A Method for Designing Robotic Gripper Parameters Based on Improved Electric Eel Foraging Optimization

Abstract

This invention relates to a method for designing robot gripper parameters based on an improved electric eel foraging optimization, belonging to the field of mechanical engineering technology. First, the robot gripper parameter design problem is represented as a parameter optimization problem. Then, the traditional electric eel foraging optimization algorithm is improved by introducing a good point set initialization strategy, a differential evolution strategy, a stochastic boundary control strategy, and a solution enhancement strategy, resulting in an improved electric eel foraging optimization algorithm. Finally, based on the improved electric eel foraging optimization algorithm, the optimal parameter combination for the parameter optimization problem is obtained. This invention integrates multiple strategies to provide the electric eel foraging optimization algorithm with a high-quality initial population, enhanced local search depth, and the ability to escape local optima, aiming to solve the problems of existing robot gripper parameter design problems, such as easy getting trapped in local optima, poor optimization accuracy, and slow convergence speed.

Description

Technical Field

[0001] This invention relates to a method for designing robot gripper parameters based on improved electric eel foraging optimization, belonging to the field of mechanical engineering technology. Background Art

[0002] As the complexity of engineering problems continues to increase, ordinary metaheuristic algorithms can get trapped in local optima during the search process. This is especially true when dealing with high-dimensional complex problems, where they may fail to converge precisely to the global optimum or obtain a high-quality solution close to the global optimum. Once trapped in a local optimum, the algorithm struggles to escape that region and find a better solution. The design of robot grippers is crucial in industrial applications. The flexibility and versatility of grippers make them an indispensable component of industrial production systems, enabling them to optimize production processes, precisely manipulate workpieces, adapt to diverse tasks, and play a key role in various industrial scenarios, thereby ensuring production efficiency and stability.

[0003] Since the design of a robot gripper is a complex engineering task, where the decision variables of the model are the geometry of the gripper, which is subject to lateral constraints and constraints arising from the gripper structure, this task can often be regarded as an optimization problem to find the optimal robot gripper parameters or structure. Therefore, it is necessary to conduct in-depth research on efficient and accurate optimization algorithms.

[0004] The Electric Eel Foraging Optimization (EEFO) algorithm is a metaheuristic algorithm inspired by the foraging behavior of electric eels. During optimization, the algorithm's mathematical model utilizes four key foraging behaviors for exploration and exploitation: interaction, rest, hunting, and migration. Furthermore, EEFO incorporates an energy factor to manage the shift from global to local search, achieving a balance between exploration and exploitation within the search space. The algorithm's effectiveness is demonstrated using 23 benchmark functions, the CEC2011 test suite, and the CEC2017 test suite. Comparisons with 12 other algorithms in various aspects prove that EEFO outperforms them. While EEFO offers advantages such as simple parameter settings and high solution accuracy compared to some classic metaheuristic methods, it suffers from drawbacks including insufficient solution diversity in the early stages, excessively fast convergence speed, low convergence accuracy in complex high-dimensional problems, and a tendency to get trapped in local optima. Therefore, further improvements are needed to enhance the performance of the Electric Eel Foraging Optimization algorithm when designing robot gripper parameters to improve its parameter selection effectiveness in complex problems. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a robot gripper parameter design method based on improved electric eel foraging optimization, which aims to solve the problems of existing robot gripper parameter design problems such as easy getting trapped in local optima, poor optimization accuracy and slow convergence speed.

[0006] The technical solution of this invention is: a robot gripper parameter design method based on improved electric eel foraging optimization. First, in the initialization phase, a uniformly distributed initial population is generated through a good point set strategy, increasing the diversity of the population during initialization and covering a wider solution space, which helps discover more potential excellent solutions. Second, in the exploration phase, a differential evolution strategy is integrated. Mutation operations generate new mutation vectors by performing specific transformations on individuals in the population, thereby guiding the algorithm to explore a wider region in the search space. Crossover plays a role in information fusion and local optimization, while selection ensures that each evolutionary step moves towards improving fitness, enabling the algorithm to possess both global search capabilities and meticulous local optimization when solving complex optimization problems, exhibiting high efficiency and robustness. Then, a better boundary control is proposed to ensure the search process takes place within the legal region while improving search efficiency. Finally, in the development phase, a solution enhancement strategy is introduced to increase the chance of EEFO escaping local optima, thereby improving the quality of the optimal solution in each iteration and avoiding getting trapped in local optima. The specific steps are as follows:

[0007] Step 1: Represent the robot gripper parameter design problem as a parameter optimization problem, which includes variable parameters, constraints, and an objective function, wherein the objective function is obtained based on the variable parameters and the constraints;

[0008] Step 2: Improve the traditional electric eel foraging optimization algorithm to obtain the improved electric eel foraging optimization algorithm, including:

[0009] Improvement Strategy 1: In the initialization phase, introduce a good point set initialization strategy to increase the diversity of the population;

[0010] Improvement Strategy 2: In the exploration phase, introduce a differential evolution strategy to increase the breadth of exploration and improve global search and local optimization capabilities;

[0011] Improvement Strategy 3: In the iteration phase, introduce a random boundary control strategy to ensure that the search process is within the preset search boundary;

[0012] Improvement Strategy 4: In the development phase, introduce a solution enhancement strategy to avoid getting trapped in local optima;

[0013] Step 3: Based on the improved electric eel foraging optimization algorithm, perform parameter optimization on the parameter optimization problem to obtain the optimal parameter combination for the parameter optimization problem, including:

[0014] Based on the population size N, N combinations of parameters for the parameter optimization problem are generated as the initial population according to the good point set initialization strategy.

