Dynamic parameter identification method based on mechanical arm excitation track optimization

Abstract

The invention discloses a mechanical arm excitation trajectory optimization-based kinetic parameter identification method, which comprises the following steps of: constructing a corresponding Newton-Euler kinetic model based on a target mechanical arm, and obtaining a linear kinetic model through linear transformation and parameter recombination; based on the linear dynamics model, a staged periodic Fourier series excitation track based on all joint positions of the target mechanical arm is constructed; a quantum behavior and Levy flight hybrid particle swarm optimization algorithm is adopted to optimize the excitation trajectory, and constraint conditions of a regression matrix in the linear dynamic model are obtained; and based on the constraint conditions, adopting an improved hyperbolic sine and cosine optimization algorithm, and identifying the minimum parameter set and the joint torque of the linear dynamics model. According to the method, continuous excitation of the kinetic parameters in robot system recognition is achieved by improving the meta-heuristic algorithm, the decoupling problem of the kinetic parameters is solved, and therefore the precision of the mechanical arm kinetic model is improved.

Description

Technical Field

[0001] The present invention relates to the field of robotics technology, and more particularly to a dynamic parameter identification method based on robot arm excitation trajectory optimization. Background Art

[0002] Currently, accurate robot dynamics models are a fundamental prerequisite for achieving high-performance control. They are particularly critical in advanced applications such as model-based compliant control, sensorless collision detection, computed torque control, high-precision control, and surgical robots. In human-robot collaboration scenarios involving dragging, the compliance required for dragging operations further highlights the importance of accurate dynamic models. However, manufacturers generally do not provide the robot's dynamic parameters, and the parameters obtained through 3D modeling software often deviate significantly from the actual values. Therefore, experimental identification is considered a reliable method for obtaining the dynamic parameters of the robotic arm.

[0003] A typical experimental identification process includes four key steps: dynamic modeling, excitation trajectory design, parameter identification and model verification.

[0004] Among them, the Newton-Euler recursion formula is widely used in dynamic modeling. By decoupling the joint angle-related terms from the parameters to be identified, the linear expression of the dynamic characteristics is achieved. To improve the identification accuracy, Khalil and other scholars adopted a parameter simplification strategy to linearly combine the complete parameter set to form a minimum parameter set, eliminate redundant dynamic parameters and construct the corresponding regression matrix. Dynamic modeling needs to consider the joint friction characteristics at the same time. Although the traditional Coulomb-viscous friction model is widely used, its representation of friction characteristics under extremely low joint speed conditions has deviations and cannot reflect the nonlinear nature of friction. For this reason, the improved Coulomb-viscous friction model and the Stribeck model have been introduced into the field of dynamic parameter identification to more accurately fit the joint friction behavior and improve the accuracy of the dynamic model.

[0005] Excitation trajectory design plays a key role in dynamic parameter identification by ensuring continuous excitation of the system dynamics. Its optimization goal is to minimize the condition number of the regression matrix while fully stimulating all dynamic model information. Fifth-order polynomial excitation trajectories, parameterized using boundary constraints (initial and final velocities and accelerations are zero), have proven effective in single-motion scenarios. However, their limitations in repeated excitation applications have prompted researchers to turn to periodic Fourier series excitation trajectories with well-defined spectral characteristics to improve signal processing. Fifth-order periodic Fourier series trajectories combine the advantages of both, offering both parameter flexibility and periodicity. Previous studies have employed swarm intelligence algorithms such as particle swarm optimization, whale optimization, and cuckoo search algorithms to optimize such trajectories. However, Fourier series parameter optimization remains challenging in high-dimensional spaces. These methods suffer from issues such as premature convergence and insufficient exploration-exploitation balance, resulting in generally poor optimization results.

[0006] Parameter identification methods traditionally rely on least squares and weighted least squares estimators. Despite their theoretical sophistication, numerical instabilities caused by ill-conditioned regression matrices and sensitivity to measurement noise limit their effectiveness. While metaheuristic algorithms such as genetic algorithms, differential evolution, and hyperbolic sine-cosine optimization have shown promise in nonlinear identification tasks, these algorithms lack adaptability when dealing with high-dimensional dynamic identification tasks, limiting their effectiveness in dynamic environments.

[0007] Therefore, it is an urgent problem for those skilled in the art to provide a method for optimizing the excitation trajectory and identifying the dynamic parameters based on a meta-heuristic algorithm to obtain more accurate dynamic parameters of the robotic arm. Summary of the Invention

[0008] In view of this, the present invention provides a dynamic parameter identification method based on robot arm excitation trajectory optimization, which obtains more accurate robot arm dynamic parameters by optimizing the generation of continuous excitation and low noise sensitivity trajectory and combining it with an efficient parameter identification algorithm.

