Industrial robot trajectory robust optimization method under multi-source uncertainty and precision constraint

Abstract

The invention relates to the field of industrial robot trajectory design, in particular to an industrial robot trajectory robust optimization method under multi-source uncertainty and precision constraints, which considers multi-source uncertainty parameters influencing motion performance indexes such as industrial robot trajectory precision, energy consumption and motion stability in an open environment. The method comprises the following steps: parameterizing a motion curve of each joint of a robot through a B-spline interpolation method, taking motion time, energy consumption and motion stability as optimization targets, and taking joint angular velocity, joint angular acceleration, joint torque and track precision as constraints, and constructing an industrial robot track multi-target robustness optimization model; and solving the model by adopting a volumetric formula and a sequential quadratic programming algorithm to obtain an optimal trajectory parameter, and outputting an optimal trajectory. According to the industrial robot trajectory multi-target robustness optimization method provided by the invention, the influence of the physical parameters of the robot body and the load uncertainty on the motion performance of the robot is fully considered, and the motion performance and trajectory precision of the industrial robot are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of industrial robot trajectory design, and specifically to a robust optimization method for industrial robot trajectories under multi-source uncertainties and accuracy constraints. Background Technology

[0002] Industrial robots, as core intelligent equipment in the factory of the future, are indispensable units for achieving automation, flexibility, and intelligence in the production process. The efficient and high-quality completion of complex tasks in the factory of the future heavily relies on the accuracy and stability of the motion trajectories of various industrial robots on the production line. However, in the open environment of the factory of the future, the motion performance of robot systems is affected by multiple sources of uncertainty, such as errors in body parameters, fluctuations in drive control parameters, and load changes. These uncertainties are coupled and amplified through multi-level propagation, leading to problems such as nonlinear trajectory abrupt changes, motion instability, and inaccurate end-effector positioning, seriously affecting the operational accuracy of industrial robots and the quality of processed products. Therefore, it is urgent to study robust optimization methods for industrial robot trajectories considering accuracy constraints in the open environment of the factory of the future. Summary of the Invention

[0003] To address the aforementioned problems in the existing technology, this invention aims to provide a robust optimization method for industrial robot trajectories under multi-source uncertainties and accuracy constraints. The specific technical solution is as follows:

[0004] A robust optimization method for industrial robot trajectory under multi-source uncertainties and accuracy constraints includes the following steps:

[0005] Step 1: Obtain the uncertainty parameters of the industrial robot system, including: kinematic parameters, dynamic parameters, and load parameters; obtain the statistical information of the uncertainty parameters, including the parameter values ​​and distribution information of each uncertainty parameter, wherein the statistical information of the uncertainty parameters constitutes the parameter probability space;

[0006] Step 2: Based on several key path points of the robot's task, parameterize the robot's joint motion information using the B-spline interpolation method;

[0007] Step 3: Establish an objective function for optimizing robot trajectory robustness based on robot motion time, mechanical energy consumption, and motion stability indices;

[0008] Step 4: Establish a constraint function for robust optimization of robot trajectory, using the angular velocity, angular acceleration, joint torque, and trajectory accuracy of each joint as constraints;

[0009] Step 5: Based on the objective function in Step 3 and the constraint function in Step 4, establish a robust optimization model for the robot trajectory;

[0010] Step 6: Solve the robot trajectory robustness optimization model using the volume formula and sequential quadratic programming algorithm to obtain the optimal trajectory parameters.

[0011] Furthermore, in step 1, when the uncertainty parameter follows a normal distribution, it is the mean and standard deviation; when it follows a uniform distribution, it is the upper bound and lower bound.

[0012] Furthermore, step 2 specifically includes:

[0013] Step 2.1: Establish the joint angular displacement function:

[0014]

[0015] Among them, B s,p,ξ(υ) (t) represents the basis function, and p represents the order of the B-spline. It is represented as the node vector at discrete moments of the robot trajectory. n represents the difference between discrete time points, used as a design variable. t =N P -1 indicates the number of time intervals, N P P represents the number of critical path points. s This represents a multidimensional control point, where k represents the number of control points;

[0016] Step 2.2: Obtain the first, second, and third derivatives of formula (1) through the recursive formula, namely the joint angular velocity function, angular acceleration function, and impact function during the motion process, specifically:

[0017]

[0018] Where d represents the order of the derivative. The control points of the derivative can be obtained from formula (3).

