Large heavy-load double-robot leveling system multi-target trajectory planning method based on novel intelligent optimization algorithm

Abstract

The invention discloses a large-scale heavy-load double-robot leveling system multi-target trajectory planning method based on a novel intelligent optimization algorithm. The method comprises the following steps: 1) constructing a leveling trajectory of a workpiece by using a quintic B-spline curve; 2) constructing a trajectory optimization model of the workpiece; and 3) solving the trajectory optimization model to obtain a group of optimal solution sets. And 4) evaluating the optimal solution set by using a comprehensive evaluation method to obtain a movement track with optimal impact and time average in the leveling process. By changing the distance between the two parallel robots, the leveling requirements of workpieces of different sizes can be met.

Description

Technical Field

[0001] The present invention relates to the field of leveling system trajectory planning, and specifically to a multi-objective trajectory planning method for a large-scale heavy-load dual-robot leveling system based on a novel intelligent optimization algorithm. Background Art

[0002] For large-scale leveling platforms, especially those with a load of dozens of tons or even hundreds of tons, the span may exceed ten meters, and usually a six-point or multi-point support method is adopted to enhance the platform rigidity and reduce deformation. However, with the increase in the number of legs, the traditional connection method with the legs perpendicular to the platform will lead to an increase in the number of static indeterminacies. The existence of static indeterminacy makes it difficult to clearly distinguish in actual operation which of the various support rods are the actual legs bearing the load and which are the virtual legs not participating in load transfer. In addition, the lack of motion coordination between the support rods and the significant coupling phenomenon result in the fact that the multi-point adjustment technology that should work in coordination actually degrades to single-point adjustment, thus limiting the efficiency and accuracy of the leveling process. Further, due to the limitation of the support structure, an accurate control mathematical model cannot be established, which makes a series of advanced control strategies difficult to be applied in the leveling process. The existence of these problems not only affects the rapidity of the leveling operation but also limits the accuracy of the leveling system. In view of the limitations of the traditional support structure, some scholars have proposed using a six-degree-of-freedom parallel mechanism as the support structure of the automatic leveling system, successfully solving the above problems. However, in the leveling process, usually only the movement of three degrees of freedom is required to achieve the horizontal adjustment of the workpiece. Compared with the former, the parallel mechanism with fewer degrees of freedom is a more ideal choice for the leveling mechanism due to its simple structure, high operating efficiency, and easy maintenance. In addition, the existing leveling systems usually only apply to equipment of specific sizes and cannot meet the requirements of leveling workpieces of different sizes.

[0003] To sum up, in the coordinated leveling operation of dual robots, the main goal is to adjust the postures of the two leveling mechanisms according to the feedback information of the inclination sensors to achieve the adjustment of the workpiece to be detected from a non-horizontal state to a horizontal state. However, the existing leveling methods do not comprehensively consider the requirements of large-scale heavy-load workpieces for smoothness and efficiency. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-objective trajectory planning method for a large-scale heavy-load dual-robot leveling system based on a novel intelligent optimization algorithm, including the following steps:

[0005] 1) Construct the leveling trajectory of the workpiece using a fifth-degree B-spline curve;

[0006] 2) Construct the trajectory optimization model of the workpiece;

[0007] 3) Solve the trajectory optimization model to obtain a set of optimal solution sets.

[0008] 4) Evaluate the optimal solution set using the comprehensive evaluation method to obtain the motion trajectory that is optimal in terms of impact and time average during the leveling process; the motion trajectory includes the spatial motion trajectory of the workpiece and the motion trajectories of each leveling support leg.

[0009] Furthermore, the quintic B-spline curve is defined by a set of control point sets and time node increments

[0010] {Δt1, Δt2, Δt3, Δt4, Δt5, Δt6, Δt7, Δt8,..., Δt M-5}}.

[0011] Furthermore, the steps of constructing the leveling trajectory of the workpiece using the quintic B-spline curve include:

[0012] 1.1) Select the number of control points as M, and define the three-dimensional generalized coordinates of the i-th control point as That is:

[0013]

[0014] 1.2) Based on the quintic clamped B-spline curve, construct the leveling trajectory expression, that is:

[0015]

[0016] In the formula, (P z (t), P α (t), P β (t)) are the leveling trajectory coordinates;

[0017] Among them, the basis function N i,5 (t) is as follows:

[0018]

[0019] In the formula, k = 1, 2, 3, 4, 5;

[0020] 1.3) Use the 0th control point of the B-spline curve as the initial pose of the leveling trajectory, and the last control point as the target pose of the leveling trajectory, that is:

[0021]

[0022] In the formula, P ini = [P iniz , P iniα , P iniβ is the initial pose of the leveling trajectory;

[0023] P fin = [P finz , P finα , P finβis the target pose of the leveling trajectory;

[0024] 1.4) Set the generalized coordinates and initial poses of the first three control points to be equal, and the generalized coordinates and target poses of the last three control points to be equal, i.e.:

[0025]

[0026] 1.5) Use the interval ratio mapping method to determine the coordinates of the i-th control point, i.e.:

[0027]

[0028] where w n is a randomly generated control point parameter; D i is an intermediate parameter;

[0029] 1.6) Generate the leveling trajectory based on equation (5) - equation (7).

[0030] Furthermore, the trajectory optimization model F(x) of the workpiece is as follows:

[0031]

[0032] where f1(x) is the impact during the leveling process, f2(x) is the total time of leveling, T represents the total time of the leveling motion, J i represents the jerk of the i-th driving joint, Δl i represents the telescopic amount of the i-th leg driving joint; Δl + and Δl - represent the maximum allowable telescopic range of the screw lift, Δl + > 0, Δl - < 0, v li and a li respectively represent the real-time speed and acceleration of the i-th leg driving joint; ν max and a max respectively represent the maximum allowable speed and maximum allowable acceleration of the leg driving joint, τ i represents the driving force of the i-th leg driving joint; τ max represents the maximum limit value of the driving force. Δt i represents the time step.

