Robot dynamics identification method based on improved red-mouth blue-magpie optimization algorithm

Abstract

The invention discloses a robot dynamics identification method based on an improved red-beak blue-magpie optimization algorithm. The method comprises the following steps: step 1, introducing a Halton sequence to optimize and initialize a search population; step 2, constructing a search strategy in a search stage of food group search; step 3, constructing an attack prey group predation stage search strategy; 4, designing a switching function of group exploration / predation and group exploration / predation; and step 5, designing a robot dynamics identification algorithm based on an improved red-mouth blue-magpie optimization algorithm. According to the method, the parameter convergence speed and optimization precision can be improved, and the industrial robot kinetic parameter identification precision can be improved on the whole.

Description

Technical Field

[0001] The present invention belongs to the field of industrial robots and relates to a method for identifying robot dynamics by improving the red-billed blue magpie optimization algorithm. Background Art

[0002] Industrial robots are regarded as the pearl on the crown of manufacturing. They are widely used in application scenarios such as polishing and grinding, shaft-hole assembly, and human-robot interaction. These application scenarios require high trajectory tracking accuracy and force perception ability. To improve the trajectory tracking accuracy, based on the robot dynamics model, a trajectory tracking control algorithm can be designed to improve the trajectory tracking accuracy. For traditional external force perception, an external force sensor needs to be added. The force sensor is expensive and will cause the stiffness of the robot to decrease. The external force estimation algorithm based on the robot dynamics model can enable the robot to have the ability of external force perception and can meet the control requirements with low force control accuracy, thus avoiding the installation of a force sensor and reducing costs. The requirements of these two scenarios are both based on a high-precision dynamics model.

[0003] The joint torque of a robot consists of inertial torque, Coriolis force, centrifugal force, gravity, and friction. The parameters of the robot dynamics model are numerous and show non-linear characteristic coupling. Although the traditional least squares algorithm has the advantages of low computational complexity and simple implementation, its anti-interference ability to measurement noise is weak. The neural network algorithm has a strong non-linear fitting ability, but its black-box characteristic leads to insufficient physical interpretability of the model, and it faces the inherent defects of dependence on a large amount of training data, high computational complexity, and large amount of calculation. The swarm intelligence algorithm has better global optimization ability. Although it has the deficiencies of slow convergence speed and easy to fall into local optimum, through optimizing the optimization process, this deficiency can be overcome to a certain extent. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art and improve the identification accuracy of industrial robot dynamics parameters, the present invention provides a method for identifying robot dynamics by improving the red-billed blue magpie optimization algorithm. For the population initialization of the red-billed blue magpie optimization algorithm, the Halton sequence is used to optimize the initialized population to improve the randomness of population initialization; in the group search stage of searching for food, the food position is used to replace the search agent position to improve the convergence speed; while in the group predation stage of attacking prey, the search agent position is used to replace the food position to avoid falling into local optimum and improve the diversity of the population in the later stage of search; in the classical red-billed blue magpie optimization algorithm, the selection of group exploration of food, group exploration of food, group predation, and group predation is set as a specific coefficient. In this patent, the conversion coefficient is set as an adaptive coefficient that changes with the number of iterations. In the initial stage of search, it focuses on group exploration of food and group predation, and in the later stage of search, it focuses on group exploration and group predation to improve the search efficiency and avoid falling into local optimum.

[0005] In view of the above technical problems, the technical solution proposed by the present invention is as follows:

[0006] A method for identifying the dynamics of a robot by improving the red-billed blue magpie optimization algorithm, comprising the following steps:

[0007] Step 1, introducing the Halton sequence to optimize the initialization of the search population;

[0008] Step 2, constructing a search strategy for the search phase of the food search group;

[0009] Step 3, constructing a search strategy for the predation phase of the prey attack group;

[0010] Step 4, designing a switching function for group exploration / predation and individual exploration / predation;

[0011] Step 5, constructing a food storage strategy;

[0012] Step 6, designing a robot dynamics identification algorithm based on the improved red-billed blue magpie optimization algorithm.

