Parameter identification method of robot joint friction model based on improved grey wolf algorithm

Abstract

The robot joint friction model parameter identification method based on the improved gray wolf algorithm belongs to the field of motor system identification, including establishing a friction model of the robot joint under no-load state; establishing a fitness function; initializing the population, inputting the population size, problem dimension, and maximum number of iterations; gradually increasing the robot joint rotation speed from the lower limit of the range, and measuring the output torque of the robot joint when it rotates at a uniform speed at the rotation speed; identifying the robot joint friction model through the improved gray wolf algorithm to obtain the model parameters. The neighbor effect strategy in the improved gray wolf algorithm improves the local search ability of the gray wolf algorithm, the random dispersion strategy improves the global search ability of the gray wolf algorithm, and the co-evolution mechanism balances the exploration and development ability of the gray wolf algorithm. The present invention applies the gray wolf algorithm to the identification of the robot joint friction model, and effectively realizes the identification of the friction model through the improved gray wolf algorithm, thereby improving the identification accuracy, convergence speed, and stability.

Description

Technical Field

[0001] The invention belongs to the technical field of motor system identification, and in particular relates to a robot joint friction model parameter identification method based on an improved grey wolf algorithm. Background Art

[0002] Parameter identification refers to fitting the experimental measured data with the selected mathematical model to determine the unknown parameter values ​​in the mathematical model. Parameter identification methods can be divided into classical identification methods and swarm intelligence identification methods. Classical identification methods mainly include least squares method, step response method, maximum likelihood method, spectral analysis method, etc. Complex systems usually have the characteristics of nonlinearity, discontinuity, and non-differentiability. Classical identification methods have high computational costs, are prone to fall into local optimality, and have limitations. In recent years, swarm intelligence identification methods combined with metaheuristic algorithms have become a research hotspot, such as particle swarm system identification method, genetic algorithm system identification method, neural network system identification method, etc. These emerging swarm intelligence identification methods have fast convergence speed, high identification accuracy, and strong robustness, and have been successfully applied to the identification of power, mechanical and other systems. The friction model of robot joints is a nonlinear complex system, and the use of swarm intelligence identification methods can improve the accuracy of identification.

[0003] The Gray Wolf Algorithm is a new type of swarm intelligence algorithm that simulates the social class and hunting mechanism of gray wolves in nature. However, the traditional Gray Wolf Algorithm has disadvantages such as low population diversity and premature convergence, which limits its application in parameter identification.

[0004] So far, there has been no report on the application of the Grey Wolf Algorithm in the parameter identification of robot joint friction model. Summary of the invention

[0005] In view of the limitations of classical identification methods and the shortcomings of the Grey Wolf Algorithm, the present invention aims to provide a robot joint friction model parameter identification method based on an improved Grey Wolf Algorithm.

[0006] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0007] The robot joint friction model parameter identification method based on the improved grey wolf algorithm of the present invention mainly comprises the following steps:

[0008] S1: Establish the friction model of the robot joint under no-load state;

[0009] S2: Establish fitness function;

[0010] S3: Initialize the population, input the population size, problem dimension, and maximum number of iterations;

[0011] S4: gradually increase the robot joint rotation speed from the lower limit of the range, and measure the output torque of the robot joint when it rotates at a uniform speed at this speed;

[0012] S5: By improving the Grey Wolf algorithm, the robot joint friction model is identified and the model parameters are obtained.

[0013] Furthermore, in step S1, the established robot joint friction model is as follows:

[0014]

[0015]

[0016]

[0017] Where θ is the motor angle, τ mf is the friction torque converted to the motor end, z is the average deformation of the bristle, σ0 is the bristle stiffness, σ1 is the bristle damping coefficient, σ2 is the viscous friction coefficient, is the Stribeck effect, F c is the Coulomb friction force, F s is the maximum static friction, ω s is the Stribeck speed, is the rate of change of bristle shape, is the motor speed.

[0018] Furthermore, in step S2, the fitness function formula established is as follows:

[0019]

[0020] Among them, f i and f di are the i-th estimated friction and actual friction respectively, i=1,2,…,N, N is the population size.

[0021] Furthermore, in step S3, random numbers are generated within the value range of each identification parameter to form a vector as a search agent, and the formula is as follows:

[0022] X ij =rand×(ub j -lb j )+lb j (26)

[0023] Among them, rand is a random number in the interval [0,1], ub j is the upper limit of the value of the jth identification parameter, lb jis the lower limit of the value of the jth identification parameter; j = 1, 2, ..., k, k is the problem dimension; i = 1, 2, ..., N, N is the population size.