[0033] Furthermore, the steps for solving the trajectory optimization model include:

[0034] 3.1) Population initialization: Set the multi-objective optimization function and boundary conditions according to the trajectory optimization model, realize the recognition of antigens, and randomly generate p antibodies according to real number coding to form the initial antibody population P 1 , calculate P 1For the objective function value of each initial antibody, perform non-dominated sorting and crowding distance evaluation on the antibodies, and store the first-generation non-dominated antibodies in the mature cell set P Y 1 and the memory cell set, and store the remaining antibodies in the immature cell set to complete the initialization of the population, and set the maximum number of iterations N max ;

[0035] 3.2) Constraint condition judgment: Judge whether each antibody in the i-th generation antibody population P i meets the constraint conditions of the workpiece trajectory optimization model. If not, it will be punished and eliminated;

[0036] 3.3) Antibody population cloning: The antibodies in the mature cell set are cloned to form a population The cloning ratio is dynamically adjusted according to the crowding degree;

[0037] 3.4) Antibody population crossover: Group the antibody population in pairs, and perform crossover operations on each pair of antibodies using the two-point crossover method to obtain the antibody population

[0038] 3.5) Antibody population mutation: Perform adaptive mutation operations on the antibodies in to obtain the antibody population

[0039] 3.6) According to the linear decreasing extinction strategy, eliminate d antibodies in the immature cell set, and then randomly generate d new antibodies to replace them to form a new antibody set

[0040] 3.7) Antibody population update: Combine the antibody population and to generate the next generation antibody population P i+1 ;

[0041] 3.8) Mature cell set update: Perform fast non-dominated sorting and crowding distance evaluation on the (i + 1)-th generation antibody population P i+1 to select θ optimal antibodies and store them in the mature cell set The remaining antibodies are stored in the immature cell set;

[0042] 3.9) Memory cell set update: Copy the non-dominated solutions in P i+1 to the memory cell set, perform fast non-dominated sorting and crowding distance evaluation on the antibodies in the memory cell set, and delete the dominated antibodies and duplicate antibodies;

[0043] 3.10) Iterative condition determination: Determine whether it is the maximum number of iterations. If so, terminate the iteration and output the current set of memory cells; otherwise, jump to step 3.2) to continue the iteration.

[0044] Furthermore, the steps for non - dominated sorting of antibodies include:

[0045] 4.1) Assign two parameters \(G\) m and \(G\) n to each antibody \(x\) in the population. The value of \(G\) m represents the set of antibodies dominated by \(x\), and the value of \(G\) n represents the set of antibodies that dominate \(x\). Initialize the counter \(i\) to 1.

[0046] 4.2) Find all antibodies in the population that are not dominated by other antibodies, that is, antibodies with \(G\) n equal to 0, put them into set \(A\), and assign these antibodies a sorting value of 1.

[0047] 4.3) Check the \(G\) m set of each antibody in set \(A\). For each antibody in \(G\) m , decrement its \(G\) n by 1; if the \(G\) n value of any individual becomes 0, add it to set \(B\).

[0048] 4.4) Update the counter \(i\) to \(i + 1\), copy the individuals in set \(B\) to \(A\), and empty \(B\). Set the sorting value of these individuals to \(i + 1\).

[0049] 4.5) Determine whether set \(A\) is empty. If not, return to step 4.3); if so, the sorting process ends.

[0050] Furthermore, the crowding distance of the boundary solutions is twice the maximum crowding distance among all non - boundary solutions in the population;

[0051] The crowding distance \(c\) i of non - boundary solutions is as follows:

[0052]

[0053] In the formula, \(f\) j (x i+1 ) and \(f\) j (x i-1 ) represent the objective function values of two individuals adjacent to antibody \(i\); \(f\) j (x) max and \(f\) j (x) min represent the maximum and minimum values of objective function \(j\) respectively; \(b\) is the number of objective functions.

[0054] Furthermore, the cloning ratio \(\mu\)i As follows:

[0055]

[0056] Where: p is the number of initialized antibodies; c i represents the crowding distance of antibody x i ; represents the sum of the crowding distances of all antibodies to be cloned; round represents rounding.

[0057] Furthermore, the adaptive mutation operation is as follows:

[0058]

[0059] Where: N is the current iteration number; N max is the maximum iteration number; ε is the mutation factor, satisfying ε > 1, and the mutation range is proportional to the size of ε; x max and x min represent the upper and lower limit values of the decision variable respectively; δ up and δ lo represent the upper and lower limit values of the mutation respectively. λ is an intermediate parameter; Δx is the mutation step size; x is the decision variable.

[0060] The linear decreasing extinction strategy is as follows:

[0061]

[0062] Where: ξ is a constant and satisfies 0 < ξ < 1; d is the number of linear decreasing extinctions.

[0063] Furthermore, the optimal motion trajectory minF of the impact and time average during the leveling process * is as follows:

[0064]

[0065] Where, f i (x) represents the value of the i-th sub-objective function of the Pareto optimal solution; f i (x) max and f i (x) min represent the maximum and minimum values of the i-th sub-objective function in the Pareto optimal solution set respectively; ω i is the weight coefficient.

[0066] The technical effects of the present invention are beyond doubt. The present invention proposes a design scheme for a dual-robot leveling system. Each robot is a three-degree-of-freedom parallel mechanism, and by changing the distance between the two parallel robots, it can meet the leveling requirements of workpieces of different sizes. The present invention uses a multi-objective trajectory planning method to obtain a leveling trajectory that is optimal in terms of impact and time average.

[0067] Based on the traditional immune clonal selection algorithm, the present invention introduces an improved strategy to obtain a new type of intelligent optimization algorithm, so as to enhance the global search ability of the algorithm, accelerate the convergence process, and improve the quality of the solution set. Brief Description of the Drawings

[0068] Figure 1 It is a flow chart of a new type of intelligent optimization algorithm

[0069] Figure 2 It is the Pareto front optimized by the new type of intelligent optimization algorithm

[0070] Figure 3 It is the Pareto front optimized by the traditional immune clonal selection algorithm

[0071] Figure 4 It is the displacement trajectory of each leveling leg that is average optimal

[0072] Figure 5 It is the velocity trajectory of each leveling leg that is average optimal

[0073] Figure 6 It is the acceleration trajectory of each leveling leg that is average optimal

[0074] Figure 7 It is the jerk trajectory of each leveling leg that is average optimal

[0075] Figure 8 It is a dual-robot leveling system

[0076] Figure 9 It is a schematic diagram of a single leveling robot mechanism. Detailed Embodiments

[0077] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject scope of the present invention is limited to the following embodiments. Without departing from the above-mentioned technical idea of the present invention, various substitutions and changes made according to the common general knowledge and customary means in the art should be included within the protection scope of the present invention.

[0078] Embodiment 1:

[0079] See Figures 1 to 9 , a multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new type of intelligent optimization algorithm, including the following steps:

[0080] 1) Construct the leveling trajectory of the workpiece using a quintic B-spline curve;

[0081] 2) Construct the trajectory optimization model of the workpiece;

[0082] 3) Solve the trajectory optimization model to obtain a set of optimal solution sets.

[0083] 4) Evaluate the optimal solution set using the comprehensive evaluation method to obtain the motion trajectory with the optimal impact and time average during the leveling process; the motion trajectory includes the spatial motion trajectory of the workpiece and the motion trajectories of each leveling leg.

