Speed planning optimization method and system for repeated path operation of industrial robot

Abstract

The invention relates to a speed planning optimization method and system for industrial robot repeated path operation, and the method comprises the steps: carrying out the constraint iterative learning speed planning based on path arc length coordinates, building a precise rigid-flexible coupling dynamic model of a robot, and obtaining the motion constraint condition of the robot; calculating the speed planning motion performance of the robot through the motion performance evaluation function, and updating the parameters of the motion performance evaluation function based on a dynamic linear scaling mechanism; an intelligent iterative learning mechanism based on arc length coordinate parameterization, dynamic constraint on-line satisfaction and provable monotonic convergence performance is realized through an updating law of an iterative learning motion performance evaluation function; and outputting the optimal speed curve of the robot. Track deviation, vibration data and energy consumption characteristics are automatically recorded when a task is executed each time, the root of a problem is autonomously analyzed, key parameters such as an acceleration curve and joint torque distribution are dynamically adjusted, and dependence on manual parameter adjustment in repeated operation is eliminated.

Description

Technical Field

[0001] This invention belongs to the field of speed planning for industrial robots, specifically relating to a speed planning optimization method and system for repetitive path operation of industrial robots. Background Technology

[0002] As global manufacturing moves towards higher precision, higher efficiency, greater flexibility, and greater intelligence, the application scope of industrial robots is constantly expanding, playing an irreplaceable role in fields such as automobile manufacturing, electronic assembly, and precision machining. Industrial robot speed planning refers to how to plan a suitable speed curve on a given task path to ensure that the industrial robot meets trajectory accuracy requirements during movement, while maximizing motion efficiency, reducing energy consumption, and ensuring smooth and safe movement.

[0003] Current industrial robots face highly repetitive motions, and the existing speed planning optimization process relies heavily on experience-based adjustments. This requires manual analysis of tracking errors, mechanical vibrations, and energy consumption data during the motion process, repeatedly trying and failing to determine the correction parameters for the speed curve. This experience-driven adjustment method, based on static offline pre-generation and servo dynamic compensation, has the following bottlenecks:

[0004] First, the parameter optimization process requires multiple iterative cycles of offline simulation and actual verification, and each parameter adjustment is time-consuming, which severely restricts the dynamic response capability of the production line. Second, the effectiveness of the adjustment strategy depends excessively on the engineer's understanding of the multi-physics coupling effect, and there are significant differences in the parameter adjustment results among different personnel.

[0005] Traditional industrial robot speed planning methods are typically based on the robot's kinematics and dynamics models, utilizing optimal control, trajectory interpolation, and constraint optimization. Optimal control methods are widely used in industrial robot speed planning, such as Pontryagin's maximum principle, dynamic programming, and model predictive control. These methods optimize trajectory parameters using the robot's dynamics model and constraints to achieve time-optimal or energy-optimal speed planning. Trajectory interpolation techniques are also widely used, such as B-spline interpolation, Bezier curves, and NURBS curves. These methods generate smooth trajectories between discrete path points through curve fitting, ensuring the continuity and stability of motion. However, traditional speed planning uses an offline planning approach, lacking automatic adjustment and optimization capabilities, and lacking autonomous correction capabilities under dynamic environments, leading to drastic performance degradation under conditions such as sudden load changes and thermal drift.

[0006] Iterative learning control (ILC) is a control method for repetitive tasks that dynamically adjusts the control input using historical error data to gradually improve the system's tracking accuracy. In the field of industrial robotics, ILC is widely used for trajectory tracking, motion compensation, and accuracy improvement due to its high efficiency in repetitive trajectory tasks. The core advantage of ILC lies in its ability to compensate for system model uncertainties and external disturbances by iteratively correcting the control signal. Early research focused on the trajectory tracking problem of robot end-effectors, such as the P-type iterative learning control (ILC) algorithm proposed by foreign scholars, which achieves exponential convergence of trajectory errors by successively updating the control input. To address the practical constraints of industrial robots, some researchers have attempted to combine constraint optimization with ILC, transforming joint angle and speed limitations into inequality constraints and using gradient projection to solve for the optimal learning gain online, ensuring that physical constraints are met during iteration. However, iterative learning techniques have long been limited to single-dimensional compensation of trajectory tracking errors, rarely delving into the core aspect of speed planning, resulting in the inability of the speed curve to autonomously iteratively optimize based on historical operating data. Summary of the Invention

[0007] This invention provides speed planning optimization for repetitive path operation of industrial robots, aiming to solve at least one of the technical problems existing in the prior art.

[0008] The technical solution of this invention is a speed planning and optimization method for repetitive path operation of industrial robots, the method comprising the following steps:

[0009] S100. Constrained iterative learning velocity planning based on path arc length coordinates is used to establish an accurate rigid-flexible coupling dynamic model of the robot, and the precise rigid-flexible coupling dynamic model is identified to obtain the motion constraints of the robot.

