A safe formation optimization method for multi-robot collaborative handling based on differential evolution

Abstract

A differential evolution-based method for optimizing safe formations for multi-robot collaborative handling is characterized by the following steps: 1. Establishing a three-dimensional coordinate system based on the bottom surface of a rectangular bracket carrying a large component, with the contact points between the mobile robots and the bracket serving as the support coordinates of the mobile robots; 2. Optimizing the number of robots in the formation based on the weight of the large component and the scheduling of various types of mobile robots; 3. Using a stability cone to represent the anti-tilting capability of the entire formation; 4. Establishing a safe formation optimization model for multi-robot collaborative handling using anti-tilting capability as the objective function; and 5. Optimizing the safe handling formation using a differential evolution algorithm. This invention aims to improve the safety of multi-robot collaborative handling while optimizing the scheduling of robot handling operations.

Description

Technical Field

[0001] The present invention relates to a robotics technology, in particular to a method for configuring a handling robot, specifically a method for optimizing a safe formation for collaborative handling of multiple robots based on differential evolution, which belongs to a method for designing a safe formation for collaborative handling of multiple robots. The goal is to improve the safety of collaborative handling of multiple robots from the perspective of formation design, while optimizing the scheduling of mobile robot handling operations. Background Art

[0002] When handling large components like long cylinders, columns, and large wing-shaped parts, a single mobile robot, limited by its load-bearing capacity and overall dimensions, cannot meet transportation requirements. Therefore, collaborative handling by multiple robots is necessary. When multiple robots collaborate to handle large, heavy components, factors such as inertia during cornering, asynchronous lifting, and uncoordinated steering can cause overloading during transport, creating the risk of tipping. To address these tipping issues, current approaches focus more on formation control rather than formation design to comprehensively improve the safety of multi-robot collaborative handling.

[0003] This invention optimizes the scheduling of mobile robot handling operations and schedules different types of mobile robots to collaboratively carry large components. It optimizes the formations of different types of mobile robots working together to carry heavy objects, aiming to improve the safety of multi-robot collaborative handling and optimize the scheduling of mobile robot handling operations. Summary of the Invention

[0004] The purpose of the present invention is to target the scenario of multi-robot collaborative transportation of large components. From the perspective of improving the anti-rollover ability of the formation and ensuring that large-sized and heavy-loaded large components are safely transported to the target location, a multi-robot collaborative transportation safety formation optimization method based on differential evolution is invented. The stability cone method is used to represent the anti-rollover ability of the stability cone according to the tilting angle of the large component along each side. The differential evolution algorithm is used to optimize the formation of multi-robot collaborative transportation in high-dimensional nonlinear space. It can more effectively explore continuous space, thereby showing higher solution efficiency when dealing with continuous optimization problems, quickly solving the optimal formation, and improving the safety of the multi-robot collaborative transportation process.

[0005] The technical solution of the present invention is:

[0006] A method for optimizing the safe formation of multi-robot collaborative handling based on differential evolution is characterized by: first, establishing a three-dimensional coordinate system based on the bottom surface of the bracket carrying the large component; selecting a minimum number of idle mobile robots of the same or different models based on the weight of the large component to be handled and the scheduling of various types of mobile robots; using a stability cone to represent the anti-rollover ability of the entire formation, and establishing a multi-robot collaborative handling safe formation optimization model with anti-rollover ability as the objective function; and using a differential evolution algorithm to achieve safe handling formation optimization.

[0007] The specific steps include:

[0008] Step 1: Establish a three-dimensional coordinate system based on the bottom surface of the bracket that carries the large component, and obtain the three-dimensional coordinates of the center of mass of the large component;

[0009] Step 2: Based on the weight of the large component and the scheduling of each mobile robot, optimize the scheduling of a minimum number n of idle mobile robots to ensure that the total safe load-bearing capacity of all mobile robots exceeds the weight of the large component and the bracket. Obtain information such as the dimensions of the n mobile robots and the floating radius of the floating platform, and establish a multi-robot collaborative handling model. The contact center between the mobile robot and the bracket is used as the support coordinate of the mobile robot, and the three-dimensional coordinates of each mobile robot's support point are obtained.