[0084] The quintic B-spline curve is defined by a set of control point sets and the time node increments

[0085] {Δt1, Δt2, Δt3, Δt4, Δt5, Δt6, Δt7, Δt8,..., Δt M-5}.

[0086] The steps of constructing the leveling trajectory of the workpiece using the quintic B-spline curve include:

[0087] 1.1) Select the number of control points as M, and define the three-dimensional generalized coordinates of the i-th control point as That is:

[0088]

[0089] 1.2) Based on the quintic clamped B-spline curve, construct the leveling trajectory expression, that is:

[0090]

[0091] In the formula, (P z (t), P α (t), P β (t)) are the leveling trajectory coordinates;

[0092] Among them, the basis function N i,5 (t) is as follows:

[0093]

[0094] In the formula, k = 1, 2, 3, 4, 5;

[0095] 1.3) Take the 0th control point of the B-spline curve as the initial pose of the leveling trajectory and the last control point as the target pose of the leveling trajectory, that is:

[0096]

[0097] In the formula, P ini = [Piniz , P iniα , P iniβ is the initial pose of the leveling trajectory; P fin = [P finz , P finα , P finβ is the target pose of the leveling trajectory;

[0098] 1.4) Set the generalized coordinates and initial poses of the first three control points to be equal, and the generalized coordinates and target poses of the last three control points to be equal, i.e.:

[0099]

[0100] 1.5) Use the interval ratio mapping method to determine the coordinates of the i-th control point, i.e.:

[0101]

[0102] where w n is a randomly generated control point parameter; D i is an intermediate parameter;

[0103] 1.6) Generate the leveling trajectory based on equation (5) - equation (7).

[0104] The trajectory optimization model F(x) of the workpiece is as follows:

[0105]

[0106] where f1(x) is the impact during the leveling process, f2(x) is the total leveling time, T represents the total time of the leveling motion, J i represents the jerk of the i-th driving joint, Δl i represents the telescopic amount of the i-th leg driving joint; Δl + and Δl - represent the maximum allowable telescopic range of the screw lift, Δl + > 0, Δl - < 0, v li and a li respectively represent the real-time speed and acceleration of the i-th leg driving joint; ν max and a max respectively represent the maximum allowable speed and maximum allowable acceleration of the leg driving joint, τ i represents the driving force of the i-th leg driving joint; τ max represents the maximum limit value of the driving force. Δt i represents the time step.

[0107] The steps for solving the trajectory optimization model include:

[0108] 3.1) Population initialization: Set the multi-objective optimization function and boundary conditions according to the trajectory optimization model, achieve antigen recognition, and randomly generate p antibodies with real number coding to form the initial antibody population P 1 , calculate P 1 The objective function values of each initial antibody in it, perform non-dominated sorting and crowding distance evaluation on the antibodies, and store the first-generation non-dominated antibodies in the mature cell set and the memory cell set, and store the remaining antibodies in the immature cell set, complete the population initialization, and set the maximum number of iterations N max ;

[0109] 3.2) Constraint condition judgment: Judge whether each antibody in the i-th generation antibody population P i meets the constraint conditions of the workpiece trajectory optimization model. If not, it will be punished and eliminated;

[0110] 3.3) Antibody population cloning: Clone the antibodies in the mature cell set to form a population The cloning ratio is dynamically adjusted according to the crowding degree;

[0111] 3.4) Antibody population crossover: Group the antibody population in pairs, and perform crossover operations on each pair of antibodies using the two-point crossover method to obtain the antibody population

[0112] 3.5) Antibody population mutation: Perform adaptive mutation operations on the antibodies in to obtain the antibody population

[0113] 3.6) According to the linear decreasing extinction strategy, eliminate d antibodies in the immature cell set, and then randomly generate d new antibodies to replace them to form a new antibody set

[0114] 3.7) Antibody population update: Combine the antibody population and to generate the next-generation antibody population P i+1 ;

[0115] 3.8) Mature cell set update: Perform fast non-dominated sorting and crowding distance evaluation on the (i + 1)-th generation antibody population P i+1 and select θ optimal antibodies to store in the mature cell set The remaining antibodies are stored in the immature cell set;

[0116] 3.9) Memory cell set update: Store P i+1Copy the non-dominated solutions in [ ] into the memory cell set, perform fast non-dominated sorting and crowding distance evaluation on the antibodies in the memory cell set, and delete the dominated antibodies and duplicate antibodies;

[0117] 3.10) Iteration condition determination: Determine whether it is the maximum number of iterations. If so, terminate the iteration and output the current memory cell set; otherwise, jump to step 3.2) to continue the iteration.

[0118] The steps for non-dominated sorting of antibodies include:

[0119] 4.1) Assign two parameters G m and G n to each antibody x in the population. The value of G m represents the set of antibodies dominated by x, and the value of G n represents the set of antibodies that dominate x. Initialize the counter i to 1;

[0120] 4.2) Find all the antibodies in the population that are not dominated by other antibodies, that is, the antibodies with G n equal to 0, put them into set A, and assign a sorting value of 1 to these antibodies;

[0121] 4.3) Check the G m set of each antibody in set A. For each antibody in G m , subtract 1 from its G n ; if the G n value of any individual becomes 0, add it to set B;

[0122] 4.4) Update the counter i to i + 1, copy the individuals in set B to A, and empty B. The sorting values of these individuals are set to i + 1;

[0123] 4.5) Determine whether set A is empty. If not, return to step 4.3); if so, the sorting process ends.

[0124] The crowding distance of the boundary solution is twice the maximum crowding distance among all non-boundary solutions in the population;

[0125] The crowding distance c i of the non-boundary solution is as follows:

[0126]

[0127] In the formula, f j (x i+1 ) and f j (x i-1 ) represent the objective function values of two adjacent individuals to antibody i; f j (x) max and f j (x)min respectively represent the maximum and minimum values of the objective function j; b is the number of objective functions.

[0128] Cloning ratio μ i is as follows:

[0129]

[0130] where: p is the number of initialized antibodies; c i represents the crowding distance of antibody x i ; represents the sum of the crowding distances of all antibodies to be cloned; round represents rounding.

[0131] The adaptive mutation operation is as follows:

[0132]

[0133] where: N is the current number of iterations; N max is the maximum number of iterations; ε is the mutation factor, satisfying ε > 1, and the mutation range is proportional to the size of ε; x max and x min respectively represent the upper limit value and the lower limit value of the decision variable; δ up and δ lo respectively represent the upper limit value and the lower limit value of the mutation. λ is an intermediate parameter; Δx is the mutation step size; x is the decision variable.