[0015] The fitness value of each electric eel individual in the initial population is calculated as the value of the objective function of the parameter optimization problem, and the electric eel individual that minimizes the value of the objective function is saved as the optimal electric eel individual;

[0016] The process of generating an energy factor E for position update involves updating the position of the optimal electric eel individual based on the differential evolution strategy and the random boundary control strategy when the energy factor is greater than or equal to a preset threshold, and updating the position of the optimal electric eel individual based on the solution enhancement strategy and the random boundary control strategy when the energy factor is less than the preset threshold.

[0017] Compare the fitness values ​​of the optimal electric eel individuals before and after the position update, and select the one with the larger fitness value as the new optimal electric eel individual, thus ending the first position update process for the optimal electric eel individual.

[0018] The energy factor is regenerated to update the position of the new optimal electric eel individual. When the number of iterations of the position update process reaches the maximum number of iterations, the fitness value and position of the current electric eel individual are obtained as the optimal parameter combination for the parameter optimization problem. Otherwise, the position update process continues.

[0019] Optionally, the variable parameters include the lengths a, b, and c of the three links of the gripper, the displacement e of the vertical link, the vertical distance f from the first robotic arm node to the actuator, and the horizontal distance from the actuator to the joint. The angle δ between the second rod b and the third rod c of the gripper, and a total of 7 variable parameters, are used as the objective function to minimize the difference between the maximum and minimum clamping forces within the displacement range of the gripper end, under the following 7 constraints. The expression of the objective function is as follows:

[0020]

[0021] in, The working range of the clamp is z∈[0, ], For the target variable, Represents the clamping force, expressed as:

[0022]

[0023] in, The force applied to the drive rod;

[0024] in:

[0025]

[0026]

[0027] definition The expressions for the seven constraints are obtained as follows:

[0028]

[0029] in, This represents the limit of the gripper at its maximum working stroke. The minimum displacement at the end must not be less than ; Ensure that the end does not descend to a negative displacement when it is at its farthest position, and ensure that no collision occurs; Ensure that the end position at the initial position does not exceed the maximum permissible displacement. ; This indicates that the initial end displacement must not be lower than the minimum height required for gripping. ; It represents the relationship between two sides of a triangle, preventing structural dimensions from exceeding the limits; Ensure the geometric reachability of the position of maximum displacement at the end; The maximum working stroke is limited to the horizontal distance from the actuator to the joint. .

[0030] Optionally, the improved strategy one introduces a good point set initialization strategy to initialize the population, and the expression for generating the population by the good point set initialization strategy is:

[0031]

[0032] in, It is the i-th individual, where i is an integer and its value ranges from 1 to 2. , represents the index of a point in the set of good points, and N represents the population size. It is a point in d-dimensional space. represent The value of the j-th dimension is given by the formula Determined, where p is the parameter used to construct the direction vector, and is a prime number greater than the dimension d. express The decimal part.

[0033] Optionally, the differential evolution strategy introduced in the improved strategy two includes mutation, crossover, and selection operations, wherein the mutation operation specifically includes:

[0034] Three distinct individuals are randomly selected from the population. The difference vectors of two of these individuals are scaled and added to the position of the third individual to generate a new mutant individual, as shown in the following expression:

[0035]

[0036]

[0037] in, This represents a new electric eel individual resulting from the mutation. , , These are three individuals randomly selected from the electric eel population. Indicates the mutation ratio factor. It is a constant. MaxIt is the number of iterations;

[0038] The crossover operation specifically refers to:

[0039] After the mutation operation is completed, the original electric eel target individual and the mutated individual are cross-referenced in each dimension using a preset crossover probability CR to determine whether to select the value of the target individual or the mutated individual. Specifically, one dimension is randomly selected to forcibly inherit the mutated individual's value, while the remaining dimensions are selected from the target individual or the mutated individual based on the crossover probability. The expression for the crossover operation is as follows:

[0040]

[0041] in, Let be the target individual, and represent the value of the j-th dimension of the i-th individual in the t-th iteration. A mutated individual, For new individuals generated by crossover, Represents a random number between 0 and 1. Represent a random dimension D is the total number of dimensions, ensuring At least from To obtain a parameter;

[0042] The selection operation is specifically as follows:

[0043] For each pair of target individuals and mutant individuals, the fitness values ​​of the electric eels were compared. To retain the superior electric eel individuals, the expression for the selection operation is as follows:

[0044]

[0045] If the electric eel individual is produced Its fitness value is better than that of the current individual electric eel. Then in subsequent iterations, It will be retained as a new electric eel individual. Otherwise, retain the existing electric eel individuals. .

[0046] Optionally, the improved strategy three introduces a random boundary control strategy to process individuals that exceed the preset search boundary. This processing involves adjusting the positions of individuals exceeding the preset search boundary by combining the positions of the best and second-best performing individuals in the current population. The expression is:

[0047]

[0048] in, , These represent the positions of the optimal solution and the second-best individual in the current iteration, respectively. This means selecting a random number between (0,1). , All are random numbers in the range [0,1]. and These are the upper and lower limits, respectively.

[0049] Optionally, the fourth improvement strategy introduces a solution enhancement strategy to increase the chances of the improved electric eel foraging optimization algorithm escaping local optima, specifically:

[0050] Calculate the average of the three random solutions Then compare it with the current optimal solution. Combined to generate new candidate solutions And generated using the following formula The expression is as follows:

[0051]

[0052]

[0053]

[0054]

[0055] in, For random numbers that follow a normal distribution, It involves randomly selecting a number from -1 to 2 and then rounding it down. A random number in the range (0, 2). These are three solutions randomly selected from the population. This is an intermediate transition value. " is a constant", "Represents dot product operation, It is a new solution generated by enhancing the original optimal solution through an enhancement strategy;

[0056] If the generated new solution is not better than the current solution, another new candidate solution is constructed. :

[0057]

[0058]

[0059]

[0060] In the formula, j, k, and s are constants, and SF and This serves as an intermediate transition value, where SF is used to control the balance between exploration and development, varying with the number of iterations. It decreases as it increases.