[0024] Furthermore, in step S5, the improved grey wolf algorithm has three strategies, including:

[0025] Strategy 1: Neighborhood Effect Strategy

[0026]

[0027]

[0028]

[0029]

[0030] in, is the change in individual position caused by the neighbor effect, M is the neighbor of the ith individual, K i and K j are the fitness values ​​of the i-th individual and the j-th neighbor, respectively, K worst and K best is the fitness value of the best and worst two individuals in the current population, X i and X j are the positions of the ith individual and the jth neighbor, ε = 10 -8 , is the sensing distance of individual i, N is the population size, and the definition of neighbors is: if the distance between two individuals Smaller than the sensing distance Then they are neighbors to each other; is the fitness difference between individual i and individual j, is the position difference between individual i and individual j;

[0031] Strategy 2: Random Dispersion Strategy

[0032]

[0033] in, is the individual position change caused by random dispersion, X m and X n are two individuals randomly selected from the current population, ρ~N(0.5,0.1 2 ) is a random number;

[0034] Strategy 3: Co-evolutionary mechanism

[0035]

[0036] U i =Xa +F(X b +X c ) (19)

[0037]

[0038]

[0039] Among them, α is the best solution in the GWO population, DE_best and DE_worst are the best and worst solutions in the DE population, respectively. and are the positions corresponding to the best and worst solutions in the DE population, respectively. is the fitness value corresponding to the best solution in the DE population, K α is the fitness value corresponding to the best solution in the GWO population, X a , X b and X c are three individuals randomly selected from the DE population, F is a random number in the interval [0,1], CR=0.4 is the crossover probability, rand(j) is a random number in the interval [0,1], rnbr(i) is a random number in the set {1,2,…,k}, k is the problem dimension, t is the number of iterations, and U i is the variant of individual i, V ij is the intersection of individual i, X ij is the parameter value corresponding to the jth dimension of individual i, U ij is the parameter value corresponding to the jth dimension of variant i, X(t+1) is the position of individual i at the t+1th iteration, X(t) is the position of individual i at the tth iteration, V(t) is the position of intersection i at the tth iteration, K X is the fitness value of individual i, K V is the fitness value of the intersection i.

[0040] Furthermore, the strategy 3, i.e. the co-evolution mechanism, comprises the following steps:

[0041] (1) The initial population is copied into two copies, one as the initial population of the DE algorithm and the other as the initial population of the GWO algorithm;

[0042] (2) In the DE algorithm, use formulas (19) to (21) to update the population, calculate the fitness value of each individual according to the fitness function formula, and output the best solution DE_best and the worst solution DE_worst;

[0043] (3) In the GWO algorithm, the traditional grey wolf algorithm and update formula are used to update the population and output the best solution α;

[0044] (4) Compare the best solutions in the two populations: If the best solution in the DE population is better than the best solution in the GWO population, let DE_best replace α in the GWO population; otherwise, let α replace DE_worst in the DE population; and use formula (18) to perform the migration operation;

[0045] (5) Return to step (2) until the number of iterations t equals the maximum number of iterations MaxIter, and the best solution α and the corresponding fitness value are obtained.

[0046] Furthermore, in step (2), firstly, the mutation operation is performed using formula (19), then the crossover operation is performed using formula (20), and finally the selection operation is performed using formula (21).

[0047] Furthermore, in step (3), the traditional grey wolf algorithm is as follows:

[0048] D=|C·X p (t)-X(t)| (4)

[0049] X(t+1)=X p (t)-A·D (5)

[0050] A=2a·r1-a (6)

[0051] C=2·r2 (7)

[0052] a(t)=2-2t / MaxIter (8)

[0053] X1=X α -A1·|C1·X α -X| (9)

[0054] X2=X β -A2·|C2·X β -X| (10)

[0055] X3=X δ -A3·|C3·X δ -X| (11)

[0056] X(t+1)=(X1(t)+X2(t)+X3(t)) / 3 (12)

