Robot trajectory and pose optimization method and device based on comprehensive pose performance index

Abstract

The application provides a robot trajectory posture optimization method and device based on a comprehensive posture performance index, and belongs to the technical field of robot control and artificial intelligence. The method comprises the following steps: constructing a translation deformation vector based on a robot joint stiffness model, constructing a deformation energy model according to the translation deformation vector and external force analysis of a grinding wheel; constructing an operability index according to a translation speed and a joint penalty factor; constructing a comprehensive posture performance index according to the deformation energy model and the operability index; constructing a discrete point set based on a grinding trajectory, taking the maximum sum of indexes of the discrete point set and the minimum cumulative amount of joint changes on the grinding trajectory as an optimization target, and constructing a grinding trajectory optimization model in combination with joint angle limiting and joint rated speed constraints; and solving the model by using an M-LSHADE algorithm improved based on Q-learning to obtain an optimized trajectory posture. The improved algorithm is used to solve the grinding trajectory optimization model, and the stability and quality of robot grinding trajectory execution are greatly improved.

Description

Technical Field

[0001] This application relates to the fields of robot control and artificial intelligence technology, and in particular to a method and apparatus for optimizing robot trajectory and posture based on comprehensive posture performance indicators. Background Technology

[0002] With technological advancements, the research and application of robotic grinding technology are continuously progressing. In practical applications, such as grinding aero-engine blades, the robot's end effector needs to maintain continuous and stable contact with the workpiece surface to ensure uniform material removal, contour accuracy, and surface quality. Robot stiffness is a crucial factor affecting processing stability and quality, and the optimization of robot trajectory and posture is closely related to its stiffness performance. Currently, the increasing market demand for high-precision, high-stability grinding has driven research progress in robot trajectory and posture optimization design based on comprehensive posture performance indicators.

[0003] Existing robot trajectory and posture optimization design methods mainly employ three approaches. The first approach is stiffness modeling and parameter identification, which establishes a quantitative relationship between robot configuration, joint flexibility, and end effector deformation. This is primarily achieved through structural modeling, experimental measurement, and transmission chain mechanism analysis to characterize the impact of joint flexibility on end effector deformation. The second approach is stiffness performance index construction, which evaluates the robot's performance differences under different configurations and processing conditions using indicators such as stiffness, flexibility, deformation error, or machining error. Evaluation indicators such as stiffness, flexibility, deformation error, or machining error are established around specific processing tasks to quantitatively characterize the robot's stiffness characteristics under different configurations and processing conditions. The third approach is stiffness pose optimization, which, based on stiffness or deformation evaluation results, improves the robot's stiffness performance and motion stability during processing by adjusting processing posture, toolpath direction, and trajectory parameters.

[0004] However, the three methods mentioned above share two common problems. First, focusing solely on improving local stiffness or single-point posture performance can enhance local performance at discrete processing points, but it may lead to uneven posture transitions between adjacent processing points, abrupt joint motion changes, or the robot approaching joint limits, thus weakening the overall stability of the grinding trajectory. Second, when dealing with continuous curved surface grinding trajectories involving multiple processing points and multidimensional posture variables, the algorithms' global search capability, local exploitation capability, and parameter adaptive adjustment capability are all insufficient. These problems make it difficult for the robot to meet the requirements of high-precision and high-stability grinding. Summary of the Invention

[0005] In view of this, this application provides a robot trajectory and posture optimization method and apparatus based on comprehensive posture performance indicators to solve the problem that robots are unable to meet the requirements of high precision and high stability grinding.

[0006] Specifically, this application is implemented through the following technical solution:

[0007] The first aspect of this application provides a method for optimizing robot trajectory and posture based on comprehensive posture performance indicators, the method comprising:

[0008] Based on the robot joint stiffness model, a translational deformation vector for the robot operating in a non-singular configuration is constructed, and a deformation energy model is constructed based on the translational deformation vector and the external force analysis of the grinding wheel.

[0009] An operability index is constructed based on the translation speed and joint penalty factor during the robot's polishing process, wherein the joint penalty factor is used to characterize scalability.

[0010] A comprehensive attitude performance index is constructed based on the deformation energy model and the operability index.

[0011] Based on the grinding trajectory of the robot, a discrete point set including several grinding points is constructed. The optimization objective is to maximize the sum of the comprehensive posture performance index of the discrete point set and minimize the cumulative amount of joint changes on the grinding trajectory. Combining joint angle limit constraints and joint rated speed constraints, a grinding trajectory optimization model is constructed.

[0012] The grinding trajectory optimization model is solved using the M-LSHADE algorithm, which is an improvement on the Q-learning model.

[0013] In a preferred embodiment of the present invention, the robot trajectory posture optimization method based on comprehensive posture performance indicators is characterized in that the stiffness model is configured as follows:

[0014] ;

[0015] in, , It is the i-th joint angle of the robot. It is the Jacobian matrix of the robot. It is the joint stiffness matrix. It is a robot stiffness model.

[0016] The process of constructing the deformation vector for the robot to operate in non-singular configurations based on the robot joint stiffness model includes:

[0017] The flexibility matrix is ​​constructed based on the robot joint stiffness model, specifically as follows:

[0018] ;

[0019] Based on the force conditions experienced by the robot during the polishing process and the compliance matrix, the translational deformation vector is constructed as follows:

[0020] ;

[0021] in, The translation deformation vector, yes The vector in the tool direction, yes In the plane, F is a vector representing a unidirectional axial force. , , These represent the three directions in which unidirectional axial force causes parallel deformation on the grinding wheel. This represents the component of the compliance matrix in the tool direction.

[0022] In another preferred embodiment of the present invention, the step of constructing a deformation energy model based on the deformation vector and the external force analysis of the grinding wheel includes:

[0023] Construct a first expression for the deformation energy with respect to the deformation vector and the external force:

[0024] ;

[0025] in, This is a deformation energy model.

[0026] Based on the balance of forces and the law of conservation of energy, a second expression is constructed according to the first expression. The second expression characterizes the relationship between the deformation energy and the vector of the planar direction:

[0027] ;

[0028] in, It is a symmetric matrix.

[0029] Based on the assumption that the robot link is rigid, the second expression is converted to the joint coordinate system to obtain the deformation energy expression in the joint coordinate system:

[0030] ;

[0031] Based on the deformation energy expression in the joint coordinate system and the force and torque analysis of the robot, the deformation energy model is obtained:

[0032] ;

[0033] in, For force / torque components.

[0034] In another preferred embodiment of the present invention, the construction of the operability index includes:

[0035] According to the robot's grinding translation speed We obtain the Jacobian determinant of the operator:

[0036] ;

[0037] Let be the operable Jacobian matrix of the robot.

[0038] An operability index is constructed based on a joint penalty factor, which is used to characterize scaling operability.

[0039] ;

[0040] in, The robot's operability index. This is a penalty factor.

[0041] In another preferred embodiment of the present invention, the construction comprising a discrete point set including a plurality of grinding points includes:

[0042] Obtain the grinding points on the grinding trajectory, wherein the grinding points include the starting point, the ending point, and the target point within the preset area of ​​the grinding trajectory.

[0043] For the blank areas between the polishing points, discrete points on the planned polishing trajectory are selected to fill in the gaps, thus obtaining the discrete point set.

[0044] In another preferred embodiment of the invention, the cumulative amount of joint change on the grinding trajectory is configured as follows:

[0045] ;

[0046] ;

[0047] in, This represents the cumulative amount of joint changes. Let be the average change in the angle of each joint over the entire trajectory, where The robot's first One joint, , It is the first The joint in the first The joint angle at each polishing point. It is the joint between adjacent grinding points. Angular difference;

[0048] The joint rated speed constraint satisfies:

[0049] ;

[0050] ;

[0051] in, The rated speed of each joint, For safety reasons, , For the first The first polishing point and the first The time interval between each polishing point The distance between the two polishing points. For feed rate;

[0052] The construction of the grinding trajectory optimization model includes:

[0053] Based on the aforementioned optimization objectives and constraints, a grinding trajectory optimization model is established:

[0054] ;

[0055] in, A comprehensive attitude performance index characterizing the entire grinding trajectory. For the first A polishing point , It is the first Attitude matrix at each polishing point The inverse kinematics function of the robot is used to solve for the robot's joint angles. For the robot's first One joint, Characterized as the first The joint in the first The joint angle at each polishing point. This represents the average change in the angle of each joint along the entire trajectory. , Initial attitude matrix, It is at point The rotation angle around the tool axis Z, It is the robot joint angle. The upper and lower limits of satisfaction.