[0019]

[0020] Furthermore, step 3 specifically includes:

[0021] Step 3.1: Use the robot's task execution time as the first objective function:

[0022]

[0023] Step 3.2: Use the upper bound of the robot's mechanical energy consumption confidence as the second objective function:

[0024]

[0025] Where μ represents the mean calculation, σ represents the standard deviation calculation, m represents the robot's degrees of freedom, and τ m(X,υ,t) represents the torque of joint m, and X represents the dynamic and load uncertainty parameter vector;

[0026] Step 3.3: Represent the robot's motion stability through joint impact, which is the third objective function:

[0027]

[0028] Furthermore, step 4 specifically includes

[0029] Step 4.1: Establish the robot's physical motion constraint function based on the angular velocity, angular acceleration, and torque of each joint. The joint angular velocity constraint function is as follows:

[0030]

[0031] in, Represents the joint velocity vector.

[0032] This represents the maximum permissible velocity vector of the joint;

[0033] The joint angular acceleration constraint function is:

[0034]

[0035] in, Represents the joint acceleration vector.

[0036] This represents the maximum allowable acceleration vector of the joint;

[0037] The joint torque constraint function is:

[0038] g3(X,υ,t)=|μ(τ(X,υ,t))|+3σ(τ(X,υ,t))-τ max ≤0 (9)

[0039] Among them, μ(τ(X,υ,t))=[μ1(τ1(X,υ,t)),...,μ m (τ m [(X,υ,t))] represents the mean vector of joint torques at a certain moment, σ(τ(X,υ,t))=[σ1(τ1(X,υ,t)),...,σ m (τ m [X,υ,t)] represents the standard deviation vector of the joint torque at a certain moment, τ max =[τ max-1 ,τ max-2 ,...,τ max-m ] represents the maximum allowable torque vector of the joint;

[0040] Step 4.2: Considering the uncertainty of kinematic parameters, establish the trajectory accuracy constraint function:

[0041]

[0042] Where e represents the kinematic uncertainty parameter, r represents the accuracy tolerance, and G(e,υ,t) represents the robot end-effector positioning error:

[0043]

[0044] Where, x actual (e,υ,t), y actual (e,υ,t) and z actual (e, υ, t) represent the actual positions of the robot in the x, y, and z directions at any time t, respectively; x ideal (t), y ideal (t) and z ideal (t) represent the ideal positions of the robot in the x, y and z directions at any time t;

[0045] Furthermore, in step 5, the robot trajectory robustness optimization model is specifically expressed as follows:

[0046]

[0047] in, υ and ω1, ω2, and ω3 represent the lower and upper bounds of the design variables, respectively. ω1, ω2, and ω3 represent the importance coefficients of the three different objectives, respectively. ω1 + ω2 + ω3 = 1. θ1, θ2, and θ3 represent the scaling factors of each objective, ensuring the scale consistency of the three objectives.

[0048] Furthermore, in step 6, the robust optimization model for the robot trajectory is solved, and each iteration specifically includes:

[0049] Step 6.1: Under fixed design variables, calculate the mean and standard deviation of the joint torque using the volumetric formula, specifically as follows:

[0050]

[0051] Where, η l Let R represent the Gaussian-Hermitian multidimensional integral node. -1 (·) denotes the Rosenblatt inverse transform, w l N represents the weighting coefficient. l Indicates the number of integration nodes;

[0052] Step 6.2: Under fixed design variables, calculate the mean value of the positioning error using the volume formula:

[0053]

[0054] Step 6.3: Based on the optimization objectives of formulas (4)-(6) and the mean joint torque of formula (13), solve the objective function f(X,υ,t) in the optimization model formula (12) under fixed design variables;

[0055] Step 6.4: Based on the constraints of formulas (7)-(10) and the mean value of joint torque, standard deviation and mean value of positioning error of formulas (13)-(15), solve the four constraint functions in formula (12) of the optimization model under fixed design variables;

[0056] Step 6.5: Check the difference between the objective function value in the current iteration and the objective function value in the previous iteration. For the first iteration, this difference is defined as the objective function value of the first generation. If the difference is less than the convergence threshold, output the updated design variables; otherwise, repeat steps 6.1 to 6.4.

