Track optimization method and system considering redundancy characteristics of robot macro-micro force control grinding and polishing system

Abstract

The invention belongs to the field of robot trajectory optimization, and particularly relates to a trajectory optimization method and system considering redundancy characteristics of a robot macro-micro force control grinding and polishing system. The method comprises the following steps: S1, generating an initial grinding and polishing track based on a CAD model, and providing a discrete point curvature estimation method to estimate the curvature of each path point; s2, on the basis of the curvature of the discrete points, a mixed optimization target of a curve energy item and a curvature change rate about curvature square is constructed, arc length and redundancy direction optimization constraints are considered, and an adjusted grinding and polishing track is generated through a nonlinear optimization method; s3, on the basis of the optimized initial points, an initial dominant point selection method based on an angle-chord height-chord length joint criterion is adopted, and the trajectory precision is kept while the number of dominant points is reduced; and S4, on the basis of the optimized curved surface dominant points, an improved least square iterative approximation method is provided to generate a parameterized B-spline grinding and polishing path generation method, and final grinding and polishing track generation is achieved.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of robot trajectory optimization, and particularly relates to a trajectory optimization method and system that takes into account the redundancy characteristics of a robot's macro-micro force-controlled grinding and polishing system. Background Technology

[0002] Robotic macro-micro force-controlled grinding and polishing systems are widely used in grinding and polishing complex curved surfaces due to their advantages of high flexibility, high adaptability, and high force control precision. The generation and smoothing of the robot's grinding and polishing trajectory is a crucial step in ensuring the smoothness of robot motion. Existing robot grinding and polishing trajectory generation typically considers the theoretical model of the part to be ground and polished, generating the trajectory through discretization using B-spline direct interpolation. This approach does not consider the motion redundancy inherent in macro-micro robot force-controlled grinding and polishing systems. Utilizing this motion redundancy can effectively improve the actual smoothness of the grinding and polishing trajectory and the speed accuracy of grinding. Furthermore, the improved smoothness of the actual grinding and polishing trajectory further reduces the interference of the robot body on the force control actuator, which helps improve the precision of grinding force control during the grinding and polishing process. Moreover, existing B-spline direct interpolation methods for generating parametric curves do not consider the curvature distribution of the trajectory, easily leading to local curvature oscillations.

[0003] The relevant patent found is CN118848975A (A method and device for trajectory planning and optimization of a grinding robot based on machine vision).

[0004] This patent discloses a method for optimizing robot grinding trajectory planning, mainly including:

[0005] Point cloud data of the polishing area is acquired using a 3D vision inspection system to determine the Cartesian coordinates of the joints and the joint coordinates obtained through inverse kinematics.

[0006] Based on the identified features of the polishing area (such as straight lines / arcs in the edge area, and planes / simple or complex surfaces in the surface area), a trajectory planning strategy (linear interpolation, circular interpolation, or B-spline interpolation) is determined and trajectory generation is performed.

[0007] A multi-objective optimization function is established, which includes constraints on joint angle, angular velocity, angular acceleration, angular jerk, and joint torque. An improved multi-objective genetic algorithm is then used to solve for the optimal trajectory.

[0008] Existing technical problems:

[0009] 1. Redundant degrees of freedom and redundant directional constraints were not adequately considered.

[0010] Although this patent combines visual recognition and inverse kinematics, and constructs optimization targets using joint motion indicators (angle, velocity, acceleration, torque), it does not specifically optimize redundant directions or redundant space utilization for redundant degrees of freedom of the robot system (e.g., arm DOF is greater than the task space dimension). In other words, in trajectory planning, it lacks constraints and objectives on how redundant joints are optimized in the free subspace (e.g., avoiding joint limits, avoiding singularities, optimizing Jacobian condition numbers, or joint loads).

[0011] 2. The integration of path geometric features (such as curvature and rate of change of curvature) and parametric B-spline trajectory generation is relatively low.

[0012] While this patent proposes selecting interpolation methods (straight lines, circular arcs, B-splines) based on the characteristics of the polishing zone for trajectory planning, its focus is on visual recognition, joint motion optimization, and multi-objective genetic algorithms. It involves less attention to path geometry discretization (e.g., extracting at constant arc length, calculating the curvature of discrete points, and constructing optimization objectives based on curvature or the rate of change of curvature) and coupling it with parametric B-spline trajectory generation methods. In other words, its technical development in trajectory smoothness, geometric continuity (e.g., C² continuity), and the optimization conversion from discrete points to parametric curves (B-splines) is insufficient. Summary of the Invention

[0013] To address the problems existing in the prior art, this invention provides a trajectory optimization method and system that considers the redundancy characteristics of a robot macro-micro force-controlled grinding and polishing system.

