A mechanical arm rigid-flexible coupling dynamics parameter identification method based on pattern search and swarm intelligence optimization

Abstract

A kind of mechanical arm rigid-flexible coupling dynamics parameter identification method based on pattern search and swarm intelligence optimization, it contains: the establishment includes dissipative force rigid-flexible coupling multi-degree-of-freedom robot Lagrange dynamics model;Solve the minimum parameter set of dynamics, and obtain the observable matrix by reorganization through linear relationship, obtain the identifiable robot linearized dynamics model;Based on finite fourier series and quintic polynomial, establish dynamics parameter identification excitation trajectory model;With the condition number of observable matrix and the combination of singular value as the objective function of excitation trajectory optimization;The final excitation trajectory best parameter is obtained by iterative optimization using pattern search algorithm and swarm intelligence optimization algorithm;The state parameters generated by the best excitation trajectory operation are identified by least square method, and the dynamics parameters of the robot are obtained.The invention improves the search ability in the global feasible region and the late local search convergence ability, improves the anti-interference ability to measurement signal noise, and improves the accuracy of parameter identification.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robots, in particular to a mechanical arm rigid-flexible coupling dynamics parameter identification method based on pattern search and swarm intelligence optimization. BACKGROUND

[0002] The dynamics parameters obtained by dynamics parameter identification are of great significance for robot simulation and control. For robot simulation, an accurate dynamics model can make the motion simulation more consistent with the actual situation, facilitating the simulation experiment test of the algorithm; for robot control, the known dynamics model of the robot can realize the model-based feedforward control algorithm or model prediction algorithm, etc., improving the robustness and dynamic performance of the control algorithm. However, due to the structural errors of the modeling parameters and the complex physical laws that are not mathematically modeled, such as coupling joints, flexible joints, assembly conditions, etc., there is an inevitable deviation between the identified robot dynamics model and the actual situation. Therefore, it is very important to establish an accurate dynamics model for rigid-flexible coupling mechanical arms and to perform effective parameter identification compensation.

[0003] The invention patent application CN115042190A discloses an optimization method for excitation trajectory of serial robot dynamics parameter identification, which is performed according to the following steps: Step 1: establishing a Newton-Euler dynamics model of the serial robot; Step 2: linearizing the nonlinear terms in the dynamics model in Step 1 and obtaining a linear dynamics model based on the improved DH method; Step 3: solving the minimum parameter set of the multi-joint robot dynamics to obtain a simplified model of the multi-joint robot dynamics model; Step 4: reorganizing the standard parameters through QR decomposition or numerical methods of linear relationship mapping to obtain an observation matrix W; Step 5: establishing a mathematical model for excitation trajectory of serial robot dynamics parameter identification based on Fourier series; Step 6: introducing Hadamard inequality optimization criterion as one of the constraint conditions, and taking the condition Cond(W) of the observation matrix as the optimization standard of the identification excitation trajectory optimization objective function, so as to obtain the optimal excitation trajectory fully representing the mechanical characteristics of the actual robot system, and the optimal excitation trajectory is used for parameter identification of the dynamics of the multi-joint robot. The main purpose of this patent document is to model and linearize the rigid dynamics parameters of the robot, to solve the minimum parameter set for identification, to optimize the excitation trajectory by introducing the Hadamard inequality optimization criterion, to obtain the excitation trajectory representing the rigid parameter dynamics characteristics of the robot system, and to use this excitation trajectory for rigid body dynamics parameter identification, thereby reducing the required condition number and reducing the complexity in the calculation process.

[0004] It can be seen that, for the problem of to be identified dynamic model establishment, the existing method is mainly to model the rigidity parameters, and since the flexible characteristics exist in the joint transmission link of the robot, the established dynamic model does not conform to the real physical law, and the optimization and identification of the excitation trajectory based on such model will lead to the decrease of the effectiveness of the identification effect and the weakening of the control effect, which is a problem to be solved in the prior art. For the optimization problem of the excitation trajectory used for identifying the parameters, the mainstream solution method at present is to use the swarm intelligence optimization algorithm such as genetic algorithm, particle swarm algorithm and differential evolution algorithm to optimize the objective function, and these heuristic algorithms have strong global optimization capability when the population size and the number of generations are large, but have the problems of weak local search capability, slow convergence speed and poor precision in the later stage of the algorithm. The pattern search algorithm is a direct search algorithm independent of derivative, and is more efficient in local search than the swarm intelligence optimization algorithm, but is more dependent on the given initial point and is easy to fall into a local optimal solution. SUMMARY

[0005] The application provides a mechanical arm rigid-flexible coupling dynamic parameter identification method based on pattern search and swarm intelligence optimization to overcome the prior art.