[0057] The beneficial effects of this invention are as follows:

[0058] I. A multi-objective robust optimization model for industrial robot trajectory considering multi-source uncertainties and accuracy constraints was established. With running time, energy consumption, and motion stability as objectives, and robot physical mechanisms and trajectory accuracy as constraints, it fully considers the interference of multi-source uncertainties in future factory environments and the various performance index requirements for robots to perform complex tasks efficiently and with high quality.

[0059] Second, high-order B-spline curves are used to parametrically fit joint motions under the influence of uncertainties, effectively suppressing nonlinear abrupt changes in the robot's motion trajectory and improving motion stability. The volumetric formula method is used to efficiently perform kinematic and dynamic uncertainty propagation analysis of the robot, and combined with a sequential quadratic programming optimization algorithm, efficient, low-cost, highly stable, and high-precision design of the robot trajectory is achieved.

[0060] Third, an uncertainty design paradigm for industrial robot trajectory optimization is proposed, which can effectively characterize the transmission law of multi-source uncertainty, realize the comprehensive improvement of robot motion performance in open environment, and ensure the accuracy and quality of robot-assisted processing products. Attached Figure Description

[0061] Figure 1 A flowchart illustrating a robust optimization method for industrial robot trajectory under multi-source uncertainties and accuracy constraints provided in an embodiment of the present invention;

[0062] Figure 2 The optimized spatial trajectory diagram of the industrial robot provided in the embodiments of the present invention;

[0063] Figure 3An industrial robot trajectory accuracy analysis diagram provided for an embodiment of the present invention;

[0064] Figure 4 The graph shows the results of the uncertainty analysis of the trajectory accuracy of an industrial robot provided in an embodiment of the present invention. Detailed Implementation

[0065] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. It should also be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0066] It should be noted that, unless otherwise specified, the embodiments and technical features described in this invention can be combined with each other. The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0067] This invention provides a robust optimization method for industrial robot trajectories under multi-source uncertainties and accuracy constraints, such as... Figure 1 As shown, it includes the following steps:

[0068] Step 1: Obtain the uncertainty parameters of the industrial robot system, including: kinematic parameters, dynamic parameters, and load parameters; obtain the statistical information of the uncertainty parameters, including the parameter values ​​and distribution information of each uncertainty parameter, wherein the statistical information of the uncertainty parameters constitutes the parameter probability space;

[0069] In step 1, when the uncertainty parameter follows a normal distribution, it is the mean and standard deviation; when it follows a uniform distribution, it is the upper bound and lower bound.

[0070] Optionally, in this embodiment, the uncertainty parameters follow normal and uniform distributions. If they follow a normal distribution, parameter 1 is the mean and parameter 2 is the standard deviation. If they follow a uniform distribution, parameter 1 is the upper bound and parameter 2 is the lower bound, as shown in Table 1, but not limited thereto.

[0071] Table 1: Uncertainty Parameter Information of Industrial Robot Systems

[0072]

[0073]

[0074] Step 2: Based on the N of the task P =33 critical path points, and the robot joint motion information is parameterized using the B-spline interpolation method, specifically including:

[0075] Step 2.1: Establish the joint angular displacement function:

[0076]

[0077] Among them, B s,p,ξ(υ) (t) represents the basis function, and p represents the order of the B-spline. It is represented as the node vector at discrete moments of the robot trajectory. n represents the difference between discrete time points, used as a design variable. t =N P -1 = 32 represents the number of time intervals, P s This represents a multidimensional control point, where k represents the number of control points;

[0078] Step 2.2: The first, second, and third derivatives of (1) can be obtained according to the recursive formula, namely the joint angular velocity function, angular acceleration function, and impact function during the motion process. The specific calculation is as follows:

[0079]

[0080] Where d = 1, 2, 3 represents the order of the derivative. The control points of the derivative can be obtained from (3).

