Mechanical arm parameter stable estimation method based on average distribution sliding window
By constructing the total observation matrix using the Jacobian matrix and performing four-layer smoothing optimization, the stability and noise suppression problems of the robotic arm parameter estimation were solved, enabling high-precision motion control and trajectory planning for the robotic arm.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- FOSHAN UNIVERSITY
- Filing Date
- 2026-04-27
- Publication Date
- 2026-06-05
AI Technical Summary
Existing robotic arm parameter estimation methods are susceptible to the selection of initial values, have slow convergence speed, are prone to divergence, and are easily affected by noise and abnormal data, resulting in unstable control accuracy and difficulty in achieving high-precision motion control.
A stable estimation method for robot arm parameters based on a sliding window with average distribution is adopted. The total observation matrix is constructed by the Jacobian matrix. Combined with regularization solution and four-layer smoothing optimization, the stable convergence of parameters and noise suppression are achieved. The sliding window average smoothing and damping factor control the parameter update to ensure the stability of the estimation results.
It improves the stability and accuracy of robotic arm parameter estimation, ensures the real-time performance and accuracy of robotic arm motion control, and provides high-precision trajectory planning support.
Smart Images
Figure CN122143043A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of robotic arm motion control technology, and in particular to a method for stabilizing and estimating robotic arm parameters based on an average distribution sliding window. Background Technology
[0002] In industrial production, medical surgery, logistics sorting, and service robotics, the motion control accuracy of robotic arms directly determines their work quality and operational reliability. The DH link parameter error of the robotic arm is a core factor affecting kinematics solutions and control accuracy. Accurate and stable parameter estimation is a prerequisite for achieving high-precision forward and inverse kinematics solutions and trajectory planning for robotic arms. Currently, the mainstream robotic arm parameter estimation schemes mainly include extended Kalman filtering, recursive least squares, and traditional batch least squares. However, these methods have the following limitations in practical applications: Extended Kalman filtering estimates parameters recursively, which is susceptible to errors due to the selection of initial values, resulting in slow convergence and potential estimation divergence in nonlinear robotic arm systems. Recursive least squares (RLS) updates parameters sequentially, lacking data accumulation and smoothing, making it difficult to converge quickly to stable values. Furthermore, the single-step update nature of RLS makes it highly susceptible to individual abnormal observations and environmental noise, leading to poor stability and irregular fluctuations in parameter estimation results. Traditional batch least squares (BLS) does not perform targeted noise reduction on the data, and noise accumulation reduces estimation accuracy. BLS uses all observation data over a period of time for estimation, lacking criteria for judging parameter convergence, which can easily lead to oscillations in parameter estimation results, making it impossible to determine the optimal estimate and stop updating, thus affecting the real-time control performance of the robotic arm.
[0003] In view of this, this proposal puts forward a stable estimation method for robot arm parameters based on a uniformly distributed sliding window to solve the above problems. Summary of the Invention
[0004] The purpose of this invention is to provide a stable estimation method for robotic arm parameters based on an average distribution sliding window, so as to solve the problems mentioned in the background art.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for stable estimation of robotic arm parameters based on a uniformly distributed sliding window, comprising the following operational steps: The first step is to establish the coordinate system of the robotic arm links based on the DH parameter method; The second step is to configure the control parameters and initial DH parameters for the robotic arm parameter estimation, and store all parameters. The third step involves synchronously collecting the joint angle input data and end-effector actual pose data of the robotic arm over the most recent N time steps through encoders, vision sensors, and motion control systems, and then preprocessing the collected data. The fourth step is to construct the Jacobian matrix based on the DH parameter estimates, and then concatenate the Jacobian matrices of each time step according to the time series to construct the total observation matrix. The fifth step is to perform regularization and then smooth the solution. The sixth step is to iteratively process the parameter estimates based on the parameters configured in the second step until the parameter convergence iteration ends. The seventh step is to calculate and output the optimized DH parameters based on the converged parameters, and then perform motion control and trajectory planning for the robotic arm.