[0056] In another preferred embodiment of the present invention, the step of solving the grinding trajectory optimization model using the M-LSHADE algorithm based on the Q-learning model specifically includes:

[0057] In the M-LSHADE algorithm, the optimal solution is output when the number of function evaluations is greater than or equal to the maximum allowed value.

[0058] In the M-LSHADE algorithm, when the number of function evaluations is less than the maximum allowed value, the Q-learning model is coupled to generate crossover rate and scaling factor sampling based on successful historical data, and based on the crossover rate and scaling factor, mutation and crossover operations are performed on individuals in the population to obtain a new candidate set;

[0059] An adaptive evaluation is performed on the new candidate set, and the function evaluation count is updated based on the number of adaptive evaluations.

[0060] Based on the results of the adaptive assessment, a Q-learning state is constructed, and the Q-value table is updated according to the learning state. Successful historical data is then updated based on the updated Q-value table.

[0061] The next generation size is updated using a linear population reduction strategy, and the number of times the current function is evaluated is returned to check if it is less than the maximum allowed value, until the optimal solution is output.

[0062] In another preferred embodiment of the present invention, the successful historical data is characterized as the next generation generated by the M-LSHADE algorithm based on multi-objective environment selection and Pareto relation, wherein the next generation is represented by the Pareto solution set:

[0063] ;

[0064] EnvSelect indicates that individuals with lower rank are preferred. This represents the merging of the parent and child generations, where... Indicates the parent generation. It is represented as offspring.

[0065] In another preferred embodiment of the present invention, obtaining a new candidate set includes:

[0066] For each individual First, Q-learning selects the index. Then, the crossover rate and scaling factor are generated:

[0067] ;

[0068] ;

[0069] in, Indicates a normal distribution. Represents the Cauchy distribution sampling operator;

[0070] The mutation operator adopts the current-to-pbest / 1 form and introduces external memory A. The best subset of the current population is randomly selected. and randomly select and Construct the mutation vector:

[0071] ;

[0072] The This is the new candidate set.

[0073] In another preferred embodiment of the present invention, the new candidate set is subjected to adaptive evaluation, and the function evaluation count is updated based on the number of adaptive evaluations, including:

[0074] The new candidate set is adaptively evaluated based on the Q-learning algorithm, and the number of function evaluations is assigned according to the number of adaptive evaluations.

[0075] In another preferred embodiment of the present invention, updating the next generation size through a linear population reduction strategy includes:

[0076] ;

[0077] in, This refers to the size of the G+1 generation population. This is a rounding function. This represents the initial population size for the algorithm. For the minimum allowed population size, The number of times the function has been evaluated so far. The maximum number of function evaluations is preset for the algorithm, when At that time, The algorithm reduces the number of solutions based on the non-dominated level and the crowding distance until the size constraint is met, and then outputs the optimal solution.

[0078] A second aspect of this application provides a robot trajectory and posture optimization device based on comprehensive posture performance indicators, the device comprising:

[0079] The first construction module is used to construct the translational deformation vector of the robot running in a non-singular configuration based on the robot joint stiffness model, and to construct the deformation energy model based on the translational deformation vector and the external force analysis of the grinding wheel.

[0080] The second construction module is used to construct an operability index based on the translation speed and joint penalty factor of the robot grinding process, wherein the joint penalty factor is used to characterize scaling operability.

[0081] The third construction module is used to construct a comprehensive attitude performance index based on the deformation energy model and the operability index.

[0082] The fourth construction module is used to construct a discrete point set including several grinding points based on the grinding trajectory of the robot. The optimization objective is to maximize the sum of the comprehensive posture performance index of the discrete point set and minimize the cumulative amount of joint changes on the grinding trajectory. Combined with joint angle limit constraints and joint rated speed constraints, a grinding trajectory optimization model is constructed.

[0083] The grinding trajectory optimization model solving module is used to solve the grinding trajectory optimization model using the M-LSHADE algorithm based on the Q-learning model to obtain the optimized trajectory pose.

[0084] The robot trajectory and posture optimization method and apparatus based on comprehensive posture performance index provided in this application use comprehensive posture performance index to optimize the robot trajectory and posture design. Building upon existing methods for improving posture performance metrics, the design method presented in this application employs a comprehensive posture performance metric. This metric integrates deformation energy models, operability indices, and joint limit penalty factors to achieve unified quantification of multi-dimensional performance of the robot at a single-point posture. Based on the optimization of the comprehensive posture performance metric, this application establishes a multi-objective point grinding trajectory posture optimization model. By introducing a dual objective function that maximizes the sum of the comprehensive posture performance metrics across the entire path and minimizes the cumulative amount of joint changes, supplemented by joint angle limits and dynamic velocity constraints, this effectively eliminates trajectory jumps caused by local optimal postures, achieving coordinated optimization of single-point performance and the continuity of the entire trajectory. Furthermore, based on the multi-objective point grinding trajectory posture optimization model, an improved M-LSHADE algorithm based on Q-learning is introduced to address the problems of numerous variables and complex constraints in grinding trajectory optimization. While maintaining the M-LSHADE success history adaptive mechanism and linear population reduction strategy, Q-learning is introduced to strategically select historical memory indices. By dynamically adjusting the crossover rate and scaling factor, a uniformly distributed and convergent Pareto optimal solution set is output, providing diverse optimization schemes. By adopting a robot trajectory attitude optimization method based on comprehensive attitude performance indicators, the stability of robot grinding trajectory execution and grinding quality can be significantly improved. Attached Figure Description

[0085] Figure 1 This is a flowchart illustrating a robot trajectory and posture optimization method based on comprehensive posture performance indicators, according to an exemplary embodiment.

[0086] Figure 2 This is a schematic diagram illustrating the compliance error vector in a Cartesian coordinate system according to an exemplary embodiment;

[0087] Figure 3 This is a schematic diagram illustrating the robot polishing trajectory and optimization variables according to an exemplary embodiment;

[0088] Figure 4 This is a flowchart illustrating an improved M-LSHADE algorithm based on Q-learning, according to an exemplary embodiment.

[0089] Figure 5 This is a schematic diagram illustrating the learning framework of Q-learning for each iteration according to an exemplary embodiment;

[0090] Figure 6 This is a schematic diagram illustrating the PCA dimensionality reduction distribution of training and testing tasks according to an exemplary embodiment;

[0091] Figures 7 to 9 This is a schematic diagram illustrating the training curves of the QM-LSHADE algorithm on a training task regarding archive oversize, success update rate, and average round reward, according to an exemplary embodiment.

[0092] Figures 10 to 12 This is a schematic diagram of the Pareto front on a representative edge grinding test task obtained according to different processing methods;

[0093] Figures 13 to 16 This is a schematic diagram showing the changes in robot joint angles obtained from different processing methods;

[0094] Figures 17 to 20 This is a schematic diagram of pose deformation contour lines obtained according to different processing methods;

[0095] Figures 21 to 24 These are schematic diagrams of the test specimens after grinding, obtained according to different processing methods;

[0096] Figure 25 This is a schematic diagram illustrating the removal depth of an aero-engine blade according to an exemplary embodiment;

[0097] Figure 26 This is a schematic diagram illustrating the surface roughness of an aero-engine blade according to an exemplary embodiment;

[0098] Figure 27 This is a block diagram of an electronic device according to an exemplary embodiment. Detailed Implementation

[0099] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0100] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0101] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0102] The following specific embodiments are given to illustrate the technical solution of this application in detail.