[0057] Among them, X p is the location of the prey, i.e. the global optimal solution, X is the location of the wolf, i.e. the search agent, t is the number of iterations, r1 and r2 are random numbers in the interval [0,1], MaxIter is the maximum number of iterations, X α , X β , X δare the positions of wolves α, β, and δ respectively, D is the distance between the prey and the gray wolf, C is a random number in [0,2], X p (t) is the position of the prey in the tth iteration, A is the weight value that determines the influence of D on the distance of the gray wolf's movement, a(t) is the weight value that affects the change of A in the tth iteration, X1, X2, and X3 are the distances of the gray wolf's movement caused by α, β, and δ, respectively, A1, A2, and A3 are the weight values ​​in the distances of the gray wolf's movement caused by α, β, and δ, respectively, C1, C2, and C3 are the random values ​​in the distances of the gray wolf's movement caused by α, β, and δ, respectively, X1(t), X2(t), and X3(t) are the distances of the gray wolf's movement caused by α, β, and δ in the tth iteration, respectively.

[0058] Furthermore, in step (3), the update formula is as follows:

[0059]

[0060]

[0061]

[0062] B2(t)=1-B1(t)(25)

[0063] Among them, ρ1, ρ2~N(0.5, 0.1 2 ) is a random number, μ = 1.5, X i (t+1) is the position of individual i in the t+1th iteration, B1 and B2 are the weights that determine the leader effect and the random dispersion in the movement of individual i, respectively. is the movement of individual i caused by leaders α, β and δ (leader effect), B1(t) is the influence factor of the leader effect on the movement of individual i in the tth iteration, and B2(t) is the influence factor randomly dispersed in the movement of individual i in the tth iteration.

[0064] Furthermore, the specific operation process of step (3) is as follows:

[0065] Initialize parameters α, A, C, B1, B2, and calculate the fitness value of each individual according to the fitness function formula (27); set the best three solutions α, β and δ; calculate the movement caused by the leader through formula (23); calculate the movement caused by the neighbors through formula (13); calculate the movement caused by random dispersion through formula (17); update the position of each individual through formula (22), and calculate the fitness value of each individual according to the fitness function formula (27); update the positions of α, β and δ.

[0066] The beneficial effects of the present invention are:

[0067] Compared with the existing inventions, the present invention has the following advantages:

[0068] (1) The present invention uses a swarm intelligence algorithm to identify the robot joint friction model. Compared with classical identification methods such as the least squares method and the maximum likelihood method, the swarm intelligence algorithm has the advantages of low computational cost, fast convergence speed, high convergence accuracy, strong robustness, and high feasibility. It is more suitable for the identification of complex systems with nonlinear characteristics such as friction models.

[0069] (2) The present invention improves the traditional gray wolf algorithm. On the basis of the traditional gray wolf algorithm, three strategies are integrated: neighbor effect strategy, random dispersion strategy, and co-evolution mechanism. The neighbor effect strategy improves the local search capability of the gray wolf algorithm, the random dispersion strategy improves the global search capability of the gray wolf algorithm, and the co-evolution mechanism balances the development and exploration capabilities of the gray wolf algorithm. These three strategies improve and balance the development and exploration capabilities of the gray wolf algorithm. The improved gray wolf algorithm has stronger performance than the classic gray wolf algorithm, with faster convergence speed and higher convergence accuracy, and is more suitable for the identification of complex systems.

[0070] (3) The present invention applies the Grey Wolf Algorithm to the identification of the robot joint friction model for the first time, and effectively realizes the identification of the friction model by improving the Grey Wolf Algorithm. The identification results show that the improved Grey Wolf Algorithm is superior to the traditional Grey Wolf Algorithm in terms of identification accuracy, convergence speed and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a flow chart of the robot joint friction model parameter identification method based on the improved grey wolf algorithm of the present invention.

[0072] Figure 2 It is a flow chart of the improved grey wolf algorithm in the present invention.

[0073] Figure 3 Schematic diagram of the hunting mechanism of the gray wolf algorithm. DETAILED DESCRIPTION

[0074] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0075] like Figure 1 As shown, the robot joint friction model parameter identification method based on the improved grey wolf algorithm of the present invention specifically includes the following steps:

[0076] S1: Establish the friction model of the robot joints in the no-load state.