[0010] Step 3: Based on the definition of the stability cone, the coordinates of all mobile robot support points are obtained as the corner points of the stability cone. The coordinates of the center of mass of the large component are obtained as the vertex of the stability cone. The minimum angle required for the vertex to tilt along the bottom edges of the stability cone is calculated to measure the anti-tilting ability of the entire formation.

[0011] Step 4: Using the minimum tilting angle of the stability cone along each side of the bottom polygon as the evaluation index for the safe formation design of multi-robot collaborative handling, a formation optimization design model is established;

[0012] Step 5: Taking the horizontal and vertical coordinates of n mobile robots as unknown quantities, obtain the initial population through the improved initial population generation method and set the differential evolution algorithm parameters;

[0013] Step 6: Generate offspring population through improved crossover and mutation operations;

[0014] Step 7: Calculate the fitness of the offspring population generated by step 6 based on the objective function of the multi-robot collaborative handling safety formation optimization design. By comparing the fitness values ​​of the original population and the offspring population, select excellent individuals to join the next generation population. If the maximum number of iterations is reached, execute step 8; otherwise, execute step 6.

[0015] Step 8: According to the optimal fitness value, obtain the corresponding population individual value and map it into the coordinates of n mobile robots, that is, the optimal formation representation.

[0016] The beneficial effects of the present invention are:

[0017] This invention can quickly select the minimum number of mobile robots capable of safely lifting a large component based on its weight and the scheduling of each mobile robot. Based on the coordinates of the large component's center of mass, the coordinates of each mobile robot are adjusted using a differential evolution algorithm. This makes the stabilization cone formed by the large component's center of mass and the mobile robots more resistant to tipping, thereby improving the safety of multi-robot collaborative handling through formation design. It also optimizes the scheduling of robot handling operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and implementation examples.

[0020] like Figure 1 shown

[0021] A method for optimizing the safe formation of multi-robot collaborative handling based on differential evolution is proposed. First, a three-dimensional coordinate system is established based on the bottom surface of the bracket carrying the large component. Then, the minimum number of idle mobile robots (which may be of different models) is optimally scheduled according to the weight of the large component being handled and the scheduling status of various types of mobile robots. The anti-rollover capability of the entire formation is represented by a stability cone, and a multi-robot collaborative handling safe formation optimization model is established with the formation's anti-rollover capability as the objective function. Finally, a differential evolution algorithm is used to achieve safe formation optimization.

[0022] Figure 1 This is a flow chart of the present invention, which specifically includes the following steps:

[0023] Step 1: Establish a three-dimensional coordinate system based on the bottom surface of the bracket that carries the large component, and obtain the three-dimensional coordinates of the center of mass of the large component; that is, according to the bottom surface of the bracket that carries the large component in actual application, establish a three-dimensional coordinate system, with the center of the rectangular bottom surface as the coordinate origin, the bottom surface of the bracket as the XY plane, and the Z axis perpendicular to the XY plane through the origin to obtain the coordinates of the center of mass of the large component as (X p ,Y p ,Z p ).

[0024] Step 2: Based on the weight of the large component and the scheduling status of each mobile robot, optimize the scheduling of the minimum number n of idle mobile robots to ensure that the total safe load-bearing capacity of all mobile robots is greater than the weight of the large component and the bracket. Obtain information such as the size of the n mobile robots and the floating radius of the floating platform, establish a multi-robot collaborative handling model, and use the contact center between the mobile robot and the bracket as the support coordinate of the mobile robot to obtain the three-dimensional coordinates of the support point of each mobile robot; assume that there are k types of mobile robots, and the maximum safe load-bearing capacity of each mobile robot is G i , i=1,2,3,4...k, the size of each mobile robot is different, and the minimum circumscribed circle radius of each mobile robot is r i , i=1,2,3,4...k. The weight of the large component is G, and ni mobile robots of type i are selected so that and The value is the smallest. Assume that the total number of mobile robots is n, and the set of mobile robots that can collaboratively lift large components is M = {M1, M2, M3, ..., M n The position and type information of the mobile robots in the multi-robot collaborative transport team are expressed as formula (1). The position and size information of each mobile robot are represented by a four-dimensional vector:

[0025] M i =[X i ,Y i ,R i ,r i ] T (1)

[0026] In formula (1), X i ,Y i is the horizontal and vertical coordinates of the contact point between the i-th mobile robot and the large component, R i is the minimum circumscribed circle radius of the i-th mobile robot, r i is the floating radius of the floating platform of the i-th mobile robot.