[0103] Example 1:

[0104] Figure 1 This is a flowchart of an embodiment of the robot trajectory and posture optimization method based on comprehensive posture performance indicators provided in this application. Please refer to... Figure 1 The method provided in this embodiment includes steps S1 to S5:

[0105] Step S1: Based on the robot joint stiffness model, construct the translational deformation vector of the robot running in a non-singular configuration, and construct the deformation energy model according to the translational deformation vector and the external force analysis of the grinding wheel.

[0106] In step S1, the robot joint stiffness model refers to a mathematical model that describes "how stiff each joint of the robot is in different postures". It uses mathematical language to describe the ability of each joint of the robot to resist torsional deformation when subjected to force.

[0107] The translational deformation vector refers to the displacement change of the robot end effector (center point of the grinding wheel) in the Cartesian coordinate system due to the force applied to the end effector.

[0108] The deformation energy model refers to the quantitative relationship model between the deformation of a robot under force and energy dissipation in the joint coordinate system. It is the physical basis and core quantitative tool of attitude optimization technology.

[0109] Non-singular configuration refers to a robot in a state where the Jacobian matrix is ​​full rank, meaning that the robot's end effector has full motion capability in all directions and there is no "jamming" or "loss of control" phenomenon in any direction.

[0110] Optionally, step S1 specifically includes:

[0111] Step S11: Construct the translational deformation vector for the robot to operate in a non-singular configuration.

[0112] Based on a Cartesian stiffness model proposed by Salibury, each joint in the robot is considered as a torsional spring, resulting in the following robot stiffness model:

[0113] ;

[0114] in, , It is the i-th joint angle of the robot. It is the Jacobian matrix of the robot. This is the joint stiffness matrix:

[0115] ;

[0116] The joint stiffness matrix refers to a 6×6 diagonal matrix corresponding to the six joints of a six-DOF industrial robot, providing fundamental physical parameters for stiffness performance evaluation, posture optimization, and grinding quality improvement. The stiffness of the j-th joint is determined by adding a complementary stiffness matrix based on the load applied to the end effector. Thus, we obtain the second equation for the stiffness model:

[0117] ;

[0118] Among them, the flexibility matrix Used to avoid errors caused by calculating the inverse Jacobian matrix:

[0119] ;

[0120] The flexibility matrix is ​​the inverse of the stiffness matrix and is used to map forces to deformations.

[0121] Based on the robot's operation in a non-singular configuration, The influence is negligible. By relating the external force / moment to the deformation using the compliance matrix, the total deformation is obtained:

[0122] ;

[0123] in, The total deformation vector includes the translational deformation vector. and rotational deformation vector , The force / torque components include external force F and external torque M. During the grinding process, torque is negligible. Translational deformation is dominant. .

[0124] Considering only the axial force, the total deformation can be rewritten as a translational deformation vector:

[0125] ;

[0126] The translation deformation vector is decomposed into two vectors: , that is, the vector of the tool direction; and , that is, a vector in the plane direction.

[0127] Step S12: Construct a deformation energy model based on the translational deformation vector and the external force analysis of the grinding wheel.

[0128] Based on the obtained vector of the plane direction, such as Figure 2 As shown, a first expression for the deformation energy is constructed with respect to the deformation vector and the external force.

[0129] ;

[0130] Since F is determined by the feed rate and spindle speed, it can be approximated as a constant under given process conditions, based on force balance:

[0131] ;

[0132] By minimizing deformation energy To minimize Specifically, it includes:

[0133] According to the law of conservation of energy, the energy generated by the external force is converted into the robot's deformation energy. The first expression for the deformation energy with respect to the deformation vector and the external force is transformed into:

[0134] ;

[0135] The balance of binding forces is transformed into:

[0136] ;

[0137] in, It is a symmetric matrix.

[0138] Assuming it is in a non-singular configuration, Diagonalization transforms the first expression into:

[0139] ;

[0140] in For Frobenius 2-norm, It is by A diagonal matrix composed of the eigenvalues ​​of . It is an orthogonal matrix, and The column elements are The corresponding feature vector, yes The smallest eigenvalue of is such that minimize.

[0141] Assuming the robot's links are rigid, we obtain the second expression:

[0142] ;

[0143] in, For the first Deformation angle of each joint;

[0144] The torque of the joint. .

[0145] Combined with the external torque acting on the end effector With joint torque The relationship between them The deformation energy model in the joint coordinate system is obtained as follows:

[0146] ;

[0147] Step S1 transforms the stiffness performance, which cannot be directly measured, into a scalar function that can be accurately calculated by constructing a deformation energy model. It also rigorously proves the engineering intuition that "different postures at the same grinding point will produce different stiffnesses," providing an existence proof for posture optimization and avoiding the blindness of "blindly adjusting postures."

[0148] See you again Figure 1 Execute after step S1:

[0149] Step S2: Construct an operability index based on the translation speed and joint penalty factor during the robot's grinding process. The joint penalty factor is used to characterize scaling operability.

[0150] In step S2, the operability index is an indicator that measures the flexibility of the robot's movement in each direction under its current posture. The larger the value, the more flexible the end effector. When the value is zero, the robot enters a singular configuration and its movement is "stuck".

[0151] The joint penalty factor, also known as the joint limit penalty factor, is specifically used to quantify the safety margin of a robot's distance from the physical limit of a joint in its current posture.

[0152] Optionally, step S2 specifically includes:

[0153] Since translational speed performance is more important than rotational performance during the grinding process of aero-engine blade edges, and to avoid mixed elements and related non-uniformity issues, translational speed is used. The operability is configured using three rows of the corresponding Jacobian determinant:

[0154] ;

[0155] in, It is the operable Jacobian matrix of the robot.

[0156] Maneuverability evaluation alone may overlook the risk of joint over-limits. To ensure that the optimized robot posture is both flexible and safe, a penalty factor is introduced to scale maneuverability:

[0157] ;

[0158] in, It is a scaling factor used to adjust behavior near joint limits. It is a joint Current location and These are the upper and lower limits of joint movement, respectively. It is a joint The penalty factor.

[0159] By calculating the penalty factor for each joint under a specific pose, and selecting the smallest one as the penalty factor for calculating overall operability, The robot's operability number is:

[0160] ;

[0161] Step S2 introduces a penalty factor into the operability index to avoid ignoring the risk of joint over-limits, ensuring that the optimized robot posture is both flexible and safe.

[0162] See you again Figure 1 Execute after step S2:

[0163] Step S3: Construct a comprehensive attitude performance index based on the deformation energy model and the operability index.

[0164] In step S3: The comprehensive posture performance index refers to a composite index used to evaluate the robot's stiffness, flexibility and safety under a single point posture using a single numerical value. The larger the index value, the better the comprehensive performance of the posture.

[0165] Due to the deformation energy model With operability index Since the physical dimensions, numerical scales, and optimization preference directions are inconsistent, a corresponding type of signal-to-noise ratio transformation is adopted to unify the deformation energy index ("the smaller the better") and the operability index ("the larger the better") into an evaluation form of "the larger the better". The signal-to-noise ratio is:

[0166] ;

[0167] in It refers to the deformation energy at the i-th discrete point.

[0168] The signal-to-noise ratio is:

[0169] ;

[0170] in It refers to the operability index of the i-th discrete point.

[0171] Signal-to-noise ratio (SNR) is a key indicator for quantifying the impact of noise on quality characteristics, and a higher value indicates better performance. The SNR of the robot's deformation energy and maneuverability within the machining plane is normalized as follows:

[0172] ;

[0173] ;

[0174] The two performance indicators were made comparable, and after fusion, the comprehensive posture performance index of the grinding robot was obtained:

[0175] ;

[0176] in, This is a comprehensive attitude performance index for a single posture during the robotic polishing process.