[0009] In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] A method for identifying dynamic parameters based on robot arm excitation trajectory optimization includes the following steps:

[0011] S1. Construct a corresponding Newton-Euler dynamics model based on the target robotic arm, and obtain a linear dynamics model through linear transformation and parameter reorganization; the linear dynamics model includes a relevant minimum parameter set and a regression matrix of the target robotic arm; the relevant minimum parameter set includes: the mass of each joint of the target robotic arm, the inertia tensor, the first-order moment, the motor moment of inertia, and the friction force;

[0012] S2. Based on the linear dynamics model, construct a staged periodic Fourier series excitation trajectory based on the position of each joint of the target manipulator; and optimize the excitation trajectory using a quantum behavior and Lévy flight hybrid particle swarm optimization algorithm to obtain the constraints of the regression matrix in the linear dynamics model; the constraints include motion constraints of each joint angle, velocity, and angular velocity;

[0013] S3. Based on the constraints, an improved hyperbolic sine-cosine optimization algorithm is used to identify the numerical value of the minimum parameter set and the joint torque value of the linear dynamics model.

[0014] Furthermore, the quantum behavior and Lévy flight hybrid particle swarm optimization algorithm is used to optimize the Fourier coefficients of the excitation trajectory to obtain the constraint conditions of the regression matrix in the linear dynamics model; specifically including:

[0015] S21, initialize the particle swarm corresponding to each position and speed of each joint of the target manipulator, and calculate the initial fitness; take the current position of each particle as the individual optimal position, and take the current fitness as the individual optimal fitness;

[0016] S22. Randomly select the quantum behavior update mechanism or the Lévy flight update mechanism for iterative optimization; update the position of each particle as the individual optimal position, calculate and evaluate the fitness of the new position, and perform boundary checks until the global optimal position of each particle is found;

[0017] S23. Calculate and retain the corresponding iterative results to obtain the optimal position of each joint of the target robotic arm; and adjust the Fourier coefficient to optimize the excitation trajectory; obtain the constraint conditions that meet the angle, speed and angular velocity of each joint of the target robotic arm.

[0018] Furthermore, the quantum behavior update mechanism specifically includes:

[0019] Calculate the average value based on the individual optimal positions corresponding to each joint of the target manipulator as the center of the potential well;

[0020] The individual optimal position of each particle is mixed with the global optimal position to generate a new potential well center as the local potential well center of each particle;

[0021] Based on the quantum contraction and expansion coefficient and logarithmic perturbation, the position of each particle is dynamically adjusted and updated.

[0022] Furthermore, the Lévy flight update mechanism specifically includes:

[0023] Dynamically adjust the Lévy step size parameters and coefficients to generate the Lévy step size;

[0024] The current particle position corresponding to each joint of the target robot arm is updated by fusing the current particle position, the global optimal position and the Lévy step length.

[0025] Further, the boundary check is performed until the global optimal position of each particle is found, and specifically includes:

[0026] After updating the particle position corresponding to each joint of the target robot arm each time, the out-of-bound particle position is corrected and randomly reset to the search space;

[0027] Two escape mechanisms are introduced to avoid falling into a local optimum.

[0028] The first escape mechanism includes: when the number of iterations reaches a first threshold, the individual optimal position of an unimproved particle is fused with the position of a random particle to generate a new position, which is evaluated as the updated individual optimal position.

[0029] The second escape mechanism includes: when the number of iterations reaches a second threshold and the optimal position is not updated each time, the Lévy flight update mechanism is used to re-generate and evaluate.

[0030] Further, the step S3 specifically includes:

[0031] S31, based on the constraint condition, the improved hyperbolic sine cosine optimization algorithm is used to set the iteration parameters and control parameters in the parameter solving process of each joint of the target robot arm, and parameter initialization and mixed population initialization are performed;

[0032] S32, the initial population fitness is calculated, the optimal solution and the suboptimal solution are recorded, and the individual adaptive weight is established;

[0033] S33, the global search is performed in the iteration process, and the control parameters and individual positions are updated;

[0034] S34, the population fitness value is updated to obtain the corresponding global optimal solution and suboptimal solution, and the weight is adjusted according to the individual performance;

[0035] S35, periodic local search is performed in the iteration process, and population diversity maintenance and adaptive restart mechanism are used for enhanced optimization to obtain the optimal fitness and optimal parameter solution in the population iteration process;

[0036] S36, by determining the optimal fitness and optimal parameter solution, the corresponding numerical value of the minimum parameter set of the target robot arm and the torque value of each joint are obtained.

[0037] Further, in step S31,

[0038] The iteration parameters include: population size, maximum number of iterations, parameter boundary and dimension;

[0039] The control parameters include: hyperbolic function value, exploration coefficient, utilization coefficient, exploration intensity and attenuation coefficient;

[0040] The mixed population initialization includes: performing uniform random distribution initialization, chaotic sequence initialization and reverse learning initialization on all populations according to proportion.

[0041] Furthermore, step S33 specifically includes:

[0042] Perform global search during the iteration process, update the hyperbolic function value according to the current iteration progress ratio, and dynamically adjust the exploration coefficient and utilization coefficient;

[0043] If bounded search is triggered, the search range is narrowed; if bounded search is not triggered, the position update of the exploration-exploitation phase is performed;

[0044] For individuals that cross the boundary, a boundary rebound mechanism is adopted, and a mechanism of moving closer to the optimal solution is introduced to update the individual position.

[0045] Furthermore, step S35 specifically includes:

[0046] S351. Perform periodic local search during the iteration process and introduce parameter sensitivity analysis to prioritize the search for sensitive parameters.

[0047] S352. Introduce a diversity monitoring and maintenance mechanism. When the population diversity falls below a threshold, diversify the non-elite individuals.