[0061] Optionally, before performing parameter optimization on the parameter optimization problem based on the improved electric eel foraging optimization algorithm, the algorithm further includes defining parameters, including the upper limit Up and lower limit Low of the solution space, the population size N, and the maximum number of iterations MaxIt. The upper limit Up and lower limit Low of the solution space are the upper and lower limits of the variable parameters in the parameter optimization problem.

[0062] Optionally, the improved electric eel foraging optimization algorithm includes interactive operations, migration operations, resting operations, and hunting operations, wherein:

[0063] When the energy factor E At time 1, the interactive operation is performed to update the current position of the electric eel individual, and the position of the electric eel individual is updated again based on the differential evolution strategy. Boundary detection is performed on the updated position of the electric eel individual. Based on the random boundary control strategy, the position of the electric eel individual that exceeds the upper limit Up and lower limit Low of the solution space is updated for the last time.

[0064] When the energy factor E < 1, if rand < 1 / 3, perform a rest operation and update the current electric eel individual's position; if 1 / 3 rand If 2 / 3, perform a migration operation to update the current electric eel individual's position. If rand > 2 / 3, perform a hunting operation to update the current electric eel individual's position. Then, based on the solution enhancement strategy, update the updated electric eel individual's position again. Perform boundary detection on the electric eel individual's position updated after the above rand judgment. Based on the random boundary control strategy, update the position of electric eel individuals that exceed the upper limit Up and lower limit Low of the solution space.

[0065] Optionally, the energy factor is generated using the following formula:

[0066]

[0067] in, t is the current iteration number, and T is the maximum iteration number. It is a random number in the range (0, 1).

[0068] The beneficial effects of this invention are as follows: By improving the electric eel foraging optimization algorithm through multiple strategies, the algorithm can solve the robot gripper parameter design problem more efficiently and accurately. This invention uses a good point set initialization strategy to obtain a high-quality and uniformly distributed initial population, helping the algorithm quickly locate the region near the optimal solution in the search space, thereby accelerating the discovery of the global optimum. Secondly, the stochastic boundary control strategy ensures that the algorithm can effectively control the search range during iteration, thus improving the convergence speed and avoiding unnecessary waste of computational resources. Furthermore, the differential evolution strategy expands the search range by introducing a local search mechanism, enhancing the algorithm's global search capability and enabling it to more accurately approximate the global optimum. Finally, to address the algorithm's tendency to get trapped in local optima, a solution quality enhancement strategy is introduced to further increase the diversity of solutions, helping the algorithm escape the local optimum trap and obtain a better solution. Attached Figure Description

[0069] Figure 1 This is a schematic diagram of the structure of the present invention;

[0070] Figure 2 This is a schematic diagram of the robot gripper parameter design of the present invention;

[0071] Figure 3 This is a comparison diagram of the good point set initialization strategy of this invention and the original initialization strategy;

[0072] Figure 4 This is a radar chart showing the ranking of the CEC2017 function in 30 dimensions using the present invention and different optimization algorithms.

[0073] Figure 5 This is a comparison of the convergence curves of the present invention and other different algorithms on the F1 function in the 30-dimensional CEC2017 test function;

[0074] Figure 6 This is a comparison of the convergence curves of the present invention and other different algorithms on the F3 function in the 30-dimensional CEC2017 test function;

[0075] Figure 7 This is a comparison of the convergence curves of the present invention and other different algorithms on the F4 function in the 30-dimensional CEC2017 test function;

[0076] Figure 8 This is a comparison of the convergence curves of the present invention and other different algorithms on the F10 function in the 30-dimensional CEC2017 test function;

[0077] Figure 9This is a comparison of the convergence curves of the present invention and other different algorithms on the F20 function in the 30-dimensional CEC2017 test function;

[0078] Figure 10 This is a comparison of the convergence curves of the present invention and other different algorithms on the F23 function in the 30-dimensional CEC2017 test function;

[0079] Figure 11 This is a comparison of the convergence curves of the present invention and other different algorithms on the F24 function in the 30-dimensional CEC2017 test function. Detailed Implementation

[0080] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0081] Example 1: As Figure 1 As shown, a method for designing robot gripper parameters based on improved electric eel foraging optimization is described, and its steps are as follows:

[0082] Step 1: Represent the robot gripper parameter design problem as a parameter optimization problem, which includes variable parameters, constraints, and an objective function, wherein the objective function is obtained based on the variable parameters and the constraints;

[0083] Specifically, the structural diagram of the robot gripper parameter design problem is as follows: Figure 2 As shown, the variable parameters include the lengths a, b, and c of the three links of the gripper, the displacement e of the vertical link, the vertical distance f from the first robotic arm node to the actuator, and the horizontal distance from the actuator to the joint. The angle δ between the second rod b and the third rod c of the gripper, and a total of 7 variable parameters, are used as the objective function to minimize the difference between the maximum and minimum clamping forces within the displacement range of the gripper end, under the following 7 constraints. The expression of the objective function is as follows:

[0084]

[0085] in, The working range of the clamp is z∈[0, ], The target variable is the individual electric eel in the population. Represents the clamping force, expressed as:

[0086]

[0087] in, The force applied to the drive rod;

[0088] in:

[0089]

[0090]

[0091] definition The expressions for the seven constraints are obtained as follows:

[0092]

[0093] in, This represents the limit of the gripper at its maximum working stroke. The minimum displacement at the end must not be less than ; Ensure that the end does not descend to a negative displacement when it is at its farthest position, and ensure that no collision occurs; Ensure that the end position at the initial position does not exceed the maximum permissible displacement. ; This indicates that the initial end displacement must not be lower than the minimum height required for gripping. ; It represents the relationship between two sides of a triangle, preventing structural dimensions from exceeding the limits; Ensure the geometric reachability of the position of maximum displacement at the end; The maximum working stroke is limited to the horizontal distance from the actuator to the joint. .