[0177] Step S3 integrates the two physical quantities, stiffness performance (deformation energy) and flexibility safety (operability index), into a dimensionless scalar evaluation index through signal-to-noise ratio transformation and normalization operations, providing the algorithm with a clear and optimizable single objective function.

[0178] See you again Figure 1 Execute after step S3:

[0179] Step S4: Based on the robot's grinding trajectory, construct a discrete point set including several grinding points. The optimization objective is to maximize the sum of the comprehensive posture performance indicators of the discrete point set and minimize the cumulative amount of joint changes on the grinding trajectory. Combine the joint angle limit constraints and the joint rated speed constraints to construct a grinding trajectory optimization model.

[0180] In step S4: the discrete point set refers to the set of grinding trajectory optimization points, which consists of key feature points and supplementary discrete points, representing those representative positions on the entire continuous grinding trajectory that need to be evaluated and optimized point by point.

[0181] Joint variation refers to the change in the angle of each joint between adjacent grinding points.

[0182] Joint angle limit constraints refer to the maximum range of rotation angles allowed for each joint of a robot in terms of physical structure. These are hard physical boundaries that must be followed to prevent joints from exceeding their limits, which could lead to mechanical failures or anomalies.

[0183] The rated speed constraint of a joint refers to the safe multiple by which the rate of change of the angle of each joint of a robot must not exceed the rated maximum speed when the joints move between adjacent grinding points. It is a kinematic safety boundary to prevent joint overspeed from causing dynamic instability.

[0184] The grinding trajectory optimization model is a multi-objective optimization mathematical model used to find an end-effector trajectory that optimizes the robot's stiffness performance and makes its motion most stable while satisfying the robot's physical constraints.

[0185] Optionally, step S4 specifically includes:

[0186] Step S41: Obtain the grinding points on the grinding trajectory, the grinding points including the starting point, ending point and target point within the preset area of ​​the grinding trajectory.

[0187] By combining expert experience with rule constraints, key feature points are selected to determine n polishing points. This ensures that the optimized model accurately focuses on key performance targets.

[0188] Key feature points refer to nodes on the continuous grinding trajectory that cover the starting point, the ending point, and the core area (such as the point of geometric change in trajectory and the area where grinding force is concentrated) that plays a decisive role in grinding accuracy.

[0189] Step S42: Fill the blank areas between the polishing points by selecting discrete points on the planned polishing trajectory to obtain the discrete point set.

[0190] For the gaps between key feature points, the discrete points determined in the trajectory planning stage can be directly reused as supplements. These preset discrete points have fully considered the workpiece contour coverage and robot motion continuity during trajectory planning, and can directly fill the spatial gaps between feature points, forming a complete set of discrete points covering the entire path together with the key feature points.

[0191] Combination Figure 3 As shown, the dashed line represents the normal direction of the blade edge surface, and Z is the tool axis. These are the optimization variables for the robot's posture at the polishing point. It is at point The rotation angle around the tool axis Z, Rotating clockwise is considered positive.

[0192] Step S43: Establish the cumulative function of joint changes on the grinding trajectory.

[0193] The smooth transition of robot posture depends on the continuous and stable change of joint angles in the joint space. To optimize the posture smoothness in the scenario of robotic grinding of aero-engine blade edges, this paper focuses on the joint angle increments between adjacent grinding path points. The core optimization objective is to minimize the cumulative sum of all joint angle changes along the entire machining trajectory, and thus establishes the objective function:

[0194] ;

[0195] ;

[0196] in, This represents the average change in the angle of each joint along the entire trajectory. The robot's first One joint, , It is the first The joint in the first The joint angle at each polishing point. It is the joint between adjacent grinding points. The angle difference.

[0197] Step S44: Construct joint angle limit constraints and joint rated speed constraints.

[0198] Based on the robot's performance parameters, the following constraints should be met during the optimization process: robot joint angles The upper and lower limits and the rate of change of each joint should be less than their rated speed. Therefore, the constraints are as follows:

[0199] ;

[0200] ;

[0201] in, The rated speed of each joint, For safety reasons, , For the first The first polishing point and the first The time interval between each polishing point and These represent the distance between the two grinding points and the feed rate, respectively.

[0202] Step S45: Based on the optimization objective and constraints, establish a grinding trajectory optimization model.

[0203] Based on the aforementioned optimization objectives and constraints, a grinding trajectory optimization model is established:

[0204] ;

[0205] in, A comprehensive attitude performance index characterizing the entire grinding trajectory. For the first A polishing point It is the sum of the overall attitude performance indicators at all polishing points. It refers to the number of polishing points along the entire trajectory. Is the robot in the first The attitude matrix at each polishing point.

[0206] , It is the first Attitude matrix at each polishing point The inverse kinematics function of the robot is used to solve for the robot's joint angles. For the robot's first One joint, Characterized as the first The joint in the first The joint angle at each polishing point. This represents the average change in the angle of each joint along the entire trajectory. , Initial attitude matrix.

[0207] Step S4 transforms the engineering intuition of "how to plan the optimal grinding trajectory posture" into a constrained optimization mathematical model by constructing a grinding trajectory optimization model, providing a clear optimization objective for the algorithm.

[0208] See you again Figure 1 Execute after step S4:

[0209] Step S5: The M-LSHADE algorithm based on the improved Q-learning model is used to solve the grinding trajectory optimization model to obtain the optimized trajectory pose.

[0210] Q-learning is an off-track reinforcement learning algorithm that uses a Q-value table to store the value of states and actions. It employs ε-greedy to select actions to obtain rewards, iteratively updates Q-values ​​according to a formula, and selects the optimal Q-value for the next state to calculate the target value. After repeated iterations and convergence, it looks up the optimal action in the table to achieve the best decision.

[0211] The Q-value table is a two-dimensional lookup table maintained internally by the Q-learning module. It stores the "long-term expected return of taking a specific strategy (action) under a specific environment (state)". It is the knowledge base for the algorithm to "learn" the optimal parameter scheduling strategy.

[0212] The M-LSHADE algorithm is an improved adaptive differential evolution algorithm that relies on multi-strategy collaborative balancing of global exploration and local optimization. In general, the steps of the M-LSHADE algorithm include:

[0213] Step 1: Initialize the population, parameters, and external memory;

[0214] Step 2: Adaptively select three types of mutation formulas to generate mutated individuals, and construct candidate solutions through cross-validation;

[0215] Step 3: Greedy selection, the winning individual updates parameters and external memory;

[0216] Step 4: Linearly reduce the population size and iteratively converge.

[0217] Here, the population refers to the set of all candidate solutions in the current generation of the differential evolution algorithm, and each individual represents a set of polishing posture parameters.

[0218] Mutation refers to the use of known good solutions to guide the search direction within a population;

[0219] Crossover refers to the offspring inheriting some characteristics from the parent, while also receiving new characteristics brought about by mutation operations, forming entirely new polishing posture parameters;

[0220] The linear population reduction strategy refers to a strategy in which the population size gradually shrinks from the initial value to the minimum value according to a linear law as iterations proceed, thereby achieving a search mode switch of "extensive exploration with a large population in the early stage and refined development with a small population in the later stage".

[0221] In this application, the two algorithms above are combined. Specifically, the Q-learning algorithm is combined in steps 2 and 3 of the M-LSHADE algorithm.

[0222] Optionally, step S5 includes:

[0223] Step S51: In the M-LSHADE algorithm, the optimal solution is output in response to the function evaluation count exceeding the maximum allowed value.

[0224] Before starting S51, let's first introduce the definition of Pareto dominance:

[0225] If all objectives are satisfied If at least one objective is strictly less than , then a is said to dominate b, denoted as . Ranking is obtained by performing a non-dominated ranking on the candidate set based on dominance relationships. And calculate the crowd distance To characterize the local solution density.