[0048] S353, introduce an adaptive restart mechanism to re-search non-elite individuals when falling into a local optimum;

[0049] S354. After the iteration is completed, the optimal fitness and optimal parameter solution are obtained.

[0050] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for identifying dynamic parameters based on robot arm excitation trajectory optimization, which has the following beneficial effects:

[0051] The present invention optimizes the excitation trajectory of the robotic arm by constructing a staged Fourier series structure and using a hybrid particle swarm optimization algorithm of quantum behavior and Lévy flight; the generated excitation trajectory has a smaller regression matrix condition number, stronger continuous excitation, and higher robustness to measurement noise.

[0052] The present invention improves the hyperbolic sine-cosine optimization algorithm. During the dynamic parameter identification, the nonlinear constraint problem of the excitation trajectory is solved through multi-strategy initialization, adaptive stage search, sensitivity-guided local fine search, and stagnation detection restart, which significantly improves the convergence speed and estimation accuracy in the constrained dynamic parameter identification task.

[0053] The present invention organically combines optimized excitation trajectory generation with robust parameter identification. Compared with existing technologies, it can more effectively obtain a high-precision robotic arm dynamics model, laying a more reliable foundation for model-based advanced control applications (such as compliant control, high-precision trajectory tracking, sensorless collision detection, etc.), and has good generalization capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0055] Figure 1 A flow chart of a dynamic parameter identification method based on robot arm excitation trajectory optimization provided by an embodiment of the present invention.

[0056] Figure 2 The spatial trajectory diagram of the end effector of the optimized excitation trajectory provided by the embodiment of the present invention.

[0057] Figure 3 This is a graph of joint angles versus time for the optimized excitation trajectory provided by an embodiment of the present invention.

[0058] Figure 4 This is a graph showing the angular velocity of each joint versus time for the optimized excitation trajectory provided by an embodiment of the present invention.

[0059] Figure 5 This is a graph of the angular acceleration-time curves of each joint of the optimized excitation trajectory provided by an embodiment of the present invention.

[0060] Figure 6 Flowchart of the quantum behavior and Lévy flight hybrid particle swarm optimization algorithm provided by an embodiment of the present invention.

[0061] Figure 7 Flowchart of the improved hyperbolic sine-cosine optimization algorithm provided by an embodiment of the present invention.

[0062] Figure 8 A comparison chart of the estimated and measured values ​​of each joint torque obtained through identification provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work belong to the scope of protection of the present application.

[0064] The embodiment of the present application discloses a dynamic parameter identification method based on mechanical arm excitation trajectory optimization, as shown in the figure, Figure 1 The embodiment of the present application discloses a dynamic parameter identification method based on mechanical arm excitation trajectory optimization, as shown in the figure,

[0065] S1, a corresponding Newton-Euler dynamic model is constructed based on a target mechanical arm, and a linear dynamic model is obtained through linear transformation and parameter reorganization; the linear dynamic model includes a related minimum parameter set and a regression matrix of the target mechanical arm; the related minimum parameter set includes the mass, inertia tensor, first moment, motor rotational inertia and friction force of each joint of the target mechanical arm;

[0066] S2, based on the linear dynamic model, a stage-by-stage periodic Fourier series excitation trajectory based on the position of each joint of the target mechanical arm is constructed; and a quantum behavior and Lévy flight hybrid particle swarm optimization algorithm is used to optimize the excitation trajectory, to obtain the constraint conditions of the regression matrix in the linear dynamic model; the constraint conditions include the motion constraints of the joint angle, speed and angular speed;

[0067] S3, based on the constraint conditions, an improved hyperbolic sine cosine optimization algorithm is used to identify the numerical value of the minimum parameter set and the joint torque value of the linear dynamic model.

[0068] The embodiment of the present application provides a solution scheme of fusing an improved meta-heuristic algorithm, aiming at the problems of poor excitation trajectory optimization effect and insufficient dynamic parameter identification accuracy, generates a continuous excitation trajectory with low noise sensitivity through optimization, and obtains more accurate dynamic parameters by combining a robust and efficient parameter identification algorithm, to finally obtain a high-precision mechanical arm dynamic model.

[0069] The embodiment is applied before high-precision operation of a robot (a serial rigid mechanical arm with n degrees of freedom), and the working precision and performance of the robot need to be improved before use. The robot is required to have high repeat positioning accuracy and high absolute position accuracy. The absolute position accuracy depends on its kinematic parameters, and the dynamic parameter identification process of a serial rigid mechanical arm with n degrees of freedom is described in detail.

[0070] The implementation steps of the embodiment will be described in detail below.

[0071] Step one, establish the Newton-Euler dynamic model of the serial rigid manipulator;

[0072] Firstly, according to the Newton-Euler recursive formula, the dynamic model of the n-DOF serial rigid manipulator is expressed as:

[0073]

[0074] where, represents the joint friction force / torque vector; respectively represent the joint position, velocity, and acceleration vectors; represents the positive definite symmetric inertia matrix; represents the Coriolis force and centrifugal force matrix; represents the gravity vector;

[0075] represents the friction vector.

[0076] In this embodiment, the joint friction of the manipulator adopts the Coulomb-viscous friction model, which is expressed as:

[0077]

[0078] where, c and F v respectively represent the Coulomb coefficient and viscous coefficient diagonal matrices; F o represents the asymmetric bias term of Coulomb friction during forward and reverse rotation; sign(·) is the sign function.