[0081]

[0082] Step 3: Establish the objective function for robust robot trajectory optimization, which includes:

[0083] Step 3.1: Use the robot's task execution time as the first objective function:

[0084]

[0085] Step 3.2: Use the upper bound of the robot's mechanical energy consumption confidence as the second objective function:

[0086]

[0087] Where m = 6 represents the robot's degrees of freedom, τ m (X,υ,t) represents the torque of joint m, and X represents the dynamic and load uncertainty parameter vector;

[0088] Step 3.3: Represent the robot's motion stability through joint impact, which is the third objective function:

[0089]

[0090] Step 4: Construct robust optimization constraint functions for robot trajectory, specifically including:

[0091] Step 4.1: Establish the robot's physical motion constraint function based on the angular velocity, angular acceleration, and joint torque of each joint. The joint angular velocity constraint function is as follows:

[0092]

[0093] in, Represents the joint velocity vector.

[0094] This represents the maximum permissible velocity vector of the joint; joint angle plus...

[0095] The velocity constraint function is:

[0096]

[0097] in, Represents the joint acceleration vector.

[0098] Represents the maximum allowable acceleration vector of the joint; joint torque constraint function

[0099] The number is:

[0100] g3(X,υ,t)=|μ(τ(X,υ,t))|+3σ(τ(X,υ,t))-τ max ≤0 (9)

[0101] Among them, μ(τ(X,υ,t))=[μ1(τ1(X,υ,t)),...,μ m (τ m [(X,υ,t))] represents the mean vector of joint torques at a certain moment, σ(τ(X,υ,t))=[σ1(τ1(X,υ,t)),...,σ m (τ m [X,υ,t)] represents the standard deviation vector of the joint torque at a certain moment, τ max =[300,300,300,200,50,50]Nm represents the maximum allowable torque vector of the joint;

[0102] Step 4.2: Considering the uncertainty of kinematic parameters, establish the trajectory accuracy constraint function:

[0103]

[0104] Where e represents the kinematic uncertainty parameter, r = 0.5 mm represents the accuracy tolerance, and G(e,υ,t) represents the robot end-effector positioning error.

[0105]

[0106] Where, x actual (e,υ,t), y actual (e,υ,t) and z actual(e, υ, t) represent the actual positions of the robot in the x, y, and z directions at any time t, respectively, which can be obtained through the robot's kinematic model. ideal (t), y ideal (t) and z ideal (t) represent the ideal positions of the robot in the x, y and z directions at any time t;

[0107] Step 5: Establish a robust optimization model for the robot trajectory, taking robot motion time, energy consumption, and stability as optimization objectives, and motion physics mechanisms and accuracy as key constraints. Specifically:

[0108]

[0109] in, υ =1 32 and These represent the lower and upper bounds of the design variables, respectively. ω1 = 1 / 3, ω2 = 1 / 3 and ω3 = 1 / 3 represent the importance coefficients of the three different objectives, respectively. ω1 + ω2 + ω3 = 1; θ1 = 10, θ2 = 40 and θ3 = 1 represent the scaling factors of each objective, ensuring the scale consistency of the three objectives.