[0094] Optionally, in some specific implementations, the above variables can take the following values: The range of values ​​for the variable parameter can be: .

[0095] Step 2: Improve the traditional electric eel foraging optimization algorithm to obtain the improved electric eel foraging optimization algorithm, including:

[0096] Improvement Strategy 1: In the initialization phase, introduce a good point set initialization strategy to increase the diversity of the population;

[0097] Optionally, in EEFO, the initial position of each electric eel is randomly generated by a random initialization strategy, which cannot effectively guarantee the diversity of the randomly generated initial population, thus affecting convergence accuracy and search efficiency. Therefore, this embodiment introduces a good point set initialization strategy to initialize the population. The expression for generating the population by the good point set initialization strategy is:

[0098]

[0099] in, It is the i-th individual, where i is an integer and its value ranges from 1 to 2. , represents the index of a point in the set of good points, and N represents the population size. It is a point in d-dimensional space. represent The value of the j-th dimension is given by the formula Determined, where p is the parameter used to construct the direction vector, and is a prime number greater than the dimension d. express The decimal part.

[0100] Alternatively, assuming the population size is 100 and the search domain is [-100, 100], Figure 3 The study compares the distribution of population initialization in two-dimensional space between the good point set strategy and the random number generation strategy. It is clear that the population generated by the random initialization strategy is chaotic and even has many overlapping parts, while the population generated by the good point set initialization strategy is significantly more uniform and has more diversity in the search space.

[0101] Understandably, this embodiment uses a good point set initialization strategy to initialize each particle, which can increase the diversity of the population and improve the algorithm's global search capability and convergence speed.

[0102] Improvement Strategy 2: In the exploration phase, introduce a differential evolution strategy to increase the breadth of exploration and improve global search and local optimization capabilities;

[0103] Optionally, the differential evolution strategy introduced in the improved strategy two includes mutation, crossover, and selection operations, wherein the mutation operation specifically includes:

[0104] Three distinct individuals are randomly selected from the population. The difference vectors of two of these individuals are scaled and added to the position of the third individual to generate a new mutant individual, as shown in the following expression:

[0105]

[0106]

[0107] in, This represents a new electric eel individual resulting from the mutation. , , These are three individuals randomly selected from the electric eel population. Indicates the mutation ratio factor. It is a constant. Let be the number of iterations, and MaxIt be the maximum number of iterations. In some specific embodiments, however... 0.5 can be taken;

[0108] The crossover operation specifically refers to:

[0109] After the mutation operation is completed, the original electric eel target individual and the mutated individual are cross-referenced in each dimension using a preset crossover probability CR to determine whether to select the value of the target individual or the mutated individual. Specifically, one dimension is randomly selected to forcibly inherit the mutated individual's value, while the remaining dimensions are selected from the target individual or the mutated individual based on the crossover probability. The expression for the crossover operation is as follows:

[0110]

[0111] in, Let be the target individual, and represent the value of the j-th dimension of the i-th individual in the t-th iteration. A mutated individual, For new individuals generated by crossover, Represents a random number between 0 and 1. Represent a random dimension D is the total number of dimensions, ensuring At least from A parameter is obtained, wherein, in some specific embodiments, CR can be 0.3;

[0112] The selection operation is specifically as follows:

[0113] For each pair of target individuals and mutant individuals, the fitness values ​​of the electric eels were compared. To retain the superior electric eel individuals, the expression for the selection operation is as follows:

[0114]

[0115] If the electric eel individual is produced Its fitness value is better than that of the current individual electric eel. Then in subsequent iterations, It will be retained as a new electric eel individual. Otherwise, retain the existing electric eel individuals. .

[0116] Understandably, since EEFO tends to search near the population mean during the exploration phase, it may limit the breadth of the algorithm's exploration. This embodiment introduces a differential evolution strategy during the exploration phase. Mutation operation generates new mutated individuals by performing specific transformations on individuals in the population, thereby guiding the algorithm to explore a wider area in the search space. Crossover plays a role in information fusion and local optimization, while selection ensures that each step of evolution is in the direction of improving fitness. This enables the algorithm to have both global search capabilities and meticulous local optimization when solving complex optimization problems, demonstrating high efficiency and robustness.

[0117] Improvement Strategy 3: In the iteration phase, introduce a random boundary control strategy to ensure that the search process is within the preset search boundary;

[0118] Optionally, during the iteration process, some individuals may exceed the predetermined search boundary, causing the algorithm to explore in the invalid solution space, affecting the efficiency and stability of the optimization process. Traditional methods typically ensure that all individuals remain within the effective search range by forcibly adjusting the coordinates of individuals exceeding the boundary to the upper or lower limit of the set boundary value. While this method guarantees the validity of the solution space, it does not fully utilize the existing excellent solution information in the population. This embodiment introduces a random boundary control strategy to handle individuals exceeding the preset search boundary. The handling involves adjusting the position of individuals exceeding the preset search boundary by combining the positions of the best and second-best performing individuals in the current population. The expression is:

[0119]

[0120] in, , These represent the positions of the optimal solution and the second-best individual in the current iteration, respectively. This means selecting a random number between (0,1). , All are random numbers in the range [0,1]. and These are the upper and lower limits, respectively.

[0121] It is understandable that in this embodiment, when an individual exceeds the boundary, it does not simply adjust it to the boundary value, but rather combines the positions of the best and second-best performing individuals in the current population with a probability to make more precise positional adjustments to the individuals that exceed the boundary. This prevents the search process from becoming too localized, which would limit the algorithm's global search capability. Therefore, this embodiment can effectively guide individuals toward the global optimal solution while avoiding premature convergence.

