Complex curved surface robot processing redundancy angle and process parameter joint optimization method and equipment

Abstract

The present application belongs to the technical field of robot machining deformation optimization, and discloses a redundant angle and process parameter joint optimization method and equipment for robot machining of complex curved surfaces, (1) joint motion limit constraints, pose singularity constraints and machining deformation error constraints corresponding to a robot machining system constitute multi-domain composite constraints, and based on the multi-domain composite constraints, fusion modeling is carried out in a redundant angle space, so as to map the constraints of different spaces and different dimensions into a unified fusion potential field; (2) a dynamics equation is established with a virtual torque generated by the fusion potential field as a driving input, and based on the obtained dynamics equation and a numerical solving method, the redundant angles of each tool position are sequentially solved, and then a continuous and smooth redundant angle trajectory is obtained; (3) based on the obtained redundant angle trajectory, an optimization algorithm is used to iteratively solve an optimization model to obtain an optimal machining parameter combination. The present application realizes the collaborative optimization of process parameters and redundant angles.

Description

Technical Field

[0001] This invention belongs to the technical field of robot machining deformation, and more specifically, relates to a method and equipment for joint optimization of redundant angles and process parameters in robot machining of complex curved surfaces. Background Technology

[0002] In the fields of aerospace and high-end equipment manufacturing, complex curved surface components, such as aero-engine blades and marine propellers, exhibit three main characteristics: first, drastic changes in surface curvature limit machining accessibility; second, redundant degrees of freedom in multi-axis linkage pose challenges to attitude planning; and third, strong coupling of multi-dimensional process parameters affects machining quality. The robotic machining of these components faces a dual technological bottleneck.

[0003] At the kinematic level, the solution space of redundant joint degrees of freedom in robots exhibits highly nonlinear characteristics. Optimizing redundant robot postures requires simultaneously satisfying multi-domain conditions such as geometric reachability constraints, kinematic singularity constraints, and mechanical machining deformation constraints. Traditional hierarchical progressive optimization methods decouple posture planning from process parameters, leading to a mismatch between redundant postures and process parameters during actual machining. At the process optimization level, cutting parameter optimization involves multiple nonlinearly coupled dimensions such as rotational speed, feed rate, and cut width. Existing research often employs local-perspective optimization strategies, lacking comprehensive consideration of multi-domain constraints in the machining process, making it difficult to construct a global collaborative optimization system for process parameters and redundant joint space. This segmented optimization paradigm restricts the improvement of machining accuracy for complex curved surface parts; therefore, it is necessary to establish a joint optimization theoretical framework that integrates redundant planning and parameter optimization. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and equipment for joint optimization of redundant angles and process parameters in the machining of complex curved surfaces by robots. It aims to solve the problem that the existing technology is difficult to achieve global collaborative optimization of process parameters and redundant angles.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for jointly optimizing redundant angles and process parameters in the machining of complex curved surfaces by robots is provided, the method comprising the following steps:

[0006] (1) The joint motion limit constraints, pose singularity constraints and processing deformation error constraints corresponding to the robot processing system constitute multi-domain composite constraints. Based on the multi-domain composite constraints, a fusion model is performed in the redundant angular space to map the constraints of different dimensions in different spaces into a unified fusion potential field. Among them, the joint motion limit constraints include the joint angle constraints and angular velocity constraints.

[0007] (2) Establish a dynamic equation with the virtual torque generated by the fusion potential field as the driving input, and solve the redundant angles of each tool position sequentially based on the obtained dynamic equation and numerical solution method, and then obtain a continuous and smooth redundant angle trajectory.

[0008] (3) Based on the obtained redundant angular trajectories, the optimization model is iteratively solved using an optimization algorithm to obtain the optimal combination of processing parameters; the optimization model is constructed with minimizing the global deformation index as the optimization objective and the processing parameters as the optimization variables.

[0009] Furthermore, the robot redundancy angle is set as... By using robot inverse kinematics, the multi-domain composite constraint is transformed into a form with redundant angles as independent variables. The mathematical form of the multi-domain composite constraint is:

[0010]

[0011] In the formula, This indicates the angles and angular velocities of each joint. This represents the minimum limit of the angle of each joint. These represent the maximum limits for the angle and angular velocity of each joint, respectively.

[0012] Furthermore, multi-domain composite constraints are decomposed into basic constraint forms. Calculate the distance metric between the constraint value and the boundary. Constructing a potential function transforms the constraints into a potential field:

[0013]

[0014] in, These are standardized parameters determined based on the distribution of different constraints. These are weight parameters determined based on the importance of different constraints under different operating conditions. It is the fundamental potential field transformation function.