[0077] The experiments involved in the present invention are all carried out under the premise that the robot joints are unloaded and placed horizontally, for the following reasons:

[0078] The dynamic equations of a typical robot joint system are as follows:

[0079]

[0080] When the robot joint is unloaded, the load moment τ l =0; when the joint is placed horizontally, the gravity term G(q)=0, M(q) is the mass matrix of the motor, is the motor speed. Therefore, as long as the robot joints rotate at a constant speed, the centrifugal force Acceleration Then τ=τ f , that is, the output torque τ of the joint is the internal friction torque τ f .

[0081] The friction model adopted in the present invention is the LuGre friction model, which not only takes into account the static friction characteristics, but also takes into account the dynamic friction characteristics near the speed zero point, and has a more comprehensive description of the friction.

[0082] The robot joint friction model established in step S1 is as follows:

[0083]

[0084]

[0085]

[0086] Where θ is the motor angle, τ mf is the friction torque converted to the motor end, z is the average deformation of the bristle, σ0 is the bristle stiffness, σ1 is the bristle damping coefficient, σ2 is the viscous friction coefficient, is the Stribeck effect, F c is the Coulomb friction force, F s is the maximum static friction, ω s is the Stribeck speed, is the rate of change of the bristle-type variable, is the motor speed.

[0087] Among them, the model parameters that need to be identified include: Coulomb friction force F c , Maximum static friction F s 、Stribeck speed ω s , bristle stiffness σ0, bristle damping coefficient σ1 and viscous friction coefficient σ2.

[0088] S2: Establish fitness function.

[0089] In this implementation, the square error is specifically used as the fitness evaluation index. The square error is used as the fitness function, and the fitness function formula established is as follows:

[0090]

[0091] Among them, f i and f di are the i-th estimated friction (calculated by the friction model through the speed value) and the actual friction (measured by the torque sensor), i = 1, 2, ..., N, N is the population size. This problem is a minimum optimization problem. The smaller the fitness value J, the closer the search agent is to the optimal solution.

[0092] S3: First initialize the population, input the population size, problem dimension, and maximum number of iterations.

[0093] Generate random numbers within the range of each identification parameter value to form a vector as a search agent. The formula is as follows:

[0094] X ij =rand×(ub j -lb j )+lb j (26)

[0095] Among them, rand is a random number in the interval [0,1], ub j is the upper limit of the value of the jth identification parameter, lb j is the lower limit of the value of the jth identification parameter; j = 1, 2, ..., k, k is the problem dimension; i = 1, 2, ..., N, N is the population size.

[0096] In this implementation, in the friction parameter identification, the number of model parameters that need to be identified is 6, so the problem dimension k is set to 6, the population size N is set to 30, and the maximum number of iterations MaxIter is set to 500.

[0097] S4: gradually increase the robot joint rotation speed from the lower limit of the range, and use the torque sensor to measure the output torque of the robot joint when it rotates at a constant speed at this speed.

[0098] From the analysis of step S1, it can be known that the output torque is the friction torque of the robot joint. In specific implementation, the range should be determined according to the speed range of the robot joint, the number of torque samples should be sufficient, and finally the average value is taken to obtain the speed-torque data.

[0099] S5: By improving the Grey Wolf algorithm, the robot joint friction model is identified and the model parameters are obtained.

[0100] The overall framework of the improved grey wolf algorithm of the present invention is that the differential evolution algorithm (DE) and the classical grey wolf algorithm (GWO) run in parallel, and the optimal solution is transferred through the migration operator.

[0101] In the specific implementation, the input of the friction model is the speed value in step S4. After substituting the 6 parameters identified by the improved grey wolf algorithm, the friction torque value at the speed is calculated (i.e., the estimated friction force f i ); the actual friction force f measured by the torque sensor di With f i Substituting into the fitness function formula (27), the fitness value of the set of identification parameters can be obtained; according to the fitness value, the population of the improved grey wolf algorithm is updated until the maximum number of iterations is met, and the optimal identification parameters and corresponding fitness are output.