[0110] Step 6: Solve the robust optimization design model of robot trajectory (12) using the volume formula and sequential quadratic programming algorithm. Each iteration specifically includes:

[0111] Step 6.1: Under fixed design variables, calculate the mean and standard deviation of the joint torque using the volumetric formula, specifically as follows:

[0112]

[0113] Where, η l Let R represent the Gaussian-Hermitian multidimensional integral node. -1 (·) denotes the Rosenblatt inverse transform, w l N represents the weighting coefficient. l =43 indicates the number of integration nodes;

[0114] Step 6.2: Under fixed design variables, calculate the mean value of the positioning error using the volume formula:

[0115]

[0116] Step 6.3: Solve for the objective function f(X,υ,t) in formula (12) under fixed design variables according to formulas (4)-(6) and formula (13);

[0117] Step 6.4: Solve for the four constraint functions in formula (12) under fixed design variables according to formulas (7)-(10) and (13)-(15);

[0118] Step 6.5: Check the difference between the objective function value in the current iteration and the objective function value in the previous iteration. For the first iteration, this difference is defined as the objective function value of the first generation. If this difference is less than the convergence threshold of 1×10⁻⁶, the objective function value is considered to be within the first generation. -6 If the result is positive, output the updated design variables; otherwise, repeat steps 6.1 to 6.4.

[0119] Table 2 compares the objective function value after implementing the trajectory optimization method of the present invention with the initial design scheme. It can be seen that the method of the present invention can significantly reduce the time and energy consumption of robot operation and effectively improve motion stability.

[0120] Table 2: Objective function values ​​after implementing the robot trajectory optimization method of the present invention

[0121]

[0122]

[0123] Figure 2 To optimize the robot's working trajectory, Figure 3 and Figure 4 The accuracy improvement and uncertainty analysis results of the industrial robot trajectory after implementing the method proposed in this invention are presented respectively. It can be seen that the method proposed in this invention effectively improves the trajectory accuracy of the industrial robot during processing operations. The calculation results verify the effectiveness and engineering applicability of the robust optimization method for industrial robot trajectory under multi-source uncertainty and accuracy constraints proposed in this invention.

[0124] It should be stated that the content and specific embodiments of this invention are intended to demonstrate the practical application of the technical solutions provided by this invention, and should not be construed as limiting the scope of protection of this invention. Any modifications and changes made to this invention within the spirit and scope of the claims fall within the protection scope of this invention.

Claims

1. A robust optimization method for industrial robot trajectory under multi-source uncertainty and accuracy constraints, characterized in that, Includes the following steps: Step 1: Obtain the uncertainty parameters of the industrial robot system, including: kinematic parameters, dynamic parameters, and load parameters; obtain the statistical information of the uncertainty parameters, including the parameter values ​​and distribution information of each uncertainty parameter, wherein the statistical information of the uncertainty parameters constitutes the parameter probability space; Step 2: Based on several key path points of the robot's task, parameterize the robot's joint motion information using the B-spline interpolation method; Step 3: Establish an objective function for optimizing robot trajectory robustness based on robot motion time, mechanical energy consumption, and motion stability indices; Step 4: Establish a constraint function for robust optimization of robot trajectory, using the angular velocity, angular acceleration, joint torque, and trajectory accuracy of each joint as constraints; Step 5: Based on the objective function in Step 3 and the constraint function in Step 4, establish a robust optimization model for the robot trajectory; Step 6: Solve the robot trajectory robustness optimization model using the volume formula and sequential quadratic programming algorithm to obtain the optimal trajectory parameters.

2. The robust optimization method for industrial robot trajectory as described in claim 1, characterized in that, In step 1, when the uncertainty parameter follows a normal distribution, it is the mean and standard deviation; when it follows a uniform distribution, it is the upper bound and lower bound.

3. The robust optimization method for industrial robot trajectory as described in claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Establish the joint angular displacement function: Among them, B s,p,ξ(υ) (t) represents the basis function, and p represents the order of the B-spline. It is represented as the node vector at discrete moments of the robot trajectory. n represents the difference between discrete time points, used as a design variable. t =N P -1 indicates the number of time intervals, N P P represents the number of critical path points. s This represents a multidimensional control point, where k represents the number of control points; Step 2.2: Obtain the first, second, and third derivatives of formula (1) through the recursive formula, namely the joint angular velocity function, angular acceleration function, and impact function during the motion process, specifically: Where d represents the order of the derivative. The control points of the derivative can be obtained from formula (3).