[0014] This invention is implemented as follows: a trajectory optimization method considering the redundancy characteristics of a robot's macro-micro force-controlled grinding and polishing system, the method comprising:

[0015] S1. Based on the CAD model, the initial polishing trajectory is generated, and a discrete point curvature estimation method is proposed to estimate the curvature of each path point.

[0016] S2, based on discrete point curvature, constructs a hybrid optimization objective of curve energy term and curvature change rate with respect to the square of curvature, considers arc length and redundant direction optimization constraints, and generates the adjusted grinding and polishing trajectory through nonlinear optimization method;

[0017] S3, based on the optimized initial point, adopts an initial dominant point selection method based on the joint criterion of angle-chord height-chord length, which reduces the number of dominant points while maintaining trajectory accuracy;

[0018] S4. Based on the selected dominant points of the surface, an improved least-squares iterative approximation method is proposed to generate a parameterized B-spline polishing path generation method, thereby realizing the final polishing trajectory generation.

[0019] Furthermore, step S1 specifically includes:

[0020] Based on the CAD model of the initially polished part, according to a constant arc length interval Generate the initial point of the polishing trajectory , Let represent the i-th path point, and n represent the number of path points; use The deflection angle of path point i can be calculated using the following formula:

[0021] (1)

[0022] in Let i and i represent the (i-1), i, and i+1th path points, respectively.

[0023] Based on geometric relationships, the curvature at trajectory point i can be calculated using the following expression. :

[0024] (2)

[0025] Furthermore, the specific steps in step S2 are as follows:

[0026] Step S1 above can estimate the curvature of discrete path points; in order to achieve trajectory smoothing considering the redundancy characteristics of robot macro-micro force-controlled grinding and polishing, the following optimization objective function is first established:

[0027] (3)

[0028] in Let be the objective function. and These are the weighting coefficients. Based on the discrete curvature estimation method of the curves mentioned above, the optimization objective can be expressed in discrete form as follows:

[0029] (4)

[0030] To ensure that the grinding and polishing positions remain unchanged before and after optimization, the optimization direction should be consistent with the redundancy direction of the grinding and polishing system; that is, the line connecting the optimized path point and the initial path point must coincide with the direction of the normal vector of the initial point on the curved part.

[0031] (5)

[0032] in Indicates the optimized path points. This represents the normal vector at a path point. This represents the offset of the path point, and is also the optimization variable in the formula;

[0033] Meanwhile, to ensure that the optimized grinding path does not deviate significantly from the original path length, thereby guaranteeing the robot's motion efficiency, the following constraint is applied to the optimized arc length:

[0034] (6)

[0035] in, This represents the total arc length of the optimized path point. This represents the total length of the initial path. It is the allowable deviation of arc length. and It can be calculated using the following formula:

[0036] (7)

[0037] Meanwhile, to ensure that the optimized grinding and polishing trajectory points remain within the working range of the force-controlled actuator, the following smooth boundary constraints were applied:

[0038] (8)

[0039] The final trajectory optimization equation for robotic grinding and polishing considering the redundancy characteristics of macro- and micro-force-controlled grinding and polishing is expressed as follows:

[0040] (9)

[0041] The above optimization can be solved using a nonlinear programming algorithm to obtain the optimal path points that satisfy the constraints.

[0042] Furthermore, step S3 specifically involves the following steps:

[0043] Because the spacing between the adjusted initial points is very small, directly performing spline interpolation may cause the curve to bend sharply to pass through all path points, potentially leading to high-frequency curvature oscillations. To address this issue, an initial dominant point selection method based on a joint criterion of angle-chord height-chord length is adopted for subsequent spline fitting. This method effectively preserves the geometric features of the path, such as corners, turns, and line segment transitions. It has stronger shape preservation capabilities and can reduce the number of control points while maintaining trajectory accuracy. The specific steps are as follows:

[0044] (1) The initial dominant point is set as all discrete trajectory points optimized in step S2. Set the allowed angle threshold chord height threshold Chord length threshold ;

[0045] (2) Select three consecutive data points starting from the initial point. , and Then calculate the vector and Angle between Chord height String length and :

[0046] (10)

[0047] (3) If , and If all conditions are met, then Deemed redundant and deleted; set the next point as new. , and ,if If the data does not exist, the data selection process is complete; otherwise, please continue to step (2).

[0048] (4) If , and Not all conditions are met, settings and Set the next new location ,if If the data does not exist, the data selection process is complete; otherwise, please continue to step (2).