[0010] S200, through the motion performance evaluation function J k The motion performance of the robot is calculated based on velocity planning, and the motion performance evaluation function J is updated based on a dynamic linear scalarization mechanism. k Parameters;

[0011] S300, Learning the motion performance evaluation function J through iterative learning. k The update law is based on the constrained iterative learning velocity planning method, and an iterative learning framework for velocity planning is constructed to realize an intelligent iterative learning mechanism based on arc length coordinate parameterization, online satisfaction of dynamic constraints, and provable monotonic convergence performance.

[0012] S400 outputs the optimal speed curve of the robot.

[0013] Furthermore, step S100 includes:

[0014] S110. By introducing the elastic deformation compensation term of the flexible joint and the temperature drift friction model, the accurate rigid-flexible coupling dynamic model of the industrial robot is obtained.

[0015] S120. An online identification framework that integrates LSTM neural network and extended Kalman filter (EKF) is adopted. The robot joint position, velocity and motor current are taken as inputs. The nonlinear mapping relationship of dynamic parameters is learned through LSTM neural network and then real-time parameter calibration and confidence evaluation are performed through extended Kalman filter (EKF).

[0016] S130. The joint velocity, acceleration and torque constraints are uniformly transformed into a quadratic inequality form, and the real-time feasible region determination algorithm based on gradient projection is derived. The real-time feasible region determination algorithm dynamically calculates the motion constraint boundary under the current state in every millisecond control cycle to ensure that the subsequent speed planning strictly meets the physical limit and avoids the risk of overspeed or overload.

[0017] Furthermore, in step S110, the precise rigid-flexible coupling dynamic model is:

[0018]

[0019] Where q is an n-dimensional vector representing the position state of the robot's joints, and n is the robot's degrees of freedom. Represents the velocity vector of a robot joint. M represents the acceleration vector of the robot joint, C is the inertia matrix, G is the Coriolis force, and F is the gravity force. f For the friction model, KΔθ is the flexible joint compensation term, and τ is the control torque of the robot joint.

[0020] Further, step S200 includes:

[0021] S210: Collect high-frequency vibration data of the robot, contour error data between the actual trajectory and the commanded trajectory, task cycle duration data, and motor energy consumption data.

[0022] S220, by integrating high-frequency vibration data, contour error data between actual and commanded trajectories, task cycle duration data, and motor energy consumption data, a motion performance evaluation function J is constructed. k ;

[0023] S230, iterative execution steps S210 to S220: based on the relative degradation degree of high-frequency vibration data, contour error data between actual trajectory and command trajectory, task cycle duration data and motor energy consumption data in each iteration, automatically increase the weight coefficient of significant degradation items. When a certain indicator is significantly improved and does not cause degradation of other indicators, its weight can be actively reduced, and optimization resources can be shifted to other potential targets.

[0024] Furthermore, in step S210, the high-frequency vibration data is collected by an IMU sensor installed at the end of the robot and the vibration energy data for quantifying the main resonant frequency band of motion stability is extracted by short-time Fourier transform. The contour error data between the actual trajectory and the command trajectory is collected by an encoder installed on the robot. The task cycle duration data is obtained by collecting electricity meter data and performing cycle scoring calculation.

[0025] In step S220, the motion performance evaluation function J k for:

[0026] J k = α * Contour error data between actual trajectory and commanded trajectory + β * High-frequency vibration data + γ * Motor energy consumption data + δ * Task cycle duration data

[0027] In this context, α, β, γ, and δ are all variable positive numbers.

[0028] Furthermore, the method S300 includes:

[0029] S310. Planning iterative learning update law, wherein the iterative learning update law includes at least the following along the motion performance evaluation function J. k Update control point P with negative gradient direction i The gradient-type iterative learning update law, the difference-type iterative learning update law that estimates the Jacobian matrix by performing difference budgeting on historical data, and the least squares-type iterative learning update law that fits the optimal parameters based on multiple rounds of data.

[0030] S320. To satisfy the dynamic constraints, the gradient projection operator is called after each iteration update to project the control point P. i Map to the feasible region;

[0031] S330. Construct the Lyapunov energy function and prove the monotonic convergence of iterative learning under joint torque constraints, ensuring that the velocity curve is continuously optimized during repeated execution.

[0032] S340, If the motion performance evaluation function J is satisfied... k If the rate of change is less than a preset first threshold or the number of iterations is greater than a preset second threshold, the iteration is terminated.

[0033] Furthermore, in method S310, the path arc length s is used as a fixed reference coordinate, and a fifth-order B-spline curve is used to parametrically model the velocity curve v. The number of control points is adaptively set according to the path complexity.

[0034]

[0035] Where v(s) is the velocity-time rate, P iThese are control points. During the first iteration, control points P are evenly distributed according to the path length s. i Location, control point P i The quantity is adaptively set according to the path complexity, B i,5 For a fifth-order B-spline basis function, the subscript i is the control point index, which ranges from 0 to n, where n depends on the path complexity. It identifies the position of the control point corresponding to this basis function. Each P... i The initial value is set to the upper limit of the robot's safe speed;

[0036] The differential iterative learning update law is defined as follows:

[0037]

[0038] Where μ is the differential gain, J represents the control point parameters of the B-spline velocity curve at the k-th iteration. k It is the performance evaluation function value of the k-th iteration.