[0013] Furthermore, in Step 1, the rand function is used in the original algorithm to randomize the initial population. Although the constructed initial population has a high degree of randomness, it may not be evenly distributed between the upper and lower bounds of the search, resulting in a slow population search speed and insufficient diversity. Therefore, the Halton sequence is introduced to optimize the initialization of the search population, enabling the population individuals to be evenly distributed in the search space and improving the diversity of the population. The mathematical model is shown in the following formula:

[0014]

[0015] ρ n = H(n)(ρ U - ρ L ) + ρ L (4)

[0016] where n ∈ [1, N], N is the number of the population, p is a prime number, p ≥ 2, b i is a constant coefficient, m determines the number of digits in the base expansion, i represents the dimension of the Halton sequence, H(n) is a D-dimensional uniform Halton sequence, ρ U , ρ L are the upper and lower bounds of the population, and ρ n is the initialized red-billed blue magpie population;

[0017] Furthermore, in step 2, during the traditional process of searching for food, red-billed blue magpies usually act in small groups (2 to 5 individuals) or large groups (more than 10 individuals) to improve search efficiency. They employ various techniques, such as hopping, walking on the ground, or scavenging for food resources in trees. This adaptability and flexibility enable red-billed blue magpies to adopt diverse hunting strategies according to environmental conditions and available resources, ensuring an adequate food supply.

[0018] When a small group explores for food, its mathematical model is as follows:

[0019]

[0020] where t is the current iteration number, ρ i (t + 1) represents the latest search position, l represents the number of red-billed blue magpies randomly selected in a group of 2 to 5 individuals, ρ s represents the randomly selected s-th individual, ρ i represents the i-th individual, ρ rs represents the search position randomly selected in the current iteration, Rand represents a random number used to generate a standard normal distribution (mean 0, standard deviation 1);

[0021] When searching in a large group, its mathematical model is as follows:

[0022]

[0023] where: j represents the number of search positions during large-group search, ranging from 10 to N, and is also randomly selected from the entire population;

[0024] During the overall search process of small-group exploration and large-group exploration, it tends to exploration, resulting in a slow overall convergence speed and a lack of the ability to communicate with excellent individuals. Therefore, the food position is introduced in the large-group search stage, and its mathematical model is as follows:

[0025]

[0026] where is the food position.

[0027] Furthermore, in step 3, during the stage of attacking prey groups for predation, red-billed blue magpies show a high level of hunting proficiency and cooperation spirit when chasing prey. They adopt tactics such as quickly pecking, jumping to catch prey, or flying to catch insects. In small-group actions, the targets are small prey or plants, and its mathematical model is as follows:

[0028]

[0029] where, T is the iteration number;

[0030] When acting in a group, the red-billed blue magpie can jointly target larger prey, such as large insects or small vertebrates. This predatory hunting behavior emphasizes the various strategies and skills possessed by the red-billed blue magpie, making it a versatile predator capable of successfully obtaining food in various scenarios. Its mathematical model is shown as follows:

[0031]

[0032] Although small groups and clusters can jointly target prey during the predation stage, the diversity is poor during the search process and it is easy to fall into local optima. Therefore, the current search position is introduced during cluster actions to maintain search diversity. Its mathematical model is shown as follows:

[0033]

[0034] In step 4, since classical red-billed blue magpies use fixed values for switching during small-group search, group search switching, and small-group attack and group attack on prey, with a value of 0.5, this type of algorithm completely evenly divides the process of small-group search and group search. According to the existing algorithm, if fixed-value search is used, it will lead to poor diversity in population search in the early stage of search and poor convergence in the later stage of search; during the attack stage, the convergence is poor in the early stage of search and the diversity is poor in the later stage of search. Therefore, a switching adaptive factor is designed, and its mathematical model is shown as follows:

[0035]

[0036] Among them, γ1 and γ2 are switching factor coefficients.

[0037] In step 5, in addition to searching for and attacking food, the red-billed blue magpie will also store excess food for future consumption. This process helps to find the global optimum, and its mathematical model is shown as follows:

[0038]

[0039] Among them, and respectively represent the fitness values before and after the position update of the i-th red-billed blue magpie.