[0079] The dynamic term in the dynamic model expression is a non-diagonal matrix, that is, there is coupling between each joint, and it is difficult to directly identify the dynamic parameters. In this embodiment, the dynamic model of the manipulator is linearly transformed, and the linearized dynamic form is:

[0080]

[0081] where, represents the regression matrix; represents the set of all dynamic parameters; N is the number of parameters in the set of all dynamic parameters.

[0082] For a serial rigid manipulator, there are usually multiple dynamic parameters (such as inertia, mass, friction coefficient, etc.) for each joint, and an n-DOF manipulator has N = 14n dynamic full parameters. In this embodiment, a 6-DOF manipulator is established.

[0083] After linearization, since the regression matrix is not full rank, the least squares method and other methods cannot be used to solve the set of dynamic parameters. Therefore, in this embodiment, the inertia parameters of the regression matrix are linearly reorganized, and the dynamic model of the manipulator obtained by using the least inertia parameters is:

[0084]

[0085] wherein, is the regression matrix corresponding to the minimum parameter set; is the minimum parameter set; N b is the number of parameters in the minimum parameter set of dynamics.

[0086] The minimum inertial parameter set Φ b containing N b parameters and its corresponding regression matrix N b = 58 in this embodiment.

[0087] Step two, the design and optimization of the excitation trajectory of the robot arm;

[0088] The main goal of the design and optimization of the excitation trajectory in this embodiment is to maximize the excitation information of the dynamic model through the carefully designed motion trajectory, to reduce the condition number of the regression matrix as much as possible, and to suppress the interference of the measurement noise.

[0089] This embodiment provides a phased five-order periodic Fourier series excitation trajectory, which includes low-speed, uniform-speed, high-speed and variable-speed stages; and a hybrid particle swarm optimization algorithm based on quantum behavior and Lévy flight is proposed to optimize the specific parameters of the five-order Fourier series, which fully excites the dynamic characteristics of the robot arm, improves the noise suppression ability, and realizes the generation of high-precision dynamic parameter identification excitation trajectory; as shown in Figure 2 , the end effector space trajectory graph of the optimized excitation trajectory is displayed; the XYZ axes are the three-dimensional axes based on the target robot arm, and the corresponding regression matrix condition number and fitness are as shown in Figure 2 .

[0090] The periodic five-order Fourier series excitation trajectory constructed in this embodiment is as follows:

[0091]

[0092] wherein, q 0i represents the initial value of joint i; N represents the order of the Fourier series; ω = 2π / T is the motion fundamental frequency; a ij and b ij are Fourier coefficients; α j (t) is the adjustment function of each stage j.

[0093] In this embodiment, the number of joints of the robot arm is i=6; the order of the Fourier series is N=5; the trajectory operation period is T=20s; and the fundamental frequency of the motion is ω=π / 10. Figure 3 As shown, the horizontal axis is time and the vertical axis is angle, showing the angle-time curve of each joint of the optimized excitation trajectory. Figure 4 As shown, the horizontal axis is time and the vertical axis is speed, showing the angular velocity-time curve of each joint of the optimized excitation trajectory. Figure 5 As shown, the horizontal axis is time and the vertical axis is angular velocity, which shows the angular acceleration-time curve of each joint of the optimized excitation trajectory.

[0094] The objective function of this embodiment is constructed based on the penalty function of Lagrange multipliers. By dynamically adjusting the penalty factor, it can handle nonlinear constrained optimization problems. The higher the degree of constraint violation, the more severe the penalty imposed, thus guiding the search process to converge within the feasible region.

[0095] The objective function of this embodiment is expressed as follows:

[0096] J=cond(Y b (·))+k1·ρ

[0097] Among them, cond(Y b (·)) is the condition number of the regression matrix; k1 is the penalty factor; and ρ is a penalty function based on Lagrange multipliers. The penalty factor k1 is dynamically adjusted, with larger penalties for more severe constraint violations. A smaller J value increases the coverage of the excitation trajectory within the feasible motion space, resulting in higher identification accuracy and greater robustness against measurement noise.

[0098] Therefore, the optimization problem of the excitation trajectory can be expressed as a problem of solving the minimum value of Ξ under nonlinear constraints, which is specifically expressed as follows:

[0099] minΞ=min[cond(Y b (·))+k1·ρ]

[0100]

[0101] Among them, q imin and q imax are the minimum and maximum values ​​of the robot arm joint angle; and are the minimum and maximum values ​​of the robot arm joint velocity; and are the minimum and maximum angular velocities of the robot joints.

[0102] These constraints ensure the safety and feasibility of the robotic arm during movement.

[0103] The embodiment is based on a hybrid particle swarm optimization algorithm of quantum behavior and Lévy flight, and optimizes an objective function by dynamically adjusting a penalty factor, and then optimizes an excitation function, so as to process a nonlinear constraint optimization problem.