[0039] Furthermore, in method S320, the next control point satisfy:

[0040]

[0041] in, These are the control point parameters of the B-spline velocity curve in the (k+1)th iteration. J is the control point parameter of the B-spline velocity curve at the k-th iteration. k It is a motion performance evaluation function, where η is a positive real number, and η is used to control the control point P. i The update step size, Πc is the constraint projection operator based on gradient projection, and ΔP is the initial update vector calculated only based on the performance gradient in the current iteration;

[0042] The constraint projection operator Πc is used to ensure that the velocity-time rate v(s) satisfies the following dynamic constraints:

[0043]

[0044] in,

[0045]

[0046] Where s is the arc length, is the derivative of arc length with respect to time, q is an n-dimensional vector representing the position state of the robot joint, and a(s) is the tangential acceleration along the path. and These are the minimum and maximum permissible values ​​for the joint velocity, M(q), respectively.

[0047] The inertia matrix, G(q) is the Coriolis force term, G(q) is the gravity term, and τ is the force term. min and τ max These are the minimum and maximum allowable values ​​for joint torque;

[0048] The constrained projection operator Π C This is achieved using non-extended mapping theory, mapping the velocity control point P(i) to the dynamic feasible region:

[0049]

[0050] Where C is the convex set defined by the velocity / acceleration / torque constraints, and x and y are the original input vector and the projected input vector, respectively, i.e., the control point P after gradient update. i And a feasible solution that satisfies the dynamic constraints, ‖x―y‖ is the shortest Euclidean distance between x and y.

[0051] Furthermore, in method S330, the Lyapunov energy function is used as follows:

[0052] V k =|e k | 2 ,

[0053] Among them, V k To learn the residual energy, e k To track errors,

[0054] e k =v d (s)―v k (s),

[0055] Tracking error e k satisfy:

[0056]

[0057] Among them, v d (s) is the desired velocity profile, v d (s) represents the ideal velocity distribution along the path arc length, v k (s) is the actual velocity profile of the k-th iteration. Performance evaluation function J k The gradient of λ is the convergence coefficient.

[0058] Furthermore, this invention also discloses a speed planning and optimization system for repetitive path operation of industrial robots. This system is used to implement the speed planning and optimization method for repetitive path operation of industrial robots. The speed planning and optimization system for repetitive path operation of industrial robots includes:

[0059] The dynamics module is used to build and update dynamic models;

[0060] The motion performance evaluation module is used to calculate and update the motion performance evaluation function J. k The motion performance evaluation module is connected to the dynamics module;

[0061] An iterative calculation module is used to optimize the dynamic model established by the dynamics module. The dynamics module and the motion performance evaluation module are respectively connected to the iterative calculation module.

[0062] The beneficial effects of this invention are as follows:

[0063] This invention proposes a velocity planning optimization algorithm based on iterative learning. For industrial robots running repetitive trajectories, the algorithm automatically records trajectory deviation, vibration data, and energy consumption characteristics each time a task is performed. It autonomously analyzes the root causes of problems and dynamically adjusts key parameters such as acceleration curves and joint torque distribution, thus eliminating the reliance on manual parameter tuning in repetitive tasks.

[0064] This invention overcomes the static nature and manual dependence of traditional methods by deeply embedding Iterative Learning Control (ILC) into the speed planning stage, achieving autonomous evolution and dynamic optimization of the speed curve in repetitive operation scenarios for industrial robots. Its core advantages and technical effects are reflected in the following aspects:

[0065] (1) Dynamic autonomous optimization capability: This invention decouples the velocity curve in the time domain into iterable parameters in the spatial domain through path arc length parameterized modeling. By utilizing the local support characteristics of the fifth-order B-spline curve, it achieves fine-grained control of the velocity profile. Specifically, the velocity curve is transformed into a set of control point parameters directly driven by the path's geometric features. Through an iterative learning mechanism, the parameter weights are continuously corrected, enabling the velocity distribution to autonomously adapt to dynamic factors such as path curvature and inertial load.

[0066] (2) Real-time guarantee mechanism with full constraints: This invention proposes a projection optimization framework that maps multiple types of constraints, such as velocity, acceleration, and torque, to the feasible domain boundary of control point parameters. This framework decomposes the complex multi-constraint coupled problem into multiple sub-problems that can be solved independently, and uses projection operators to correct the iteration parameters in real time, ensuring that the velocity curve after each update strictly meets the physical limits and safety thresholds.

[0067] Furthermore, additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0068] Figure 1This is a general flowchart of a speed planning and optimization method for repetitive path operation of industrial robots according to an embodiment of the present invention.

[0069] Figure 2 This is a general schematic diagram of a speed planning and optimization method for repetitive path operation of industrial robots according to an embodiment of the present invention.

[0070] Figure 3 This is a schematic diagram of the dynamic modeling scheme of the speed planning and optimization method for repetitive path operation of industrial robots according to an embodiment of the present invention.

[0071] Figure 4 This is a schematic diagram of a motion performance evaluation scheme for a speed planning optimization method for repetitive path operation of industrial robots according to an embodiment of the present invention.