[0049] Furthermore, step S4 specifically involves the following steps:

[0050] As described above, after selecting from the initial path points, a set of refined initial dominant points is obtained. This method preserves the key features of the path while reducing redundancy. Traditional spline generation methods usually rely on direct interpolation of initial control points to generate trajectories. Although this ensures that the generated spline accurately passes through discrete points, it often introduces local curvature oscillations due to overfitting, especially in regions where the points are closely spaced. To obtain a smoother trajectory, an improved least-squares asymptotic iterative approximation method is used to perform spline fitting on the selected path points.

[0051] First, the centripetal method is used to construct the normalized parameter values ​​for each path point.

[0052] (11)

[0053] Where m is the number of initial dominators;

[0054] To achieve a parameterized representation of the spline trajectory, a cubic B-spline is used to construct the polishing trajectory; an iterative method is employed to adjust the control points of the B-spline fitting. The initial form of the B-spline curve is defined as follows:

[0055] (12)

[0056] in This represents the control points of the B-spline curve, whose initial values ​​are set to the dominant point f selected in step S3, and k is the iteration number. It is a basis function of the spline curve and can be calculated as:

[0057] (13)

[0058] in It is a node vector, which can be calculated using the following formula:

[0059] (14)

[0060] Combining the above formulas, the trajectory spline points fitted relative to the parameters can be calculated using the following expression:

[0061] (15)

[0062] To achieve high-precision fitting of the initial path points, traditional least-squares iterative approximation fitting methods typically optimize by minimizing the position error:

[0063] (16)

[0064] Traditional fitting methods only minimize the distance between path points and spline curves without constraining the changing trend of the control point sequence; this often leads to oscillations in the control points, resulting in unwanted curvature fluctuations. To suppress this geometric irregularity, this patent introduces a regularization term based on the second-order difference of the control points:

[0065] (17)

[0066] Furthermore, through mathematical transformations, the second-order difference matrix can be reformulated as:

[0067] (18)

[0068] By combining the introduced second-order difference regularization term with the traditional fitting method, the optimization objective of the improved least squares fitting method proposed in this patent can be expressed as:

[0069] (19)

[0070] in This is the smoothing weight parameter; the larger the value, the smoother the fitted spline curve; the iterative update equation is given by the following formula:

[0071] (20)

[0072] in It is the convergence factor. It is a matrix eigenvalue calculation function;

[0073] The maximum pointwise fitting error is introduced as the stopping criterion; at iteration number k, the fitting error is defined as:

[0074] (twenty one)

[0075] The iteration terminates when the maximum fitting error falls below a predefined threshold.

[0076] (twenty two)

[0077] in This is a user-specified tolerance, set to 0.01mm in this patent;

[0078] By employing the improved least-squares-based iterative approximation method described above, the discrete robot path can be parameterized to obtain the final position spline; similarly, the orientation spline can also be calculated using the same processing method.

[0079] Another objective of this invention is to provide a trajectory optimization system that considers the redundancy characteristics of a robot's macro-micro force-controlled grinding and polishing system, for implementing the aforementioned trajectory optimization method that considers the redundancy characteristics of such a system. This system includes:

[0080] The initial point adjustment module for the grinding and polishing trajectory establishes a curvature-based hybrid objective equation based on the robot's initial motion path, thereby optimizing the initial grinding and polishing trajectory by considering the redundant kinematics of macro-micro systems.

[0081] The grinding and polishing trajectory parameterized B-spline construction module adjusts the initial path points generated by the initial point adjustment module based on the initial point of the grinding and polishing trajectory, selects the final dominant path point based on the joint criterion of angle-chord height-chord length, and generates the final smooth grinding and polishing path through an improved least squares iterative approximation method.

[0082] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, the computer program being executed by the processor causing the processor to perform the steps of the trajectory optimization method considering the redundancy characteristics of the robot macro-micro force control grinding and polishing system.

[0083] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the trajectory optimization method that takes into account the redundancy characteristics of a robot macro-micro force-controlled grinding and polishing system.

[0084] Another objective of this invention is to provide an information data processing terminal, characterized in that the information data processing terminal is used to implement the trajectory optimization system that takes into account the redundancy characteristics of the robot's macro-micro force control grinding and polishing system.

[0085] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0086] This invention addresses a typical robot path planning problem by considering the redundancy characteristics in a compliant force-controlled grinding and polishing system for macro and micro robots, thereby achieving a smooth grinding and polishing path.

[0087] The expected benefits and commercial value of the technical solution of this invention after transformation are as follows: This invention proposes a trajectory optimization method that considers the redundancy characteristics of a robot's macro-micro force-controlled grinding and polishing system. In practical commercial applications, it can be mainly applied to the field of industrial automation to improve the trajectory smoothness of the robot's compliant force-controlled grinding and polishing, improve processing quality, and increase product yield.