[0104] The hybrid particle swarm optimization algorithm of quantum behavior and Lévy flight in the embodiment is specifically introduced below, and reference is made to Fig. Figure 6

[0105] Firstly, an initialization stage is entered; a particle swarm is initialized, and an initial fitness is calculated; a current position of each particle is taken as an individual optimal position, and a current fitness is taken as an individual optimal fitness; and the initialization specifically includes:

[0106] (1) setting algorithm parameters;

[0107] The number of particles of the optimization objective, the problem dimension, the maximum number of iterations, the lower bound and the upper bound of the search space are determined.

[0108] (2) initializing a particle position;

[0109] An initial position of each particle is randomly generated in the search space.

[0110] (3) initializing a particle speed;

[0111] An initial speed of each particle is randomly generated in a preset speed range.

[0112] (4) calculating an initial fitness;

[0113] Objective function values of all particles are evaluated, and the number of evaluated times is recorded.

[0114] (5) initializing an optimal record;

[0115] A current position is taken as an individual optimal position Pbest, and a current fitness is taken as an individual optimal fitness; and a global optimal position Gbest and a global optimal fitness are selected.

[0116] Secondly, an iterative optimization stage is entered (cyclically executed until the maximum number of iterations is reached); a quantum behavior updating mechanism or a Lévy flight updating mechanism is randomly selected for iterative optimization; a position of each particle is updated as an individual optimal position, a fitness of the new position is calculated and evaluated, and a boundary check is performed until a global optimal position of each particle is found; and the iterative optimization specifically includes:

[0117] (1) firstly, strategy selection is performed;

[0118] In the embodiment, a random number A is generated, if A<0.5, a quantum behavior strategy (2) is executed; otherwise, a Lévy flight strategy (3) is executed.

[0119] ​(2) Quantum behavior strategy; calculate the average of all individual optimal positions (potential well center), mix the individual optimal position of each particle with the global optimal position to generate a new potential well center, update the particle position based on the quantum shrinkage expansion coefficient and logarithmic perturbation.

[0120] First, calculate the potential well center C and the local potential well center ZX of each particle:

[0121]

[0122] ZX k = φ · Pbest k + (1 - φ) · Gbest

[0123] where φ is a random number in [0, 1]. Then, the particle position is updated as follows:

[0124]

[0125] where r and rand are both random numbers in (0, 1], and α CE is the shrinkage-expansion coefficient, which is dynamically adjusted with iterations:

[0126]

[0127] where α CE0 and α CE1 represent the initial and final quantum shrinkage-expansion coefficients, respectively; t represents the current iteration number; T Max is the maximum number of iterations.

[0128] (3) Lévy flight strategy; dynamically adjust the Lévy step length parameter and coefficient, generate Lévy random step length (combined with normal distribution and Gamma function), and update the position by fusing the current particle position, global optimal position, and Lévy step length.

[0129] The particle position is updated as follows:

[0130] X k (t+1) = C1 · X k (t) + λ · Gbest + 0.01 · L(β) · (Gbest - X r )

[0131] where X r is a randomly selected reference particle; L(β) is the Lévy flight step length, which is generated as follows:

[0132]

[0133] where u and v are subject to normal distribution N(0, σ u) and N(0, 1), σ u is calculated by the following equation:

[0134]

[0135] The parameters λ and C1 are dynamically adjusted with iterations:

[0136]

[0137] (4) Boundary treatment;

[0138] After updating the particle position each time, a boundary check is performed, and the out-of-boundary particles are reinitialized randomly within the search space. The algorithm iterates until a preset maximum number of iterations T is reached Max .

[0139] To prevent the algorithm from falling into a local optimum, two escape mechanisms are introduced in this embodiment.

[0140] The first escape mechanism includes:

[0141] When the number of iterations exceeds a first preset threshold, for a particle whose fitness is not better than the global optimum, a new candidate solution is generated by performing a crossover operation with the individual optimal position of another particle selected randomly, and is evaluated and updated.

[0142] The second escape mechanism includes: when the number of iterations exceeds a second preset threshold and the global optimal solution is not updated, the global optimal solution is disturbed by Lévy flight to generate a new candidate solution:

[0143] Nbest = Gbest + L(β) · (Gbest - Pbest d )

[0144] where Pbest d is the individual optimal position of the randomly selected particle.

[0145] In this embodiment, for (5) individual optimal disturbance, according to the first escape mechanism, when the number of iterations is more than half and every 50 generations, for the particle that is not improved, a new solution is generated by fusing the individual optimal position and the position of a random particle. The new solution is evaluated and the individual optimal position is updated.

[0146] (6) Update the optimal position and evaluate the fitness of all new positions.

[0147] Update the individual optimal position and the global optimal position. If the global optimal solution is not updated for 201 consecutive times, perform (7).

[0148] (7) Global optimal disturbance; according to the second escape mechanism, a new solution of the global optimal position is generated by Lévy flight.

[0149] Evaluate the new solution, if better than the current global optimum, then update the global optimal position.

[0150] (8) Record and output; save the current global optimal fitness, display the iteration information (iteration number, optimal fitness, etc.).

[0151] Finally, the output result stage, return the global optimal solution, optimal fitness, total evaluation number and iteration optimal record; calculate and keep the corresponding iteration result as the optimization parameter of the global optimal solution, dynamically adjust the penalty factor, and then optimize the incentive function to meet the physical limit constraint and boundary constraint.

[0152] Step three, identify the minimum parameter set of the mechanical arm dynamics model and the joint torque.