[0072] Figure 5 This is a schematic diagram of the iterative learning algorithm design scheme for a speed planning optimization method for repetitive path operation of industrial robots according to an embodiment of the present invention. Detailed Implementation

[0073] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with the embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention.

[0074] It should be noted that, unless otherwise specified, when a feature is referred to as "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature, or indirectly fixed or connected to the other feature. The singular forms "a," "described," and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. Furthermore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this specification is for the purpose of describing particular embodiments only and not for limiting the invention. The term "and / or" as used herein includes any combination of one or more of the associated listed items.

[0075] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various elements, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from one another. For example, a first element may also be referred to as a second element without departing from the scope of this disclosure, and similarly, a second element may also be referred to as a first element. Any and all instances or exemplary language (“e.g.,” “such as,” etc.) provided herein are intended only to better illustrate embodiments of the invention and, unless otherwise required, do not impose a limitation on the scope of the invention.

[0076] Reference Figures 1 to 5 In some embodiments, the speed planning optimization method for repetitive path operation of industrial robots according to the present invention refers to... Figures 1 to 2 The speed planning optimization method for repetitive path operation of industrial robots includes the following steps:

[0077] S100. Constrained iterative learning velocity planning based on path arc length coordinates is used to establish an accurate rigid-flexible coupling dynamic model of the robot, and the precise rigid-flexible coupling dynamic model is identified to obtain the motion constraints of the robot.

[0078] S200, through the motion performance evaluation function J k The motion performance of the robot is calculated based on velocity planning, and the motion performance evaluation function J is updated based on a dynamic linear scalarization mechanism. k Parameters;

[0079] S300, Learning the motion performance evaluation function J through iterative learning. k The update law is based on the constrained iterative learning velocity planning method, and an iterative learning framework for velocity planning is constructed to realize an intelligent iterative learning mechanism based on arc length coordinate parameterization, online satisfaction of dynamic constraints, and provable monotonic convergence performance.

[0080] S400 outputs the optimal speed curve of the robot.

[0081] In a specific embodiment, the specific iterative learning speed planning optimization steps are as follows: A dynamic model of the robot is established and identified to obtain the robot's motion constraints. The motion performance of the speed planning is evaluated using a motion performance evaluation function based on measured performance index data. A constrained iterative learning speed planning method with rigorous theoretical guarantees is proposed, and an iterative learning framework for speed planning is constructed, realizing an intelligent iterative learning mechanism based on arc-length coordinate parameterization, online satisfaction of dynamic constraints, and provable monotonic convergence performance.

[0082] The beneficial effects of this invention are as follows:

[0083] This invention proposes a velocity planning optimization algorithm based on iterative learning. For industrial robots running repetitive trajectories, the algorithm automatically records trajectory deviation, vibration data, and energy consumption characteristics each time a task is performed. It autonomously analyzes the root causes of problems and dynamically adjusts key parameters such as acceleration curves and joint torque distribution, thus eliminating the reliance on manual parameter tuning in repetitive tasks.

[0084] This invention overcomes the static nature and manual dependence of traditional methods by deeply embedding Iterative Learning Control (ILC) into the speed planning stage, achieving autonomous evolution and dynamic optimization of the speed curve in repetitive operation scenarios for industrial robots. Its core advantages and technical effects are reflected in the following aspects:

[0085] (1) Dynamic autonomous optimization capability: This invention decouples the velocity curve in the time domain into iterable parameters in the spatial domain through path arc length parameterized modeling. By utilizing the local support characteristics of the fifth-order B-spline curve, it achieves fine-grained control of the velocity profile. Specifically, the velocity curve is transformed into a set of control point parameters directly driven by the path's geometric features. Through an iterative learning mechanism, the parameter weights are continuously corrected, enabling the velocity distribution to autonomously adapt to dynamic factors such as path curvature and inertial load.

[0086] (2) Real-time guarantee mechanism with full constraints: This invention proposes a projection optimization framework that maps multiple types of constraints, such as velocity, acceleration, and torque, to the feasible domain boundary of control point parameters. This framework decomposes the complex multi-constraint coupled problem into multiple sub-problems that can be solved independently, and uses projection operators to correct the iteration parameters in real time, ensuring that the velocity curve after each update strictly meets the physical limits and safety thresholds.

[0087] Specifically, the present invention addresses the following deficiencies of the prior art:

[0088] (1) Arc length coordinate parameterization: solves the spatial inconsistency problem in repeated paths in traditional time domain planning;

[0089] (2) Constrained projection operator: For the first time, non-extended mapping theory is applied to velocity planning iterative learning, strictly ensuring that physical constraints are satisfied;

[0090] (3) Multi-type update law compatibility: Gradient type / difference type / least square type can be dynamically switched to adapt to different working conditions;

[0091] (4) Convergence proof: The first rigorous proof of convergence of iterative learning with dynamic constraints is given by using the Lyapunov function.

[0092] The research contents of the invention have different focuses and are interconnected: Step S100 solves the fundamental problem of real-time and accurate dynamic constraints required for the velocity planning algorithm; Step S200 establishes a dynamic performance evaluation system and intelligent multi-objective trade-off method for velocity planning, providing target guidance for the iterative optimization in Step S300; Step S300 studies the core constraint iterative learning theory and algorithm, and uses the dynamic constraints provided in Step S100 and the evaluation index in Step S200 to achieve intelligent optimization of the velocity curve.

