robot to the target point. It introduces the scaling parameters, translation parameters, and rotation parameters of the initial desired graphic to construct a matching model between the target point of the desired graphic and the robot. The matching model is transformed into a relaxation problem using a spatial branch and bound algorithm. The optimal solution of the matching model is solved, and the optimal allocation matrix between the robot and the target point is determined based on the optimal solution of the matching model. Finally, a bio-inspired neural network algorithm is used to plan the collision-free motion path of the robot.

[0021] First, in an obstacle environment, let the obstacle's position be denoted as... Initially, the robot's position is recorded as follows: The target point in the desired figure is denoted as Since obstacles affect the formation of the desired pattern, determining the optimal allocation matrix between the robot and the target point is crucial. When doing so, it is necessary to establish constraints on the obstacle environment, specifically including three constraints:

[0022] (1) The desired graphic should be located in the application area, i.e.

[0023] Formula (1)

[0024] in, These are the minimum and maximum boundary values ​​along the X-axis of the given region, respectively. Let be the minimum and maximum boundary values ​​along the Y-axis of the given region, and let r be the radius of the robot. For the j-th target point x-axis position, For the j-th target point The y-axis position.

[0025] This application introduces a scaling parameter for the desired graphic. Translation parameters and rotation parameters Therefore, the j-th target point Location Expressed as a formula:

[0026] Formula (2)

[0027] Among them, rotation parameters The The angle difference between the desired shape after rotation and the initial desired shape.

[0028] Translation parameters ,in, The translation parameter representing the x-axis, This is the translation parameter for the y-axis.

[0029] Then the above formula (1) is equivalent to

[0030] Formula (3)

[0031] (2) The desired shape should not be inside the obstacle, i.e.

[0032] Formula (4)

[0033] in, Represents the j-th target point Location, Represents the m-th obstacle Location, Let be the radius of the obstacle.

[0034] (3) The distance between all target points in the desired graphic is greater than twice the robot radius, i.e.

[0035] Formula (5)

[0036] in, Represents the i-th target point Location, Represents the j-th target point The location.

[0037] Secondly, with the objective of minimizing the sum of squared distances from the robot to the target point, a scaling parameter for the initial desired shape is introduced. Translation parameters and rotation parameters Establish a matching model between the target point of the desired graphic and the robot, as shown in the following formula (6).

[0038] Formula (6)

[0039] in

[0040] Formula (7)

[0041] Formula (8)

[0042] Formula (9)

[0043] Introducing the scaling parameter of the desired graphic Translation parameters and rotation parameters After that, the j-th target point Location Expressed as formula (2), substituting formula (2) and formula (9) into formula (6), we obtain the matching model as follows:

[0044] Formula (10),

[0045] in, For proportional parameters, For translation parameters, For rotation parameters, for The assignment matrix; n is the number of robots or target points; This represents the position of the i-th robot; Represents the j-th target point The location.

[0046] According to formula (10), the matching problem between the target point of the desired graphic and the robot can be transformed into a hybrid nonlinear programming problem. The constraints (formulas (3), (4), and (5)) are nonconvex, so the spatial branch and bound algorithm can be used to solve the model. That is, the matching model is transformed into the corresponding relaxation problem, and then the optimal solution of the relaxation problem is solved. If the optimal solution of the relaxation problem meets the constraints of the obstacle environment, that is, formulas (3), (4), and (5), the optimal solution of the relaxation problem is the optimal solution of the matching model. Conversely, the optimal solution of the relaxation problem is used as the upper bound of the matching model solution. The entire feasible solution space of the matching model is repeatedly divided into several subsets, and the minimum value of the matching model in the subset is used as the lower bound of the matching model solution. The process is repeated iteratively to continuously reduce the upper bound and the lower bound of the matching model solution until the minimum value of the matching model in all subsets is greater than the lower bound of the matching model solution, thus obtaining the optimal solution of the matching model.

[0047] The optimal allocation matrix between the robot and the target point can be determined based on the optimal solution of the matching model. The goal is for the robot to move to the target point without collision. This invention uses a bio-inspired neural network algorithm to plan the robot's collision-free movement path.