[0134] The linear decreasing extinction strategy is as follows:

[0135]

[0136] where: ξ is a constant and satisfies 0 < ξ < 1; d is the number of linear decreasing extinctions.

[0137] The optimal motion trajectory minF of impact and time average during the leveling process * is as follows:

[0138]

[0139] where, f i (x) represents the value of the i-th sub-objective function of the Pareto optimal solution; f i (x) max and f i (x) min respectively represent the maximum and minimum values of the i-th sub-objective function in the Pareto optimal solution set; ω i is the weight coefficient.

[0140] Example 2:

[0141] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm, comprising the following steps:

[0142] 1) Construct the leveling trajectory of the workpiece using a quintic B-spline curve;

[0143] 2) Construct the trajectory optimization model of the workpiece;

[0144] 3) Solve the trajectory optimization model to obtain a set of optimal solution sets.

[0145] 4) Evaluate the optimal solution set using the comprehensive evaluation method to obtain the motion trajectory with the best impact and time average during the leveling process; the motion trajectory includes the spatial motion trajectory of the workpiece and the motion trajectories of each leveling leg.

[0146] Example 3:

[0147] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm, the technical content is the same as that of Example 2. Further, the quintic B-spline curve is defined by a set of control point sets and the time node increments {Δt1, Δt2, Δt3, Δt4, Δt5, Δt6, Δt7, Δt8,..., Δt M-5}.

[0148] Example 4:

[0149] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm, the technical content is the same as any one of Examples 2-3. Further, the steps of constructing the leveling trajectory of the workpiece using the quintic B-spline curve include:

[0150] 1.1) Select the number of control points as M, and define the three-dimensional generalized coordinates of the i-th control point as That is:

[0151]

[0152] 1.2) Based on the quintic clamped B-spline curve, construct the leveling trajectory expression, that is:

[0153]

[0154] Among them, the basis function N i,5 (t) is as follows:

[0155]

[0156] In the formula, k = 1, 2, 3, 4, 5;

[0157] 1.3) Take the 0th control point of the B-spline curve as the initial pose of the leveling trajectory, and the last control point as the target pose of the leveling trajectory, i.e.:

[0158]

[0159] 1.4) Set the generalized coordinates and initial poses of the first three control points to be equal, and the generalized coordinates and target poses of the last three control points to be equal, i.e.:

[0160]

[0161] 1.5) Use the interval ratio mapping method to determine the coordinates of the ith control point, i.e.:

[0162]

[0163] In the formula, w n is a randomly generated control point parameter; D i is an intermediate parameter;

[0164] 1.6) Generate the leveling trajectory based on equations (5)-(7).

[0165] Example 5:

[0166] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Examples 2-4. Further, the trajectory optimization model of the workpiece is as follows:

[0167]

[0168] In the formula, f1(x) is the impact during the leveling process, f2(x) is the total leveling time, T represents the total time of the leveling movement, J i represents the jerk of the ith driving joint, Δl i represents the telescopic amount of the ith leg driving joint; Δl + and Δl - represent the maximum allowable telescopic range of the screw jack, Δl + > 0, Δl - < 0, v li and a li respectively represent the real-time speed and acceleration of the ith leg driving joint; ν max and a max respectively represent the maximum allowable speed and maximum allowable acceleration of the leg driving joint, τ i represents the driving force of the ith leg driving joint; τ max represents the maximum limit value of the driving force.

[0169] Example 6:

[0170] A multi-objective trajectory planning method for a large-scale heavy-load dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Embodiments 2-5. Further, the steps for solving the trajectory optimization model include:

[0171] 3.1) Population initialization: Set the multi-objective optimization function and boundary conditions according to the trajectory optimization model, realize the recognition of antigens, and randomly generate p antibodies according to real number coding to form an initial antibody population P 1 , calculate P 1 The objective function values of each initial antibody in are calculated, the antibodies are non-dominated sorted and crowded distance evaluated, and the first-generation non-dominated antibodies are stored in the mature cell set and the memory cell set, and the remaining antibodies are stored in the immature cell set to complete the initialization of the population, and set the maximum number of iterations N max ;

[0172] 3.2) Constraint condition judgment: Judge whether each antibody in the i-th generation antibody population P i satisfies the constraint conditions of the workpiece trajectory optimization model. If not, it will be punished and eliminated;

[0173] 3.3) Antibody population cloning: The antibodies in the mature cell set are cloned to form a population The cloning ratio is dynamically adjusted according to the crowding degree;

[0174] 3.4) Antibody population crossover: The antibody population is grouped in pairs, and the two-point crossover method is used to perform crossover operations on each group of antibodies to obtain the antibody population

[0175] 3.5) Antibody population mutation: Adaptive mutation operations are performed on the antibodies in to obtain the antibody population

[0176] 3.6) According to the linear decreasing extinction strategy, d antibodies in the immature cell set are eliminated, and then d new antibodies are randomly generated to replace them to form a new antibody set

[0177] 3.7) Antibody population update: The antibody population and are merged to generate the next-generation antibody population P i+1 ;

[0178] 3.8) Mature cell set update: Perform fast non-dominated sorting and crowded distance evaluation on the (i + 1)-th generation antibody population P i+1 , and select θ optimal antibodies to store in the mature cell set The remaining antibodies are stored in the immature cell set;

[0179] 3.9) Memory cell set update: Copy the non-dominated solutions in P i+1 to the memory cell set, perform fast non-dominated sorting and crowding distance evaluation on the antibodies in the memory cell set, and delete the dominated antibodies and duplicate antibodies;

[0180] 3.10) Iteration condition determination: Determine whether it is the maximum number of iterations. If so, terminate the iteration and output the current memory cell set; otherwise, jump to step 3.2) to continue the iteration.

[0181] Example 7:

[0182] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Examples 2-6. Further, the steps for performing non-dominated sorting on antibodies include:

[0183] 4.1) Assign two parameters G m and G n to each antibody x in the population. The value of G m represents the set of antibodies dominated by x, and the value of G n represents the set of antibodies that dominate x, and initialize the counter i to 1;

[0184] 4.2) Find all antibodies in the population that are not dominated by other antibodies, that is, antibodies with G n equal to 0, put them into set A, and assign these antibodies a sorting value of 1;

[0185] 4.3) Check the G m set of each antibody in set A. For each antibody in G m , subtract 1 from its G n ; if the G n value of any individual becomes 0, add it to set B;

[0186] 4.4) Update the counter i to i + 1, copy the individuals in set B to A, and empty B. The sorting value of these individuals is set to i + 1;

[0187] 4.5) Determine whether set A is empty. If not, return to step 4.3); if so, the sorting process ends.