[0088] The technical solution of this invention fills a technical gap in the industry both at home and abroad: existing robotic macro-micro force-controlled grinding and polishing systems do not consider the redundancy characteristics that exist in the grinding and polishing process when making path planning, which makes it impossible for macro-micro robots to fully achieve smooth motion, thus affecting the grinding and polishing quality.

[0089] The method provided in this invention solves several problems of existing technologies in industrial applications and brings about significant technological advancements. The following is a detailed explanation of these advancements and problem-solving: 1) Solving technical problems: Full utilization of redundant degrees of freedom in macro-micro systems: Existing methods do not consider this redundant degree of freedom when optimizing compliant force-controlled grinding and polishing paths, limiting the smoothness of the planned grinding and polishing path and the actual processing quality. 2) Technological advancements: Improving the smoothness of grinding and polishing trajectories: By considering the redundant degrees of freedom in grinding and polishing, the curvature of the robot path during actual grinding and polishing can be reduced, improving grinding and polishing efficiency and quality. The technical solution of this invention, while solving the problems of existing technologies, brings about significant technological advancements and provides strong support for the industrial applications of robots. Attached Figure Description

[0090] Figure 1 This is a flowchart of the robot grinding and polishing path optimization provided in an embodiment of the present invention;

[0091] Figure 2 A schematic diagram of the grinding and polishing blade path provided for the implementation of this invention;

[0092] Figure 3 A comparison of the path and path curvature provided in the embodiments of the present invention with the comparison method;

[0093] Figure 4The present invention provides a comparison of the planning and polishing force and speed of the comparative method. Detailed Implementation

[0094] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0095] like Figure 1 As shown, this embodiment of the invention provides a robot time-optimal velocity planning method based on two-step linear programming, the method comprising:

[0096] S1. Based on the CAD model, the initial polishing trajectory is generated, and a discrete point curvature estimation method is proposed to estimate the curvature of each path point.

[0097] S2, based on discrete point curvature, constructs a hybrid optimization objective of curve energy term and curvature change rate with respect to the square of curvature, considers arc length and redundant direction optimization constraints, and generates the adjusted grinding and polishing trajectory through nonlinear optimization method;

[0098] S3, based on the optimized initial point, adopts an initial dominant point selection method based on the joint criterion of angle-chord height-chord length, which reduces the number of dominant points while maintaining trajectory accuracy;

[0099] S4. Based on the selected dominant points of the surface, an improved least-squares iterative approximation method is proposed to generate a parameterized B-spline polishing path generation method, thereby realizing the final polishing trajectory generation.

[0100] Furthermore, step S1 generates an initial grinding and polishing trajectory based on the CAD model, and proposes a discrete point curvature estimation method to estimate the curvature of each path point. Specifically, based on the CAD model of the initial grinding and polishing part, the curvature is estimated according to a constant arc length interval. Generate the initial point of the polishing trajectory , Let represent the i-th path point, and n represent the number of path points. The deflection angle of path point i can be calculated using the following formula:

[0101] (1)

[0102] in Let i and i represent the (i-1), i, and i+1th path points, respectively.

[0103] Based on geometric relationships, the curvature at trajectory point i can be calculated using the following expression. :

[0104] (2)

[0105] Furthermore, in step S2, a hybrid optimization objective is constructed based on the curvature of discrete points, which combines the curve energy term with the rate of change of curvature, considering arc length and redundant direction optimization constraints. An adjusted grinding and polishing trajectory is then generated using a nonlinear optimization method. Specifically, step S1 above can estimate the curvature of discrete path points. To achieve trajectory smoothing that considers the redundancy characteristics of the robot's macro- and micro-force-controlled grinding and polishing, the following optimization objective function is first established:

[0106] (3)

[0107] in Let be the objective function. and These are the weighting coefficients. Based on the discrete curvature estimation method for the above curves, the optimization objective can be expressed in discrete form as follows:

[0108] (4)

[0109] To ensure that the grinding and polishing positions remain unchanged before and after optimization, the optimization direction should be consistent with the redundancy direction of the grinding and polishing system. That is, the line connecting the optimized path point and the initial path point must coincide with the direction of the normal vector of the initial point on the curved part.

[0110] (5)

[0111] in Indicates the optimized path points. This represents the normal vector at a path point. This represents the offset of the path point and is also the optimization variable in the formula.