[0015] Furthermore, the fusion potential field is represented as:

[0016] .

[0017] Furthermore, the obtained dynamic equation is:

[0018]

[0019] In the formula, M is the virtual moment of inertia; C is the virtual rotational damping; and K is the virtual rotational stiffness.

[0020] Furthermore, based on toolpath functions Discrete time series, virtual modal parameters, and initial redundant state corresponding to the initial tool position. The redundant state of the next tool position is obtained by solving. The continuous and smooth redundant angular trajectory is obtained by iterative solution.

[0021] Furthermore, the expression for the optimization model is:

[0022]

[0023] In the formula, This represents the variance of the deformation values ​​at various points on the machined surface. This represents the average deformation value at various points on the machined surface. This refers to the tool rotation speed in the process parameters. This refers to the feed rate in the process parameters.

[0024] Furthermore, the joint motion limit constraint is expressed as:

[0025]

[0026] In the formula, This indicates the angles and angular velocities of each joint. This represents the minimum limit of the angle of each joint. These represent the maximum limits for the angle and angular velocity of each joint, respectively.

[0027] The present invention also provides a system for jointly optimizing redundant angles and process parameters for robotic machining of complex curved surfaces. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the method for jointly optimizing redundant angles and process parameters for robotic machining of complex curved surfaces as described above.

[0028] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method for jointly optimizing redundant angles and process parameters for complex surface robot machining as described above.

[0029] In summary, compared with the prior art, the method and equipment for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces provided by this invention have the following advantages:

[0030] 1. The joint motion limit constraints, pose singularity constraints, and machining deformation error constraints corresponding to the robot machining system constitute multi-domain composite constraints. Based on the multi-domain composite constraints, a fusion model is performed in the redundant angle space to map constraints of different dimensions in different spaces into a unified fusion potential field. This realizes the representation of multiple constraints in a unified space, provides a foundation for multi-constraint redundant angle planning, and further realizes the synergistic optimization of redundant angles and process parameters.

[0031] 2. A dynamic equation is established with the virtual torque generated by the fused potential field as the driving input. Based on the obtained dynamic equation and numerical solution method, the redundant angles of each tool position are solved sequentially, and then a continuous and smooth redundant angle trajectory is obtained. This redundant angle trajectory satisfies multiple constraints, which effectively improves the motion stability and trajectory accuracy of the robot machining process.

[0032] 3. Based on the obtained redundant angle trajectory, the optimization model is iteratively solved using an optimization algorithm to obtain the optimal combination of processing parameters. Specifically, a global processing deformation optimization index is constructed based on statistical principles, and an optimization algorithm is used to optimize multi-objective processing parameters. The algorithm obtains the process parameter combination that makes the global processing deformation distribution optimal, realizing the synergistic optimization of redundant angles and process parameters, and can provide a performance-optimized process parameter configuration scheme for actual processing. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method for jointly optimizing redundant angles and process parameters in the machining of complex curved surfaces by a robot, provided by the present invention.

[0034] Figure 2 This is a schematic diagram of the fusion potential field from the perspective of the processing trajectory;

[0035] Figure 3 It is the trajectory curve of the smoothed redundant angle driven by the potential field;

[0036] Figure 4 It is a graph showing the shape of the workpiece to be processed and the curve trajectory of its test processing;

[0037] Figure 5 It is a set of redundant angle trajectories obtained after redundancy angle planning driven by potential field for each trajectory;

[0038] Figure 6 (1) and (2) are Pareto optimal boundary map and deformation error distribution map after optimization based on NSGA-Ⅱ multi-objective optimization, respectively. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0040] Please see Figure 1 The present invention provides a method for jointly optimizing redundant angles and process parameters in the machining of complex curved surfaces by robots, which mainly includes the following steps:

[0041] Step 1: Based on the robot machining system, construct joint motion limit constraints, pose singularity constraints, and machining deformation error constraints; among which, joint motion limit constraints include joint angle constraints and angular velocity constraints.

[0042] Regarding the construction of joint motion limit constraints: In robot motion, establishing joint motion limit constraints is a necessary step to ensure system safety. Joint motion limit constraints typically include angular constraints and angular velocity constraints for each joint. If these constraints are not imposed during movement, the robotic arm may suffer mechanical damage or control instability due to exceeding physical limits.

[0043] The limit constraints of joint motion are expressed as follows:

[0044]

[0045] In the formula, This indicates the angles and angular velocities of each joint. This represents the minimum limit of the angle of each joint. These represent the maximum limits for the angle and angular velocity of each joint, respectively.