[0006] Preferably, the parameters configured in the second step include batch size, regularization parameter, initial learning rate, damping factor, sliding window size, convergence threshold, convergence judgment window, and initial DH parameter. The batch size is the number of time steps used for each estimated observation data; The regularization parameter is set to 1e-2; The initial learning rate is set to 0.01-0.02; The damping factor is set to 0.98-0.99; The size of the sliding window is set to 10-12; The convergence threshold is set to 1e-6; The convergence judgment window is set to 20-22; The initial DH parameters are based on the physical structure of the robotic arm, and initial values (a1, a2, d1, d4, d6) are set.
[0007] Preferably, after the parameters are configured, the robotic arm data acquisition module, parameter calculation module, and result output module are started simultaneously.
[0008] Preferably, the data preprocessing involves filtering out invalid, missing, and abruptly changed abnormal data from the collected data, and then organizing the processed data according to time series to form a dataset.
[0009] Preferably, the Jacobian matrix performs a linear mapping between the joint angular velocity and the end effector linear velocity of the robotic arm.
[0010] Preferably, the regularization solution performs singularity and overfitting processing on the total observation matrix to obtain the initial update amount of the DH parameters to be estimated for the robotic arm.
[0011] Preferably, after obtaining the initial update amount, four layers of smoothing optimization are performed sequentially to gradually suppress noise interference and control the update rhythm.
[0012] Preferably, the four-layer smoothing optimization process includes the following specific operations: S1, introduce an adaptive learning rate and apply the learning rate to the initial update amount to control the magnitude of a single update; S2, set the parameter update amplitude threshold; S3, introduce a damping factor to perform damped smoothing on the update amount; S4, construct a window set and calculate the average as the final estimate.
[0013] Preferably, during the iterative process, convergence is determined based on a convergence threshold. When the iteration needs to continue, the process returns to the third step to collect data again and continue processing.
[0014] The technical effects and advantages of this invention are as follows: This invention embeds core formulas for DH coordinate transformation, forward kinematics, and parameter solving. The parameter estimation results can be directly substituted into the kinematic model without secondary transformation. Furthermore, it incorporates a four-layer progressive smoothing optimization combined with a quantized convergence criterion formula, balancing convergence speed and stability to address parameter oscillation issues. Simultaneously, it utilizes large-scale data accumulation combined with sliding window averaging smoothing and regularization constraints to effectively dilute environmental noise and abnormal data interference, significantly improving parameter estimation stability. Finally, it achieves quantitative assessment of parameter estimation uncertainty through the error covariance matrix, providing precise data support for subsequent optimization of robotic arm control strategies. Attached Figure Description
[0015] Figure 1 This is a flowchart illustrating the operation of the estimation method of the present invention.
[0016] Figure 2 This is a schematic diagram of the DH parameter modeling of the robotic arm of the present invention. Detailed Implementation
[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0018] This invention provides, for example Figure 1 The robot arm parameter stabilization estimation method based on a uniformly distributed sliding window, as shown, includes the following steps: The first step is to establish the linkage coordinate system of the robotic arm based on the DH parameter method, and to provide a matching DH parameter table for the 6-DOF robotic arm. At the same time, the core kinematic formulas are clarified to provide a mathematical basis for subsequent parameter estimation. The DH parameter table is shown in Table 1 below. Table 1 DH Parameter Table
[0019] Modeling based on DH parameters, such as... Figure 2 As shown, the DH coordinate transformation formula is: Adjacent link coordinate system V i To V i-1 The homogeneous transformation matrix T(i-1,i) is the core formula of the robotic arm's kinematics, composed of four basic rotational and translational transformations. The specific formula is as follows: (1); (2); Expanding into a specific matrix form, it can be represented as follows: (3); The forward kinematics formula is: the total homogeneous transformation matrix T(0,6) from the robot arm base coordinate system {0} to the end effector coordinate system {6} is the product of the transformation matrices of each link, reflecting the mapping relationship between the end effector pose and the joint angles. The formula is: (4); The above total transformation matrix can be decomposed into the end position vector P=[x,y,z] and the attitude rotation matrix R, which are the core mathematical basis for subsequent parameter estimation.