[0040] The process of step 6 is as follows:

[0041] 6.1 Construct a robot dynamics model

[0042] Construct a robot dynamics model according to Newton-Euler's theorem, and its mathematical model expression is

[0043]

[0044] where τ is the robot joint torque, M(q) is the inertia matrix, is the centrifugal and Coriolis force matrix, G(q) is the gravity, is the friction force, and the traditional Stribeck friction model is

[0045]

[0046] where, f c , f s , σ are the Coulomb friction, static friction, and viscous friction coefficients respectively, is an empirical parameter with a value range of 0.5 - 2, q e is the Stribeck velocity coefficient. The traditional friction model uses one Stribeck velocity coefficient to characterize the Stribeck velocity characteristics of Coulomb friction and static friction, which is not accurate enough. Therefore, two parameters are introduced to describe the Stribeck velocity characteristics, and its mathematical model expression is:

[0047]

[0048] where q e1 , q e2 are the Stribeck velocity coefficients of Coulomb friction and static friction respectively;

[0049] 6.2 Design the excitation trajectory

[0050] Design the excitation trajectory to fully stimulate the dynamic characteristics of the robot, reduce the influence of measurement noise, and avoid exceeding the motion limit. Design a periodic fifth-order Fourier series as the estimation expression, and the trajectories of the robot joint position, velocity, and acceleration are shown as follows:

[0051]

[0052] where, q i0 is the offset of the i-th joint position, a il , b il are the amplitudes of the sine and cosine functions of the i-th joint, ω f is the fundamental frequency of the Fourier series, and S is the number of harmonic terms of the Fourier series. Set the robot motion limits such as joint position, velocity, and acceleration to avoid equipment damage;

[0053] 6.3 Construct the fitness function of the improved red-billed blue magpie

[0054] Execute the robot excitation trajectory, collect the positions and torques of the six joints, calculate the speeds and accelerations of the robot joints, and filter the joint torques. Obtain the data required for identification, design a fitness function, and make the fitness function value approach the minimum. At this time, the identification error also approaches the minimum. The designed fitness function is:

[0055]

[0056] Wherein, are the values of the torque estimated according to the identification model and the filtered torque collected respectively. ψ i is a weight between 0 and 1, and the search goal is to obtain the minimum value of the fitness value.

[0057] The technical concept of the present invention is: for the identification of industrial robot dynamic parameters, design a Stribeck friction model. For the traditional red-billed blue magpie algorithm, introduce the Halton sequence to optimize the initialization of the search population to improve the diversity of the population; in the group search stage of looking for food, introduce the food position to improve the convergence speed. Introduce the current search position in the stage of attacking the prey group for predation to maintain the diversity of the search; when switching between group, group search and predation, design an adaptive factor to improve the convergence speed and population diversity, improve the convergence speed and estimation effect of the algorithm, and improve the accuracy of dynamic parameter identification.

[0058] The beneficial effects of the present invention are: compared with the traditional red-billed blue magpie algorithm, the initialization of the search population is optimized by the Halton sequence to improve the diversity of the population; designing to introduce the food position in the group search stage improves the convergence speed, and introducing the current search position in the group predation stage improves the diversity of the population. By designing the switching factor between groups and groups, the convergence speed and population diversity are improved. Generally, the convergence speed and fitting accuracy of the algorithm can be improved, and the identification accuracy of the dynamic model can be improved. Description of the Drawings

[0059] Figure 1 is the robot excitation trajectory designed based on the fifth-order Fourier series. Among them, (a) represents the position, (b) represents the speed, and (c) represents the acceleration;

[0060] Figure 2 is the schematic diagram of the torque filtering for the robot joint to execute the excitation trajectory;

[0061] Figure 3 is the schematic diagram of the robot identification effect based on the improved red-billed blue magpie algorithm;

[0062] Figure 4 is the schematic diagram of the identification process of the present invention. Detailed Embodiments

[0063] The present invention will be further described below in conjunction with the accompanying drawings.