[0112] Meanwhile, to ensure that the optimized grinding path does not deviate significantly from the original path length, thereby guaranteeing the robot's motion efficiency, the following constraint is applied to the optimized arc length:

[0113] (6)

[0114] in, This represents the total arc length of the optimized path point. This represents the total length of the initial path. It is the allowable deviation of arc length. and It can be calculated using the following formula:

[0115] (7)

[0116] Meanwhile, to ensure that the optimized grinding and polishing trajectory points remain within the working range of the force-controlled actuator, the following smooth boundary constraints were applied:

[0117] (8)

[0118] The final trajectory optimization equation for robotic grinding and polishing considering the redundancy characteristics of macro- and micro-force-controlled grinding and polishing is expressed as follows:

[0119] (9)

[0120] The above optimization can be solved using a nonlinear programming algorithm to obtain the optimal path points that satisfy the constraints.

[0121] Furthermore, in step S3, based on the optimized initial points, an initial dominant point selection method based on the angle-chord height-chord length joint criterion is adopted to maintain trajectory accuracy while reducing the number of dominant points. Specifically, since the spacing between the adjusted initial points is very small, directly performing spline interpolation may cause the curve to bend sharply to pass through all path points, potentially leading to high-frequency curvature oscillations. To address this issue, this patent employs an initial dominant point selection method based on the angle-chord height-chord length joint criterion for subsequent spline fitting. This method effectively preserves the geometric features of the path, such as corners, turns, and line segment transitions. It has stronger shape preservation capabilities and can reduce the number of control points while maintaining trajectory accuracy. The specific steps are as follows:

[0122] 1. The initial dominant points are set as all discrete trajectory points optimized in step S2. Set the allowed angle threshold. chord height threshold Chord length threshold .

[0123] 2. Select three consecutive data points starting from the initial point. , and Then, calculate the vector. and Angle between Chord height String length and :

[0124] (10)

[0125] 3. If , and If all conditions are met, then It was deemed redundant and deleted. The next location was set as the new one. , and ,if If the data does not exist, the data selection process is complete; otherwise, please continue to step 2.

[0126] 4. If , and Not all conditions are met, settings and Set the next new location ,if If the data does not exist, the data selection process is complete; otherwise, please continue to step 2.

[0127] Furthermore, in step S4, based on the selected dominant points of the surface, an improved least-squares iterative approximation method is proposed to generate a parameterized B-spline polishing path, thus achieving the final polishing trajectory generation. The specific steps are as follows:

[0128] As described above, after selecting from the initial path points, a refined set of initial dominant points is obtained. This method preserves the key features of the path while reducing redundancy. Traditional spline generation methods typically rely on direct interpolation of initial control points to generate the trajectory. While this ensures that the generated spline accurately passes through discrete points, it often introduces local curvature oscillations due to overfitting, especially in regions where the points are closely spaced. To obtain a smoother trajectory, this patent employs an improved least-squares asymptotic iterative approximation method to perform spline fitting on the selected path points.

[0129] First, the centripetal method is used to construct the normalized parameter values ​​for each path point.

[0130] (11)

[0131] To achieve a parameterized representation of the spline trajectory, this work uses cubic B-splines to construct the grinding and polishing trajectory. An iterative method is employed to adjust the control points for the B-spline fitting. The initial form of the B-spline curve is defined as follows:

[0132] (12)

[0133] in represents the control points of the B-spline curve, whose initial values ​​are set to the dominant point f selected in step S3. k is the iteration number. It is a basis function of the spline curve and can be calculated as:

[0134] (13)

[0135] in It is a node vector, which can be calculated using the following formula:

[0136] (14)

[0137] Combining the above formulas, the trajectory spline points fitted relative to the parameters can be calculated using the following expression:

[0138] (15)

[0139] To achieve high-precision fitting of the initial path points, traditional least-squares iterative approximation fitting methods typically optimize by minimizing the position error:

[0140] (16)

[0141] Traditional fitting methods only minimize the distance between path points and spline curves without constraining the changing trend of the control point sequence. This often leads to oscillations in the control points, resulting in unwanted curvature fluctuations. To suppress this geometric irregularity, this patent introduces a regularization term based on the second-order difference of the control points:

[0142] (17)

[0143] Furthermore, through mathematical transformations, the second-order difference matrix can be reformulated as:

[0144] (18)

[0145] By combining the introduced second-order difference regularization term with the traditional fitting method, the optimization objective of the improved least squares fitting method proposed in this patent can be expressed as:

[0146] (19)

[0147] in This is the smoothing weight parameter; the larger the value, the smoother the fitted spline curve. The iterative update equation is given by the following formula:

[0148] (20)

[0149] in It is the convergence factor. It is a matrix eigenvalue calculation function.