[0020] The second step involves configuring the control parameters and initial DH parameters for the robotic arm parameter estimation, and storing all parameters. The parameters configured in this step include batch size, regularization parameter, initial learning rate, damping factor, sliding window size, convergence threshold, convergence judgment window, and initial DH parameters. The batch size is the number of time steps used for each estimation of observation data; in this implementation, the batch size is set to 100, meaning each estimation uses 100 time steps of observation data. The regularization parameter is set to 1e-2 to prevent overfitting during estimation. The initial learning rate is set to 0.01-0.02 to control the parameter update speed. The damping factor is set to 0.98-0.9. 9. To enhance the stability of parameter convergence; the sliding window size is set to 10-12 to smooth the estimation results; the convergence threshold is set to 1e-6 as the criterion for parameter convergence; the convergence judgment window is set to 20-22 to continuously verify whether the parameters have reached the convergence state; the initial DH parameters are based on the physical structure of the robotic arm, and initial values (a1, a2, d1, d4, d6) are set; after the parameters are configured, the robotic arm data acquisition module, parameter calculation module and result output module are started simultaneously to complete the linkage and readiness of various hardware devices and software functional modules, ensuring the coordinated operation of data acquisition, calculation and judgment processes, and preparing for subsequent batch data processing and parameter iterative calculation.
[0021] The third step involves synchronously collecting the joint angle input data of the robotic arm over the most recent N time steps (N=100 in this scheme) using encoders, vision sensors, and a motion control system. Compared with the actual observed pose data of the end effector The collected data is preprocessed; the preprocessing involves filtering out invalid, missing, and abruptly changed abnormal data, and then organizing the processed data into a time series to form a dataset, providing effective data support for subsequent matrix construction and solution.
[0022] The fourth step is to calculate the theoretical end-effector pose P based on the estimated DH parameters and substitute them into the forward kinematics formula. cal Construct the Jacobian matrix J. The Jacobian matrix reflects the linear mapping relationship between joint angular velocity and end-effector linear velocity, and is the core of parameter error solution. The formula is defined as follows: (5); Where q represents the DH parameter vector to be estimated, q=[a1,a2,d1,d4,d6], and each column of the Jacobian matrix corresponds to the partial derivative of a single DH parameter; then, the Jacobian matrices of each time step are concatenated according to the time series to construct the total observation matrix H, realizing the mathematical correlation between joint input, end observation and the parameter to be estimated, and establishing the error equation: (6); Where e represents the end-effector pose observation error vector, This represents the correction amount of the DH parameter to be solved.
[0023] The fifth step involves regularization followed by smoothing optimization. The regularization solution addresses the singularity and overfitting of the total observation matrix by introducing a regularization term and constructing a regularized least squares objective function. The optimal parameter correction is then calculated by minimizing the sum of squared errors. The objective function formula is as follows: (7); In the formula, λ=1e-2 is the regularization parameter. Taking the derivative of the objective function and setting the derivative to zero, we obtain the closed-form solution of the parameter correction, which is expressed as: (8); Where I represents the identity matrix, H T The transpose of the observation matrix is used to obtain the initial update amount of the DH parameters to be estimated for the robotic arm through formula (8). After obtaining the initial update amount, four-layer smoothing optimization is performed sequentially to solve the problems of parameter estimation fluctuation and unstable convergence. Noise interference suppression and update rhythm control are gradually implemented to ensure smooth convergence of parameter estimation results. The four-layer smoothing optimization includes the following specific operations: S1 introduces an adaptive learning rate, which is applied to the initial update amount to control the magnitude of each update. Specifically, an adaptive learning rate η is introduced, with an initial value of 0.01, which decays exponentially with the number of iterations, as shown in the formula. k represents the number of iterations, and τ represents the decay coefficient. The learning rate is applied to the parameter update amount to control the magnitude of a single update, achieving rapid approximation in the early stage and fine-tuning in the later stage. S2, Set the parameter update amplitude threshold, specifically, set the parameter update amplitude threshold δ max =0.0001, if |Δq i |>δ max Then it is truncated to Δq i =sign(Δq i )·δ max This prevents significant parameter fluctuations from the source. S3, introduce a damping factor β=0.98 to perform damped smoothing on the update amount, the formula is Δq k =β·Δq (k-1) +(1-β)·Δq new This reduces the estimated oscillation trend; S4, construct a window set and calculate the average as the final estimate; specifically, set a 10-step sliding window, combine the parameter estimates of the current iteration and the previous 9 iterations into a window set, and calculate the arithmetic mean as the final estimate, using the formula q. avg =(1 / 10)·Σq i (Summation interval i=k-9 to k) completely eliminates the influence of high-frequency noise.