[0226] In each generation, the parent generation with offspring Merge into:

[0227] ;

[0228] right Perform non-dominated sorting and crowding distance calculation, and use the environmental selection operator to retain the top NP individuals to form the next generation:

[0229] ;

[0230] EnvSelect indicates that individuals with low rank are preferred to be retained. The last layer is a standard multi-objective selection rule based on the crowding distance from large to small, which ensures that the algorithm outputs a Pareto solution set approximation rather than a single-point optimal solution.

[0231] Based on this, step S51 specifically includes:

[0232] The number of function evaluations refers to the total number of times the algorithm calls the comprehensive attitude performance index to optimize the objective function during the entire optimization process.

[0233] Referring to Figure 4, an initial population is generated and parameters are initialized during the algorithm's preparation phase. In the Gth generation, the population is represented as:

[0234] ;

[0235] For population size, For dimensions. Initialization command. Generate the initial population And calculate the multi-objective vector for each individual:

[0236] ;

[0237] The cumulative number of function evaluations is denoted as NFEs.

[0238] M-LSHADE's two success history storages are:

[0239] ;

[0240] ;

[0241] in, For storage length, For crossover probability, The scaling factor represents the initial crossover probability. Initial scaling factor External memory Used to store the replaced parent individual, initially .

[0242] The scaling factor is a core parameter in the differential evolution algorithm that controls the "variable length". It determines the factor by which the differential vector is magnified, i.e. "how far to go in each exploration".

[0243] Crossover rate is a probability parameter in differential evolution that controls "what proportion of offspring genes come from the mutation vector", determining the extent to which new individuals inherit the new characteristics generated by the mutation operation.

[0244] Solve the function and record the number of function evaluations; if the number of function evaluations exceeds the maximum allowed value, output the optimal solution.

[0245] Step S52: In the M-LSHADE algorithm, in response to the function evaluation count being less than the maximum allowed value, the coupled Q-learning model generates crossover rate and scaling factor sampling based on successful historical data, and performs mutation and crossover operations on individuals in the population based on the crossover rate and scaling factor to obtain a new candidate set.

[0246] The candidate set refers to the set of all experimental vectors (offspring individuals) generated through mutation and crossover operations in each generation iteration.

[0247] In the algorithm preparation phase, an initial population is generated and parameters are initialized; the function is solved, and the number of function evaluations is recorded; if the number of function evaluations is less than the maximum allowed value, Q-learning is introduced in the parameter generation phase, where the action set corresponds one-to-one with the historical index:

[0248] ;

[0249] in For action, An index for historical memory.

[0250] The historical memory index refers to the slot number in the memory bank, i.e., the array index, which is used to guide parameters.

[0251] state by father With test vector The Pareto relation construction includes three cases: , And they do not control each other.

[0252] Using the Softmax strategy to select actions:

[0253] ;

[0254] in, For successful historical data, The Q value includes the state. and actions T is the temperature parameter; the return is defined as:

[0255] ;

[0256] Successful historical data refers to two memory banks maintained by the algorithm: the crossover rate memory bank and the scaling factor memory bank. These banks are specifically used to store the center values ​​of parameter distributions that have historically generated better offspring, serving as a reference benchmark for subsequent parameter sampling.

[0257] For each individual First, Q-learning selects the index. Then, the crossover rate and scaling factor are generated:

[0258] ;

[0259] ;

[0260] in, and Let A and B represent the sampling operators for the normal distribution and Cauchy distribution, respectively. The mutation operator adopts the current-to-pbest / 1 form and is introduced into the external memory A.

[0261] Randomly select from the superior subset of the current population and randomly select and Construct the mutation vector:

[0262] ;

[0263] Binomial cross-validation is used to generate test vectors. The components:

[0264] ;

[0265] in for Uniform random numbers, This is used to ensure that at least one component comes from the mutation vector, and the candidate set is composed of all the test vectors generated in the current iteration.

[0266] Step S53: Perform an adaptive evaluation on the new candidate set, and update the function evaluation count based on the number of adaptive evaluations.

[0267] The objective function is called to solve the new candidate set to calculate the value of the comprehensive attitude performance index, and the function evaluation count is updated based on the number of function calls.

[0268] Step S54: Based on the results of the adaptive assessment, construct the Q-learning state, update the Q-value table according to the learning state, and update the success history data based on the updated Q-value table.

[0269] Q-learning states refer to three discrete states (+1 for success, 0 for neutrality, and -1 for failure) based on the Pareto dominance relationship between the experimental vector and the parent. They are "environmental snapshots" for Q-learning to understand the current evolutionary environment and are used to guide parameter selection strategies.

[0270] The formula for calculating the updated Q value is:

[0271] ;

[0272] in, and These are two parameters between 0 and 1. For learning rate, This is the discount factor.

[0273] It is a state and actions The Q value.

[0274] In the environmental state Execute action at time The rewards received.

[0275] The state in the Q table is The maximum Q value at that time The action that maximizes the Q value in the current state is selected, and the action selection depends on the Q value.

[0276] Q-learning framework combined Figure 5 As shown, the Q-learning state is updated based on the fitness evaluation of the candidate set. The Q value is updated to:

[0277] ;

[0278] To ensure consistency between successful historical data updates and multi-objective goals, success is defined as the improvement of the parent generation in the Pareto sense by the experimental vector:

[0279] ;

[0280] For all successful samples, construct a set respectively. and The improved parent individual will be incorporated into external memory A.

[0281] To assign different contributions to successful samples, a multi-objective improvement quantity is defined:

[0282] ;

[0283] in, For multi-objective improvements, weights are assigned accordingly:

[0284] ;

[0285] Wherein, represents the probability weight of the k-th position (or k-th action) in the history memory bank being selected in the current iteration, and the sum of the weights of all slots is 1.

[0286] This represents the degree of improvement the algorithm achieves on the objective function after generating parameters based on the k-th memory slot.

[0287] This indicates the size of the memory set currently participating in the statistics. The length of the memory is H, meaning there are H slots participating in the weight calculation.

[0288] This means that the performance improvement from all memory slots is summed up and used as the baseline for normalization.

[0289] Based on this, the weighted Lehmer mean is used:

[0290] ;

[0291] in, Indicates weight-based Set of computations Specific statistics;

[0292] Successful update history data:

[0293] ;

[0294] ;

[0295] Then, index k is updated in a loop, when... season This ensures that parameter memory updates are driven by multi-objective improvements without introducing ambiguous single-objective scalarization biases.

[0296] Step S55: Update the next generation size using a linear population reduction strategy, return the number of times the current function has been evaluated to see if it is less than the maximum allowed value, until the optimal solution is output.

[0297] The linear population reduction strategy refers to a strategy in which the population size gradually shrinks from the initial value to the minimum value according to a linear law as iterations proceed, thereby achieving a search mode switch of "extensive exploration with a large population in the early stage and refined development with a small population in the later stage".

[0298] By updating the next generation size using a linear population reduction strategy, the efficiency of later convergence can be improved.

[0299] ;

[0300] in, This refers to the size of the G+1 generation population. This is a rounding function. This represents the initial population size for the algorithm. For the minimum allowed population size, The number of times the function has been evaluated so far. The maximum number of function evaluations is preset for the algorithm, when At that time, The algorithm reduces the number of components based on the non-dominated level and the crowding distance until the size constraint is met, and simultaneously constrains the upper limit of the capacity of the external memory A to ensure the stability of the differential vector sampling process, and outputs the optimal solution.

[0301] Step S5, through a precise loop of "Q-learning perception decision → mutation and crossover to generate high-quality candidates → fitness evaluation to consume budget → experience feedback to update knowledge → population reduction to focus on elites," systematically solves a complex multi-objective trajectory optimization problem within limited computing resources. It surpasses the "mechanical search" of traditional differential evolution algorithms, achieving a true intelligent breakthrough of "learning while searching, becoming smarter with each iteration."

[0302] In summary, this embodiment provides a robot trajectory posture optimization method based on comprehensive posture performance indicators. By constructing a multi-target point grinding trajectory posture optimization model and introducing an improved M-LSHADE algorithm based on Q-learning to solve the model, the robot trajectory posture is optimized, effectively eliminating trajectory jumps caused by local optimal postures and significantly improving the stability of robot grinding trajectory execution and grinding quality.