[0188] Example 8:

[0189] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Examples 2-7. Further, the crowding distance of the boundary solutions is twice the maximum crowding distance of all non-boundary solutions in the population;

[0190] The crowding distance of non-boundary solutions is as follows:

[0191]

[0192] In the formula, f j (x i+1 ) and f j (x i-1 ) represent the objective function values of two individuals adjacent to antibody i; f j (x) max and f j (x) min represent the maximum and minimum values of objective function j respectively; b is the number of objective functions.

[0193] Example 9:

[0194] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Examples 2-8. Further, the cloning ratio is as follows:

[0195]

[0196] Among them: p is the number of initialized antibodies; c i represents the crowding distance of antibody x i ; represents the sum of the crowding distances of all antibodies to be cloned; round represents rounding.

[0197] Example 10:

[0198] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Examples 2-9. Further, the adaptive mutation operation is as follows:

[0199]

[0200] Among them: N is the current iteration number; N max is the maximum iteration number; ε is the mutation factor, satisfying ε > 1, and the mutation range is proportional to the size of ε; x max and x min represent the upper limit value and the lower limit value of the decision variable respectively; δ up and δ lo represent the upper limit value and the lower limit value of mutation respectively.

[0201] The linear decreasing extinction strategy is as follows:

[0202]

[0203] Where: ξ is a constant and satisfies 0 < ξ < 1; d is the linearly decreasing extinction number.

[0204] Example 11:

[0205] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the technical content is the same as any one of Examples 2-10. Further, the motion trajectory with the best impact and time average during the leveling process is as follows:

[0206]

[0207] Among them, f i (x) represents the value of the i-th sub-objective function of the Pareto optimal solution; f i (x) max and f i (x) min respectively represent the maximum and minimum values of the i-th sub-objective function in the Pareto optimal solution set; ω i is the weight coefficient.

[0208] Example 12:

[0209] A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, the content is as follows:

[0210] Considering the relatively simple kinematic inverse solution of the leveling system, first plan the desired trajectory of the workpiece from the initial pose to the target pose in the Cartesian space, and then use the kinematic inverse solution method to deduce the corresponding motion trajectories of the driving joints of each leveling leg.

[0211] The present invention first parametrically describes the motion trajectory of the workpiece using a quintic B-spline curve; in view of the requirements of leveling operations for smoothness and efficiency, constructs a trajectory optimization model for the system; then proposes a novel intelligent optimization algorithm to solve the trajectory optimization model, and uses the comprehensive evaluation method to obtain the motion trajectory with the best impact and time average during the leveling process.

[0212] In the trajectory generation stage, a clamped quintic B-spline curve is used as the interpolation function to ensure the smoothness, differentiability, and local controllability of the generated trajectory. The main process of trajectory generation is as follows:

[0213] Select 13 control points, and define the three-dimensional generalized coordinates of the i-th control point as:

[0214]

[0215] Based on the quintic clamped B-spline curve, the leveling trajectory can be expressed as:

[0216]

[0217] The initial pose and the target pose of the leveling trajectory are the 0th and 12th control points of the B-spline curve respectively, and their generalized coordinates are:

[0218]

[0219] To ensure that the velocity and acceleration at the starting and ending stages of the leveling trajectory are both zero, it is necessary to set the generalized coordinates of the first three control points equal to the initial pose, and the generalized coordinates of the last three control points equal to the target pose, that is:

[0220]

[0221] To determine the remaining intermediate control points The interval ratio mapping method is adopted. This method reorders the control points randomly generated during the initialization of the optimization algorithm in a superimposed manner. A new variable D i is introduced, and its expression is:

[0222]

[0223] where: w n is the parameter of the randomly generated control point.

[0224] After interval ratio mapping, the coordinates of the i-th control point can be obtained as:

[0225]

[0226] The control points generated according to this method will satisfy monotonic orderliness. At the same time, according to the properties of the clamped B-spline curve, the first and last knots should have a multiplicity of k + 1, that is, a multiplicity of 6. Then the knot vector can be expressed as:

[0227] t = [0, 0, 0, 0, 0, 0, t1, t2, t3, t4, t5, t6, t7, t8, t8, t8, t8, t8]

[0228] In view of the irreversibility of time and the continuity of motion, the knot vector components should also satisfy the following constraint conditions:

[0229] 0 < t1 ≤ t2 ≤ t3 ≤ t4 ≤ t5 ≤ t6 ≤ t7 ≤ t8

[0230] Let the knot increment be:

[0231] Δt i = t i - t i-1 (i = 1, 2, …, 8)

[0232] After the above analysis, the leveling trajectory can be represented by a set of ordered control points and a quintic B-spline parametric curve defined by time node increments {Δt1, Δt2, Δt3, Δt4, Δt5, Δt6, Δt7, Δt8}.

[0233] Optimizing the leveling trajectory of the workpiece is the key to achieving efficient and stable leveling operations. When establishing the trajectory optimization model of the dual-robot leveling system, various performance indicators and physical constraints during the leveling process must be comprehensively analyzed to make the optimal decision. The dual-robot leveling system is used to complete the leveling task of large and heavy workpieces. To ensure the safety of the leveling process, the running trajectory of the mechanism must be smooth and stable. In addition, the leveling time is an important indicator for evaluating the leveling system. Therefore, the impact and time during the leveling process are taken as the optimization objectives. When optimizing the leveling trajectory of the workpiece, the constraints on the telescopic range, speed, acceleration, and driving force of the leveling leg drive joints also need to be comprehensively considered. Based on the above optimization objective function and constraints, the trajectory optimization model of the workpiece to be leveled can be constructed as follows:

[0234]

[0235] The immune clonal selection algorithm effectively utilizes the diversity mechanism of the immune system and demonstrates excellent global optimization search capabilities. In this algorithm, the objective function and constraints of the problem to be optimized are regarded as antigens, and the solutions to the problem are regarded as antibodies. However, this algorithm still has deficiencies in the diversity and uniformity of the solution set and the convergence speed of the algorithm. These deficiencies provide potential directions for the further improvement of the algorithm. Based on the traditional immune clonal selection algorithm, this invention introduces an improvement strategy to obtain a new type of intelligent optimization algorithm to enhance the global search ability of the algorithm, accelerate the convergence process, and improve the quality of the solution set. Specifically, a real-number coding method is adopted to improve the coding accuracy and efficiency; fast non-dominated sorting and crowding distance calculation are implemented, and the cloning ratio is dynamically adjusted, and a crossover operation is introduced to improve the diversity and uniformity of the solutions; an adaptive mutation and a strategy of decreasing the number of extinct antibodies are adopted to accelerate the convergence speed. These improvements enable the algorithm to more efficiently explore the solution space and quickly converge to a set of balanced and non-dominated solution sets when dealing with multi-objective optimization problems.