[0150] The maximum pointwise fitting error is introduced as a stopping criterion. At iteration number k, the fitting error is defined as:

[0151] (twenty one)

[0152] The iteration terminates when the maximum fitting error falls below a predefined threshold.

[0153] (twenty two)

[0154] in It is a user-specified tolerance, which is set to 0.01mm in this patent.

[0155] By employing the improved least-squares-based iterative approximation method described above, the discrete robot path can be parameterized to obtain the final position spline. Similarly, the orientation spline can be calculated using the same method.

[0156] Industrial Application Example 1: Robotic Compliant Force-Controlled Grinding and Polishing

[0157] In robotic compliant force-controlled grinding and polishing applications, further smoothing of the robot's grinding and polishing trajectory and further reduction of path curvature can effectively improve grinding and polishing efficiency, improve force and speed accuracy during the grinding and polishing process, and ultimately improve grinding and polishing quality.

[0158] The specific implementation steps include:

[0159] 1) Discrete curvature estimation of initial points: Based on the robot's grinding and polishing path, the initial curvature of each point is generated by the discrete point curvature estimation method.

[0160] 2) Path point adjustment method considering redundancy in macro-micro systems: Based on the curvature of discrete points, a hybrid optimization objective is constructed, which combines the curve energy term with the rate of change of curvature and the curvature square. Considering the optimization constraints of arc length and redundant direction, the adjusted grinding and polishing trajectory is generated through nonlinear optimization.

[0161] 3) B-spline parameterized fitting of polishing trajectory: Based on the optimized initial points, an initial dominant point selection method based on the angle-chord height-chord length joint criterion is adopted to reduce the number of dominant points while maintaining trajectory accuracy; based on the selected surface dominant points, an improved least squares iterative approximation method is proposed to generate a parameterized B-spline polishing path generation method to achieve the final polishing trajectory generation.

[0162] This method can effectively improve the smoothness of the robot's grinding and polishing path movement and increase grinding and polishing efficiency.

[0163] like Figure 2 The diagram shown is a schematic diagram of the grinding and polishing blade path provided in the embodiment of the present invention;

[0164] Figure 3 and Figure 4 The figure shows a comparison of the curvature of the grinding and polishing path generation path and the planned grinding and polishing force and velocity between the present invention and the traditional method. It shows that the proposed method can effectively reduce the curvature of the grinding and polishing trajectory, improve the smoothness of the grinding and polishing, and thus improve the grinding and polishing efficiency.

[0165] This invention provides a trajectory optimization method and system considering the redundancy characteristics of a robot's macro-micro force-controlled grinding and polishing system. The system includes:

[0166] Initial point adjustment module for grinding and polishing trajectory: Based on the robot's initial motion path, a curvature-based hybrid objective equation is established to optimize the initial grinding and polishing trajectory considering the redundant kinematics of macro and micro systems.

[0167] The grinding and polishing trajectory parameterized B-spline construction module adjusts the initial path points generated by the initial point adjustment module based on the initial point of the grinding and polishing trajectory, selects the final dominant path point based on the joint criterion of angle-chord height-chord length, and generates the final smooth grinding and polishing path through an improved least squares iterative approximation method.

[0168] This invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the trajectory optimization method that considers the redundancy characteristics of a robot macro-micro force-controlled grinding and polishing system.

[0169] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the trajectory optimization method considering the redundancy characteristics of a robot macro-micro force-controlled grinding and polishing system.

[0170] This invention provides an information data processing terminal, which is used to implement the trajectory optimization system that takes into account the redundancy characteristics of the robot's macro-micro force control grinding and polishing system.

[0171] To verify the effectiveness of the proposed trajectory optimization algorithm, it is compared with traditional path generation methods that do not consider the redundancy characteristics of macro and micro systems. Under the same parameter settings, the optimization results are as follows: Figure 3 As shown, the optimized total path length is 98.843 mm, while the original length was 97.843 mm, thus satisfying the constraint allowing for variations in path arc length. Figure 3 As shown, the maximum curvature of the two blade edge regions decreased from 1.87 mm and 5.07 mm to 0.57 mm and 0.60 mm, respectively, representing reductions of 69.52% and 8.17%. This indicates that the trajectory optimization method considering the redundancy characteristics of the robotic macro-micro force-controlled grinding and polishing system can effectively reduce curvature. Furthermore, compared to comparative methods, the proposed method significantly reduces blade curvature fluctuations. This demonstrates that the proposed dominant point selection strategy, combined with the improved least-squares iterative approximation fitting method, can generate smoother parametric splines and mitigate curvature oscillations caused by overfitting due to excessively dense trajectory points in direct interpolation methods.