[0006] A mechanical arm rigid-flexible coupling dynamic parameter identification method based on pattern search and swarm intelligence optimization comprises:

[0007] S1: a rigid-flexible coupling multi-degree-of-freedom mechanical arm Lagrange dynamic model containing a dissipation force is established;

[0008] S2: the dynamic equation obtained in step S1 is linearized, the minimum parameter set of dynamics is solved, and an observation matrix is obtained through linear reorganization to obtain an identifiable linearized dynamic model of the mechanical arm;

[0009] S3: a dynamic parameter identification excitation trajectory model is established based on a finite Fourier series and a quintic polynomial, and the finite Fourier series is compensated by the quintic polynomial so that the original function, the first derivative and the second derivative of the excitation trajectory are zero at the starting and ending time;

[0010] S4: the condition number and the singular value of the observation matrix are combined as an objective function of excitation trajectory optimization, a certain motion range of the mechanical arm is taken as a constraint condition, and the initial excitation trajectory optimal parameters satisfying the constraint condition are obtained through a swarm intelligence optimization algorithm;

[0011] S5: the initial excitation trajectory optimal parameters are used as the initial value of the pattern search algorithm, and the final excitation trajectory optimal parameters are obtained through iterative optimization of the pattern search algorithm and the swarm intelligence optimization algorithm;

[0012] S6: Least square identification is performed on the state parameters generated by the optimal excitation trajectory operation to obtain the mechanical arm dynamics parameters.

[0013] Further, the specific process of obtaining the optimal parameters of the preliminary excitation trajectory satisfying the constraint condition by the swarm intelligence optimization algorithm is as follows:

[0014] S4.1: adjustable parameters are set;

[0015] S4.2: the population position is initialized;

[0016] S4.3: the fitness of the population individuals is evaluated;

[0017] S4.4: individual crossover, mutation and selection are performed to generate new generation individuals;

[0018] S4.5: it is judged whether the constraint condition is satisfied, if yes, S4.6 is executed, otherwise, S4.3 is executed;

[0019] S4.6: the optimal parameters of the preliminary excitation trajectory are obtained.

[0020] Further, the specific process of obtaining the optimal parameters of the final excitation trajectory by the pattern search algorithm optimization is as follows:

[0021] S5.1: the optimal parameters of the preliminary excitation trajectory are set as the initial values of the pattern search algorithm;

[0022] S5.2: adjustable parameters are set, including search step, pattern matrix and tolerance;

[0023] S5.3: it is judged whether the tolerance condition is satisfied, if yes, S5.6 is executed, otherwise, S5.4 is executed;

[0024] S5.4: target function comparison is performed on the grid points near the search point;

[0025] S5.5: it is judged whether there is a grid point with better target function value than the current grid point, if yes, the search step is increased, the search point is set as the new grid point, and S5.3 is executed, otherwise, the search step is reduced, the original grid point is kept as the search point, and S5.3 is executed

[0026] S5.6: the pattern search grid point is set as the initial population of the particle swarm algorithm;

[0027] S5.7: individual position updating and selection are performed to generate new generation individuals;

[0028] S5.8: it is judged whether the precision condition or the end condition is satisfied, if yes, S5.9 is executed, otherwise, S5.1 is executed;

[0029] S5.9: the optimal parameters of the final excitation trajectory are obtained.

[0030] The beneficial effects of the present application compared with the prior art are:

[0031] 1、The present application uses Lagrange method to establish a dynamic equation containing dissipation force, considers the friction force factor and flexible transmission factor in the dynamic equation through the flexible mutual conversion of motor end and joint end, constructs a rigid-flexible coupling dynamic equation, improves the expression ability of the dynamic model, and the root mean square of the identified torque residual at the first joint and the second joint of the robot is increased by 11.35% and 4.2% respectively.

[0032] 2、The present application adopts the method of combining pattern search method and swarm intelligence optimization algorithm to optimize the identified excitation trajectory, improves the search ability in the global feasible region and the late local search convergence ability, provides a new method for multi-dimensional parameter excitation trajectory optimization, effectively optimizes the condition number of the observation matrix, improves the anti-interference ability to the measurement signal noise, improves the accuracy of parameter identification, and the ratio of the root mean square of the identified torque residual to the joint torque range is within 10%.