[0046] Regarding the construction of pose singularity constraints: In the machining process of a six-axis robot, configuration singularities can lead to rank deficiency in the Jacobian matrix, resulting in loss of motion degrees of freedom or uncontrolled joint velocities exceeding limits. To avoid such problems, pose singularity constraints based on kinematic properties need to be established. The core of this pose singularity constraint lies in constructing a mathematical index that can quantify the degree of singularity and setting its safe threshold boundary.

[0047] A robot kinematic model is established based on the standard DH parameter method. Let the joint variable vector be... The end-effector pose matrix is ​​obtained by multiplying the transformation matrices of each joint:

[0048]

[0049] Jacobian matrix of the robot By position Jacobi And direction Jacobi composition:

[0050]

[0051] The essential condition for the occurrence of singularity is The rank deficiency of a singularity can be determined by the matrix determinant or singular value decomposition. An operability index is defined as a quantitative benchmark for singularity:

[0052]

[0053] Operational indicators The volumetric measure of the terminal velocity ellipsoid reflects the terminal's ability to move in all directions. When, it indicates that the robot is in a flexible configuration, when When the robot approaches a singular configuration, it indicates that the robot's configuration is singular. To avoid robot configuration singularities, the following pose singularity constraint is established:

[0054]

[0055] Regarding the establishment of machining deformation errors: Machining deformation errors in the robot end effector are mainly caused by insufficient joint stiffness and the characteristics of the end effector stiffness. To establish constraints on machining deformation errors, starting from the robot stiffness model, we construct the constraint relationships between joint stiffness, end effector stiffness, and external loads through coordinate transformation and mechanical equilibrium equations.

[0056] The joint space stiffness matrix can be represented as a diagonal matrix. ,in For the first The stiffness coefficient of a joint, when the joint is subjected to torque. At that time, joint deformation The joint space stiffness is mapped to the robot's operating space using the robot's Jacobian matrix. Based on the principle of virtual work, the equivalent stiffness matrix of the robot's end effector is:

[0057]

[0058] The equivalent stiffness matrix of the robot's end effector represents the projection of joint stiffness into the Cartesian space of the robot's end effector, reflecting its ability to resist deformation under external forces. Furthermore, a cutting force mechanism prediction model is used to calculate the end effector force in the tool coordinate system. Typically, when calculating end effector deformation, the average cutting force, i.e., the force per revolution of the tool, is used. The average instantaneous cutting force is calculated using the following formula:

[0059]

[0060] In the formula, This is the cutting force transformation matrix, which transforms the forces to the base coordinate system. , representing radial, tangential, and axial directions, respectively.

[0061] Machining deformation error mainly focuses on the deformation of the tool in the normal direction of the cutting coordinate system. Combining the above-mentioned end stiffness and end force, the constraint form of machining deformation error is as follows:

[0062]

[0063] in, The unit normal vector represents the coordinate system tangent to the base coordinate system.

[0064] Step 2: Joint motion limit constraints, pose singularity constraints, and machining deformation error constraints constitute multi-domain composite constraints. Based on the multi-domain composite constraints, a fusion model is performed in the redundant angular space to map constraints of different dimensions in different spaces into a unified fusion potential field.

[0065] Please see Figure 2 In the process of robot processing, it is necessary to take into account multi-domain composite constraints such as joint motion limit constraints, pose singularity constraints, and processing deformation error constraints. Based on the superposition principle of potential fields, multi-domain composite constraints are fused and modeled to map constraints of different dimensions in different spaces into a unified fused potential field.

[0066] Set the robot redundancy angle to Given a redundant angle, multi-domain composite constraints can be transformed into a form with the redundant angle as the independent variable using robot inverse kinematics. The mathematical form of the multi-domain composite constraint is:

[0067]

[0068] Decompose the above constraints into basic constraint forms. Calculate the distance metric between the constraint value and the boundary. Constructing a potential function transforms the constraints into a potential field:

[0069]

[0070] in, These are standardized parameters determined based on the distribution of different constraints. These are weight parameters determined based on the importance of different constraints under different operating conditions. It is the basic potential field transformation function. The advantage of this basic potential field transformation function is that it can guarantee first-order and second-order continuity at piecewise boundaries, thus obtaining a smoother spatial potential field.

[0071] Taking into account the multi-domain composite constraints, the fused potential field is expressed as:

[0072]

[0073] By leveraging the fused potential field, redundant angles can be used for continuous trajectory planning while simultaneously considering composite constraints.

[0074] Step 3: Calculate the virtual torque generated by the fused potential field and establish the dynamic equation with the virtual torque as the driving input.