[0122] Improvement Strategy 4: In the development phase, introduce a solution enhancement strategy to avoid getting trapped in local optima;

[0123] Optionally, as the problem complexity increases, numerous nonlinear constraints make EEFO prone to getting trapped in local optima, leading to premature convergence and an inability to achieve higher convergence accuracy. To address the shortcomings of EEFO in terms of convergence accuracy and its susceptibility to local optima, this embodiment introduces a solution enhancement strategy after generating a new solution to increase the chances of the improved electric eel foraging optimization algorithm escaping local optima. Specifically:

[0124] Calculate the average of the three random solutions Then compare it with the current optimal solution. Combined to generate new candidate solutions And generated using the following formula The expression is as follows:

[0125]

[0126]

[0127]

[0128]

[0129] in, For random numbers that follow a normal distribution, It involves randomly selecting a number from -1 to 2 and then rounding it down. A random number in the range (0, 2). These are three solutions randomly selected from the population. This is an intermediate transition value. As a constant, in some specific implementations, It can be -5, "Represents dot product operation, It is a new solution generated by enhancing the original optimal solution through an enhancement strategy;

[0130] When the generated new solution is not better than the current solution, i.e. To further construct another new candidate solution :

[0131]

[0132]

[0133]

[0134] In the formula, j, k, and s are constants. In some specific implementations, j, k, and s can be 20, -12, and 2, respectively, and SF and This serves as an intermediate transition value, where SF is used to control the balance between exploration and development, varying with the number of iterations. It decreases as it increases.

[0135] It is understandable that the solution quality enhancement strategy introduced in this embodiment can move each solution to a better position, further refine the optimal solution, and at the same time avoid getting trapped in local optima to the greatest extent.

[0136] Step 3: Based on the improved electric eel foraging optimization algorithm, perform parameter optimization on the parameter optimization problem to obtain the optimal parameter combination for the parameter optimization problem, including:

[0137] Based on the population size N, N combinations of parameters for the parameter optimization problem are generated as the initial population according to the good point set initialization strategy.

[0138] The fitness value of each electric eel individual in the initial population is calculated as the objective function of the parameter optimization problem. The electric eel individual that minimizes the objective function value is saved as the optimal electric eel individual, denoted as . ;

[0139] The process of generating an energy factor E for position update involves updating the position of the optimal electric eel individual based on the differential evolution strategy and the random boundary control strategy when the energy factor is greater than or equal to a preset threshold, and updating the position of the optimal electric eel individual based on the solution enhancement strategy and the random boundary control strategy when the energy factor is less than the preset threshold.

[0140] Compare the fitness values ​​of the optimal electric eel individuals before and after the position update, and select the one with the larger fitness value as the new optimal electric eel individual. This concludes the first position update process for the optimal electric eel individual, and the position of the optimal solution is recorded. and the corresponding optimal objective function value ;

[0141] The energy factor is regenerated to update the position of the new optimal electric eel individual. When the number of iterations in the position update process reaches the maximum number of iterations, the fitness value of the current electric eel individual is obtained. and location If the optimal parameter combination is selected as the optimal parameter combination for the parameter optimization problem, then the position update process continues.

[0142] Optionally, before performing parameter optimization on the parameter optimization problem based on the improved electric eel foraging optimization algorithm, the algorithm further includes defining parameters, including the upper limit Up and lower limit Low of the solution space, the population size N, and the maximum number of iterations MaxIt. The upper limit Up and lower limit Low of the solution space are the upper and lower limits of the variable parameters in the parameter optimization problem. The improved electric eel foraging optimization algorithm is named the Improved Electric Eel Foraging Optimization Algorithm Based on Differential Evolution Strategy and Multi-Strategy Fusion (IEEFO).

[0143] Optionally, the improved electric eel foraging optimization algorithm includes interactive operations, migration operations, resting operations, and hunting operations, wherein:

[0144] When the energy factor E At time 1, the interactive operation is performed to update the current position of the electric eel individual, and the position of the electric eel individual is updated again based on the differential evolution strategy. Boundary detection is performed on the updated position of the electric eel individual. Based on the random boundary control strategy, the position of the electric eel individual that exceeds the upper limit Up and lower limit Low of the solution space is updated for the last time.

[0145] When the energy factor E < 1, if rand < 1 / 3, perform a rest operation and update the current electric eel individual's position; if 1 / 3 rand If 2 / 3, perform a migration operation to update the current electric eel individual's position. If rand > 2 / 3, perform a hunting operation to update the current electric eel individual's position. Then, based on the solution enhancement strategy, update the updated electric eel individual's position again. Perform boundary detection on the electric eel individual's position updated after the above rand judgment. Based on the random boundary control strategy, update the position of electric eel individuals that exceed the upper limit Up and lower limit Low of the solution space.

[0146] Optionally, the energy factor is generated using the following formula:

[0147]

[0148] in, t is the current iteration number, and T is the maximum iteration number. It is a random number in the range (0, 1).

[0149] Optionally, the interactive operation includes:

[0150] The electric eel interacts with a random electric eel within the population using its individual location information, updating its position by comparing its distance from the population center. It also interacts with other random electric eels in the population using search space information, updating its position based on its difference from other randomly generated electric eels in the search space. The interactions between electric eels result in random movements in different directions. The interaction model of the electric eels is expressed as follows:

[0151]

[0152]

[0153]

[0154]

[0155] , ,

[0156]

[0157]

[0158] in, This represents the electric eel's speed update value. Indicates the location of the electric eel. This represents the average position of the electric eel. This indicates the location of a randomly selected electric eel. It is a scaling factor used to control the magnitude of speed updates. It is a random number that follows a standard normal distribution. It is a binary variable. It is a vector composed of binary variables. and It is a random number within (0, 1). and Two probability thresholds are used to determine the method of speed update. It is the fitness of the i-th electric eel. It is the location of an electric eel randomly selected within the current population. Let be the dimension of the electric eel's search space, and ; It is a random number within (0, 1) used to generate random positions. .