[0153] The present embodiment proposes to improve the hyperbolic sine cosine optimization algorithm, the purpose is to solve the fixed parameter adaptability in high-dimensional dynamic parameter identification task, lack of diversity of initialization strategy, weak local search mechanism, premature loss of population diversity and oversimplified boundary processing and other limitations, which significantly improves the convergence performance and robustness in the identification process, and realizes efficient solution for the problem of dynamic parameter identification. The meta-heuristic algorithm provided in the present embodiment can obtain the specific value of the minimum parameter set and the size of the identified joint torque.

[0154] The specific process of identification in the present embodiment using the improved hyperbolic sine cosine optimization algorithm is as follows, referring to Figure 7 as shown:

[0155] First, enter the initialization stage; set the iteration parameters and control parameters in the solution process, and perform parameter initialization and mixed population initialization; calculate the initial population fitness, record the optimal solution and suboptimal solution; and establish individual adaptive weight; including:

[0156] (1) Parameter setting;

[0157] Receive population size, maximum iteration number, parameter boundary, dimension, etc. Input parameters.

[0158] (2) Adaptive parameter initialization; set the core control parameters of hyperbolic function parameters, exploration / exploitation coefficients, exploration strength / decay coefficients, etc.

[0159] In order to improve the adaptability of the algorithm, the present embodiment introduces an adaptive parameter adjustment mechanism based on iteration progress, which is expressed by the formula as follows:

[0160]

[0161] Where a1 and a2 represent the exploration and exploitation stage weight coefficients respectively, B represents the search mode selection parameter. t represents the current iteration number, T maxwhere m, n, p and q represent the exploration coefficient, exploitation coefficient, search intensity and search decay parameter, respectively, and cosh2 and sinh2 are the hyperbolic function values based on the iteration progress.

[0162] This adaptive parameter setting of the embodiment enables the algorithm to dynamically adjust the search behavior according to the optimization process.

[0163] (3) Hybrid population generation;

[0164] To enhance the diversity and quality of the initial population, the embodiment proposes a hybrid strategy of three initialization methods:

[0165] X = {X uniform ,X chaotic ,X opposition}

[0166] where X uniform The uniform random initialization is adopted, X chaotic The chaotic sequence initialization is generated by the Logistic mapping, X opposition The reverse learning initialization is adopted.

[0167] In the embodiment, 60% of the individuals are initialized by the uniform random distribution, 20% of the individuals are initialized by the chaotic sequence, and 20% of the individuals are initialized by the reverse learning strategy.

[0168] (4) Fitness evaluation; calculate the fitness of the initial population, record the optimal solution and suboptimal solution.

[0169] (5) Weight initialization: establish an adaptive weight history record for each individual.

[0170] The embodiment introduces an individual historical weight record mechanism, and dynamically adjusts the weight of the individual according to the optimization performance of the individual:

[0171]

[0172] where w l represents the weight of the lth individual, represents the fitness value of the lth individual in the tth iteration.

[0173] Then, the iteration optimization main loop is performed; in the iteration process, the global search is performed, the control parameters and the individual position are updated, the population fitness value is updated, the corresponding global optimal solution and suboptimal solution are obtained, and the weight is adjusted according to the performance of the individual; specifically including:

[0174] (1) Dynamic parameter update; calculate the current iteration progress ratio, update the hyperbolic function value, and dynamically adjust the exploration coefficient and exploitation coefficient.

[0175] (2) Bound search trigger; trigger search space contraction at preset iteration points, dynamically reduce parameter boundaries based on optimal solution and suboptimal solution, retain elite individuals, and reinitialize the rest in new intervals.

[0176] This embodiment dynamically reduces the search space according to the current optimal solution and suboptimal solution, which is expressed by the formula as follows:

[0177]

[0178] Wherein, Lb new,s and ub new,s respectively represent the new lower bound and the new upper bound of the parameter in the s dimension, X second,s represents the position of the suboptimal solution in the s dimension, and X best,s represents the position of the optimal solution in the s dimension.

[0179] The reduced search space helps the algorithm to perform more effective local fine search in the later iterations.

[0180] (3) Position update;

[0181] The early iterations belong to the exploration stage, and a large range of disturbance is generated based on the hyperbolic function, and the positive or negative exploration is randomly selected;

[0182] The later iterations belong to the utilization stage, and the fine search is performed with small step size to fine-tune the optimal solution.

[0183] (4) Boundary processing;

[0184] The out-of-bound individuals adopt the rebound strategy, and in the later iterations, they are attracted to the optimal solution, and the rebound amplitude is adaptively adjusted; for the parameter boundary constraint, this embodiment introduces an adaptive boundary rebound mechanism, and the optimal individual position is expressed by the formula as follows:

[0185]

[0186] Wherein, δ represents the out-of-bound distance, lb s and ub s respectively represent the lower bound and the upper bound of the parameter in the s dimension, X l,s represents the position of the optimal individual; and rand() represents a random number between 0 and 1.

[0187] In addition, in the later iterations, the boundary processing also introduces a mechanism to attract the optimal solution, which is expressed by the formula as follows:

[0188]

[0189] (5) Fitness reevaluation; update the fitness value of the population, dynamically maintain the global optimal solution and the suboptimal solution, adjust the weight according to the performance of the individual, for example, reward progress or punish stagnation.