[0303] Based on the above-mentioned robot trajectory and posture optimization method based on comprehensive posture performance indicators, an effectiveness verification experiment was conducted, as detailed below:

[0304] Experimental basis

[0305] Using a compressor blade of a certain type of aero-engine as the process test object, the grinding experiment was conducted based on the FANUC LR-Mate-200iD robotic grinding platform. This platform consists of a robot body, a grinding wheel, and sensors. The robot's repeatability is ±0.01mm, its radius of motion is ≥700mm, and its wrist can handle a mass of ≥7kg. The grinding wheel is a nylon wheel with a mesh size of P240.

[0306] To achieve multi-objective collaborative optimization of trajectory and attitude during robotic blade edge grinding, a task-level dataset oriented towards QM-LSHADE was constructed, and a corresponding training and testing process was established. For the FANUC LR-Mate-200iD industrial robot's aero-engine blade edge grinding scenario, local grinding trajectories in different regions were extracted. These trajectories were then combined with the surface normals at key feature points, the initial attitude matrix, the feasible region of inverse kinematics, joint angle constraints, and joint velocity constraints to form trajectory and attitude optimization task instances. Based on this, the rotation angle of key points around the tool axis was used as the variable to be optimized. With the dual objectives of maximizing the overall trajectory attitude performance and minimizing the cumulative joint changes, a training and testing task set consistent with the optimization model presented in this paper was constructed.

[0307] During the task set construction process, significant differences exist in curvature, normal variation, and kinematic reachability among different trajectory segments during blade edge grinding. The task set construction adopts a region coverage and parameter perturbation amplification approach. First, the blade edge trajectory is divided into several representative local segments, and key feature points are selected according to step S41 to cover the trajectory start point, end point, and intermediate regions with significant geometric changes or sensitivity to attitude adjustment. Subsequently, the trajectory length, key point spacing, initial attitude bias, and local normal variation amplitude are perturbed and amplified to form trajectory attitude optimization tasks with different difficulty levels.

[0308] Taking into account the geometric differences of different local trajectory segments at the blade edge, task coverage, and the computational cost of QM-LSHADE offline training, a task set of 150 trajectory and attitude optimization tasks was constructed. These tasks were divided into training and testing sets in a 0.7:0.3 ratio, with 105 training tasks and 45 testing tasks. To visually demonstrate the distribution characteristics of the constructed task set in terms of geometric attributes and optimization difficulty, statistical feature vectors were extracted for each trajectory and attitude optimization task, including trajectory length, number of keypoints, average curvature, rate of change of normal, initial mean CPPI, and initial cumulative joint changes. These vectors were then projected onto a two-dimensional plane using PCA. Figure 6 As shown, the training and testing tasks overlap rather than are clearly separated in the low-dimensional space, and the constructed task set has good diversity and representativeness.

[0309] The dimensionality of this optimization problem is determined by the number of key feature points, *n*. A single individual fitness evaluation requires sequentially solving inverse kinematics, calculating comprehensive posture performance indicators, and verifying joint constraints. Hyperparameter tuning must simultaneously consider population diversity and computational efficiency. Therefore, the optimal configuration of hyperparameters must satisfy two core principles: first, fully guarantee the diversity of the evolutionary population to avoid premature convergence; second, effectively control the computational cost of the algorithm while considering the execution efficiency of iterative optimization. Specific settings are shown in Table 1. Here, *n* represents the number of key feature points on the trajectory, i.e., the dimensionality of the decision variables in the trajectory posture optimization problem.

[0310] Table 1 Parameter settings for the QM-LSHADE algorithm

[0311]

[0312] After completing the task set construction and parameter setting, QM-LSHADE was trained offline on the training task set. During training, Q-learning continuously updates the selection strategy of the historical memory index, guiding the sampling of the scaling factor F and crossover rate CR to gradually adapt to the current search state, thereby improving the solution set quality on the trajectory pose optimization task. To characterize the policy convergence and search performance evolution during training, three metrics were recorded: average episode reward, Hypervolume (HV) of the non-dominated solution set of the external archive, and the success rate of updates. Figures 7 to 9 As shown in the figure, the solid line represents the mean of multiple independent runs, and the shaded area represents the standard deviation. It can be seen that as the training task progresses, the archive HV generally shows an upward trend and then stabilizes in the later stages. While the successful update ratio fluctuates somewhat, it generally shows a steady increase with training progress, stabilizing in the later stages. The average episode return increases rapidly with training progress and remains stable in the later stages. These results indicate that the parameter calling strategy after training exhibits good stability and consistency across different training tasks. The coupling of Q-learning and M-LSHADE helps improve the multi-object search performance in trajectory and pose optimization tasks.

[0313] After training, the trained QM-LSHADE is applied to a test task set to evaluate its generalization ability on tasks without training trajectories. For the test task, the algorithm outputs the corresponding Pareto solution set and calculates the external archive HV, the number of non-dominated solutions, the maximum value of the objective function F, and the objective function... The minimum value and the F and corresponding representative compromise solutions The compromise solution is defined as the Pareto solution that is closest to the ideal point in the normalized objective space. See Table 2.

[0314] Table 2 Results of QM-LSHADE on the edge grinding test task set

[0315]

[0316] Table 2 shows that the trained QM-LSHADE maintains relatively stable solution set quality on edge trajectory tasks that were not trained. The average external archive HV is 0.669, and the average number of non-dominated solutions is 17.2, indicating that the algorithm can output Pareto solution sets with good convergence and distribution. The average optimal F-value and the optimal... The values ​​are 8.06±0.27 and 884.6±57.3 respectively, and the overall fluctuation is small, indicating that the parameter calling strategy obtained through training can adapt to the pose optimization requirements of different edge local segments. The compromise solution corresponds to F and It is also relatively stable, indicating that the algorithm can provide a continuous and reasonable trade-off between overall posture performance improvement and joint changes.

[0317] To further demonstrate the generalization performance of QM-LSHADE on different edge local segments, the Pareto front distributions of three representative test tasks were plotted, corresponding to the edge initiation segment task, the edge middle segment task, and the edge termination segment task, respectively. Figures 10 to 12 As shown, QM-LSHADE can obtain clear and continuous Pareto front distributions on three representative test tasks: edge start segment, edge middle segment, and edge end segment. It is not limited to a few specific edge trajectories, but continuously outputs high-quality and reasonably distributed candidate solution sets for the differences in local curvature, normal changes, and attitude constraints between edge segments. Thus, it has the ability to adapt to different local trajectory optimization needs in the blade edge grinding scenario. Figure 10 This is a schematic diagram of the Pareto front for the edge-starting segment of the task. Figure 11 This is a schematic diagram of the Pareto front for the edge-middle segment of the mission. Figure 12 This is a schematic diagram of the Pareto front for edge-end tasks.

[0318] Experimental Task

[0319] To verify the effectiveness of the proposed method, a comparative experiment was conducted with the attitude-free optimization baseline method, the NSGA-II optimization method, and the M-LSHADE optimization method. The process parameters for all experimental groups were kept constant, specifically set as follows: grinding force 15N, robot feed speed 600mm / min, and grinding wheel spindle speed 1200r / min.