[0236] (1) Real-number coding

[0237] When dealing with optimization problems, the coding method of the optimization variables has a significant impact on the search performance. The traditional immune clonal selection algorithm usually uses the binary coding method to represent variables. However, in problems with high precision requirements, binary coding may lead to an exponential expansion of the search space, thereby exacerbating the contradiction between the coding length and the solution accuracy and affecting the execution efficiency of the algorithm.

[0238] Compared with binary coding, real - number coding directly uses real numbers to represent each antibody within the domain of definition, simplifies the decoding process, and improves computational efficiency. In addition, real - number coding is more suitable for dealing with continuous variables, which is crucial for many practical optimization problems. Based on these considerations, the present invention adopts real - number coding to more effectively address high - precision optimization problems while maintaining the efficient operation of the algorithm.

[0239] (2) Fast non - dominated sorting mechanism and crowding distance evaluation

[0240] In traditional immune clonal selection algorithms, the screening of antibody populations mainly relies on the affinity evaluation between antibodies and antigens, focusing on identifying antibodies with the highest affinity for the target antigen. However, this method fails to fully consider the diversity of the antibody population, that is, the influence of antibody concentration. To solve this problem, a selection strategy combining a fast non - dominated sorting mechanism and crowding distance calculation is adopted.

[0241] The fast non - dominated sorting mechanism is a method used to determine the sorting and dominance relationships of solutions in multi - objective optimization. The steps of this mechanism are as follows:

[0242] a1) Assign two parameters \(G^+\) m and \(G^-\) n to each antibody \(x\) in the population. The \(G^+\) m value represents the set of antibodies dominated by \(x\), and the \(G^-\) n value represents the set of antibodies that dominate \(x\), and initialize the counter \(i\) to 1;

[0243] a2) Find all antibodies in the population that are not dominated by other antibodies, that is, antibodies with \(G^-\) n equal to 0, put them into set \(A\), and assign these antibodies a sorting value of 1;

[0244] a3) Check the \(G^+\) m set of each antibody in \(A\). For each antibody in \(G^+\) m , subtract 1 from its \(G^-\) n . If the \(G^-\) n value of any individual becomes 0, add it to set \(B\);

[0245] a4) Update the counter \(i\) to \(i + 1\), copy the individuals in set \(B\) to \(A\), and empty \(B\). The sorting values of these individuals are set to \(i + 1\);

[0246] a5) If \(A\) is not empty, repeat the above steps; if \(A\) is empty, the sorting process ends.

[0247] Through the above process, each antibody in the population is assigned a sorting value. When two antibodies have the same sorting value, the crowding distance is used to measure their degree of differentiation. The crowding distance reflects the degree of crowding of a certain antibody with its surrounding antibodies. In the multi-objective optimization problem, the calculation formula for the crowding distance of antibody i is as follows:

[0248]

[0249] where: f j (x i+1 ) and f j (x i-1 ) represent the objective function values of two individuals adjacent to antibody i; f j (x) max and f j (x) min represent the maximum and minimum values of the objective function j respectively; b is the number of objective functions.

[0250] It should be noted that the crowding distance of the boundary solution cannot be directly obtained through the formula. Therefore, the crowding distance of the boundary solution is set to twice the maximum crowding distance among all non-boundary solutions in the population.

[0251] After fast non-dominated sorting and crowding distance calculation, the population can be comprehensively sorted. Specifically, if there is a difference in the sorting values of two antibodies, the antibody with the smaller sorting value is preferentially selected; if the sorting values are the same, the individual with the larger crowding distance is preferentially selected to ensure the diversity of the population is maintained. Through this method, the algorithm can more effectively identify and retain those solutions that are neither dominated nor evenly distributed, thereby improving the quality of the solution set and avoiding premature convergence.

[0252] (3) Dynamically adjust the cloning ratio

[0253] In the traditional immune clone selection algorithm, the cloning number of antibodies is fixed and lacks the ability of dynamic adjustment. To improve the search efficiency, a dynamic cloning ratio adjustment strategy based on the crowding distance is adopted. Specifically, antibodies with a larger crowding distance, that is, those antibodies that are more isolated in the objective space, will be assigned a higher cloning ratio to increase their frequency of appearance in the next generation. On the contrary, antibodies with a smaller crowding distance, that is, those antibodies located in crowded areas, will be assigned a lower cloning ratio. This approach can promote the diffusion of the population to under-searched areas while maintaining the utilization of the discovered excellent solutions. The calculation method of the cloning ratio value is as follows:

[0254]

[0255] where: p is the number of initialized antibodies; c i represents the crowding distance of antibody x i ; Denote the sum of crowding distances of all antibodies to be cloned; round means rounding.

[0256] (4) Introduce antibody population crossover

[0257] Crossover is different from mutation. Crossover is used to exchange genetic information between parents to produce offspring with new characteristics. This helps to conduct a wide search in the solution space, retain excellent characteristics in the parents, and try new combinations; mutation is used to introduce new genetic diversity, which can introduce new solutions in the offspring, help the algorithm jump out of local optimal solutions, and explore other regions of the solution space. When crossover is performed first, the algorithm first generates a series of new candidate solutions using the excellent characteristics of the parents, and then introduces randomness to these solutions through mutation, thereby increasing the diversity of the population and avoiding premature convergence.

[0258] The present invention introduces a crossover operation into the traditional immune clone selection algorithm and adopts the method of two-point crossover. The antibody population is grouped in pairs, and two random integers are generated for each pair of antibodies as crossover points, and the gene segments between the two antibodies located at the crossover points are exchanged to obtain a new antibody population after crossover.

[0259] (5) Adaptive mutation

[0260] Although common multi-point mutation methods are easy to implement, their fixed mutation degree may affect the efficiency of the algorithm. To solve this problem, an adaptive mutation strategy is adopted, that is, the mutation range of the antibody is gradually reduced according to the increase of the number of iterations to improve the convergence efficiency of the algorithm. The calculation formula is as follows:

[0261]

[0262] Where: N is the current number of iterations; N max is the maximum number of iterations; ε is the mutation factor, satisfying ε > 1, and the mutation range is proportional to the size of ε; x max and x min represent the upper limit value and the lower limit value of the decision variable respectively; δ up and δ lo represent the upper limit value and the lower limit value of mutation respectively.

[0263] (6) Decreasing extinction number

[0264] In the iterative process of the traditional immune clone selection algorithm, the number of extinct individuals retained in the population is preset, and the optimality of newly generated individuals is random, which may lead to non-optimal solutions in the later stage of the iterative process. In order to maintain population diversity in the early stage of iteration, avoid falling into local optima, not affect the convergence speed of the algorithm in the later stage of iteration, and ensure that there are no infeasible solutions in the final solution set, a linear decreasing strategy for the number of extinct antibodies is adopted:

[0265]

[0266] where: ξ is a constant and satisfies 0 < ξ < 1.