[0093] This invention discloses a speed planning optimization method for repetitive path operation of industrial robots. First, a dynamic model incorporating flexible joint effects is established, and online parameter identification is achieved through an LSTM neural network and extended Kalman filter. Second, vibration energy features are extracted based on end-effector IMU sensor data, and an evaluation system is constructed by combining trajectory contour error, operation cycle, and energy consumption. Then, using the path arc length as the reference coordinate, a fifth-order B-spline parameterized velocity curve is adopted, and an iterative learning algorithm with gradient projection constraints is designed. Finally, a dynamic weighting mechanism is used to achieve multi-objective collaborative optimization. This method enables industrial robots to autonomously improve trajectory accuracy, suppress mechanical vibration, and reduce energy consumption during repetitive operations, solving the pain points of traditional static planning, which relies on manual parameter tuning and has poor adaptability.

[0094] Furthermore, refer to Figure 3 Step S100 includes:

[0095] S110. By introducing the elastic deformation compensation term of the flexible joint and the temperature drift friction model, the accurate rigid-flexible coupling dynamic model of the industrial robot is obtained.

[0096] S120. An online identification framework that integrates LSTM neural network and extended Kalman filter (EKF) is adopted. The robot joint position, velocity and motor current are taken as inputs. The nonlinear mapping relationship of dynamic parameters is learned through LSTM neural network and then real-time parameter calibration and confidence evaluation are performed through extended Kalman filter (EKF).

[0097] S130. The joint velocity, acceleration and torque constraints are uniformly transformed into a quadratic inequality form, and the real-time feasible region determination algorithm based on gradient projection is derived. The real-time feasible region determination algorithm dynamically calculates the motion constraint boundary under the current state in every millisecond control cycle to ensure that the subsequent speed planning strictly meets the physical limit and avoids the risk of overspeed or overload.

[0098] Specifically, the precise rigid-flexible coupling dynamics model not only includes traditional rigid dynamics terms (inertia matrix, Coriolis force, gravity term), but also introduces elastic deformation compensation terms for flexible joints and temperature drift friction model to accurately describe the dynamic characteristics under high-speed motion.

[0099] An online identification framework integrating LSTM neural network and extended Kalman filter (EKF) is adopted: robot joint position, velocity, and motor current are used as inputs, the nonlinear mapping relationship of dynamic parameters is learned through LSTM network, and then EKF is used for real-time parameter calibration and confidence evaluation.

[0100] Finally, the joint velocity, acceleration, and torque constraints are uniformly transformed into a quadratic inequality form, and a real-time feasible region determination algorithm based on gradient projection is developed. This algorithm dynamically calculates the motion constraint boundary of the current state within each millisecond control cycle, ensuring that subsequent velocity planning strictly meets physical limits and avoiding the risk of overspeed or overload.

[0101] Furthermore, refer to Figure 3 In step S110, the precise rigid-flexible coupling dynamic model is:

[0102]

[0103] Where q is an n-dimensional vector representing the position state of the robot's joints, and n is the robot's degrees of freedom. Represents the velocity vector of a robot joint. Let M be the acceleration vector of the robot joint, C be the Coriolis force, G be the gravity force, and F be the acceleration vector of the robot joint. f For the friction model, KΔθ is the flexible joint compensation term, and τ is the control torque of the robot joint.

[0104] Furthermore, refer to Figure 4 Step S200 includes:

[0105] S210: Collect high-frequency vibration data of the robot, contour error data between the actual trajectory and the commanded trajectory, task cycle duration data, and motor energy consumption data.

[0106] S220, by integrating high-frequency vibration data, contour error data between actual and commanded trajectories, task cycle duration data, and motor energy consumption data, a motion performance evaluation function J is constructed. k ;

[0107] S230, iterative execution steps S210 to S220: based on the relative degradation degree of high-frequency vibration data, contour error data between actual trajectory and command trajectory, task cycle duration data and motor energy consumption data in each iteration, automatically increase the weight coefficient of significant degradation items. When a certain indicator is significantly improved and does not cause degradation of other indicators, its weight can be actively reduced, and optimization resources can be shifted to other potential targets.

[0108] Furthermore, refer to Figure 4 In step S210, the high-frequency vibration data is collected by an IMU sensor installed at the end of the robot and the vibration energy data for quantifying the main resonant frequency band of motion stability is extracted by short-time Fourier transform. The contour error data between the actual trajectory and the command trajectory is collected by an encoder installed on the robot. The task cycle duration data is obtained by collecting electricity meter data and performing cycle scoring calculation.

[0109] In step S220, the motion performance evaluation function J k for:

[0110] J k = α * Contour error data between actual trajectory and commanded trajectory + β * High-frequency vibration data + γ * Motor energy consumption data + δ * Task cycle duration data,

[0111] In this context, α, β, γ, and δ are all variable positive numbers.