[0320] Experimental results

[0321] Changes in joint angles before and after optimization, as follows Figures 13 to 16 As shown, Figure 13This is a schematic diagram of the joint angle changes in the baseline scheme. Figure 14 This is a schematic diagram of the joint angle changes in the NSGA-II scheme. Figure 15 This is a schematic diagram of the joint angle changes in the M-LSHADE scheme. Figure 16 This is a schematic diagram of the joint angle changes in the proposed scheme. Table 3 shows the cumulative joint change, total variation (TV), total squared difference (SSD), and maximum single-step joint jump variable. Compared to the baseline method without posture optimization, the proposed method reduces these four indicators by 65.42%, 69.79%, 91.18%, and 82.32%, respectively; compared to the NSGA-II optimization method, it reduces them by 42.03%, 50.01%, 75.27%, and 73.11%, respectively; and compared to the M-LSHADE optimization method, it reduces them by 16.85%, 25.66%, 48.71%, and 52.40%, respectively. Experimental results show that the joint angle trajectory obtained by the proposed method is more continuous overall, the transition between adjacent grinding points is more natural, and there are fewer local oscillations and abrupt changes. While ensuring trajectory posture performance, it can more effectively reduce the fluctuation of joint angles throughout the entire path and suppress large local jumps, thus obtaining a smoother joint movement process.

[0322] Table 3. Joint trajectory smoothness evaluation results of different algorithms

[0323]

[0324] Static analysis of the robot was performed using ANSYS, and the overall structural static stiffness of the robot under different postures was compared. Figures 17 to 20 As shown, Figure 17 This is a schematic diagram of the pose deformation contour lines obtained from the baseline scheme. Figure 18 This is a schematic diagram of the pose deformation contour lines obtained from the NSGA-II scheme. Figure 19 This is a schematic diagram of the pose deformation contour lines obtained by the M-LSHADE scheme. Figure 20 This is a schematic diagram of the pose deformation contour lines obtained by the proposed scheme.

[0325] The maximum deformation at the end effector is reduced by 40.35% compared to the baseline method without attitude optimization, by 26.75% compared to the NSGA-II optimization method, and by 23.39% compared to the M-LSHADE optimization method. The results show that the overall static stiffness of the robot is significantly improved after optimization.

[0326] Finally, the removal depth and roughness were analyzed. Figures 21 to 24 These are schematic diagrams of experimental specimens after grinding obtained through different treatment methods. Figure 21 This is a schematic diagram of the experimental specimen after grinding obtained from the baseline scheme. Figure 22 This is a schematic diagram of the experimental specimen after grinding obtained using the NSGA-II method. Figure 23 This is a schematic diagram of the experimental specimen after grinding obtained using the M-LSHADE method. Figure 24 This is a schematic diagram of the experimental specimen obtained after grinding using the proposed method. The material removal depth is shown below. Figure 25 As shown. Surface roughness results are as follows. Figure 26 As shown.

[0327] Experimental results show that the proposed method can improve the removal depth while reducing the surface roughness of the workpiece, and the removal depth and surface roughness are more uniform, effectively improving the surface quality of the polished surface. The average removal depth is improved by 82.6% compared to the baseline method without orientation optimization, by 38.2% compared to the NSGA-II optimized method, and by 15.1% compared to the M-LSHADE optimized method; the average surface roughness is reduced by 28.5% compared to the baseline method without orientation optimization, by 16.5% compared to the NSGA-II optimized method, and by 10.6% compared to the M-LSHADE optimized method.

[0328] Example 2:

[0329] A second aspect of this application provides a robot trajectory and posture optimization device based on comprehensive posture performance indicators, the device comprising:

[0330] The first construction module is used to construct the translational deformation vector of the robot running in a non-singular configuration based on the robot joint stiffness model, and to construct the deformation energy model based on the translational deformation vector and the external force analysis of the grinding wheel.

[0331] The second construction module is used to construct an operability index based on the translation speed and joint penalty factor of the robot grinding process, wherein the joint penalty factor is used to characterize scaling operability.

[0332] The third construction module is used to construct a comprehensive attitude performance index based on the deformation energy model and the operability index.

[0333] The fourth construction module is used to construct a discrete point set including several grinding points based on the grinding trajectory of the robot. The optimization objective is to maximize the sum of the comprehensive posture performance index of the discrete point set and minimize the cumulative amount of joint changes on the grinding trajectory. Combined with joint angle limit constraints and joint rated speed constraints, a grinding trajectory optimization model is constructed.

[0334] The grinding trajectory optimization model solving module is used to solve the grinding trajectory optimization model using the M-LSHADE algorithm based on the Q-learning model to obtain the optimized trajectory pose.

[0335] In summary, the robot trajectory posture optimization device based on comprehensive posture performance index provided in this embodiment optimizes the robot trajectory posture by constructing a multi-target point grinding trajectory posture optimization model and introducing the M-LSHADE algorithm based on Q-learning to solve the model. This effectively eliminates trajectory jumps caused by local optimal postures and significantly improves the stability of robot grinding trajectory execution and grinding quality.

[0336] Example 3:

[0337] Thirdly, embodiments of this application provide an electronic device, Figure 27 This is a block diagram illustrating an electronic device according to an exemplary embodiment. (e.g.) Figure 27 As shown, the electronic device may include a processor 11 and a memory 12 storing computer program instructions.

[0338] Specifically, the processor 11 may include a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0339] The memory 12 may include a large-capacity storage device for data or instructions. For example, and not limitingly, the memory 12 may include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), flash memory, an optical disk drive, a magneto-optical disk drive, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 12 may include removable or non-removable (or fixed) media. Where appropriate, the memory 12 may be internal or external to a data processing device. In a particular embodiment, the memory 12 is non-volatile memory. In a particular embodiment, the memory 12 includes read-only memory (ROM) and random access memory (RAM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), an electrically alterable read-only memory (EAROM), or flash memory, or a combination of two or more of these. Where appropriate, the RAM can be Static Random-Access Memory (SRAM) or Dynamic Random-Access Memory (DRAM). DRAM can be Fast Page Mode Dynamic Random-Access Memory (FPMDRAM), Extended Data Out Dynamic Random-Access Memory (EDODRAM), Synchronous Dynamic Random-Access Memory (SDRAM), etc.

[0340] The memory 12 can be used to store or cache various data files that need to be processed and / or communicated, as well as possible computer program instructions executed by the processor 11.

[0341] The processor 11 reads and executes computer program instructions stored in the memory 12 to implement any of the robot trajectory and posture optimization methods based on comprehensive posture performance indicators in the above embodiments.

[0342] In one embodiment, the electronic device may further include a communication interface 13 and a bus 10. Wherein, as... Figure 27 As shown, the processor 11, memory 12, and communication interface 13 are connected through bus 10 and communicate with each other.

[0343] The communication interface 13 is used to enable communication between the various modules, devices, units, and / or equipment in the embodiments of this application. The communication port 13 can also enable data communication with other components such as external devices, image / data acquisition devices, databases, external storage, and image / data processing workstations.

[0344] Bus 10 includes hardware, software, or both, that couples components of an electronic device together. Bus 10 includes, but is not limited to, at least one of the following: data bus, address bus, control bus, expansion bus, and local bus. For example, and not as a limitation, bus 10 may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand interconnect, a Low Pin Count (LPC) bus, a memory bus, a Micro Channel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local Bus (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, bus 10 may include one or more buses. Although specific buses are described and illustrated in the embodiments of this application, this application considers any suitable bus or interconnection.

[0345] The apparatus of this embodiment can be used to perform... Figure 1 The steps of the method embodiment shown are similar in principle and process, and will not be repeated here.

[0346] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0347] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0348] Fourthly, embodiments of this application provide a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the robot trajectory and posture optimization method based on comprehensive posture performance indicators provided in the first aspect.

[0349] The readable storage medium may be more specifically adopted, including but not limited to: portable disk, hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0350] In a possible implementation, this application can also be implemented as a program product comprising program code, which, when the program product is run on a terminal device, causes the terminal device to perform steps to implement the robot trajectory and posture optimization method based on comprehensive posture performance indicators provided in the first aspect.

[0351] The program code for executing this application can be written in any combination of one or more programming languages. The program code can be executed entirely on the user device, partially on the user device, as a standalone software package, partially on the user device and partially on a remote device, or entirely on a remote device.