[0190] Further, the optimization strategy is enhanced; periodic local search is performed in the iteration process, and population diversity maintenance and adaptive restart mechanism are used for enhanced optimization to obtain the optimal fitness and optimal parameter solution in the iteration process of the population; specifically including:

[0191] (1) Periodic local search;

[0192] In the iteration process, the embodiment periodically performs local fine search on the global optimal solution; which is expressed by the formula as:

[0193]

[0194] Wherein, z is the search radius coefficient, randn() represents a random number subject to standard normal distribution.

[0195] In the later stage of iteration (t>0.7*t / T max ), the local search of the embodiment also introduces parameter sensitivity analysis, and preferentially searches sensitive parameters, and the sensitivity thereof is expressed by the formula as:

[0196]

[0197] Wherein, S s represents the sensitivity of the s-dimensional parameter, x +δ,s and x -δ,s respectively represent the solution after increasing and decreasing the s-dimensional parameter.

[0198] The local search of the embodiment is triggered every 5 generations, and the parameter sensitivity analysis is performed every 2 generations in the later stage, and the sensitive parameters are simulated annealing searched.

[0199] (2) Diversity maintenance;

[0200] In order to prevent the population from converging too early, the embodiment introduces a diversity monitoring and maintenance mechanism, which is expressed by the formula as:

[0201]

[0202] Wherein, D represents the population diversity measure, represents the population center point.

[0203] When D is lower than the threshold value, the non-elite individuals are diversified, which is expressed by the formula as:

[0204]

[0205] Wherein, γ is the mutation intensity coefficient, X elite,s is the position of the elite individual in the s-dimensional.

[0206] In this embodiment, the population diversity is detected every 20 generations, and when the diversity is insufficient, the top 30% elite individuals are retained, and the remaining individuals are subjected to directional mutation or reinitialization.

[0207] (3) Adaptive restart;

[0208] When the algorithm falls into local optimum, that is, the convergence curve stagnates, partial population restart is triggered; the formula is as follows:

[0209]

[0210] Wherein, X i represents the lth individual; X new represents the individual that needs to be reinitialized.

[0211] In this embodiment, the top 30% elite individuals are kept unchanged, and the remaining individuals are reinitialized and reevaluated;

[0212] (4) Record the convergence curve and save the optimal fitness of each generation.

[0213] Finally, the result is output; the optimal parameter solution is returned, the best fitness value is output, and the convergence curve data is provided.

[0214] In this embodiment, the improved hyperbolic sine cosine optimization algorithm is used, and the final output is the minimum parameter set and the joint torque.

[0215] In this embodiment, the mechanical arm executes the excitation trajectory with a cycle length of 20s and a sampling time of 10ms; in order to suppress random noise, the data of five cycles are averaged. The joint position and motor current data are filtered by a zero-phase low-pass Butterworth filter. After extensive parameter tuning, the filter parameters are set as follows: the passband cutoff frequency is 0.12Hz, the stopband cutoff frequency is 0.2Hz, the passband attenuation is 3dB, and the stopband attenuation is 60dB. The joint speed and acceleration are obtained by off-line central difference method, and the acceleration data is further smoothed by a sliding average filter.

[0216] Subsequently, the improved hyperbolic sine cosine optimization algorithm is used to identify the minimum parameter set and joint torque of the dynamic model. Referring to Figure 8 , a comparison chart of the estimated and measured values of each joint torque identified within a period of time is shown.

[0217] In summary, the present application is a hybrid particle swarm optimization algorithm based on quantum behavior and Lévy fight (QLHPSO) for the design optimization of robot manipulator excitation trajectories, particularly its contained dual-strategy dynamic selection mechanism (quantum behavior / Lévy fight), adaptive parameter control mechanism (contraction coefficient decay / step size adjustment), and three-level escape mechanism (neighborhood recombination / Lévy jump / boundary repair) when the global optimal solution is not updated.

[0218] The present application is a modified Sinh Cosh Optimizer (MSCHO) for the identification of robot manipulator dynamics minimum parameter set and joint torques, particularly its contained multi-strategy hybrid initialization mechanism (uniform / chaotic / inverse learning), adaptive exploration-exploitation phase search strategy and its conversion mechanism, parameter sensitivity guided local search mechanism (sensitivity analysis / adaptive radius / simulated annealing criterion), and stagnation detection and restart mechanism.

[0219] The present application is a fusion of the QLHPSO optimized phased periodic Fourier series excitation trajectory and the MSCHO algorithm for robot manipulator dynamics parameter identification.

[0220] The various embodiments in the present specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same or similar parts between various embodiments can be referred to each other. For the apparatus disclosed by the embodiments, since it corresponds to the method disclosed by the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part description.