[0112] Specifically, the process involves collecting high-frequency vibration data using an IMU sensor installed at the robot's end effector, extracting the vibration energy of the main resonant frequency band using short-time Fourier transform, and quantifying motion stability. Simultaneously, it collects data on the contour error between the actual trajectory and the commanded trajectory, task cycle time, and motor energy consumption. A motion performance evaluation function J is constructed by integrating these four types of indicators. k .

[0113] To eliminate the subjectivity of manually set weights, a dynamic linear scalarization mechanism is introduced: based on the relative degradation degree of each index in each iteration, the weight coefficient of significantly degraded terms is automatically increased (e.g., if the vibration energy increases by 10% in the current iteration, the β weight is increased accordingly). This mechanism enables the robot to autonomously balance the conflicting demands of accuracy, stability, energy efficiency, and productivity, achieving multi-objective collaborative optimization.

[0114] Furthermore, refer to Figure 5 The method S300 includes:

[0115] S310. Planning iterative learning update law, wherein the iterative learning update law includes at least the following along the motion performance evaluation function J. k Update control point P with negative gradient direction i The gradient-type iterative learning update law, the difference-type iterative learning update law that estimates the Jacobian matrix by performing difference budgeting on historical data, and the least squares-type iterative learning update law that fits the optimal parameters based on multiple rounds of data.

[0116] S320. To satisfy the dynamic constraints, the gradient projection operator is called after each iteration update to project the control point P. i Map to the feasible region;

[0117] S330. Construct the Lyapunov energy function and prove the monotonic convergence of iterative learning under joint torque constraints, ensuring that the velocity curve is continuously optimized during repeated execution.

[0118] S340, If the motion performance evaluation function J is satisfied... k If the rate of change is less than a preset first threshold or the number of iterations is greater than a preset second threshold, the iteration is terminated.

[0119] Specifically, in contrast to step S300 of this invention, traditional time-domain planning is prone to spatial inconsistencies due to time offsets in repeated paths. This invention binds the arc length coordinate s to the velocity v and the path geometry, ensuring that the velocity adjustment in each iteration depends only on the path position (such as automatic speed reduction at turns).

[0120] Furthermore, refer to Figure 5 In method S310, the path arc length s is used as a fixed reference coordinate, and a fifth-order B-spline curve is used to parametrically model the velocity curve v. The number of control points is adaptively set according to the path complexity.

[0121]

[0122] Where v(s) is the velocity-time rate, P i These are control points. During the first iteration, control points P are evenly distributed according to the path length s. i Location, control point P i The quantity is adaptively set according to the path complexity, B i,5 For a fifth-order B-spline basis function, the subscript i is the control point index, which ranges from 0 to n, where n depends on the path complexity. It identifies the position of the control point corresponding to this basis function. Each P... i The initial value is set to the upper limit of the robot's safe speed;

[0123] The differential iterative learning update law is defined as follows:

[0124]

[0125] Where μ is the differential gain, J represents the control point parameters of the B-spline velocity curve at the k-th iteration. k It is the performance evaluation function value of the k-th iteration.

[0126] Furthermore, in method S320, the next control point satisfy:

[0127]

[0128] Among them, among them, These are the control point parameters of the B-spline velocity curve in the (k+1)th iteration. J is the control point parameter of the B-spline velocity curve at the k-th iteration. k It is a motion performance evaluation function, where η is a positive real number, and η is used to control the control point P. i The update step size, Πc is the constraint projection operator based on gradient projection, and ΔP is the initial update vector calculated only based on the performance gradient in the current iteration;

[0129] The constraint projection operator ∏c is used to ensure that the velocity-time rate v(s) satisfies the following dynamic constraints:

[0130]

[0131] in,

[0132]

[0133] Where s is the arc length, is the derivative of arc length with respect to time, q is an n-dimensional vector representing the position state of the robot joint, and a(s) is the tangential acceleration along the path. and These are the minimum and maximum permissible values ​​for the joint velocity, M(q), respectively.

[0134] The inertia matrix, G(q) is the Coriolis force term, G(q) is the gravity term, and τ is the force term. min and τ max These are the minimum and maximum allowable values ​​for joint torque;

[0135] The constrained projection operator Π C This is achieved using non-extended mapping theory, mapping the velocity control point P(i) to the dynamic feasible region:

[0136]

[0137] Where C is the convex set defined by the velocity / acceleration / torque constraints, and x and y are the original input vector and the projected input vector, respectively, i.e., the control point P after gradient update. i And a feasible solution that satisfies the dynamic constraints, ‖x―y‖ is the shortest Euclidean distance between x and y.

[0138] Furthermore, refer to Figure 5 In method S330, the Lyapunov energy function is used as follows:

[0139] V k =|e k | 2 ,

[0140] Among them, V k To learn the residual energy, e k To track errors,

[0141] e k =v d (s)―v k (s),

[0142] Tracking error e k satisfy:

[0143]

[0144] Among them, v d (S) is the desired velocity profile, v d (s) represents the ideal velocity distribution along the path arc length, v k (s) is the actual velocity profile of the k-th iteration. Performance evaluation function J k The gradient of λ is the convergence coefficient.