[0267] The new intelligent optimization algorithm effectively improves the global search ability, speeds up the convergence speed, and improves the quality of the solution set of multi-objective optimization problems by introducing real number coding, fast non-dominated sorting, crowding distance calculation, dynamic clone ratio adjustment, crossover operation, adaptive mutation, and the strategy of decreasing the number of extinct antibodies. Its trajectory optimization process is as Figure 1 shown, and the detailed process can be summarized as follows:

[0268] (s1) Population initialization. Set the multi-objective optimization function and boundary conditions according to the trajectory optimization model to achieve the recognition of antigens, and randomly generate p antibodies according to real number coding to form the initial antibody population P 1 , calculate the objective function values of each initial antibody in P 1 , perform non-dominated sorting and crowding distance evaluation on the antibodies, store the first-generation non-dominated antibodies in the mature cell set and the memory cell set, and store the remaining antibodies in the immature cell set to complete the initialization of the population, and set the maximum number of iterations N max ;

[0269] (s2) Constraint condition judgment. Judge whether each antibody in the i-th generation antibody population P i (i = 1, 2,... N) satisfies the constraint conditions. If not, it will be punished and eliminated;

[0270] (s3) Antibody population cloning. Clone the antibodies in the mature cell set to form a population The cloning scale is dynamically adjusted according to the crowding degree;

[0271] (s4) Antibody population crossover. Group the antibody population in pairs, and perform crossover operations on each pair of antibodies using the two-point crossover method to obtain the antibody population

[0272] (s5) Antibody population mutation. Perform adaptive mutation operations on the antibodies in to obtain the antibody population

[0273] (s6) According to the linear decreasing extinction strategy, d antibodies in the immature cell set are eliminated, and then d new antibodies are randomly generated to replace them to form a new antibody set.

[0274] (s7) Antibody population update. and Merge to generate the next generation antibody population P i+1 ;

[0275] (s8) Renewal of mature cell set. i+1 Perform fast non-dominated sorting and crowding distance evaluation to select the optimal antibodies and store them in the mature cell set The remaining antibodies were deposited in the immature cell pool;

[0276] (s9) Memory cell set update. i+1 The non-dominated solutions in the memory cell set are copied to the memory cell set, and the antibodies in the memory cell set are quickly non-dominated sorted and evaluated for crowding distance, and the dominated antibodies and duplicate antibodies are deleted;

[0277] (s10) Iteration condition determination: Determine whether the maximum number of iterations has been reached. If so, terminate the iteration and output the current memory cell set. Otherwise, jump to step s2 to continue the iteration.

[0278] A set of Pareto optimal solutions can be obtained by trajectory optimization through a new intelligent optimization algorithm. In order to select a solution that achieves a balance between time and impact as the leveling trajectory, the present invention adopts a comprehensive evaluation method, namely

[0279]

[0280] Among them, f i (x) represents the value of the ith sub-objective function of the Pareto optimal solution; f i (x) max and f i (x) min Respectively represent the maximum and minimum values ​​of the ith sub-objective function in the Pareto optimal solution set; ω i is the weight coefficient, which can be adjusted according to specific working conditions.

[0281] The dual robot leveling system is taken as the research object. Figure 8 As shown, the schematic diagram of a single leveling robot is as follows Figure 9 As shown in Figure 2, it is a 2-SPPP / UP mechanism, where S represents the ball joint, P represents the translation joint, and U represents the Hooke joint. The new intelligent optimization algorithm is used to iteratively calculate the leveling trajectory optimization model, and the Pareto optimal front end is obtained as follows:Figure 2 As shown. As a control experiment, under the same parameter configuration, the traditional immune clonal selection algorithm was used to iteratively calculate the trajectory optimization model, and the obtained Pareto optimal front was as shown in Figure 3 As shown. By comparing the two, it can be seen that the Pareto front obtained by the improved algorithm proposed in the present invention has significant advantages in terms of uniformity and diversity. Moreover, it is superior to the traditional algorithm in terms of the two indicators of the minimum time value and the minimum shock value. This result confirms the effectiveness and superiority of the improved algorithm in dealing with multi-objective optimization problems. By taking the weight coefficient ω1 as 2 and ω2 as 1, the leveling trajectory with the optimal average of shock and time can be obtained. According to the inverse kinematic model of the dual-robot leveling system, the displacement trajectory curves of each leveling leg corresponding to this average optimal leveling trajectory can be solved as shown in Figure 4 As shown, the velocity trajectory curves are as shown in Figure 5 As shown, the acceleration trajectory curves are as shown in Figure 6 As shown, and the jerk trajectory curves are as shown in Figure 7 As shown. It can be seen that the displacement, velocity, acceleration, and jerk curves of all leg drive joints are smooth without mutation, and at the initial and target pose points, the velocities and accelerations of each leveling leg drive joint are zero, meeting the stability requirements during the start-up and stop processes of the leveling system. The trajectory planning simulation results prove that the novel intelligent optimization algorithm proposed in this paper can effectively solve the multi-objective optimization problem with the goal of minimizing the leveling time and shock. According to the simulation comparison results with the traditional immune clonal selection algorithm, the advantages of the proposed algorithm in ensuring the diversity, uniformity, and effectiveness of the solution set are demonstrated.

Claims

1. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm, characterized in that It includes the following steps: 1) Construct the leveling trajectory of the workpiece using a quintic B-spline curve. 2) Construct the trajectory optimization model of the workpiece; 3) Solve the trajectory optimization model to obtain a set of optimal solution sets. 4) Evaluate the optimal solution set using the comprehensive evaluation method to obtain the motion trajectory with the optimal impact and time average during the leveling process; the motion trajectory includes the spatial motion trajectory of the workpiece and the motion trajectories of each leveling leg.

2. The multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm according to claim 1, wherein, The quintic B-spline curve passes through a set of control points and is defined by time knot increments {Δt1, Δt2, Δt3, Δt4, Δt5, Δt6, Δt7, Δt8,..., Δt M-5}.