[0064] Referring to Figures 1-4 , a robot dynamics identification method for improving the red-billed blue magpie optimization algorithm, comprising the following steps:

[0065] Step 1, introducing the Halton sequence to optimize the initial search population, the process is as follows:

[0066] Introducing the Halton sequence to optimize the initial search population, so that the population individuals can be evenly distributed in the search space, improving the diversity of the population. Its mathematical model is shown in the following formula:

[0067]

[0068]

[0069] ρ n = H(n)(ρ U -ρ L ) + ρ L (4)

[0070] where n ∈ [1, N], N is the number of the population, set to 200 groups, p is a prime number, p ≥ 2, b i is a constant coefficient, m determines the number of digits of the base expansion, i represents the dimension of the Halton sequence, H(n) is a D-dimensional uniform Halton sequence (D is the number of dynamic parameters), ρ U , ρ L are the upper and lower bounds of the population, ρ n is the initial red-billed blue magpie population;

[0071] Step 2, constructing a search strategy for the search stage of the food search group, the process is as follows:

[0072] When the group explores food, its mathematical model is shown in the following formula

[0073]

[0074] where t is the current iteration number, ρ i (t + 1) represents the latest search position, l represents the number of red-billed blue magpies randomly selected in a group of 2 to 5, ρ s represents the s-th individual randomly selected, ρ i represents the i-th individual, ρ rs represents the search position randomly selected in the current iteration, Rand represents a random number used to generate a standard normal distribution (mean 0, standard deviation 1);

[0075] And when the group searches, its mathematical model is shown in the following formula:

[0076]

[0077] Among them: j represents the number of search positions during group search, which is between 10 and N. Similarly, it is also randomly selected from the entire population;

[0078] During the overall search process of group exploration and population exploration, the search is biased towards exploration, resulting in a slow overall convergence speed and a lack of the ability to communicate with excellent individuals. Therefore, during the group search stage, the food position is introduced, and its mathematical model is shown as follows:

[0079]

[0080] Among them is the food position;

[0081] Step 3, construct the search strategy for the stage of attacking prey groups and preying, and the process is as follows:

[0082] In small group actions, the main targets are usually small prey or plants, and its mathematical model is shown as follows:

[0083]

[0084] Among them, T is the number of iterations, which is set to 1000 times. When acting in a group, the red-billed blue magpie can jointly target larger prey, such as large insects or small vertebrates. This predatory hunting behavior emphasizes the various strategies and skills possessed by the red-billed blue magpie, making it a versatile predator that can successfully obtain food in various scenarios, and its mathematical model is shown as follows:

[0085]

[0086] Although small groups and group actions can jointly target prey during the predation stage, the diversity during the search process is poor and it is easy to fall into local optima. Therefore, the current search position is introduced during group actions to maintain the diversity of the search, and its mathematical model is shown as follows:

[0087]

[0088] Step 4, design the switching function between group exploration / prey and population exploration / prey, and the process is as follows;

[0089] According to the existing algorithm, if fixed-value search is adopted, it will lead to poor diversity of the population search in the early stage of the search, poor convergence in the later stage of the search, poor convergence in the early stage of the attack stage, and poor diversity in the later stage of the search. Therefore, a switching adaptive factor is designed, and its mathematical model is shown as follows:

[0090]

[0091] where γ1 and γ2 are switching factor coefficients;

[0092] Step 5, construct a food storage strategy, the process is as follows:

[0093] In addition to searching for and attacking food, the red-billed blue magpie will also store excess food for future consumption. This process helps to find the global optimum, and its mathematical model is shown as follows:

[0094]

[0095] where, and represent the fitness values before and after the position update of the i-th red-billed blue magpie respectively;

[0096] Step 6, design a robot dynamics identification algorithm based on the improved red-billed blue magpie optimization algorithm, the process is as follows:

[0097] 6.1 Construct a robot dynamics model according to Newton-Euler theorem, and its mathematical model expression is

[0098]

[0099] where τ is the robot joint torque, M(q) is the inertia matrix, is the centrifugal and Coriolis force matrix, G(q) is the gravity, is the friction force, and the traditional Stribeck friction model is

[0100]

[0101] where, f c , f s , σ are the Coulomb friction, static friction and viscous friction coefficients respectively, is an empirical parameter, and its value range is 0.5 - 2, q e is the Stribeck velocity coefficient. The traditional method uses a single Stribeck velocity coefficient to represent the Stribeck velocity characteristics of Coulomb friction and static friction, which is not accurate enough. Therefore, two parameters are introduced, and its mathematical model expression is:

[0102]