[0027] Step 3: According to the definition of the stability cone, the coordinates of the support points of all mobile robots are obtained as the corner points of the stability cone, the coordinates of the center of mass of the large component are obtained as the vertex of the stability cone, and the minimum angle required for the vertex to tilt along the bottom edge of the stability cone is calculated to measure the anti-tilting ability of the entire formation; According to the definition of the stability cone, the coordinates of the support points of all mobile robots are used as the corner points A of the stability cone. i ,i=1,2,...,n, the coordinates of the centroid of the large component are used as the vertex P of the stable cone. The stable cone requires that the bottom polygon is a convex polygon. This patent uses the vector outer product to determine whether the angle between two vectors is non-obtuse. Through formulas (2) and (3), it is concluded that if any edge of the bottom polygon satisfies formula (4), the bottom polygon can be judged to be a convex polygon.

[0028]

[0029] (x i+1 -x i )(y i+2 -y i+1 )-(y i+1 -y i )(x i+2 -x i+1 )>0 (4)

[0030] Among them, A i is the i-th vertex of the bottom polygon, x i ,y i is the horizontal and vertical coordinates of the i-th vertex of the bottom polygon. The bottom polygon is represented by a vector, as shown in formula (5):

[0031]

[0032] Therefore, the vector passing through the vertex P and perpendicular to the tipping edge can be expressed by formula (6):

[0033]

[0034] in The angle at which the stability cone tilts along the edge can be determined by the centroid vector Perpendicular vector to the tipping edge The angle between the two is calculated as shown in formula (7):

[0035]

[0036] Step 4: The minimum tilting angle of the stabilizing cone along each side of the bottom polygon is used as the evaluation index for the design of the multi-robot collaborative handling safety formation, and a formation optimization design model is established; the tilting angles of the stabilizing cone along each side obtained in step 3 are used to find the minimum angle. The minimum tilting angle of the stabilizing cone is made as large as possible, indicating that the less likely the stabilizing cone is to tilt, that is, the stronger the anti-tilting ability of the multi-robot collaborative handling safety formation is. Therefore, the objective function is shown in formula (8):

[0037]

[0038] Step 5: Using the horizontal and vertical coordinates of n mobile robots as unknown quantities, an improved initial population generation method is used to obtain an initial population, and differential evolution algorithm parameters are set. Based on the minimum number of mobile robots n obtained in Step 2, the horizontal and vertical coordinates of each mobile robot are variable parameters, for a total of 2n variable parameters. The initial population is generated using the improved initial population generation method of the present invention. Specifically, horizontal and vertical coordinates are randomly generated for each mobile robot within the reach of the large component. If a position allocation scheme meets the conditions, this position allocation scheme is used as an individual in the initial population. Two mobile robots are selected to exchange their coordinates. If the conditions are met, they are added to the initial population. Generating the initial population based on this concept can significantly reduce the time spent on initial population generation. Before the algorithm begins, the algorithm parameters are set as follows: population size NP = 100, mutation operator α = 0.09, crossover operator CR = 0.6, and maximum evolutionary generation number GEN = 200.

[0039] Step 6: Generate the offspring population through the improved crossover and mutation operations; perform mutation operations on the parent population. For each individual in the population, randomly select three different individuals from the population, calculate their difference vectors, and then linearly combine the difference vectors with the current population individuals to obtain new individuals. The calculation method of the mutant individuals is shown in formula (9):

[0040] Q=P i +α(P j -P k ) (9)

[0041] Among them, P i ,P j ,P k are three random individuals in the current population, and α is the mutation operator;

[0042] Then, a value is randomly generated in the range of (0, 1). When the value is less than the value of the crossover operator CR, the mutant individual is selected and the current individual is crossovered to form a new individual, as shown in formula (10):

[0043]

[0044] Step 7: Calculate the fitness of the offspring population generated by step 6 according to the objective function of the multi-robot collaborative handling safety formation optimization design. By comparing the fitness values ​​of the original population and the offspring population, select excellent individuals to join the next generation population. If the maximum number of iterations is reached, execute step 8, otherwise execute step 6. For the offspring population generated in step 6, calculate the fitness value of each individual according to the objective function. For the population individual corresponding to the maximum fitness value, copy S copies and add them to the new population. The remaining NP-S population individuals are generated by roulette, that is, the new population is generated by combining the elite retention strategy and the roulette algorithm. At the same time, record the optimal fitness value and average fitness value of each generation population.