3. A multi-objective trajectory planning method for a large-scale heavy-load dual-robot leveling system based on a new intelligent optimization algorithm according to claim 1, characterized in that, The steps of constructing the leveling trajectory of the workpiece using a quintic B-spline curve include: 1) Select the number of control points as M, and define the three-dimensional general coordinates of the i-th control point as d i p , that is: 2) Based on the quintic clamped B-spline curve, construct the leveling trajectory expression, i.e.: where (P z (t), P α (t), P β (t)) are the coordinates of the leveling trajectory; Among them, the basis function N i,5 (t) is as follows: where k = 1, 2, 3, 4, 5; u is a parameter; 3) Use the 0th control point of the B-spline curve as the initial pose of the leveling trajectory, and the last control point as the target pose of the leveling trajectory, i.e.: wherein, P ini = [P iniz , P iniα , P iniβ is the initial pose of the leveling trajectory; P fin = [P finz , P finα , P finβ is the target pose of the leveling trajectory; 4) Set the generalized coordinates and initial poses of the first three control points to be equal, and the generalized coordinates and target poses of the last three control points to be equal, i.e.: 5) Use the interval proportional mapping method to determine the coordinates of the ith control point, i.e.: where w n is the randomly generated control point parameter; D i is the intermediate parameter; 6) Generate the leveling trajectory based on steps (5) - formula (7).

4. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm according to claim 1, characterized in that, The trajectory optimization model F(x) of the workpiece is as follows: where, f1(x) is the impact during the leveling process, f2(x) is the total leveling time, T represents the total time of the leveling movement, J i represents the jerk of the i-th driving joint, Δl i represents the telescopic amount of the i-th leg driving joint; Δl + and Δl - represent the maximum allowable telescopic range of the screw lift. Δl + > 0, Δl - < 0, v li and a li represent the real-time speed and acceleration of the i-th leg drive joint respectively; ν max and a max represent the maximum allowable speed and maximum allowable acceleration of the leg drive joint respectively. τ i represents the driving force of the i-th leg drive joint; τ max represents the maximum limit value of the driving force; Δt i represents the time step.

5. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm according to claim 1, characterized in that, The steps of solving the trajectory optimization model include: 1) Population initialization: Set the multi-objective optimization function and boundary conditions according to the trajectory optimization model to achieve the recognition of antigens, and randomly generate p antibodies by real number coding to form the initial antibody population P 1 , calculate P 1 the objective function values of each initial antibody in, perform non-dominated sorting and crowding distance evaluation on the antibodies, and store the first-generation non-dominated antibodies in the mature cell set and the memory cell set, and store the remaining antibodies in the immature cell set, complete the population initialization, and set the maximum number of iterations N max ; 2) Constraint condition judgment: Determine whether each antibody in the i-th generation antibody population P i meets the constraint conditions of the workpiece trajectory optimization model. If not, it will be penalized and eliminated; 3) Cloning of antibody population: Cloning the antibodies in the mature cell set to form a population The cloning ratio is dynamically adjusted according to the degree of crowding; 4) Antibody population crossover: Divide the antibody population into pairs, and perform crossover operations on each pair of antibodies using the two-point crossover method to obtain the antibody population 5) Antibody population variation: Perform an adaptive mutation operation on the antibodies in to obtain an antibody population 6) According to the linear decreasing extinction strategy, eliminate d antibodies in the immature cell concentration, and then randomly generate d new antibodies to replace them, forming a new antibody set 7) Antibody population update: Combine the antibody populations and to generate the next-generation antibody population P i+1 ; 8) Mature cell set update: For the i+1th generation antibody population P i+1 Perform fast non-dominated sorting and crowding distance evaluation, and select θ optimal antibodies to be stored in the mature cell set The remaining antibodies are stored in the immature cell set; 9) Memory cell set update: Copy the non-dominated solutions in P i+1 to the memory cell set, perform fast non-dominated sorting and crowding distance evaluation on the antibodies in the memory cell set, and delete the dominated antibodies and duplicate antibodies; 10) Iteration condition determination: Determine whether it is the maximum number of iterations. If so, terminate the iteration and output the current memory cell set. Otherwise, jump to step 2) to continue the iteration.

6. The multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm according to claim 5, wherein, The steps of non-dominated sorting of antibodies include: 1) Assign two parameters \(G_{x}\) and \(G_{x}^{-}\) to each antibody \(x\) in the population. The \(G_{x}\) value represents the set of antibodies dominated by \(x\), and the \(G_{x}^{-}\) value represents the set of antibodies that dominate \(x\). Initialize the counter \(i\) to 1. m and \(G_{x}^{-}\) n , \(G_{x}\) m value represents the set of antibodies dominated by \(x\), \(G_{x}^{-}\) n value represents the set of antibodies that dominate \(x\), and initialize the counter \(i\) to 1; 2) Find all the antibodies in the population that are not dominated by other antibodies, i.e., antibodies with a value of G n equal to 0, put them into set A, and assign a ranking value of 1 to these antibodies; 3) Check the G of each antibody in set A m set. For each antibody in G m , subtract 1 from its G n ; if the G n value of any individual becomes 0, add it to set B; 4) Update the counter i to i + 1, copy the individuals in set B to A, and empty B. The sorting values of these individuals are set to i + 1; 5) Determine whether set A is empty. If not, return to step 3). If so, the sorting process ends.

7. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a novel intelligent optimization algorithm according to claim 5, characterized in that, The crowding distance of the boundary solutions is twice the maximum crowding distance among all non-boundary solutions in the population; Crowding distance c of non-boundary solutions i As shown below: Where, f j (x i+1 ) and f j (x i-1 ) represent the objective function values of two individuals adjacent to antibody i; f j (x) max and f j (x) min represent the maximum and minimum values of objective function j respectively; b is the number of objective functions.

8. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm according to claim 5, characterized in that, Cloning ratio μ i is as follows: Where: p is the number of initialized antibodies; c i represents the crowding distance of antibody x i ; represents the sum of the crowding distances of all antibodies to be cloned; round means rounding.

9. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm according to claim 5, characterized in that The adaptive mutation operation is as follows: Where: N is the current number of iterations; N max is the maximum number of iterations; ε is the mutation factor, satisfying ε > 1, and the mutation range is proportional to the magnitude of ε; x max and x min represent the upper limit value and the lower limit value of the decision variable respectively; δ up and δ lo represent the upper limit value and the lower limit value of the mutation respectively; λ is an intermediate parameter; Δx is the mutation step size; x is the decision variable. The linear decreasing extinction strategy is as follows: where: ξ is a constant and satisfies 0 < ξ < 1; d is the number of linearly decreasing extinctions.

10. A multi-objective trajectory planning method for a large-scale heavy-duty dual-robot leveling system based on a new intelligent optimization algorithm according to claim 1, characterized in that, Optimal motion trajectory minF with impact and time averaging during leveling * As shown below: Among them, f i (x) represents the value of the i-th sub-objective function of the Pareto optimal solution; f i (x) max and f i (x) min represent the maximum and minimum values of the i-th sub-objective function in the Pareto optimal solution set respectively; ω i is the weight coefficient.

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