4. The robust optimization method for industrial robot trajectory as described in claim 3, characterized in that, Step 3 specifically includes: Step 3.1: Use the robot's task execution time as the first objective function: Step 3.2: Use the upper bound of the robot's mechanical energy consumption confidence as the second objective function: Where μ represents the mean calculation, σ represents the standard deviation calculation, m represents the robot's degrees of freedom, and τ m (X,υ,t) represents the torque of joint m, and X represents the dynamic and load uncertainty parameter vector; Step 3.3: Represent the robot's motion stability through joint impact, which is the third objective function:

5. The robust optimization method for industrial robot trajectory as described in claim 4, characterized in that, Step 4 specifically includes Step 4.1: Establish the robot's physical motion constraint function based on the angular velocity, angular acceleration, and torque of each joint. The joint angular velocity constraint function is as follows: in, Represents the joint velocity vector. This represents the maximum permissible velocity vector of the joint; The joint angular acceleration constraint function is: in, Represents the joint acceleration vector. This represents the maximum allowable acceleration vector of the joint; The joint torque constraint function is: g3(X,υ,t)=|μ(τ(X,υ,t))|+3σ(τ(X,υ,t))-τ max ≤0 (9) Among them, μ(τ(X,υ,t))=[μ1(τ1(X,υ,t)),...,μ m (τ m [(X,υ,t))] represents the mean vector of joint torques at a certain moment, σ(τ(X,υ,t))=[σ1(τ1(X,υ,t)),...,σ m (τ m [X,υ,t)] represents the standard deviation vector of the joint torque at a certain moment, τ max =[τ max-1 ,τ max-2 ,...,τ max-m ] represents the maximum allowable torque vector of the joint; Step 4.2: Considering the uncertainty of kinematic parameters, establish the trajectory accuracy constraint function: Where e represents the kinematic uncertainty parameter, r represents the accuracy tolerance, and G(e,υ,t) represents the robot end-effector positioning error: Where, x actual (e,υ,t), y actual (e,υ,t) and z actual (e, υ, t) represent the actual positions of the robot in the x, y, and z directions at any time t, respectively; x ideal (t), y ideal (t) and z ideal (t) represents the ideal position of the robot in the x, y and z directions at any time t.

6. The robust optimization method for industrial robot trajectory as described in claim 5, characterized in that, In step 5, the robot trajectory robustness optimization model is specifically expressed as follows: findυ st g3(X,υ,t)=|μ(τ(X,υ,t))|+3σ(τ(X,υ,t))-τ max ≤0 in, υ and ω1, ω2, and ω3 represent the lower and upper bounds of the design variables, respectively. ω1, ω2, and ω3 represent the importance coefficients of the three different objectives, respectively. ω1 + ω2 + ω3 = 1. θ1, θ2, and θ3 represent the scaling factors of each objective, ensuring the scale consistency of the three objectives.

7. The robust optimization method for industrial robot trajectory as described in claim 6, characterized in that, In step 6, the robust optimization model for robot trajectory is solved, and each iteration specifically includes: Step 6.1: Under fixed design variables, calculate the mean and standard deviation of the joint torque using the volumetric formula, specifically as follows: Where, η l Let R represent the Gaussian-Hermitian multidimensional integral node. -1 (·) denotes the Rosenblatt inverse transform, w l N represents the weighting coefficient. l Indicates the number of integration nodes; Step 6.2: Under fixed design variables, calculate the mean value of the positioning error using the volume formula: Step 6.3: Based on the optimization objectives of formulas (4)-(6) and the mean joint torque of formula (13), solve the objective function f(X,υ,t) in the optimization model formula (12) under fixed design variables; Step 6.4: Based on the constraints of formulas (7)-(10) and the mean value of joint torque, standard deviation and mean value of positioning error of formulas (13)-(15), solve the four constraint functions in formula (12) of the optimization model under fixed design variables; Step 6.5: Check the difference between the objective function value in the current iteration and the objective function value in the previous iteration. For the first iteration, this difference is defined as the objective function value of the first generation. If the difference is less than the convergence threshold, output the updated design variables; otherwise, repeat steps 6.1 to 6.4.

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