[0221] The above description of disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for identifying dynamic parameters based on robot arm excitation trajectory optimization, characterized in that: The following steps are involved: S1. Construct a corresponding Newton-Euler dynamics model based on the target manipulator, and obtain a linear dynamics model through linear transformation and parameter reorganization; The linear dynamics model includes a relevant minimum parameter set and a regression matrix of the target manipulator; The relevant minimum parameter set includes: the mass of each joint of the target manipulator, the inertia tensor, the first-order moment, the motor moment of inertia and the friction force; S2. Based on the linear dynamics model, construct a staged periodic Fourier series excitation trajectory based on the position of each joint of the target manipulator; and optimize the excitation trajectory using a quantum behavior and Lévy flight hybrid particle swarm optimization algorithm to obtain the constraints of the regression matrix in the linear dynamics model; the constraints include motion constraints of each joint angle, velocity, and angular velocity; S3. Based on the constraints, an improved hyperbolic sine-cosine optimization algorithm is used to identify the numerical value of the minimum parameter set and the joint torque value of the linear dynamics model.

2. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 1, characterized in that: The method uses a quantum behavior and Lévy flight hybrid particle swarm optimization algorithm to optimize the Fourier coefficients of the excitation trajectory to obtain the constraint conditions of the regression matrix in the linear dynamics model; specifically includes: S21, initialize the particle swarm corresponding to each position and speed of each joint of the target manipulator, and calculate the initial fitness; take the current position of each particle as the individual optimal position, and take the current fitness as the individual optimal fitness; S22. Randomly select the quantum behavior update mechanism or the Lévy flight update mechanism for iterative optimization; update the position of each particle as the individual optimal position, calculate and evaluate the fitness of the new position, and perform boundary checks until the global optimal position of each particle is found; S23. Calculate and retain the corresponding iterative results to obtain the optimal position of each joint of the target robotic arm; and adjust the Fourier coefficient to optimize the excitation trajectory; obtain the constraint conditions that meet the angle, speed and angular velocity of each joint of the target robotic arm.

3. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 2, characterized in that: The quantum behavior update mechanism specifically includes: Calculate the average value based on the individual optimal positions corresponding to each joint of the target manipulator as the center of the potential well; The individual optimal position of each particle is mixed with the global optimal position to generate a new potential well center as the local potential well center of each particle; Based on the quantum contraction and expansion coefficient and logarithmic perturbation, the position of each particle is dynamically adjusted and updated.

4. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 2, characterized in that: The Lévy flight update mechanism specifically includes: Dynamically adjust the Lévy step size parameters and coefficients to generate the Lévy step size; The position of each joint of the target manipulator corresponding to the current particle, the global optimal position and the Lévy step size are fused to update the position of the current particle.

5. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 2, characterized in that: The boundary check is performed until the global optimal position of each particle is found; specifically, it includes: After each update of the particle positions corresponding to each joint of the target manipulator, the positions of the out-of-bounds particles are corrected and randomly reset to the search space; Introducing two escape mechanisms to avoid falling into local optimality; The first escape mechanism includes: when the number of iterations reaches a first threshold, for the unimproved particles, the individual optimal position is fused with the position of the random particle to generate a new position and evaluate it as the updated individual optimal position; The second escape mechanism includes: when the number of iterations reaches a second threshold and the optimal position is not updated each time, regenerating and evaluating using the Lévy flying update mechanism.

6. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 1, characterized in that: The step S3 specifically includes: S31. Based on the constraints, an improved hyperbolic sine-cosine optimization algorithm is used to set iteration parameters and control parameters in the process of solving the parameters of each joint of the target robotic arm, and perform parameter initialization and mixed population initialization; S32. Calculate the initial population fitness, record the optimal solution and suboptimal solution; and establish individual adaptive weights; S33, perform global search in the iterative process, and update control parameters and individual positions; S34, update the population fitness value, obtain the corresponding global optimal solution and suboptimal solution, and adjust the weight according to individual performance; S35. Perform periodic local search during the iteration process, and use population diversity maintenance and adaptive restart mechanism to perform enhanced optimization to obtain the optimal fitness and optimal parameter solution during the population iteration process; S36. By determining the optimal fitness and the optimal parameter solution, the corresponding values ​​of the minimum parameter set of the target robotic arm and the torque value of each joint are obtained.

7. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 6, characterized in that: In step S31, The iteration parameters include: population size, maximum number of iterations, parameter boundaries and dimensions; The control parameters include: hyperbolic function value, exploration coefficient, utilization coefficient, exploration intensity and attenuation coefficient; The mixed population initialization includes: performing uniform random distribution initialization, chaotic sequence initialization and reverse learning initialization on all populations according to proportion.

8. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 6, characterized in that: Step S33 specifically includes: Perform global search during the iteration process, update the hyperbolic function value according to the current iteration progress ratio, and dynamically adjust the exploration coefficient and utilization coefficient; If bounded search is triggered, the search range is narrowed; if bounded search is not triggered, the position update of the exploration-exploitation phase is performed; For individuals that cross the boundary, a boundary rebound mechanism is adopted, and a mechanism of moving closer to the optimal solution is introduced to update the individual position.

9. The method for identifying dynamic parameters based on robot arm excitation trajectory optimization according to claim 8, characterized in that: Step S35 specifically includes: S351. Perform periodic local search during the iteration process and introduce parameter sensitivity analysis to prioritize the search for sensitive parameters. S352. Introduce a diversity monitoring and maintenance mechanism. When the population diversity falls below a threshold, diversify the non-elite individuals. S353, introduce an adaptive restart mechanism to re-search non-elite individuals when falling into a local optimum; S354. After the iteration is completed, the optimal fitness and optimal parameter solution are obtained.

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