[0033] The technical solutions of the present application will be further described below in combination with the drawings and embodiments: DESCRIPTION OF DRAWINGS

[0034] Figure 1 It is a flow chart of the combination of pattern search optimization and swarm intelligence optimization of the present application;

[0035] Figure 2 It is a result graph of iterative optimization of excitation trajectory parameters combined with pattern search and swarm intelligence optimization;

[0036] Figure 3 It is a graph of planned position and actual running position of three joints;

[0037] Figure 4 It is a graph of planned speed and actual running speed of three joints;

[0038] Figure 5 It is a graph of planned acceleration and actual running acceleration of three joints;

[0039] Figure 6 It is a comparison graph of actual torque and predicted torque of the first joint;

[0040] Figure 7 It is a comparison graph of actual torque and predicted torque of the second joint;

[0041] Figure 8 It is a comparison graph of actual torque and predicted torque of the third joint. DETAILED DESCRIPTION

[0042] The following examples are only used to more clearly illustrate the technical solutions of the present application. Unless otherwise specified, the technical terms or scientific terms used in the present application should be understood as the common meanings understood by those skilled in the art to which the present application belongs.

[0043] In combination Figure 1 It is explained that the mechanical arm rigid-flexible coupling dynamics parameter identification method based on pattern search and swarm intelligence optimization in the embodiment comprises:

[0044] S1: a rigid-flexible coupling multi-degree-of-freedom mechanical arm Lagrange dynamics model containing dissipative force is established; a dynamics model sufficiently characterizing inertial parameters, friction force parameters and flexible transmission parameters of the mechanical arm is obtained;

[0045] S2: the dynamics equation obtained in step S1 is linearized, the minimum parameter set of dynamics is solved, and an observation matrix is obtained through linear reorganization, so as to obtain an identifiable linearized dynamics model of the mechanical arm;

[0046] S3: a dynamics parameter identification excitation trajectory model is established based on a finite Fourier series and a quintic polynomial, the finite Fourier series is compensated by the quintic polynomial, the original function, the first derivative and the second derivative of the excitation trajectory at the starting and ending time are zero, that is, the angles, angular velocities and angular accelerations of the joints of the mechanical arm at the starting and ending time are zero, and vibration at the starting and stopping time of the mechanical arm is avoided;

[0047] S4: the combination of the condition number and the singular value of the observation matrix in step S2 is used as the objective function of excitation trajectory optimization, the anti-noise interference ability of the excitation trajectory and the excitation ability of the less affected dynamics parameters are fully considered, a certain motion range of the mechanical arm is used as a constraint condition, and the preliminary excitation trajectory optimal parameters meeting the constraint condition are obtained through a swarm intelligence optimization algorithm;

[0048] S5: the preliminary excitation trajectory optimal parameters in step S4 are used as the initial value of the pattern search algorithm, and the final excitation trajectory optimal parameters are obtained through iterative optimization of the pattern search algorithm and the swarm intelligence optimization algorithm; the optimization method has global optimization ability and local search ability of better values, and the optimization efficiency and optimization effect are improved, and the specific optimization process is as shown in Figure 1 ;

[0049] S6: the state parameters generated by the operation of the optimal excitation trajectory in step S5 are identified through the least square method, and the dynamics parameters of the mechanical arm are obtained.

[0050] Further, the rigid-flexible coupling multi-degree-of-freedom mechanical arm Lagrange dynamics model in step S1 is:

[0051]

[0052] where V is the potential energy of the system, T is the kinetic energy of the system, r is the displacement related to the potential energy, F non is a non-conservative force, q i is a generalized coordinate, and is taken as a joint position in a robot dynamics model, is a joint angular velocity.

[0053] Further, the relationship between the dynamics minimum parameter set and the observation matrix obtained in step S2 is as follows:

[0054]

[0055] where τ is a joint output torque, is an observation matrix, and ρ b is a minimum inertia parameter set.

[0056] Further, the dynamics parameter identification excitation trajectory model in step S3 is as follows:

[0057]

[0058] where, is a finite Fourier series coefficient, w f is a fundamental frequency, and N is a number of harmonics, is a constant term of a trajectory, is a quintic polynomial function coefficient, t c is a variable calculated from a sampling time, k represents a harmonic order, i represents a joint number, and j represents a term number in a polynomial.