[0103] where q e1 , q e2 are the Stribeck velocity coefficients of Coulomb friction and static friction respectively;

[0104] 6.2 Design an excitation trajectory

[0105] Design an excitation trajectory to fully stimulate the dynamic characteristics of the robot, reduce the influence of measurement noise, and avoid exceeding the motion limit. Design a periodic fifth-order Fourier series as the trajectory expression. The trajectories of the robot joint positions, velocities, and accelerations are shown as follows:

[0106]

[0107] where q i0 is the offset of the position of the i-th joint, a il , b il are the amplitudes of the sine and cosine functions of the i-th joint, ω f is the fundamental frequency of the Fourier series, set to 62.5 Hz, the period is set to 10 s, S is the number of harmonic terms of the Fourier series, set to 5; set the motion limits of the robot such as joint positions, velocities, and accelerations to avoid equipment damage;

[0108] 6.3 Construct the fitness function of the improved red-billed blue magpie

[0109] Execute the robot excitation trajectory, collect the positions and torques of the 6 joints. According to the trajectory period of 10 s and the frequency of 62.5 Hz, 625 groups of data are collected, calculate the velocities and accelerations of the robot joints, and filter the joint torques; obtain the data required for identification, design the fitness function, make the fitness function value approach the minimum, and at this time the identification error also approaches the minimum. Design its fitness function as:

[0110]

[0111] where are the values of the torque estimated according to the identification model and the filtered values of the collected torque respectively. ψ i is a weight between 0 and 1, and the search goal is to obtain the minimum value of the fitness value.

[0112] To verify the effectiveness of the proposed method for robot dynamic parameter identification, an excitation trajectory of a fifth-order Fourier series is designed, as Figure 1 shown. Its position, velocity, and acceleration all start from zero to avoid sudden start and stop, causing noise interference. Regarding the problem of noise in the collected joint torques, filter the torques of the six joints to overcome the interference of noise, as Figure 2 shown. Regarding the comparison of the joint torques fitted by the identification results and the collected torques, as Figure 3 shown. It can be seen from the figure that the estimated torque and the collected torque are relatively close. To compare the identification effect of the present invention with the identification results of the traditional red-billed blue magpie algorithm, as shown in Table 1, from the overall identification error, the identification error of the present invention is less than that of the traditional red-billed blue magpie algorithm.

[0113] Table 1 shows the comparison between the identification results of the present invention and the identification results of traditional Red-billed Blue Magpies;

[0114]

[0115] In summary, the robot dynamics identification algorithm based on the improved Red-billed Blue Magpie optimization algorithm can improve the identification accuracy of industrial robot dynamics parameters.

[0116] The excellent optimization effect shown by an embodiment given by the present invention is described above. Obviously, the present invention is not limited to the above embodiment, and various deformations can be made to it on the premise of not deviating from the basic spirit of the present invention and not exceeding the scope involved in the substantial content of the present invention.

Claims

1. A method for identifying the dynamics of a robot that improves the red-billed blue magpie optimization algorithm, characterized in that, The method includes the following steps: Step 1, introducing the Halton sequence to optimize the initial search population; Step 2, constructing a search strategy for the food search stage of the search group; Step 3, constructing a search strategy for the prey hunting stage of the attacking prey group; Step 4, designing a switching function for group exploration / predation and individual exploration / predation; Step 5, constructing a food storage strategy; Step 6, designing a robot dynamics identification method based on the improved red-billed blue magpie optimization algorithm.

2. The robot dynamics identification method for improving the red-billed blue magpie optimization algorithm according to claim 1, characterized in that, In Step 1, the Halton sequence is introduced to optimize the initial search population, enabling the population individuals to be evenly distributed in the search space and improving the diversity of the population. Its mathematical model is shown as the following formula: ρ n = H(n)(ρ U - ρ L ) + ρ L (4) Where: n ∈ [1, N], N is the number of populations, p is a prime number, p ≥ 2, b i is a constant coefficient, m determines the number of digits in the base expansion, i represents the dimension of the Halton sequence, H(n) is a D-dimensional uniform Halton sequence, ρ U , ρ L is the upper and lower bounds of the population, ρ n is the initialization of the red-billed blue magpie population.