[0102] The improved grey wolf algorithm has three strategies, including:

[0103] Strategy 1 (neighborhood effect strategy, used to improve the local search ability of the gray wolf algorithm):

[0104]

[0105]

[0106]

[0107]

[0108] Among them, is the change in individual position caused by the neighbor effect, M is the neighbor of the ith individual, K i and K j are the fitness values ​​of the i-th individual and the j-th neighbor, respectively, K worst and K best is the fitness value of the best and worst two individuals in the current population, X i and X j are the positions of the ith individual and the jth neighbor, ε = 10 -8 , is the sensing distance of individual i, N is the population size, and the definition of neighbors is: if the distance between two individuals Smaller than the sensing distance Then they are neighbors to each other; is the fitness difference between individual i and individual j, is the position difference between individual i and individual j;

[0109] Strategy 2 (random dispersion strategy, used to improve the global search ability of the gray wolf algorithm):

[0110]

[0111] in, is the individual position change caused by random dispersion, X mand X n are two individuals randomly selected from the current population, ρ~N(0.5,0.1 2 ) is a random number;

[0112] Strategy 3 (co-evolution mechanism, used to balance the exploration and development capabilities of the gray wolf algorithm):

[0113]

[0114] U i =X a +F(X b +X c ) (19)

[0115]

[0116]

[0117] Among them, α is the best solution in the GWO population, DE_best and DE_worst are the best and worst solutions in the DE population, respectively. and are the positions corresponding to the best and worst solutions in the DE population, respectively. is the fitness value corresponding to the best solution in the DE population, K α is the fitness value corresponding to the best solution in the GWO population, X a , X b and X c are three individuals randomly selected from the DE population, F is a random number in the interval [0,1], CR=0.4 is the crossover probability, rand(j) is a random number in the interval [0,1], rnbr(i) is a random number in the set {1,2,…,k}, k is the problem dimension, t is the number of iterations, and U i is the variant of individual i, V ij is the intersection of individual i, X ij is the parameter value corresponding to the jth dimension of individual i, U ij is the parameter value corresponding to the jth dimension of variant i, X(t+1) is the position of individual i at the t+1th iteration, X(t) is the position of individual i at the tth iteration, V(t) is the position of intersection i at the tth iteration, K X is the fitness value of individual i, K V is the fitness value of the intersection i.

[0118] Among them, Figure 2 As shown, the strategy 3, i.e. the co-evolution mechanism, specifically includes the following steps:

[0119] (1) The initial population is copied into two copies, one as the initial population of the DE algorithm and the other as the initial population of the GWO algorithm;

[0120] (2) In the DE algorithm, the population will be updated through three steps: mutation, crossover, and selection. After the population is updated, the fitness value of each individual is calculated. After the DE population is updated, the best solution DE_best and the worst solution DE_worst in the population are selected. The specific operation process is as follows:

[0121] In the DE algorithm, the population is updated using formulas (19) to (21), that is, firstly, the mutation operation is performed using formula (19), then the crossover operation is performed using formula (20), and finally, the selection operation is performed using formula (21). The fitness value of each individual is calculated according to the fitness function formula (27), and the best solution DE_best and the worst solution DE_worst in the DE population are output;

[0122] (3) In the GWO algorithm, the traditional grey wolf algorithm and update formula are used to update the population, and the best solution α in the GWO population is output;

[0123] Among them, the specific process of the traditional grey wolf algorithm is as follows:

[0124] D=|C·X p (t)-X(t)| (4)

[0125] X(t+1)=X p (t)-A·D (5)

[0126] A=2a·r1-a (6)

[0127] C=2·r2 (7)

[0128] a(t)=2-2t / MaxIter (8)

[0129] X1=X α -A1·|C1·X α -X| (9)

[0130] X2=X β -A2·|C2·X β -X| (10)

[0131] X3=X δ -A3·|C3·X δ -X| (11)

[0132] X(t+1)=(X1(t)+X2(t)+X3(r)) / 3 (12)

[0133] Among them, X pis the location of the prey, i.e. the global optimal solution, X is the location of the wolf, i.e. the search agent, t is the number of iterations, r1 and r2 are random numbers in the interval [0,1], MaxIter is the maximum number of iterations, X α , X β , X δ are the positions of wolves α, β, and δ respectively, D is the distance between the prey and the gray wolf, C is a random number in [0,2], X p (t) is the position of the prey in the tth iteration, A is the weight value that determines the influence of D on the distance of the gray wolf's movement, a(t) is the weight value that affects the change of A in the tth iteration, X1, X2, and X3 are the distances of the gray wolf's movement caused by α, β, and δ, respectively, A1, A2, and A3 are the weight values ​​in the distances of the gray wolf's movement caused by α, β, and δ, respectively, C1, C2, and C3 are the random values ​​in the distances of the gray wolf's movement caused by α, β, and δ, respectively, X1(t), X2(t), and X3(t) are the distances of the gray wolf's movement caused by α, β, and δ in the tth iteration, respectively.