[0159] Optionally, the rest operation includes:

[0160] Normalize the search space and the electric eel's position to a range of 0-1, then randomly select one dimension of the electric eel's position and project it onto the main diagonal of the normalized search space. Treat the projected position as the center of the electric eel's resting area. The resting operation can be represented as:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167] in, Represents a random position vector. Scaling factor This means rounding random numbers to the nearest integer within a specified range. This indicates the center of the electric eel's resting area. This represents a normalized value for one dimension of the electric eel's location. It is the position vector of the best solution obtained so far. It is the dimension of the random location of an individual randomly selected from the current population. and Indicates the search space in the th order. Lower and upper limits in latitude, It is the proportion of rest areas. This is the initial proportion of the rest area. It is a random number within the range (0,1). As the iteration proceeds, It can reduce the size of the static area and improve utilization.

[0168] Optionally, the migration operation includes:

[0169]

[0170]

[0171]

[0172]

[0173]

[0174] in, It can be considered any location within the hunting area. and It is a random number in the range (0,1). This indicates that the electric eel is moving towards the hunting area. This represents the position vector of the obtained optimal solution. It is a scaling factor used to control the extent to which the electric eel moves towards the hunting area. It is a random number that follows a standard normal distribution. It is the Lévy flight function, used to avoid getting trapped in local optima. It is the standard gamma function. It is a constant, which is 1.5 in this embodiment.

[0175] Optionally, the hunting operation includes:

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] in, This represents the position update value of the electric eel as it moves towards its prey (the optimal solution). Indicates the curl factor. It is a random number in the range (0,1), and its size increases over time. This will reduce the size of the hunting area, making it easier for development. For scale The initial value.

[0182] Example 2: Based on Example 1, this example uses both the present invention (IEEFO) and the traditional electric eel foraging optimization algorithm (EEFO) to solve the robot gripper parameter design problem. It runs independently 30 times, with a parameter population size of 100 and a maximum number of iterations of 500. The solution data is shown in Table 1.

[0183] Table 1. Solution results for the robot gripper parameter design problem

[0184]

[0185] Experimental results show that the IEEFO algorithm outperforms the original EEFO algorithm and is more stable in solving the robot gripper design problem. Furthermore, the objective function value (3.0261) obtained using this invention is less than the objective function value (3.4248) obtained using the existing whale optimization algorithm. Therefore, this invention demonstrates higher parameter solving accuracy for the robot gripper parameter design problem than the original electric eel foraging optimization algorithm.

[0186] Furthermore, to verify the performance of the IEEFO algorithm, 29 benchmark functions from the CEC2017 test suite were selected for optimization. First, the IEEFO algorithm was compared with several different swarm intelligence optimization algorithms to verify its superiority. Then, it was compared with different improvement strategies to verify the effectiveness of the improvements made to the IEEFO algorithm.

[0187] Optionally, this embodiment uses four different types of benchmark functions, as shown in Table 2. F1 and F3 are unimodal benchmark functions, F4-F10 are multimodal benchmark functions, F11-F20 are mixed benchmark functions, and F21-F30 are combined functions. The optimization performance of the IEEFO algorithm is verified through different function types.

[0188] Table 2 Overview of CEC2017 Test Kit

[0189]

[0190] Furthermore, IEEFO and nine other intelligent algorithms, including Electric Eel Foraging Optimization (EEFO), Harris Eagle Optimization (HHO), Escape Optimization (ESC), Lévy Flight Distribution (LFD), Moth Flame Optimization (MFO), Exponential-Triangular Optimization (ETO), Whale Optimization (WOA), Atomic Search Optimization (ASO), and Sine-Cosine Optimization (SCA), were tested on a 30-dimensional (Dim=30) CEC2017 test suite. To ensure the fairness and validity of the experimental results, the common parameters of the algorithms were first standardized: the population size (N=50) was set to 50, and the maximum number of iterations (MaxIter=500) was set to 500. Secondly, each algorithm was run independently 30 times, and the results of these 30 runs were recorded. The optimal value, average value, and standard deviation were then used as evaluation metrics for the performance of each algorithm. The parameter settings for each selected swarm intelligent optimization algorithm are shown in Table 3.

[0191] Table 3 Algorithm Parameter Settings

[0192]

[0193] Table 4 presents the statistical data. For unimodal functions (F1, F3), IEEFO's average fitness ranks first, and its standard deviation is significantly improved compared to the original EEFO. Notably, IEEFO outperforms the recently proposed algorithms ESC and ETO on these two test cases. Since unimodal functions have a unique extremum, IEEFO possesses strong local exploitation capabilities, largely thanks to its good point set initialization strategy, which provides a high-quality initial population, giving it a significant advantage in the initial iterations. For multimodal functions (F4~F10), the randomly selected F4, F6, and F10 in this embodiment all achieved good results. For mixed test functions (F11~F20), IEEFO achieved satisfactory results on the vast majority of test functions, thanks to the excellent ability to escape local optima provided by the differential evolution strategy and solution quality enhancement strategy. For composite functions (F21~F30), experiments were conducted on F22, F23, F24, F26, F28, and F30 in this embodiment, all yielding excellent results. These results demonstrate that IEEFO exhibits superior optimization performance when solving complex high-dimensional problems. This performance improvement is attributable to the combined effect of the four strategies introduced in this embodiment. Finally, the method proposed in this embodiment achieves a Friedman average ranking of 1.47, ranking first. Figure 4The image shows a radar chart ranking all methods. It can be seen that HHO, SCA, WOA, and ETO are roughly within a circle surrounding a large shaded area, indicating their relative stability in solving optimization problems, but with room for improvement in accuracy and quality. However, IEEFO has the smallest shaded area, demonstrating its superior ranking and performance compared to similar optimizers. Overall, IEEFO has a stronger competitive advantage on the CEC2017 test suite.