[0059] Optionally, the objective function in step S4 is as follows:

[0060]

[0061] where k1 is a condition number weight in an optimization objective, k2 is a singular value weight in the optimization objective, Cond(Y) is a condition number of the observation matrix Y, and σ min is a minimum singular value of the observation matrix Y.

[0062] The constraint condition in step S4 is as follows:

[0063]

[0064] where q i (t), are an angle, an angular velocity, and an angular acceleration of the i th joint at time t, q imax is a maximum joint angle, is a maximum joint angular velocity, is a maximum joint angular acceleration, t0, t f are a start time and an end time.

[0065] Further, the specific process of obtaining the preliminary excitation trajectory optimal parameters satisfying the constraint conditions in step S4 is as follows:

[0066] S4.1: setting adjustable parameters;

[0067] S4.2: initializing population positions;

[0068] S4.3: evaluating individual fitness of the population;

[0069] S4.4: performing individual crossover, mutation and selection to generate new generation individuals;

[0070] S4.5: judging whether the constraint conditions are satisfied, if yes, executing S4.6, otherwise executing S4.3;

[0071] S4.6: obtaining the preliminary excitation trajectory optimal parameters.

[0072] Further, the specific process of obtaining the final excitation trajectory optimal parameters by using the pattern search algorithm in step S5 is as follows:

[0073] S5.1: setting the preliminary excitation trajectory optimal parameters as the initial values of the pattern search algorithm;

[0074] S5.2: setting adjustable parameters, including search step, pattern matrix and tolerance;

[0075] S5.3: judging whether the tolerance conditions are satisfied, if yes, executing S5.6, otherwise executing S5.4;

[0076] S5.4: comparing the objective functions at the grid points near the search point;

[0077] S5.5: judging whether there is a grid point with better objective function value than the current grid point, if yes, increasing the search step, setting the search point as the new grid point, and executing S5.3, otherwise, decreasing the search step, keeping the original grid point as the search point, and executing S5.3;

[0078] S5.6: setting the pattern search grid point as the initial population of the particle swarm algorithm;

[0079] S5.7: performing individual position updating and selection to generate new generation individuals;

[0080] S5.8: judging whether the precision conditions or ending conditions are satisfied, if yes, executing S5.9, otherwise executing S5.1;

[0081] S5.9: obtaining the final excitation trajectory optimal parameters.

[0082] Based on the above inventive concept, the present application is further illustrated by the following examples:

[0083] Example 1

[0084] This embodiment takes a six-degree-of-freedom serial rope-driven manipulator as an example, and the driving shaft and the driven shaft use steel wire ropes to transmit motion and power. The rigid-flexible coupled dynamics parameter identification method for the manipulator based on pattern search and swarm intelligence optimization includes the following steps:

[0085] S1: Establish a rigid-flexible coupled multi-degree-of-freedom manipulator Lagrange dynamics model containing dissipative forces;

[0086] In step S1, the dynamics of the manipulator is modeled, and the mathematical model contains dissipative forces, which is a rigid-flexible hybrid model. The dynamics model strictly characterizes the inertia parameters, friction parameters, and flexible transmission parameters of the manipulator (inertia force, Coriolis force, centrifugal force, friction force, and rope elastic force, etc. Specific physical objects) with clear physical meaning, which is positive for the identification of trajectory parameters. The rigid-flexible coupled dynamics model can be mathematically expressed as:

[0087]

[0088] In the formula, V is the potential energy of the system, T is the kinetic energy of the system, r is the displacement related to the potential energy, F non is a non-conservative force, q i is a generalized coordinate, which is taken as a joint position in the robot dynamics model, is the joint angular velocity.

[0089] In step S2, the dynamics equation is linearized. Since a part of the link dynamics parameters does not affect the dynamics characteristics of the manipulator motion, and a part of the parameters affects the dynamics characteristics through linear combination, the torque, joint state information obtained from the manipulator motion cannot be identified separately. Before identification, first find out these parameters that do not produce effects and can be linearly combined. Finally, the remaining set of inertia parameters is called the minimum inertia parameter combination. The minimum parameter set and the observation matrix are solved by the observation matrix and the reorganized inertia parameters, and the identifiable linear dynamics model of the manipulator is obtained, which is mathematically expressed as:

[0090]

[0091] In the formula, τ is the joint output torque, is the observation matrix, and ρ b is the minimum inertia parameter set.