[0134] The update formula is as follows:

[0135]

[0136]

[0137]

[0138] B2(t)=1-B1(t)(25)

[0139] Among them, ρ1, ρ2~N(0.5, 0.1 2 ) is a random number, μ = 1.5, X i (t+1) is the position of individual i in the t+1th iteration, B1 and B2 are the weights that determine the leader effect and the random dispersion in the movement of individual i, respectively. is the movement of individual i caused by leaders α, β and δ (leader effect), B1(t) is the influence factor of the leader effect on the movement of individual i in the tth iteration, and B2(t) is the influence factor randomly dispersed in the movement of individual i in the tth iteration.

[0140] Step (3) specifically includes the following process:

[0141] Initialize parameters α, A, C, B1, B2, and calculate the fitness value of each individual according to the fitness function formula (27); set the best three solutions α, β and δ; calculate the movement caused by the leader through formula (23); calculate the movement caused by the neighbors through formula (13); calculate the movement caused by random dispersion through formula (17); update the position of each individual through formula (22), and calculate the fitness value of each individual according to the fitness function formula (27); update the positions of α, β and δ.

[0142] The update formula of GWO population consists of three parts. The first term It is determined by the leaders α, β, and δ, where α, β, and δ are the optimal solution, the second optimal solution, and the third optimal solution in the GWO population, respectively. It is the only item that determines the population update in the classic GWO algorithm. This update method has limitations: the movement of other search agents is determined only by the optimal solution, which will cause most search agents to be concentrated near the optimal solution in the later iteration. If the optimal solution falls into the local optimum, it will be difficult to break through the local optimum and search for the global optimal solution. The lack of population diversity will also cause the algorithm to converge prematurely. Therefore, the improved gray wolf algorithm of the present invention adds other items that affect population update.

[0143] Item 2 The movement is caused by neighbors. The influence of a search agent's neighbors on it can be attractive or repulsive. When the neighbors are better than the search agent, an attractive effect will be generated, guiding the search agent to move toward the "prey"; when the neighbors are worse than the search agent, a repulsive effect will be generated, pushing the search agent to move toward the "prey". The neighbor effect accelerates the movement of the search agent, making it move closer to the optimal solution faster, which helps to increase the local search ability of the algorithm, and also simulates the influence of gray wolf groups on individuals in nature.

[0144] Item 3 This is called random dispersion, which simulates the situation of food scarcity in nature. When food is scarce, some wolves will leave the current search space to open up new territories in order to find more abundant food. In formula (17), two other wolves in the population are randomly selected as guides for the current wolf to disperse to the new space. Random dispersion is of great significance to increasing the exploratory nature of the algorithm. It will provide strong support for breaking through the local optimum and improving the global search capability of the algorithm.

[0145] In the population update formula of the improved grey wolf algorithm of the present invention, weight coefficients B1 and B2 are used to dynamically adjust the strength of the algorithm development ability and exploration ability during the iteration process to achieve a balance. Development ability refers to the ability of the algorithm to converge to the optimal solution accurately and quickly, and exploration ability refers to the ability of the algorithm to break through the local optimum and search for the global optimal solution. In the early stage of iteration, most search agents are scattered in various locations in the search space. At this time, development ability should be emphasized. Even if the search agent converges quickly to the vicinity of the optimal solution, B1 is set to a larger value; at the end of the iteration, the search agents have been concentrated near the optimal solution. In order to ensure that they break through the local optimum, exploration ability should be emphasized so that more agents go to the new search space, and B2 is set to a larger value.

[0146] (4) After completing the update of the GWO population, compare the best solutions in the two populations: if the best solution in the DE population is better than the best solution in the GWO population, that is, the fitness value of the best solution in the DE population is greater than the fitness value of the best solution in the GWO population, then let DE_best replace α in the GWO population; otherwise, let α replace DE_worst in the DE population; and use formula (18) to perform the migration operation.

[0147] After the GWO population is updated, its optimal solution α is compared with the optimal solution DE_best in the DE algorithm. If the optimal solution is found in the DE population, it is replaced by α, which is equivalent to the leader of the GWO population getting the opportunity to evolve; if the optimal solution is found in the GWO population, it is replaced by the worst solution in the DE population, which is equivalent to the optimization of the DE population. The motivation of this mechanism is that the DE algorithm is good at exploration, while the GWO algorithm is good at development. The two run in parallel and interact with the optimal solution, which can adaptively adjust and improve the development and exploration capabilities of the gray wolf algorithm to achieve a dynamic balance.