[0024] Step 6: Based on the parameters configured in Step 2, iterative processing of the parameter estimates is performed until the parameter convergence iteration ends. During the iteration process, convergence is judged based on the convergence threshold. Based on the preset convergence threshold ε=1e-6 and the convergence judgment window M=20, a convergence judgment formula is constructed, and the root mean square of the change in the parameter estimates within the window is continuously calculated. The formula is expressed as: (9); If σ < ε, the parameter estimation is determined to have reached a stable convergence state, and the iteration stops; if the determination condition is not met, when the iteration needs to continue, return to the third step to collect data again and continue processing to enter the next round of parameter estimation iteration process until the parameters reach stable convergence.
[0025] Step 7: Calculate and output the optimized DH parameters based on the converged parameters for robotic arm motion control and trajectory planning. Specifically, for the converged optimal parameter values, calculate the parameter estimation error covariance matrix C to quantify the estimation uncertainty. The formula is: (10); Where, in the formula The covariance matrix represents the variance of the observation error. The diagonal elements correspond to the estimated variance of a single parameter, reflecting the uncertainty of parameter estimation, while the off-diagonal elements reflect the correlation between different parameters. The final output is the optimal DH parameters and the error covariance matrix, which can be directly substituted into the DH coordinate transformation formula and the forward kinematics formula to achieve high-precision motion control and trajectory planning for the robotic arm.
[0026] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for stabilizing robot arm parameters based on a uniformly distributed sliding window, characterized in that, The following steps are included: The first step is to establish the coordinate system of the robotic arm links based on the DH parameter method; The second step is to configure the control parameters and initial DH parameters for the robotic arm parameter estimation, and store all parameters. The third step involves synchronously collecting the joint angle input data and end-effector actual pose data of the robotic arm over the most recent N time steps through encoders, vision sensors, and motion control systems, and then preprocessing the collected data. The fourth step is to construct the Jacobian matrix based on the DH parameter estimates, and then concatenate the Jacobian matrices of each time step according to the time series to construct the total observation matrix. The fifth step is to perform regularization and then smooth the solution. The sixth step is to iteratively process the parameter estimates based on the parameters configured in the second step until the parameter convergence iteration ends. The seventh step is to calculate and output the optimized DH parameters based on the converged parameters, and then perform motion control and trajectory planning for the robotic arm.
2. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 1, characterized in that, The parameters configured in the second step include batch size, regularization parameter, initial learning rate, damping factor, sliding window size, convergence threshold, convergence judgment window, and initial DH parameter. The batch size is the number of time steps used for each estimated observation data; The regularization parameter is set to 1e-2; The initial learning rate is set to 0.01-0.02; The damping factor is set to 0.98-0.99; The size of the sliding window is set to 10-12; The convergence threshold is set to 1e-6; The convergence judgment window is set to 20-22; The initial DH parameters are based on the physical structure of the robotic arm, and initial values (a1, a2, d1, d4, d6) are set.
3. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 2, characterized in that, After the parameters are configured, the robotic arm data acquisition module, parameter calculation module, and result output module are started simultaneously.
4. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 1, characterized in that, The data preprocessing involves filtering out invalid, missing, and abruptly changed abnormal data from the collected data, and then organizing the processed data according to time series to form a dataset.
5. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 1, characterized in that, The Jacobian matrix performs a linear mapping between the joint angular velocity and the end effector linear velocity of the robotic arm.
6. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 1, characterized in that, The regularization solution performs singularity and overfitting processing on the total observation matrix to obtain the initial update amount of the DH parameters to be estimated for the robotic arm.
7. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 6, characterized in that, After obtaining the initial update amount, four layers of smoothing optimization are performed sequentially to gradually suppress noise interference and control the update rhythm.
8. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 7, characterized in that, The four-layer smoothing optimization process includes the following specific operations: S1, introduce an adaptive learning rate and apply the learning rate to the initial update amount to control the magnitude of a single update; S2, set the parameter update amplitude threshold; S3, introduce a damping factor to perform damped smoothing on the update amount; S4, construct a window set and calculate the average as the final estimate.
9. The method for stabilizing robot arm parameters based on a uniformly distributed sliding window according to claim 2, characterized in that, During the iterative process, convergence is determined based on the convergence threshold. When the iteration needs to continue, the process returns to the third step to collect data again and continue processing.