[0092] In step S3, the designed motion trajectory needs to excite the parameters to the maximum extent to make them play a role in the movement process, so as to improve the signal-to-noise ratio of the signal. The practical signal can be basically decomposed into a combination of sinusoidal signals, and the combination of the finite Fourier series and the fifth order polynomial has certain advantages. The finite Fourier series signal is a periodic signal composed of a series of harmonic linear weighted sums, and appropriate selection of the fundamental frequency and the coefficient can construct an excitation trajectory that meets different conditions. The fundamental frequency determines the motion period of the trajectory, and the coefficient determines the shape of the trajectory. Due to the characteristics of the harmonic signal, the first and second derivatives of the finite Fourier series trajectory, i.e., the velocity and acceleration functions, are non-zero at the initial and end time, and have a certain step, which leads to vibration of the mechanical arm when running the trajectory, and has an adverse effect on data acquisition and mechanical arm structure. Therefore, the constant term of the finite Fourier series trajectory is replaced by the fifth order polynomial, and the excitation trajectory can meet the boundary conditions, i.e., the initial and final positions of the trajectory are consistent with the set values, and the initial and final velocities and accelerations of the trajectory are zero, by using the fifth order polynomial and its first and second derivatives. The mathematical expression is as follows:

[0093]

[0094] In the formula, is the coefficient of the finite Fourier series, w f is the fundamental frequency, and N is the number of harmonics, is the constant term of the trajectory, is the coefficient of the fifth order polynomial function, t c is a variable calculated from the sampling time, i represents the number of joints, and j represents the number of terms in the polynomial.

[0095] In step S4, the condition number and singular value of the observation matrix are combined as the objective function of the excitation trajectory optimization, and a certain motion range of the mechanical arm is used as the constraint condition. The condition number and singular value of the observation matrix are combined as the objective function to ensure the effectiveness of the excitation trajectory, to fully excite the to-be-identified parameters, and to ensure the upper limit of the output-input error, i.e., to reduce the interference of noise on identification. The objective function can be expressed in the following form.

[0096]

[0097] In the formula, k1 is the weight of the condition number in the optimization objective, k2 is the weight of the singular value in the optimization objective, Cond(Y) is the condition number of the observation matrix Y, and σ min is the minimum singular value of the observation matrix Y;

[0098] The constraint condition is:

[0099]

[0100] wherein q i (t), are the angle, angular velocity and angular acceleration of the i-th joint at time t, respectively, imax is the maximum value of the joint angle, is the maximum value of the joint angular velocity, is the maximum value of the joint angular acceleration, t0, t f are the start time and end time.

[0101] In this embodiment 1, the structure and motion space constraints are considered, the range of motion angle, velocity and acceleration of each joint are used as inequality constraints for optimization, to limit the motion of the robot arm within a reasonable range. Preferably, the specific settings are as follows:

[0102]

[0103] wherein q1, q2 and q3 represent the angle of the 1st joint, 2nd joint and 3rd joint at time t, respectively, and represent the angular velocity of the 1st joint, 2nd joint and 3rd joint at time t, respectively, and represent the angular acceleration of the 1st joint, 2nd joint and 3rd joint at time t, respectively.

[0104] Further, the specific process of obtaining the preliminary excitation trajectory optimal parameters satisfying the constraint conditions by the swarm intelligence optimization algorithm in step S4 is as follows:

[0105] S4.1: setting adjustable parameters;

[0106] S4.2: initializing population position;

[0107] S4.3: evaluating the fitness of population individuals;

[0108] S4.4: performing individual crossover, mutation and selection to generate new generation individuals;

[0109] S4.5: judging whether the constraint conditions are met, if yes, executing S4.6, otherwise executing S4.3;

[0110] S4.6: obtaining the preliminary excitation trajectory optimal parameters.

[0111] In this embodiment 1, 20 groups of initial values satisfying the nonlinear inequality motion range constraints are obtained by genetic algorithm initialization, and primary iteration optimization is performed to obtain 20 groups of preliminary excitation trajectory optimal parameters.