[0172] like Figure 4As shown, for a blade path with an arc length of 98.7 mm, the optimization results show that the average feed rate increases from 1.69 mm / s to 2.34 mm / s, the motion time decreases from 58.04 s to 42.06 s, and the grinding efficiency improves by 27.53%. This improvement is attributed to the reduction of curvature extrema achieved by the proposed trajectory optimization method that considers the redundancy characteristics of the robotic macro-micro force-controlled grinding and polishing system. It can be seen that the grinding force command planned by the proposed method is smoother. This is due to the smooth curvature of the fitted path brought about by the proposed spline parameterization smoothing method.

[0173] The specific application field of this invention is the optimization method of the grinding and polishing process path in robot compliant force-controlled grinding and polishing. It mainly optimizes the redundant degrees of freedom of the robot grinding and polishing system under the consideration of the redundancy characteristics of the macro-micro force-controlled robot grinding and polishing system to achieve further smoothing of the robot grinding and polishing path, thereby improving the accuracy of grinding and polishing force-speed coordination, improving the accuracy of grinding and polishing material removal, and realizing high-precision grinding and polishing of complex curved surface parts.

[0174] Example 1: Nonlinear Trajectory Smoothing Optimization Based on Macro-Micro Force Control Redundancy Constraints

[0175] In this embodiment, a CAD model of a complex curved surface part (such as a turbine blade) is selected as the grinding and polishing object. Initial trajectory points are extracted on the curved surface at constant arc length intervals. The local curvature is calculated using discrete three-point geometric relationships: the curvature value of each point is obtained by the ratio of the rate of change of the included angle of three adjacent points to the distance between the arc lengths of the path, thus achieving discrete estimation of the curvature distribution.

[0176] Based on this, an initial grinding and polishing trajectory is generated using computer-aided manufacturing software, and the trajectory remains consistent with the surface normal on the CAD model. This achieves the input of the initial grinding and polishing path consistent with the pose of the robot-end flange, laying the foundation for subsequent nonlinear optimization and B-spline parameterization. Supporting claims 1 and 2, this demonstrates the feasibility and necessity of the discrete point curvature estimation method in trajectory preprocessing.

[0177] To address the redundancy characteristics of the end effector in macro-micro force-controlled robots, a hybrid optimization objective function was constructed. The objective function consists of a linear combination of a curvature square term and a curvature change rate square term. The first term penalizes abrupt curvature changes, while the second term controls the curvature change rate to smooth the trajectory. Constraints include: the path point optimization direction coincides with the normal direction; and the path point offset distance does not exceed the effective stroke of the actuator.

[0178] The objective function described above is solved using a nonlinear programming algorithm (such as Sequential Quadratic Programming, SQP) to obtain the smoothed trajectory point set. Under the same parameter settings, the optimization results are as follows: Figure 3 As shown, the optimized total path length is 98.843 mm, while the original length was 97.843 mm, thus satisfying the constraint allowing for variations in path arc length. Figure 3 As shown, the maximum curvature of the two blade edge regions decreased from 1.87 mm and 5.07 mm to 0.57 mm and 0.60 mm, respectively, representing reductions of 69.52% and 8.17%. This indicates that the trajectory optimization method considering the redundancy characteristics of the robotic macro-micro force-controlled grinding and polishing system can effectively reduce curvature. Supporting claims 1 and 2, this verifies that the curvature optimization strategy based on redundant direction constraints can effectively improve the smoothness and controllability of the grinding and polishing trajectory.

[0179] Example 2: An improved least-squares iterative approximation method for generating parameterized B-spline polishing paths.

[0180] This embodiment uses a three-threshold joint judgment criterion of angle, chord height, and chord length to screen dominant points in the optimized trajectory point set. This process automatically retains points of abrupt changes in trajectory geometric features, such as corners and turning points, thus minimizing the number of dominant points while preserving the curve shape. This embodiment supports claim 3, demonstrating that the dominant point screening mechanism based on the joint criterion can effectively eliminate redundant points and maintain surface features.

[0181] After screening, the number of dominant points was reduced from the original 491 to approximately 292, and the chord height was controlled within 0.002 mm. The results show that this method significantly reduces the number of spline fitting control points while preserving the trajectory's geometric characteristics, thus improving the efficiency of subsequent spline fitting. This embodiment supports claim 5, demonstrating that the dominant point screening mechanism based on the joint criterion can effectively eliminate redundant points while maintaining surface features.

[0182] A cubic B-spline function is used to fit the dominant points, and high-precision fitting is achieved by iteratively optimizing the control point positions. The fitting objective is to minimize the squared error between the trajectory points and the spline curve, while a regularization term for the second-order difference of the control points is introduced to limit control point oscillations. The smoothing weight parameter is set to 0.3, the convergence factor is 0.8, and the maximum fitting error threshold is 0.01 mm.