3. The method for identifying robot dynamics by improving the red-billed blue magpie optimization algorithm according to claim 1 or 2, characterized in that, In Step 2, when the individual explores food, its mathematical model is shown as the following formula where t is the current iteration number, ρ i (t + 1) represents the latest search position, l represents the number of Urocissa erythrorhyncha randomly selected in a group of 2 to 5, ρ s represents the s-th individual randomly selected, ρ i represents the i-th individual, ρ rs represents the search position randomly selected in the current iteration, Rand represents a random number used to generate a standard normal distribution; While during group search, its mathematical model is shown as the following formula: Where: j represents the number of search positions during group search, ranging from 10 to N. Similarly, it is also randomly selected from the entire population; During the overall search process of individual exploration and group exploration, it is biased towards exploration, resulting in a slow overall convergence speed and a lack of communication ability with excellent individuals. Therefore, the food position is introduced during the group search stage. Its mathematical model is shown as the following formula: wherein is the food position.

4. The robot dynamics identification method for optimizing the red-billed blue magpie optimization algorithm according to claim 3, characterized in that, In Step 3, during small group actions, the target is small prey or plants. Its mathematical model is shown as the following formula: Among them, T is the number of iterations; When acting in a group, red-billed blue magpies can jointly target larger prey. This predatory hunting behavior emphasizes the various strategies and skills possessed by red-billed blue magpies, making it a versatile predator that can successfully obtain food in various scenarios. Its mathematical model is shown as the following formula: The current search position is introduced during group action to maintain the diversity of the search. Its mathematical model is shown as the following formula:

5. The method for identifying robot dynamics by improving the red-billed blue magpie optimization algorithm according to claim 4, characterized in that, In Step 4, a switching adaptive factor is designed. Its mathematical model is shown as the following formula: Where γ1 and γ2 are switching factor coefficients.

6. The method for identifying robot dynamics by improving the red-billed blue magpie optimization algorithm according to claim 5, characterized in that, In Step 5, in addition to searching for and attacking food, red-billed blue magpies will also store excess food for future consumption. This process helps to find the global optimum. Its mathematical model is shown as the following formula: Among them, and represent the fitness values of the i-th red-billed blue magpie before and after position update, respectively.

7. The method for identifying the dynamics of a robot by improving the red-billed blue magpie optimization algorithm according to claim 6, characterized in that, The process of Step 6 is as follows: 6.1 Constructing a robot dynamics model Construct a robot dynamics model according to Newton-Euler theorem. Its mathematical model expression is where τ is the robot joint torque, M(q) is the inertia matrix, is the centrifugal and Coriolis force matrix, G(q) is the gravity, is the friction force, and the traditional Stribeck friction model is where f c , f s , and σ are the Coulomb friction, static friction, and viscous friction coefficients respectively, is an empirical parameter with a value range of 0.5 - 2, and q e is the Stribeck velocity coefficient; two parameters are introduced to describe the Stribeck velocity characteristics, and its mathematical model expression is: where q e1 , q e2 are the Stribeck velocity coefficients of Coulomb friction and static friction, respectively; 6.2 Designing an excitation trajectory Design an excitation trajectory to fully stimulate the dynamic characteristics of the robot, reduce the influence of measurement noise, and avoid exceeding the motion limit. Design a periodic fifth-order Fourier series as the estimation expression. The trajectories of the robot joint positions, velocities, and accelerations are shown as the following formula: where q i0 is the offset of the i-th joint position, a il , b il are the amplitudes of the sine and cosine functions of the i-th joint, ω f is the fundamental frequency of the Fourier series, and S is the number of harmonic terms of the Fourier series; 6.3 Constructing the fitness function of the improved red-billed blue magpie Execute the robot excitation trajectory, collect the positions and torques of the 6 joints, calculate the velocities and accelerations of the robot joints, and filter the joint torques; obtain the data required for identification, design a fitness function, and make the fitness function value approach the minimum. At this time, the identification error also approaches the minimum. Design its fitness function as: Among them, are the values of the torque estimated by the identification model and the collected torque after filtering, respectively, and ψ i is a weight between 0 and 1, and the search target is to obtain the minimum value of the fitness value.

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