[0075] The fused potential field based on multi-domain composite constraints enables the robot's end effector to deflect along the tool axis under the action of virtual torque. This transformation of the redundancy angle allows the robot configuration to move in a more flexible and less deformable direction, thereby improving the robot's machining performance. The fused potential field itself exhibits highly complex semi-analytical properties. To avoid the difficulties caused by analytical differentiation, numerical methods such as symmetric difference, forward difference, or backward difference can be used to calculate the virtual torque generated by the fused potential field, and a dynamic equation with the virtual torque as the driving input can be established.

[0076]

[0077] In the formula, the dynamic characteristic of the virtual rotational inertia M is to maintain the rotational inertia of the end effector's attitude motion, allowing it to rotate smoothly and continuously along the current angular velocity direction, thereby effectively suppressing sudden changes in rotational speed. The virtual rotational damping C, by introducing velocity-related torque components, produces a significant damping effect when the end effector is far from the constraint boundary region, causing the attitude motion energy to dissipate and stabilize at a locally optimal pose, avoiding the risk of the pose re-entering the adjacent constraint boundary due to continuous rotation. The virtual rotational stiffness K, by constructing an elastic traction torque, drives the current attitude to asymptotically approach the recommended target pose. Typically, the quality of redundant attitudes varies with the state of the machining trajectory, and there is no fixed optimal redundant attitude; therefore, the K term is ignored, allowing it to automatically find its optimal value.

[0078] Step four: Based on the obtained dynamic equations and numerical solution methods, the redundant angles of each tool position are solved sequentially, and then a continuous and smooth redundant angle trajectory is obtained.

[0079] Considering the analytical complexity of the dynamic equations, the following numerical methods, based on the characteristics of the robot machining process and the fourth-order Runge-Kutta method or Euler method, are proposed for solving the problem using the toolpath function. Discrete time series Virtual modal parameters (inertia) Damping ), Initial redundancy state corresponding to the initial tool position The redundant state of the next tool position is obtained by solving. The continuous and smooth redundant angular trajectory is obtained by iterative solution.

[0080] The specific steps are as follows: First, according to the... Redundancy at each tool position point Calculating redundant angular acceleration using dynamic equations ;according to calculate Redundant angle state at the midpoint of the tool position And calculate the new redundant angular acceleration using the dynamic equations. ; Again according to calculate Redundant angle state at the midpoint of the tool position And calculate the new redundant angular acceleration using the dynamic equations. Ultimately based on calculate Redundant angle state at the tool position point And calculate the new redundant angular acceleration using the dynamic equations. The final calculation of the first... The redundant state at the tool position point is:

[0081]

[0082] Through iterative solution, a smooth redundant angular trajectory can be obtained. The curve of the smooth redundant angular trajectory driven by the potential field is shown below. Figure 3 As shown.

[0083] Step 5: With minimizing the global deformation index as the optimization objective and the processing parameters as the optimization variables, construct an optimization model. The expression of the optimization model is as follows:

[0084]

[0085] In the formula, This represents the variance of the deformation values ​​at various points on the machined surface. This represents the average deformation value at various points on the machined surface. This refers to the tool rotation speed in the process parameters. This refers to the feed rate in the process parameters.

[0086] The multi-objective collaborative optimization mechanism of the NSGA-II algorithm is adopted, which takes process parameters such as rotation speed and feed as decision variables, minimizes the global machining deformation error as the optimization objective, obtains the Pareto optimal solution set through non-dominated sorting and elite retention strategies, and makes the optimal solution decision in combination with the process knowledge base.

[0087] The optimization objective is primarily to minimize the global deformation index of the workpiece surface. Spindle speed and feed rate are mainly used as optimization variables, with the depth of cut set to a constant 0.5 mm. The width of cut, which determines the robot's joint angle variation, is set to a constant 6 mm. Simultaneously, spindle speed and feed rate are used as optimization variables for parameter optimization calculations. Considering the optimization objective is to minimize the global deformation index, a mathematical model is chosen to construct the average value and variance of milling deformation at uniform tool positions on the workpiece surface as the deformation evaluation index. The optimization model is constructed based on the range of optimization variables and the objective function.

[0088] Step 6: Based on the obtained redundant angular trajectories, use an optimization algorithm to iteratively solve the optimization model to obtain the optimal combination of processing parameters.