[0194] Table 4 Comparison of IEEFO algorithm with different optimization algorithms

[0195]

[0196] Figures 5 to 11 The convergence curves of IEEFO and nine other algorithms are shown. For unimodal functions (F1 and F3), IEEFO demonstrates a significant improvement in convergence speed and accuracy, ranking first among the algorithms in both. Notably, IEEFO shows a good advantage over the new algorithm ESC on unimodal functions. For multimodal functions (F4~F10), this embodiment ranks first in convergence accuracy on F4, F6, and F10. For mixed functions (F11~F20), observations... Figures 5 to 11 It can be seen that IEEFO ranks first in average convergence accuracy and convergence speed for the vast majority of test functions, proving that IEEFO can still maintain good optimization performance under complex conditions. For composite functions (F21~F30), this embodiment randomly selected F22, F23, F24, F28, and F30 for testing. IEEFO outperformed other algorithms in both convergence speed and convergence accuracy. Compared to EEFO, due to the high complexity of composite functions, EEFO's ability to escape local optima is limited, leading to premature convergence to local optima. In contrast, IEEFO integrates multiple strategies, possessing a stronger ability to escape local optima and a faster convergence speed.

[0197] Furthermore, to confirm the effectiveness of each strategy, the performance of EEFO, IEFFO, and four IEEFO derivatives used individually were evaluated simultaneously in the CEC2017 test suite. IEEFO-1 is an EEFO with a good point set initialization strategy, IEEFO-2 is an EEFO with a solution quality enhancement strategy, IEEFO-3 is an EEFO with a random boundary strategy, and IEEFO-4 is an EEFO with a differential evolution strategy. The results are shown in Table 5. The algorithm parameters are consistent with the original EEFO algorithm, the population size is 30, the maximum number of iterations is 500, and each algorithm is run independently 30 times. Table 5 gives the statistical results of the five improved optimization algorithms and the original EEFO algorithm running independently 30 times under 23 benchmark functions.

[0198] Table 5. Effectiveness Experiments of the Four Strategies

[0199]

[0200] According to the ranking results in the table, the contribution of each strategy to optimization performance is ranked as follows: Differential Evolution Strategy > Solution Quality Enhancement Strategy > Good Point Set Initialization Strategy > Random Boundary Control Strategy. Table 5 shows that the EEFO variant with the addition of the good point set initialization strategy performs better on complex functions than on unimodal functions. This is because the good point set initialization strategy can still provide high-quality initial solutions in complex functions. The EEFO variant with the addition of the random boundary control strategy shows a slight decrease in performance on mixed functions, but its overall performance is still better than the original EEFO algorithm. The EEFO variants with the addition of the solution quality enhancement strategy and the differential evolution strategy show improved performance in most test functions. Therefore, each EEFO variant with added strategies shows an overall performance improvement over the original EEFO, but still lacks some robustness. The IEEFO proposed in this embodiment outperforms the original algorithm and other variants in most functions, and has an average ranking of 1.20, ranking first. This proves the effectiveness of the four strategies in improving algorithm performance and demonstrates that the combined use of the four strategies improves algorithm performance more than the use of a single strategy.

[0201] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for designing robot gripper parameters based on improved electric eel foraging optimization, characterized in that, Includes the following steps: Step 1: Represent the robot gripper parameter design problem as a parameter optimization problem, which includes variable parameters, constraints, and an objective function, wherein the objective function is obtained based on the variable parameters and the constraints; Step 2: Improve the traditional electric eel foraging optimization algorithm to obtain the improved electric eel foraging optimization algorithm, including: Improvement Strategy 1: In the initialization phase, introduce a good point set initialization strategy to increase the diversity of the population; Improvement Strategy 2: In the exploration phase, introduce a differential evolution strategy to increase the breadth of exploration and improve global search and local optimization capabilities; Improvement Strategy 3: In the iteration phase, introduce a random boundary control strategy to ensure that the search process is within the preset search boundary; Improvement Strategy 4: In the development phase, introduce a solution enhancement strategy to avoid getting trapped in local optima; Step 3: Based on the improved electric eel foraging optimization algorithm, perform parameter optimization on the parameter optimization problem to obtain the optimal parameter combination for the parameter optimization problem, including: Based on the population size N, N combinations of parameters for the parameter optimization problem are generated as the initial population according to the good point set initialization strategy. The fitness value of each electric eel individual in the initial population is calculated as the value of the objective function of the parameter optimization problem, and the electric eel individual that minimizes the value of the objective function is saved as the optimal electric eel individual; The process of generating an energy factor E for position update involves updating the position of the optimal electric eel individual based on the differential evolution strategy and the random boundary control strategy when the energy factor is greater than or equal to a preset threshold, and updating the position of the optimal electric eel individual based on the solution enhancement strategy and the random boundary control strategy when the energy factor is less than the preset threshold. Compare the fitness values ​​of the optimal electric eel individuals before and after the position update, and select the one with the larger fitness value as the new optimal electric eel individual, thus ending the first position update process for the optimal electric eel individual. The energy factor is regenerated to update the position of the new optimal electric eel individual. When the number of iterations of the position update process reaches the maximum number of iterations, the fitness value and position of the current electric eel individual are obtained as the optimal parameter combination for the parameter optimization problem. Otherwise, the position update process continues. The differential evolution strategy introduced in the improved strategy two includes mutation, crossover, and selection operations, wherein the mutation operation specifically includes: Three distinct individuals are randomly selected from the population. The difference vectors of two of these individuals are scaled and added to the position of the third individual to generate a new mutant individual, as shown in the following expression: ； ； in, This represents a new electric eel individual resulting from the mutation. , , These are three individuals randomly selected from the electric eel population. Indicates the mutation ratio factor. It is a constant. MaxIt is the number of iterations; The crossover operation specifically refers to: After the mutation operation is completed, the original electric eel target individual and the mutated individual are cross-referenced in each dimension using a preset crossover probability CR to determine whether to select the value of the target individual or the mutated individual. Specifically, one dimension is randomly selected to forcibly inherit the mutated individual's value, while the remaining dimensions are selected from the target individual or the mutated individual based on the crossover probability. The expression for the crossover operation is as follows: ； in, Let be the target individual, and represent the value of the j-th dimension of the i-th individual in the t-th iteration. As a mutated individual, For new individuals generated by crossover, Represents a random number between 0 and 1. Represent a random dimension D is the total number of dimensions, ensuring At least from To obtain a parameter; The selection operation specifically refers to: For each pair of target individuals and mutant individuals, the fitness values ​​of the electric eels were compared. To retain the superior electric eel individuals, the expression for the selection operation is as follows: ； If the electric eel individual is produced Its fitness value is better than that of the current individual electric eel. Then in subsequent iterations, It will be retained as a new electric eel individual. Otherwise, retain the existing electric eel individuals. .

2. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 1, characterized in that, The variable parameters include the lengths a, b, and c of the three links of the gripper, the displacement e of the vertical link, the vertical distance f from the first robotic arm node to the actuator, and the horizontal distance from the actuator to the joint. The angle δ between the second rod b and the third rod c of the gripper, and a total of 7 variable parameters, are used as the objective function to minimize the difference between the maximum and minimum clamping forces within the displacement range of the gripper end, under the following 7 constraints. The expression of the objective function is as follows: ； in, The working range of the clamp is z∈[0, ], For the target variable, Represents the clamping force, expressed as: ； in, The force applied to the drive rod; in: ； ； definition The resulting 7 constraint expressions are: ； in, This represents the limit of the gripper at its maximum working stroke. The minimum displacement at the end must not be less than ; Ensure that the end does not descend to a negative displacement when it is at its farthest position, and ensure that no collision occurs; Ensure that the end position at the initial position does not exceed the maximum permissible displacement. ; This indicates that the initial end displacement must not be lower than the minimum height required for gripping. ; It represents the relationship between two sides of a triangle, preventing structural dimensions from exceeding the limits; Ensure the geometric reachability of the position of maximum displacement at the end; The maximum working stroke is limited to the horizontal distance from the actuator to the joint. .

3. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 1, characterized in that, The improved strategy one introduces a good point set initialization strategy to initialize the population. The expression for generating the population using the good point set initialization strategy is as follows: ； in, It is the i-th individual, where i is an integer and its value ranges from 1 to 2. , represents the index of a point in the set of good points, and N represents the population size. It is a point in d-dimensional space. represent The value of the j-th dimension is given by the formula Determined, where p is the parameter used to construct the direction vector, and is a prime number greater than the dimension d. express The decimal part.

4. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 1, characterized in that, The third improved strategy introduces a random boundary control strategy to handle individuals that exceed the preset search boundary. This handling involves adjusting the positions of individuals exceeding the preset search boundary based on the positions of the best and second-best performing individuals in the current population. The expression is as follows: ； in, , These represent the positions of the optimal solution and the second-best individual in the current iteration, respectively. This means selecting a random number between (0,1). , All are random numbers in the range [0,1]. and These are the upper and lower limits, respectively.

5. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 1, characterized in that, The fourth improvement strategy introduces a solution enhancement strategy to increase the chances of the improved electric eel foraging optimization algorithm escaping local optima. Specifically: Calculate the average of the three random solutions Then compare it with the current optimal solution. Combined to generate new candidate solutions And generated using the following formula The expression is as follows: ； ； ； ； in, For random numbers that follow a normal distribution, It involves randomly selecting a number from -1 to 2 and then rounding it down. A random number in the range (0, 2). These are three solutions randomly selected from the population. This is an intermediate transition value. " is a constant," "Represents dot product operation, It is a new solution generated by enhancing the original optimal solution through an enhancement strategy; If the generated new solution is not better than the current solution, another new candidate solution is constructed. : ； ； ； In the formula, j, k, and s are constants, and SF and This serves as an intermediate transition value, where SF is used to control the balance between exploration and development, varying with the number of iterations. It decreases as it increases.

6. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 1, characterized in that, Before performing parameter optimization on the parameter optimization problem based on the improved electric eel foraging optimization algorithm, the algorithm further includes defining parameters, including the upper limit Up and lower limit Low of the solution space, the population size N, and the maximum number of iterations MaxIt. The upper limit Up and lower limit Low of the solution space are the upper and lower limits of the variable parameters in the parameter optimization problem.

7. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 1, characterized in that, The improved electric eel foraging optimization algorithm includes interactive operations, migration operations, resting operations, and hunting operations, among which: When the energy factor E At time 1, the interactive operation is performed to update the current position of the electric eel individual, and the position of the electric eel individual is updated again based on the differential evolution strategy. Boundary detection is performed on the updated position of the electric eel individual. Based on the random boundary control strategy, the position of the electric eel individual that exceeds the upper limit Up and lower limit Low of the solution space is updated for the last time. When the energy factor E < 1, if rand < 1 / 3, perform a rest operation and update the current electric eel individual's position; if 1 / 3 rand If 2 / 3, perform a migration operation to update the current electric eel individual's position. If rand > 2 / 3, perform a hunting operation to update the current electric eel individual's position. Then, based on the solution enhancement strategy, update the updated electric eel individual's position again. Perform boundary detection on the electric eel individual's position updated after the above rand judgment. Based on the random boundary control strategy, update the position of electric eel individuals that exceed the upper limit Up and lower limit Low of the solution space.

8. The method for designing robot gripper parameters based on improved electric eel foraging optimization according to claim 7, characterized in that, The energy factor is generated using the following formula: ； in, t is the current iteration number, and T is the maximum iteration number. It is a random number in the range (0, 1).

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