[0048] First, without considering collisions between obstacles and other robots, a grid map is created, dividing the robot's movement area into... A raster map with grid cells of equal area. Calculate the neuron activity value of each cell on the raster map using the following formula:

[0049] Formula (11)

[0050] in, is the neuron activity value of the i-th grid; A, B, and D are non-negative constants, representing the decay rate of the neuron activity value, the upper and lower limits of the neuron activity value, respectively; k is the number of grid neurons in the neighborhood (adjacent to the i-th grid). The connection weights between neurons i and j; is the neuron activity value of the j-th adjacent grid. Let E and F be the external stimulation signal for the i-th neuron, where E and F are constants. .

[0051] Formula (12)

[0052] in, The stimulation signal for the grid neurons. This is the inhibitory signal for grid neurons.

[0053] make

[0054] ,and If it is a monotonically decreasing function, then

[0055] Formula (13)

[0056] in, , for the first The first neuron to the second The Euclidean distance between neurons. u is a positive constant, and the nonlinear threshold function is used. This ensures that the grid activity value of the assigned target point can be propagated throughout the entire grid map.

[0057] Further, based on the neuron activity values ​​of the grid at the robot's current position and the robot's previous position, an activation function is constructed, as follows:

[0058] Formula (14)

[0059] in, It is a constant. , Let the robot j be the current direction angle of movement. and future movement direction angle The difference.

[0060]

[0061] in, Let x and y be the x and y coordinates of the grid cell where robot j is located at the previous, current, and next time steps, respectively.

[0062] The robot always moves towards the grid cell with the highest activity value of its current grid neurons, which is calculated according to formula (14). The grid corresponding to the value.

[0063] After each robot moves one step, the activity values ​​of the grid neurons in the neighborhood of each robot's grid map are recalculated. value, and continue towards the maximum. Move the grid corresponding to the value. Repeat the iteration until all robots reach the target point.

Claims

1. A multi-robot pattern formation method based on a multi-parameter assignment model, characterized by: Under the constraints of an obstacle-prone environment, with the goal of minimizing the sum of squared distances from the robot to the target point, a matching model between the target point of the desired graphic and the robot is constructed by introducing the scaling parameters, translation parameters, and rotation parameters of the desired graphic. The matching model is then transformed into a relaxation problem using a spatial branch and bound algorithm. The optimal solution of the matching model is then solved, and the optimal allocation matrix between the robot and the target point is determined based on the optimal solution of the matching model. Finally, a bio-inspired neural network algorithm is used to plan the collision-free motion path of the robot. The matching model is as follows: in, For proportional parameters, For translation parameters, For rotation parameters, for The assignment matrix; n is the number of robots or target points; This represents the position of the i-th robot; Represents the j-th target point Location; The ; The ; the rotation parameter , the is the angle difference between the rotated desired pattern and the original desired pattern. 2.The multi-robot pattern formation method based on a multi-parameter assignment model according to claim 1, wherein: The matching model is transformed into an optimal solution for a relaxation problem using a spatial branch and bound algorithm. Specifically, this involves: when the optimal solution of the relaxation problem satisfies the constraints of the obstacle environment, the optimal solution of the relaxation problem is the optimal solution of the matching model; otherwise, the optimal solution of the relaxation problem is used as the upper bound of the matching model solution, and the entire feasible solution space of the matching model is repeatedly divided into several subsets. The minimum value of the matching model within each subset is used as the lower bound of the matching model solution. This process is repeated iteratively to continuously reduce the upper bound and the lower bound of the matching model solution until the minimum value of the matching model within all subsets is greater than the lower bound of the matching model solution, thus obtaining the optimal solution of the matching model.

3. The multi-robot pattern construction method based on a multi-parameter allocation model according to claim 1, characterized in that: Planning collision-free motion paths for robots using bio-inspired neural network algorithms includes: creating a grid map and dividing the robot's movement area into... without considering obstacles or collisions with other robots. For each of the three grid cells with the same area, the neuron activity value of each cell is calculated and propagated in the grid map. An activation function is constructed based on the neuron activity value of the cell at the robot's current position and the robot's previous position. The cell corresponding to the maximum value of the activation function is taken as the robot's next position. This process is repeated iteratively until all robots reach the target point.

Images