[0148] (5) Return to step (2) and repeat steps (2) to (4) until the number of iterations t equals the maximum number of iterations MaxIter, and finally the best solution α and the corresponding fitness value are obtained.

[0149] In the present invention, Figure 3 As shown in the figure, the hunting mechanism of the gray wolf algorithm is demonstrated. a directly affects the value of parameter A. In the gray wolf algorithm, a changes linearly from 2 to 0 with the number of iterations. The change of A reflects the process of the gray wolf attacking its prey. When |A|<1, the gray wolf will approach its prey, reflecting the local search of the algorithm; when |A|>1, the gray wolf will move away from the current prey and look for better prey, reflecting the global search of the algorithm. Parameter C changes randomly throughout the search process, which simulates the obstacles that gray wolves encounter in nature during hunting. Figure 3 As can be seen from the figure, the classic gray wolf algorithm is to lead other wolves ω to hunt by continuously approaching the prey through the three leaders α, β, and δ.

[0150] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A robot joint friction model parameter identification method based on an improved grey wolf algorithm is characterized in that: The following steps are involved: S1: Establish the friction model of the robot joint under no-load state; The established robot joint friction model is as follows: Among them, θ is the motor angle, τ mf is the friction torque converted to the motor end, z is the average deformation of the bristle, σ0 is the bristle stiffness, σ1 is the bristle damping coefficient, σ2 is the viscous friction coefficient, is the Stribeck effect, F c is the Coulomb friction force, F s is the maximum static friction, ω s is the Stribeck speed, is the rate of change of bristle shape, is the motor speed; S2: Establish fitness function; The established fitness function formula is as follows: Among them, f i and f di are the i-th estimated friction and actual friction, respectively, i = 1, 2, …, N, N is the population size; S3: Initialize the population, input the population size, problem dimension, and maximum number of iterations; Generate random numbers within the range of each identification parameter value to form a vector as a search agent. The formula is as follows: X ij =rand×(ub j -lb j )+lb j (26) Among them, rand is a random number in the interval [0,1], ub j is the upper limit of the value of the jth identification parameter, lb j is the lower limit of the value of the jth identification parameter; j = 1, 2, ..., k, k is the problem dimension; i = 1, 2, ..., N, N is the population size; S4: gradually increase the robot joint rotation speed from the lower limit of the range, and measure the output torque of the robot joint when it rotates at a uniform speed at this speed; S5: By improving the Grey Wolf algorithm, the robot joint friction model is identified and the model parameters are obtained; The improved grey wolf algorithm has three strategies, including: Strategy 1: Neighborhood Effect Strategy in, is the change in individual position caused by the neighbor effect, M is the neighbor of the ith individual, K i and K j are the fitness values ​​of the i-th individual and the j-th neighbor, respectively, K worst and K best is the fitness value of the best and worst two individuals in the current population, X i and X j are the positions of the ith individual and the jth neighbor, ε = 10 -8 , is the sensing distance of individual i, N is the population size, and the definition of neighbors is: if the distance between two individuals Smaller than the sensing distance Then they are neighbors to each other; is the fitness difference between individual i and individual j, is the position difference between individual i and individual j; Strategy 2: Random Dispersion Strategy in, is the individual position change caused by random dispersion, X m and X n are two individuals randomly selected from the current population, ρ~N(0.5,0.1 2 ) is a random number; Strategy 3: Co-evolutionary mechanism U i =X a +F(X b +X c ) (19) Among them, α is the best solution in the GWO population, DE_best and DE_worst are the best and worst solutions in the DE population, respectively. and are the positions corresponding to the best and worst solutions in the DE population, respectively. is the fitness value corresponding to the best solution in the DE population, K α is the fitness value corresponding to the best solution in the GWO population, X a , X b and X c are three individuals randomly selected from the DE population, F is a random number in the interval [0,1], CR=0.4 is the crossover probability, rand(j) is a random number in the interval [0,1], rnbr(i) is a random number in the set {1,2,…,k}, k is the problem dimension, t is the number of iterations, and U i is the variant of individual i, V ij is the intersection of individual i, X ij is the parameter value corresponding to the jth dimension of individual i, U ij is the parameter value corresponding to the jth dimension of variant i, X(t+1) is the position of individual i at the t+1th iteration, X(t) is the position of individual i at the tth iteration, V(t) is the position of crossover i at the tth iteration, K X is the fitness value of individual i, K V is the fitness value of the intersection i.