[0145] Specifically, by constructing a Lyapunov energy function, the monotonic convergence of iterative learning under joint torque constraints is rigorously proven, ensuring that the velocity curve continuously optimizes during repeated execution. After 5-10 iterations, the velocity curve can autonomously evolve to a stable optimal state.

[0146] Furthermore, this invention also discloses a speed planning and optimization system for repetitive path operation of industrial robots. This system is used to implement the speed planning and optimization method for repetitive path operation of industrial robots. The speed planning and optimization system for repetitive path operation of industrial robots includes:

[0147] The dynamics module is used to build and update dynamic models;

[0148] The motion performance evaluation module is used to calculate and update the motion performance evaluation function J. k The motion performance evaluation module is connected to the dynamics module;

[0149] An iterative calculation module is used to optimize the dynamic model established by the dynamics module. The dynamics module and the motion performance evaluation module are respectively connected to the iterative calculation module.

[0150] It should be understood that the method steps in the embodiments of the present invention can be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable storage medium. The method can use standard programming techniques. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if necessary, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can run on a programmed application-specific integrated circuit (ASIC).

[0151] Furthermore, the procedures described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by the context. The procedures described herein (or variations and / or combinations thereof) may be executed under the control of one or more computer systems configured with executable instructions, and may be implemented by hardware or a combination thereof as code (e.g., executable instructions, one or more computer programs, or one or more applications) that commonly executes on one or more processors. The computer program comprises a plurality of instructions executable by one or more processors.

[0152] Furthermore, the method can be implemented in any suitable type of computing platform, including but not limited to personal computers, minicomputers, mainframes, workstations, networked or distributed computing environments, standalone or integrated computer platforms, or in communication with charged particle tools or other imaging devices, etc. Aspects of the invention can be implemented as machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the processes described herein. Furthermore, the machine-readable code, or portions thereof, can be transmitted via wired or wireless networks. The invention described herein includes these and other different types of non-transitory computer-readable storage media when such media comprises instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. When programmed according to the methods and techniques described in the invention, the invention may also include the computer itself.

[0153] A computer program can be applied to input data to perform the functions described herein, thereby transforming the input data to generate output data stored in non-volatile memory. The output information can also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects generated on the display.

[0154] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention, as long as they achieve the technical effects of the present invention by the same means, should be included within the scope of protection of the present invention. Within the scope of protection of the present invention, the technical solutions and / or implementation methods can have various modifications and variations.

Claims

1. A speed planning and optimization method for repetitive path operation of industrial robots, characterized in that, The method includes the following steps: S100. Constrained iterative learning velocity planning based on path arc length coordinates is used to establish an accurate rigid-flexible coupling dynamic model of the robot, and the precise rigid-flexible coupling dynamic model is identified to obtain the motion constraints of the robot. S200, through the motion performance evaluation function J k The motion performance of the robot is calculated based on velocity planning, and the motion performance evaluation function J is updated based on a dynamic linear scalarization mechanism. k Parameters; S300, Learning the motion performance evaluation function J through iterative learning. k The update law is based on the constrained iterative learning velocity planning method, and an iterative learning framework for velocity planning is constructed to realize an intelligent iterative learning mechanism based on arc length coordinate parameterization, online satisfaction of dynamic constraints, and provable monotonic convergence performance. S400 outputs the optimal speed curve of the robot.

2. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 1, wherein step S100 includes: S110. By introducing the elastic deformation compensation term of the flexible joint and the temperature drift friction model, the accurate rigid-flexible coupling dynamic model of the industrial robot is obtained. S120. An online identification framework that integrates LSTM neural network and extended Kalman filter (EKF) is adopted. The robot joint position, velocity and motor current are taken as inputs. The nonlinear mapping relationship of dynamic parameters is learned through LSTM neural network and then real-time parameter calibration and confidence evaluation are performed through extended Kalman filter (EKF). S130. The joint velocity, acceleration and torque constraints are uniformly transformed into a quadratic inequality form, and the real-time feasible region determination algorithm based on gradient projection is derived. The real-time feasible region determination algorithm dynamically calculates the motion constraint boundary under the current state in every millisecond control cycle to ensure that the subsequent speed planning strictly meets the physical limit and avoids the risk of overspeed or overload.

3. In the speed planning and optimization method for repetitive path operation of industrial robots according to claim 2, in step S110, the precise rigid-flexible coupling dynamic model is: in, q is an n-dimensional vector representing the position state of the robot's joints, where n is the robot's degrees of freedom. Represents the velocity vector of a robot joint. Let M be the acceleration vector of the robot joint, C be the Coriolis force, G be the gravity force, and F be the acceleration vector of the robot joint. f For the friction model, KΔθ is the flexible joint compensation term, and τ is the control torque of the robot joint.

4. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 1, step S200 includes: S210: Collect high-frequency vibration data of the robot, contour error data between the actual trajectory and the commanded trajectory, task cycle duration data, and motor energy consumption data. S220, by integrating high-frequency vibration data, contour error data between actual and commanded trajectories, task cycle duration data, and motor energy consumption data, a motion performance evaluation function J is constructed. k ; S230, iterative execution steps S210 to S220: based on the relative degradation degree of high-frequency vibration data, contour error data between actual trajectory and command trajectory, task cycle duration data and motor energy consumption data in each iteration, automatically increase the weight coefficient of significant degradation items. When a certain indicator is significantly improved and does not cause degradation of other indicators, its weight can be actively reduced, and optimization resources can be shifted to other potential targets.

5. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 4, In step S210, the high-frequency vibration data is collected by an IMU sensor installed at the end of the robot and the vibration energy data for quantifying the main resonant frequency band of motion stability is extracted by short-time Fourier transform. The contour error data between the actual trajectory and the command trajectory is collected by an encoder installed on the robot. The task cycle duration data is obtained by collecting electricity meter data and performing cycle scoring calculation. In step S220, the motion performance evaluation function J k for: J k = α * Contour error data between actual trajectory and commanded trajectory + β * High-frequency vibration data + γ * Motor energy consumption data + δ * Task cycle duration data, in, α, β, γ and δ are all variable positive numbers.

6. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 1, wherein method S300 includes: S310. Planning iterative learning update law, wherein the iterative learning update law includes at least the following along the motion performance evaluation function J. k Update control point P with negative gradient direction i The gradient-type iterative learning update law, the difference-type iterative learning update law that estimates the Jacobian matrix by performing difference budgeting on historical data, and the least squares-type iterative learning update law that fits the optimal parameters based on multiple rounds of data. S320. To satisfy the dynamic constraints, the gradient projection operator is called after each iteration update to project the control point P. i Map to the feasible region; S330. Construct the Lyapunov energy function and prove the monotonic convergence of iterative learning under joint torque constraints, ensuring that the velocity curve is continuously optimized during repeated execution. S340, If the motion performance evaluation function J is satisfied... k If the rate of change is less than a preset first threshold or the number of iterations is greater than a preset second threshold, the iteration is terminated.

7. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 6, wherein in method S310, the path arc length s is used as a fixed reference coordinate, and a fifth-order B-spline curve is used to parametrically model the speed curve v, and the number of control points is adaptively set according to the path complexity: in, v(s) is the velocity-time rate, P i These are control points. During the first iteration, control points P are evenly distributed according to the path length s. i Location, control point P i The quantity is adaptively set according to the path complexity, B i,5 For a fifth-order B-spline basis function, the subscript i is the control point index, which ranges from 0 to n, where n depends on the path complexity. It identifies the position of the control point corresponding to this basis function. Each P... i The initial value is set to the upper limit of the robot's safe speed; The differential iterative learning update law is defined as follows: Where μ is the differential gain, J represents the control point parameters of the B-spline velocity curve at the k-th iteration. k It is the performance evaluation function value of the k-th iteration.

8. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 6, in method S320, the next control point satisfy: in, These are the control point parameters of the B-spline velocity curve in the (k+1)th iteration. J is the control point parameter of the B-spline velocity curve at the k-th iteration. k It is a motion performance evaluation function, where η is a positive real number, and η is used to control the control point P. i The update step size, Πc is the constraint projection operator based on gradient projection, and ΔP is the initial update vector calculated only based on the performance gradient in the current iteration; The constraint projection operator Πc is used to ensure that the velocity-time rate v(s) satisfies the following dynamic constraints: in, Where s is the arc length, is the derivative of arc length with respect to time, q is an n-dimensional vector representing the position state of the robot joint, and a(s) is the tangential acceleration along the path. and These are the minimum and maximum allowable values ​​for joint velocity, respectively, and M(q) is the inertia matrix. G(q) is the Coriolis force term, G(q) is the gravity term, and τ is the force term. min and τ max These are the minimum and maximum allowable values ​​for joint torque; The constrained projection operator Π C This is achieved using non-extended mapping theory, mapping the velocity control point P(i) to the dynamic feasible region: Where C is the convex set defined by the velocity / acceleration / torque constraints, and x and y are the original input vector and the projected input vector, respectively, i.e., the control point P after gradient update. i And a feasible solution that satisfies the dynamic constraints, ‖x―y‖ is the shortest Euclidean distance between x and y.

9. The speed planning and optimization method for repetitive path operation of industrial robots according to claim 6, wherein in method S330, the Lyapunov energy function is: V k =|e k | 2 , in, V k To learn the residual energy, e k To track errors, yes k =v d (s)―v k (s), Tracking error e k satisfy: Among them, v d (s) is the desired velocity profile, v d (s) represents the ideal velocity distribution along the path arc length, v k (s) is the actual velocity profile of the k-th iteration. Performance evaluation function J k The gradient of λ is the convergence coefficient.

10. A speed planning and optimization system for repetitive path operation of industrial robots, wherein the speed planning and optimization system for repetitive path operation of industrial robots is used to implement the speed planning and optimization method for repetitive path operation of industrial robots as described in any one of claims 1 to 9, characterized in that, The speed planning and optimization system for repetitive path operation of industrial robots includes: The dynamics module is used to build and update dynamic models; The motion performance evaluation module is used to calculate and update the motion performance evaluation function J. k The motion performance evaluation module is connected to the dynamics module; An iterative calculation module is used to optimize the dynamic model established by the dynamics module. The dynamics module and the motion performance evaluation module are respectively connected to the iterative calculation module.

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