[0045] Step 8: Based on the optimal fitness value, obtain the corresponding population individual value and map it into the coordinates of n mobile robots, which is the optimal formation representation. Decode the population individual corresponding to the highest fitness value obtained in step 7 and map it into the coordinates of n mobile robots to obtain the optimal formation.

[0046] The parts not involved in the present invention are the same as the existing technology or can be implemented by using the existing technology.

Claims

1. A method for optimizing the safe formation of multi-robot collaborative handling based on differential evolution, characterized by: First, a three-dimensional coordinate system is established based on the bottom surface of the bracket carrying the large component. Based on the weight of the large component being transported and the scheduling status of various types of mobile robots, a minimum number of idle mobile robots of the same or different models are selected. The anti-rollover capability of the entire formation is represented by a stability cone, and a multi-robot collaborative transport safety formation optimization model is established with anti-rollover capability as the objective function. The differential evolution algorithm is used to optimize the safe transport formation. The steps are as follows: Step 1: Establish a three-dimensional coordinate system based on the bottom surface of the bracket that carries the large component, and obtain the three-dimensional coordinates of the center of mass of the large component; Step 2: Based on the weight of the large component and the scheduling status of each mobile robot, optimize the scheduling of a minimum number n of idle mobile robots to ensure that the total safe load-bearing capacity of all mobile robots is greater than the weight of the large component and the bracket. Obtain the dimensions of the n mobile robots and the floating radius of the floating platform, establish a multi-robot collaborative handling model, and use the contact center between the mobile robot and the bracket as the support coordinate of the mobile robot to obtain the three-dimensional coordinates of each mobile robot's support point. Step 3: Based on the definition of the stability cone, the coordinates of all mobile robot support points are obtained as the corner points of the stability cone. The coordinates of the center of mass of the large component are obtained as the vertex of the stability cone. The minimum angle required for the vertex to tilt along the bottom edges of the stability cone is calculated to measure the anti-tilting ability of the entire formation. Step 4: Using the minimum tilting angle of the stability cone along each side of the bottom polygon as the evaluation index for the safe formation design of multi-robot collaborative handling, a formation optimization design model is established; Step 5: Taking the horizontal and vertical coordinates of n mobile robots as unknown quantities, obtain the initial population through the improved initial population generation method and set the differential evolution algorithm parameters; Step 6: Generate offspring population through improved crossover and mutation operations; Step 7: Calculate the fitness of the offspring population generated by step 6 based on the objective function of the multi-robot collaborative handling safety formation optimization design. By comparing the fitness values ​​of the original population and the offspring population, select excellent individuals to join the next generation population. If the maximum number of iterations is reached, execute step 8; otherwise, execute step 6. Step 8: According to the optimal fitness value, obtain the corresponding population individual value and map it into the coordinates of n mobile robots, that is, the optimal formation representation.

2. The method according to claim 1, characterized in that In step 1: According to the bottom surface of the bracket that carries large components in actual applications, the three-dimensional coordinate system is established with the center of the rectangular bottom surface as the coordinate origin, the bottom surface of the bracket is the XY plane, and the Z axis perpendicular to the XY plane through the origin is the coordinate center of the large component (X p ,Y p ,Z p ).