[0089] The optimization was performed using the NSGA-II algorithm, NSGA, or PSO, with the following parameters set: population size of 100, optimal individual coefficient of 0.4, and maximum number of iterations of 100. After solving the optimization model using MATLAB, 40 Pareto optimal solutions were obtained. Parameters can be selected according to different processing requirements. To select one of the Pareto optimal solutions, where ap represents the cut depth and ae represents the cut width, as follows: Figure 6 The Pareto optimal boundary diagram and the optimized milling deformation distribution corresponding to the selected Pareto solution are shown below. The shape of the workpiece surface to be machined and the curve trajectory of the test machining are as follows: Figure 4 As shown, the redundant angle trajectory obtained after performing potential field-driven redundant angle planning on each trajectory is as follows: Figure 5 As shown.

[0090] Calculate the optimized average and variance of milling deformation based on a single toolpath trajectory, and the initial machining parameters. By comparing the objective function calculation results of different toolpath trajectories before and after deformation optimization, it can be seen that the global deformation average value decreased by 6.8% and the uniformity increased by 12.1% after optimization. That is, after multi-parameter variable partitioning optimization, the overall milling deformation value of the curved workpiece is reduced and the distribution is more uniform.

[0091] The present invention also provides a system for jointly optimizing redundant angles and process parameters for robotic machining of complex curved surfaces. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the method for jointly optimizing redundant angles and process parameters for robotic machining of complex curved surfaces as described above.

[0092] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method for jointly optimizing redundant angles and process parameters for complex surface robot machining as described above.

[0093] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces, characterized in that, The method includes the following steps: (1) The joint motion limit constraints, pose singularity constraints and processing deformation error constraints corresponding to the robot processing system constitute multi-domain composite constraints. Based on the multi-domain composite constraints, a fusion model is performed in the redundant angular space to map the constraints of different dimensions in different spaces into a unified fusion potential field. Among them, the joint motion limit constraints include the joint angle constraints and angular velocity constraints. (2) Establish a dynamic equation with the virtual torque generated by the fusion potential field as the driving input, and solve the redundant angles of each tool position sequentially based on the obtained dynamic equation and numerical solution method, and then obtain a continuous and smooth redundant angle trajectory. (3) Based on the obtained redundant angular trajectories, the optimization model is iteratively solved using an optimization algorithm to obtain the optimal combination of processing parameters; the optimization model is constructed with minimizing the global deformation index as the optimization objective and the processing parameters as the optimization variables; Among these, machining deformation error focuses on the deformation generated by the tool's cutting coordinate system normal; considering that the optimization objective is to minimize the global deformation index, a mathematical model of the average value and variance of milling deformation at uniform tool positions on the workpiece surface is chosen as the deformation evaluation index, and the robot redundancy angle is set as... By using robot inverse kinematics, multi-domain composite constraints are transformed into a form with redundant angles as independent variables; multi-domain composite constraints are decomposed into basic constraint forms. Calculate the distance metric between the constraint value and the boundary. Constructing a potential function transforms the constraints into a potential field: in, These are standardized parameters determined based on the distribution of different constraints. These are weight parameters determined based on the importance of different constraints under different operating conditions. It is the fundamental potential field transformation function; the fused potential field is expressed as: 。 2. The method for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces as described in claim 1, characterized in that: The mathematical form of multi-domain composite constraints is: In the formula, This indicates the angles and angular velocities of each joint. This represents the minimum limit value of the angle of each joint. These represent the maximum limits for the angle and angular velocity of each joint, respectively.

3. The method for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces as described in claim 2, characterized in that: The obtained dynamic equation is: In the formula, M is the virtual moment of inertia; C is the virtual rotational damping; and K is the virtual rotational stiffness.

4. The method for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces as described in claim 1, characterized in that: Based on toolpath function Discrete time series, virtual modal parameters, and initial redundant state corresponding to the initial tool position. The redundant state of the next tool position is obtained by solving. The continuous and smooth redundant angular trajectory is obtained by iterative solution.

5. The method for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces as described in claim 1, characterized in that: The expression for the optimization model is: In the formula, This represents the variance of the deformation values ​​at various points on the machined surface. This represents the average deformation value at various points on the machined surface. This refers to the tool rotation speed in the process parameters. This refers to the feed rate in the process parameters.

6. The method for jointly optimizing redundant angles and process parameters in robot machining of complex curved surfaces as described in any one of claims 3-5, characterized in that: The limit constraints of joint motion are expressed as follows: In the formula, This indicates the angles and angular velocities of each joint. This represents the minimum limit value of the angle of each joint. These represent the maximum limits for the angle and angular velocity of each joint, respectively.

7. A system for jointly optimizing redundant angles and process parameters in robotic machining of complex curved surfaces, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the method for joint optimization of redundant angles and process parameters for complex surface robot machining as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method for joint optimization of redundancy angles and process parameters for complex surface robot machining as described in any one of claims 1-6.

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