2. The robot joint friction model parameter identification method based on the improved grey wolf algorithm according to claim 1 is characterized in that: The strategy 3, i.e. the co-evolution mechanism, comprises the following steps: (1) The initial population is copied into two copies, one as the initial population of the DE algorithm and the other as the initial population of the GWO algorithm; (2) In the DE algorithm, use formulas (19) to (21) to update the population, calculate the fitness value of each individual according to the fitness function formula, and output the best solution DE_best and the worst solution DE_worst; (3) In the GWO algorithm, the traditional grey wolf algorithm and update formula are used to update the population and output the best solution α; (4) Compare the best solutions in the two populations: If the best solution in the DE population is better than the best solution in the GWO population, let DE_best replace α in the GWO population; otherwise, let α replace DE_worst in the DE population; and use formula (18) to perform the migration operation; (5) Return to step (2) until the number of iterations t equals the maximum number of iterations MaxIter, and the best solution α and the corresponding fitness value are obtained.

3. The robot joint friction model parameter identification method based on the improved grey wolf algorithm according to claim 2 is characterized in that: In step (2), firstly, the mutation operation is performed using formula (19), then the crossover operation is performed using formula (20), and finally the selection operation is performed using formula (21).

4. The robot joint friction model parameter identification method based on the improved grey wolf algorithm according to claim 2 is characterized in that: In step (3), the traditional grey wolf algorithm is as follows: D=|C·X p (t)-X(t)| (4) X(t+1)=X p (t)-A·D (5) A=2a·r1-a (6) C＝2·r2(7) a(t)=2-2t / MaxIter (8) X1=X α -A1·|C1·X α -X| (9) X2=X β -A2·|C2·X β -X| (10) X3=X δ -A3·|C3·X δ -X| (11) X(t+1)=(X1(t)+X2(t)+X3(t)) / 3(12) Among them, X p is the location of the prey, i.e. the global optimal solution, X is the location of the wolf, i.e. the search agent, t is the number of iterations, r1 and r2 are random numbers in the interval [0,1], MaxIter is the maximum number of iterations, X α , X β , X δ are the positions of wolves α, β, and δ respectively, D is the distance between the prey and the gray wolf, C is a random number in [0,2], X p (t) is the position of the prey in the tth iteration, A is the weight value that determines the influence of D on the distance of the gray wolf's movement, a(t) is the weight value that affects the change of A in the tth iteration, X1, X2, and X3 are the distances of the gray wolf's movement caused by α, β, and δ, respectively, A1, A2, and A3 are the weight values ​​in the distances of the gray wolf's movement caused by α, β, and δ, respectively, C1, C2, and C3 are the random values ​​in the distances of the gray wolf's movement caused by α, β, and δ, respectively, X1(t), X2(t), and X3(t) are the distances of the gray wolf's movement caused by α, β, and δ in the tth iteration, respectively.

5. The robot joint friction model parameter identification method based on the improved grey wolf algorithm according to claim 4 is characterized in that: In step (3), the update formula is as follows: B2(t)=1-B1(t) (25) Among them, ρ1, ρ2~N(0.5, 0.1 2 ) is a random number, μ = 1.5, X i (t+1) is the position of individual i in the t+1th iteration, B1 and B2 are the weights that determine the leader effect and the random dispersion in the movement of individual i, respectively. is the movement of individual i caused by leaders α, β and δ, B1(t) is the influence factor of the leader effect on the movement of individual i in the tth iteration, and B2(t) is the influence factor randomly dispersed in the movement of individual i in the tth iteration.

6. The robot joint friction model parameter identification method based on the improved grey wolf algorithm according to claim 5 is characterized in that: The specific operation process of step (3) is as follows: Initialize parameters α, A, C, B1, B2, and calculate the fitness value of each individual according to the fitness function formula (27); set the best three solutions α, β and δ; calculate the movement caused by the leader through formula (23); calculate the movement caused by the neighbors through formula (13); calculate the movement caused by random dispersion through formula (17); update the position of each individual through formula (22), and calculate the fitness value of each individual according to the fitness function formula (27); update the positions of α, β and δ.

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