[0352] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A robot trajectory and posture optimization method based on comprehensive posture performance indicators, characterized in that, The method includes: Based on the robot joint stiffness model, a translational deformation vector for the robot operating in a non-singular configuration is constructed, and a deformation energy model is constructed based on the translational deformation vector and the external force analysis of the grinding wheel. An operability index is constructed based on the translation speed and joint penalty factor during the robot's polishing process, wherein the joint penalty factor is used to characterize scalability. A comprehensive attitude performance index is constructed based on the deformation energy model and the operability index. Based on the grinding trajectory of the robot, a discrete point set including several grinding points is constructed. The optimization objective is to maximize the sum of the comprehensive posture performance index of the discrete point set and minimize the cumulative amount of joint changes on the grinding trajectory. Combining joint angle limit constraints and joint rated speed constraints, a grinding trajectory optimization model is constructed. The M-LSHADE algorithm, which is an improvement on the Q-learning model, is used to solve the grinding trajectory optimization model to obtain the optimized trajectory pose.

2. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 1, characterized in that, The stiffness model is configured as follows: ； in, , It is the i-th joint angle of the robot. It is the Jacobian matrix of the robot. It is the joint stiffness matrix. It is a robot stiffness model; The process of constructing the deformation vector for the robot to operate in non-singular configurations based on the robot joint stiffness model includes: The flexibility matrix is ​​constructed based on the robot joint stiffness model, specifically as follows: ； Based on the force conditions experienced by the robot during the polishing process and the compliance matrix, the translational deformation vector is constructed as follows: ； in, The translation deformation vector, yes The vector in the tool direction, yes In the plane, F is a vector representing a unidirectional axial force. , , These represent the three directions in which unidirectional axial force causes parallel deformation on the grinding wheel. This represents the component of the compliance matrix in the tool direction.

3. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 2, characterized in that, The process of constructing a deformation energy model based on the deformation vector and the external force analysis of the grinding wheel includes: Construct a first expression for the deformation energy with respect to the deformation vector and the external force: ； in, For deformation energy model; Based on the balance of forces and the law of conservation of energy, a second expression is constructed according to the first expression. The second expression characterizes the relationship between the deformation energy and the vector of the planar direction: ； in, It is a symmetric matrix; Based on the assumption that the links of the robot are rigid, the second expression is converted to the joint coordinate system to obtain the deformation energy expression in the joint coordinate system: ； Based on the deformation energy expression in the joint coordinate system and the force and torque analysis of the robot, the deformation energy model is obtained: ； in, For force / torque components.

4. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 1, characterized in that, The construction of the operability index includes: According to the robot's grinding translation speed We obtain the Jacobian determinant of the operator: ； For the operable Jacobian matrix of the robot; An operability index is constructed based on a joint penalty factor, which is used to characterize scaling operability. ； in, The robot operability index. This is a penalty factor.

5. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 1, characterized in that, The construction includes a discrete set of several grinding points, including: Obtain the grinding points on the grinding trajectory, wherein the grinding points include the starting point, the ending point, and the target point within a preset area of ​​the grinding trajectory; For the blank areas between the polishing points, discrete points on the planned polishing trajectory are selected to fill in the gaps, thus obtaining the discrete point set.

6. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 2, characterized in that, The cumulative amount of joint changes on the grinding trajectory is configured as follows: ； ； in, This represents the cumulative amount of joint changes. Let be the average change in the angle of each joint over the entire trajectory, where The robot's first One joint, , It is the first The joint in the first The joint angle at each polishing point. It is the joint between adjacent grinding points. Angular difference; The joint rated speed constraint satisfies: ； ； in, The rated speed of each joint, For safety reasons, , For the first The first polishing point and the first The time interval between each polishing point The distance between the two polishing points. For feed rate; The construction of the grinding trajectory optimization model includes: Based on the aforementioned optimization objectives and constraints, a grinding trajectory optimization model is established: ； in, A comprehensive attitude performance index characterizing the entire grinding trajectory. For the first A polishing point , It is the first Attitude matrix at each polishing point The inverse kinematics function of the robot is used to solve for the robot's joint angles. For the robot's first One joint, Characterized as the first The joint in the first The joint angle at each polishing point. This represents the average change in the angle of each joint along the entire trajectory. , Initial attitude matrix, It is at point The rotation angle around the tool axis Z at that point. It is the robot joint angle. The upper and lower limits of satisfaction.

7. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 1, characterized in that, The method of solving the grinding trajectory optimization model using the M-LSHADE algorithm based on the Q-learning model specifically includes: In the M-LSHADE algorithm, the optimal solution is output when the number of function evaluations is greater than or equal to the maximum allowed value. In the M-LSHADE algorithm, when the number of function evaluations is less than the maximum allowed value, the Q-learning model is coupled to generate crossover rate and scaling factor sampling based on successful historical data, and based on the crossover rate and scaling factor, mutation and crossover operations are performed on individuals in the population to obtain a new candidate set; An adaptive evaluation is performed on the new candidate set, and the function evaluation count is updated based on the number of adaptive evaluations. Based on the results of the adaptive assessment, a Q-learning state is constructed, and the Q-value table is updated according to the learning state. Successful historical data is then updated based on the updated Q-value table. The next generation size is updated using a linear population reduction strategy, and the number of times the current function is evaluated is returned to check if it is less than the maximum allowed value, until the optimal solution is output.

8. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 7, characterized in that, The successful historical data is represented by the next generation generated by the M-LSHADE algorithm based on multi-objective environment selection and Pareto relation, and the next generation is represented by the Pareto solution set: ； EnvSelect indicates that individuals with lower rank are preferred. This represents the merging of the parent and child generations, where... Indicates the parent generation. Indicated as offspring.

9. A robot trajectory and posture optimization method based on comprehensive posture performance indicators according to claim 8, characterized in that, The process of obtaining a new candidate set includes: For each individual First, Q-learning selects the index. Then, the crossover rate and scaling factor are generated: ； ； in, Indicates a normal distribution. Represents the Cauchy distribution sampling operator; The mutation operator adopts the current-to-pbest / 1 form and introduces external memory A. The best subset of the current population is randomly selected. and randomly select and Construct the mutation vector: ； Among them, the This is the new candidate set.

10. A robot trajectory and posture optimization method based on comprehensive posture performance indicators according to claim 9, characterized in that, An adaptive evaluation is performed on the new candidate set, and the function evaluation count is updated based on the number of adaptive evaluations, including: The new candidate set is adaptively evaluated based on the Q-learning algorithm, and the number of function evaluations is assigned according to the number of adaptive evaluations.

11. The robot trajectory and posture optimization method based on comprehensive posture performance index according to claim 1, characterized in that, Updating the next generation size using a linear population reduction strategy includes: ； in, This refers to the size of the G+1 generation population. This is a rounding function. This represents the initial population size for the algorithm. For the minimum allowed population size, The number of times the function has been evaluated so far. The maximum number of function evaluations is preset for the algorithm, when At that time, The algorithm reduces the number of solutions based on the non-dominated level and the crowding distance until the size constraint is met, and then outputs the optimal solution.

12. A robot trajectory and posture optimization device based on comprehensive posture performance indicators, characterized in that, The device includes: The first construction module is used to construct the translational deformation vector of the robot running in a non-singular configuration based on the robot joint stiffness model, and to construct the deformation energy model based on the translational deformation vector and the external force analysis of the grinding wheel. The second construction module is used to construct an operability index based on the translation speed and joint penalty factor of the robot grinding process, wherein the joint penalty factor is used to characterize scaling operability. The third construction module is used to construct a comprehensive attitude performance index based on the deformation energy model and the operability index. The fourth construction module is used to construct a discrete point set including several grinding points based on the grinding trajectory of the robot. The optimization objective is to maximize the sum of the comprehensive posture performance index of the discrete point set and minimize the cumulative amount of joint changes on the grinding trajectory. Combined with joint angle limit constraints and joint rated speed constraints, a grinding trajectory optimization model is constructed. The solution module is used to solve the grinding trajectory optimization model using the M-LSHADE algorithm based on the Q-learning model to obtain the optimized trajectory pose.

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