[0112] The specific process of obtaining the final excitation trajectory optimal parameters by using the pattern search algorithm optimization in step S5 is as follows:

[0113] S5.1: Set the preliminary excitation trajectory optimal parameters as the initial values of the pattern search algorithm;

[0114] S5.2: Set the adjustable parameters, including search step, pattern matrix and tolerance;

[0115] S5.3: Determine whether the tolerance condition is met, if yes, execute S5.6, otherwise execute S5.4;

[0116] S5.4: Perform target function comparison on the grid points near the search point;

[0117] S5.5: Determine whether there is a grid point with better target function value than the current grid point, if yes, increase the search step, set the search point as the new grid point, and execute S5.3, otherwise, decrease the search step, keep the original grid point as the search point, and execute S5.3; S5.6: Set the pattern search grid point as the initial population of the particle swarm algorithm;

[0118] S5.7: Perform individual position update and selection to generate a new generation of individuals;

[0119] S5.8: Determine whether the precision condition or the end condition is met, if yes, execute S5.9, otherwise execute S5.1;

[0120] S5.9: Obtain the final excitation trajectory optimal parameters.

[0121] In this embodiment 1, the pattern search algorithm and the swarm intelligence optimization algorithm are iteratively optimized, and finally the results as shown in Figure 2 are obtained. After three rounds of optimization, the condition number of the optimized observation matrix is reduced from 15.4995 to 11.5561, which is reduced by 25.44%, and the anti-noise interference ability is improved, so that the final identification ability is improved.

[0122] In this embodiment 2, the difference between this embodiment 2 and embodiment 1 is that the state parameters generated by the optimal excitation trajectory operation are identified by the least square method based on the excitation trajectory operation process of embodiment 1, and the mechanical arm dynamics parameters are obtained.

[0123] In this embodiment, the excitation trajectory optimized for three consecutive cycles is used to collect motor position, torque data and joint magnetic encoder position data. First, the original data is processed by mean value to obtain single cycle data, and the random noise is reduced. The torque and position data are processed by low-pass filter, and the position data is processed by twice difference to obtain angular velocity and angular acceleration data. The actual joint running state and the planned trajectory are compared as shown in Figure 3 、 Figure 4 、 Figure 5

[0124] ​The parameter identification is performed using the filtered data. First, the least square method is used to process the mathematical model without the elastic effect of the rope, i.e. the dynamic equation contains the rigid robot dynamic term and the friction term; then the least square method is used to process the mathematical model with the elastic effect of the rope, i.e. the dynamic equation contains the rigid dynamic term, the friction term and the rope driving term, the actual joint torque and the predicted torque calculated using the parameters after the identification are as shown in Figure 6-8 The root mean square error of the actual joint torque and the predicted torque calculated using the parameters after the identification is shown in Table 1:

[0125] Table 1: Root mean square error table of the identification torque residual with and without the modeling of the elastic effect of the rope

[0126]

[0127] From the identification results, it can be seen that the comprehensive identification accuracy is more than 90%, the identification effect with the modeling of the elastic effect is better than that without the modeling of the elastic effect, the root mean square error of the identification torque residual at the first joint and the second joint of the robot is reduced by 11.35% and 4.2% respectively, and the identification effect is improved by the rigid-flexible coupling dynamic modeling.

[0128] The present application has been disclosed with the preferred embodiments as above, however, is not used to limit the present application, any person skilled in the art, without departing from the technical solution range of the present application, can make some changes or modifications to the equivalent embodiments of the equivalent changes using the above disclosed structure and technical content, which still belong to the technical solution range of the present application.

Claims

1. A method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization, characterized in that: Include: S1: Establish a Lagrange dynamics model of a rigid-flexible coupled multi-degree-of-freedom manipulator that includes dissipative forces; S2: Linearize the dynamic equations obtained in step S1, solve for the minimum set of dynamic parameters, and obtain the observation matrix by reorganizing the linear relationship to obtain an identifiable linearized dynamic model of the robotic arm. S3: Establish a dynamic parameter identification excitation trajectory model based on finite Fourier series and fifth-order polynomial; S4: Using the combination of the condition number and singular values ​​of the observation matrix as the objective function for optimizing the excitation trajectory, and using a certain range of motion of the robotic arm as a constraint, the optimal parameters of the preliminary excitation trajectory that satisfy the constraint are obtained through a swarm intelligence optimization algorithm. S5: Use the initial optimal parameters of the excitation trajectory as the initial values ​​of the pattern search algorithm, and use the pattern search algorithm and swarm intelligence optimization algorithm to iteratively optimize and obtain the final optimal parameters of the excitation trajectory; S6: The state parameters generated by the optimal excitation trajectory are identified by the least squares method to obtain the dynamic parameters of the robotic arm.

2. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1, characterized in that: The Lagrange dynamics model of the rigid-flexible coupled multi-degree-of-freedom manipulator in step S1 is as follows: In the formula, V is the system potential energy, T is the system kinetic energy, r is the displacement related to the potential energy, and F is the displacement related to the potential energy. non For non-conservative forces, q i These are generalized coordinates, taken as joint positions in the robot dynamics model. denoted as angular velocity of the joint, and i represents the number of joints.

3. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1, characterized in that: The relationship between the minimum set of dynamic parameters and the observation matrix obtained in step S2 is as follows: In the formula, τ is the joint output torque. Observation matrix, ρ b Let q be the minimum set of inertial parameters, representing the joint angle. Indicates joint angular velocity, This represents the joint angular acceleration.

4. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1, characterized in that: Step S3 involves identifying the dynamic parameters of the excitation trajectory model. In the formula, Let w be the coefficients of a finite Fourier series. f Where N is the fundamental frequency and N is the number of harmonics. For the trajectory constant term, The coefficients of the fifth-degree polynomial function, t c Let k be the variable calculated from the sampling time, i be the harmonic series number, j be the joint number, and j be the number of terms in the polynomial.

5. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1, characterized in that: The objective function in step S4 is: In the formula, k1 is the condition number weight in the optimization objective, k2 is the singular value weight in the optimization objective, Cond(Y) is the condition number of the observation matrix Y, and σ min Let q be the smallest singular value of the observation matrix Y, and let q represent the joint angle. Indicates joint angular velocity, This represents the joint angular acceleration.

6. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 5, characterized in that: The constraint conditions mentioned in step S4 are: In the formula, Let q be the angle, angular velocity, and angular acceleration of the i-th joint at time t. imax This represents the maximum joint angle. This represents the maximum value of the joint angular velocity. The maximum value of the joint angular acceleration, t0, t f These are the start and end times.

7. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1 or 5, characterized in that: The specific process by which the swarm intelligence optimization algorithm obtains the optimal parameters of the preliminary excitation trajectory that satisfy the constraints in step S4 is as follows: S4.1: Set adjustable parameters; S4.2: Initialize population location; S4.3: Assess the fitness of individuals within the population; S4.4: Perform crossover, mutation, and selection on individuals to generate a new generation of individuals; S4.5: Determine whether the constraint conditions are met. If they are met, execute S4.6; otherwise, execute S4.

3. S4.6: Obtain the optimal parameters for the initial excitation trajectory.

8. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1 or 5, characterized in that: The specific process of using the pattern search algorithm to optimize and obtain the optimal parameters of the final excitation trajectory in step S5 is as follows: S5.1: Set the optimal parameters of the initial excitation trajectory to the initial values ​​of the pattern search algorithm; S5.2: Set adjustable parameters, including search step size, pattern matrix, and tolerance; S5.3: Determine whether the tolerance condition is met. If it is met, proceed to S5.6; otherwise, proceed to S5.

4. S5.4: Compare the objective function at grid points near the search point; S5.5: Determine if there is a grid point with a better objective function value than the current grid point. If so, increase the search step size, set the search point as the new grid point, and execute S5.

3. Otherwise, decrease the search step size, keep the original grid point as the search point, and execute S5.

3. S5.6: Set the pattern search grid points as the initial population for the particle swarm optimization algorithm; S5.7: Update and select individual locations to generate a new generation of individuals; S5.8: Determine whether the precision condition or termination condition is met. If it is met, execute S5.9; otherwise, execute S5.

1. S5.9: Obtain the optimal parameters for the final excitation trajectory.

9. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 6, characterized in that: The constraints mentioned in step S4 are specifically as follows: using the range of motion angles, velocities, and accelerations of each joint as optimization inequality constraints, specifically set as follows: In the formula, q1, q2, and q3 represent the angles of the first, second, and third joints at time t, respectively. and Let represent the angular velocities of the first joint, the second joint, and the third joint at time t, respectively. and These represent the angular accelerations of the first joint, the second joint, and the third joint at time t, respectively.

10. The method for identifying the dynamic parameters of a rigid-flexible coupling robotic arm based on pattern search and swarm intelligence optimization according to claim 1, characterized in that: The rigid-flexible coupled multi-degree-of-freedom manipulator Lagrange dynamics model in S1 is a dynamic model that characterizes the manipulator's inertial parameters, friction parameters, and flexible transmission parameters.

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