3. The method according to claim 1, characterized in that In step 2: Assume that there are k types of mobile robots, and the maximum safe load of each mobile robot is G i , i=1,2,3,4...k, the size of each mobile robot is different, and the minimum circumscribed circle radius of each mobile robot is r i , i=1,2,3,4...k; the weight of the large component is G, select n respectively i The i-th type mobile robot makes and The value is the smallest. Assume that the total number of mobile robots is n, and the set of mobile robots that can collaboratively lift large components is M = {M1, M2, M3, ..., M n The position and type information of the mobile robots in the multi-robot collaborative transport team are expressed as formula (1); the position and size information of each mobile robot are expressed by a four-dimensional vector: M i＝ [X i ,Y i ,R i ,r i ] T (1) In formula (1), X i ,Y i is the horizontal and vertical coordinates of the contact point between the i-th mobile robot and the large component, R i is the minimum circumscribed circle radius of the i-th mobile robot, r i is the floating radius of the floating platform of the i-th mobile robot.

4. The method according to claim 1, wherein In step 3: According to the definition of the stability cone, the coordinates of all mobile robot support points are taken as the corner points A of the stability cone. i ,i=1,2,...,n, the coordinates of the centroid of the large component are used as the vertex P of the stable cone; the stable cone requires that the bottom polygon is a convex polygon, and the vector outer product is used to determine whether the angle between the two vectors is a non-obtuse angle. According to formulas (2) and (3), if any edge of the bottom polygon satisfies formula (4), then the bottom polygon can be judged to be a convex polygon; (x i+1 -x i )(and i+2 -and i+1 )-(and i+1 -and i )(x i+2 -x i+1 )>0 (4) Among them, A i is the i-th vertex of the bottom polygon, x i ,y i is the horizontal and vertical coordinates of the i-th vertex of the bottom polygon; the bottom polygon is represented by a vector, as shown in formula (5): Therefore, the vector passing through the vertex P and perpendicular to the tipping edge is expressed by formula (6): in The angle at which the stability cone tilts along the edge is determined by the center of gravity vector Perpendicular vector to the tipping edge The angle between the two is calculated as shown in formula (7):

5. The method according to claim 1, wherein In step 4: The minimum angle is found from the tilting angles of the stabilizing cone along each edge obtained in step 3. The minimum tilting angle of the stabilizing cone is maximized. The less likely the stabilizing cone is to tilt, the stronger the anti-tilting ability of the multi-robot collaborative handling safety formation is. Therefore, the objective function is shown in formula (8):

6. The method according to claim 1, characterized in that In step 5: According to the minimum number n of mobile robots obtained in step 2, the horizontal and vertical coordinates of each mobile robot are variable parameters, with a total of 2n variable parameters. The initial population is generated through an improved first-generation population generation method. Mainly, the horizontal and vertical coordinates are randomly generated for each mobile robot within the contact range of large components. If the conditions are met, this position allocation scheme is used as an individual in the initial population. At the same time, two mobile robots are selected to exchange their coordinates. If the conditions are met, they are added to the initial population. Generating the initial population according to this idea can greatly reduce the time spent on initial population generation; set the algorithm parameters before the algorithm starts: population size NP = 100, mutation operator α = 0.09, crossover operator CR = 0.6, maximum evolutionary generation GEN = 200.

7. The method according to claim 1, characterized in that In step 6: Perform mutation operation on the parent population. For each individual in the population, randomly select three different individuals from the population, calculate their difference vectors, and then linearly combine the difference vectors with the current population individuals to obtain new individuals. The calculation method of the mutant individuals is shown in formula (9): Q=P i +α(P j -P k ) (9) Among them, P i ,P j ,P k are three random individuals in the current population, and α is the mutation operator; Then, a value is randomly generated in the range of (0, 1). When the value is less than the value of the crossover operator CR, the mutant individual is selected and the current individual is crossovered to form a new individual, as shown in formula (10):

8. The method according to claim 1, characterized in that In step 7: For the offspring population generated in step 6, the fitness value of each individual is calculated according to the objective function. For the population individual corresponding to the maximum fitness value, S copies are added to the new population. The remaining NP-S population individuals are generated by roulette, that is, the elite retention strategy and the roulette algorithm are combined to generate a new population; at the same time, the optimal fitness value and average fitness value of each generation of the population are recorded.

9. The method according to claim 1, characterized in that In step 8: The population individuals corresponding to the best fitness values ​​obtained in step 7 are decoded and mapped into the coordinates of n mobile robots to obtain the optimal formation.

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