[0183] Experimental results show that, Figure 4 As shown, for a blade path with an arc length of 98.7 mm, the optimization results show that the average feed rate increases from 1.69 mm / s to 2.34 mm / s, the motion time decreases from 58.04 s to 42.06 s, and the grinding and polishing efficiency improves by 27.53%. This improvement is attributed to the reduction of curvature extrema achieved by the proposed trajectory optimization method that considers the redundancy characteristics of the robot's macro-micro force-controlled grinding and polishing system. It can be seen that the grinding force command planned by the proposed method is smoother. This is due to the smooth curvature of the fitted path brought about by the proposed spline parameterization smoothing method. This embodiment supports claims 6 and 7, and the proposed algorithm ensures the efficiency and accuracy of robot compliant force-controlled grinding and polishing.

[0184] To further enhance the adaptability and intelligence of this invention in robotic macro-micro force-controlled grinding and polishing systems, this invention proposes three inventive extension schemes based on claim 1 to enrich the control logic and implementation methods for trajectory optimization.

[0185] Firstly, a trajectory adjustment scheme based on curvature-force feedback dual-domain coupling optimization is proposed. This scheme, building upon traditional geometric curvature optimization, incorporates real-time feedback of normal contact force data from a force control sensor. It jointly models trajectory smoothness optimization and force stability optimization, achieving mechanical compensation-based trajectory correction by adding a "force deviation square term" to the objective function. This balances geometric consistency and force uniformity during the polishing of complex curved surfaces. This method can dynamically balance curvature energy and force energy, improving the stability and surface quality of the polishing process.

[0186] Secondly, a surface trajectory smoothing strategy based on adaptive multi-scale piecewise optimization is proposed. This scheme employs different weight parameters and optimization step sizes for regions with large curvature changes and smooth regions, independently performing nonlinear optimization within each segment, and using C² continuity constraints at segment boundaries to achieve global smooth stitching. This method significantly reduces the computational burden of single global optimization on complex surfaces, improves the adaptability of the trajectory at both macro and micro scales, and can be effectively applied to the machining of complex surface parts by multi-axis composite robots.

[0187] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0188] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A trajectory optimization method considering redundancy characteristics of a robot macro-micro force control grinding and polishing system, characterized in that, The method comprises the following steps: (1) generating an initial polishing path based on a part CAD model, extracting path points according to constant arc length intervals, and calculating discrete point curvatures; (2) constructing a hybrid optimization objective with discrete curvature squares and curvature change rates, combining arc length constraints and redundant direction constraints, and generating a smooth path through nonlinear optimization; (3) selecting initial dominant points based on angle, chord height and chord length joint criteria; (4) generating a parametric B-spline path by using an improved least squares iterative approximation method.

2. The method of claim 1, wherein, In the calculation of the discrete point curvature, the curvature is the ratio of the change rate of the angle formed by the adjacent three path points to the arc length interval; That is, the curvature estimation value is obtained by dividing the included angle change of the three adjacent points by the arc length difference between the two points.

3. The method of claim 1, wherein, The hybrid optimization objective is composed of a curvature square term and a curvature change rate term, where the optimization objective function is equal to the sum of the first weight coefficient multiplied by the curvature square sum and the second weight coefficient multiplied by the curvature change rate square sum, and the optimization variable is the offset of the path point in the normal direction.

4. The method of claim 1, wherein, The optimization constraints include: (1) the connecting line direction of the optimization path point and the initial path point is consistent with the normal direction of the part surface; (2) the difference between the total arc length of the optimized path and the total arc length of the initial path does not exceed the preset arc length allowable deviation; (3) all optimized path points are located within the working range boundary of the force control actuator.

5. The method of claim 1, wherein, The selection of the initial dominant points is based on the joint judgment rule of the angle threshold, the chord height threshold and the chord length threshold, when the angle, the chord height and the chord length among any three consecutive points are all less than the respective threshold value, the middle point is deleted, so as to reduce the number of dominant points while maintaining the geometric shape features.

6. The method of claim 1, wherein, The B-spline polishing path is generated by using an improved least squares iterative approximation method, a cubic B-spline function form is adopted, and the initial dominant points are used as the control point initial values, the path points and the curve distance are minimized, and a second-order difference regularization term of the control points is applied for smooth fitting.

7. The method of claim 6, wherein, The regularization term is the square sum of the second-order difference of the control points multiplied by a smoothing weight parameter, the smoothing weight parameter is used to adjust the smoothness of the curve, and the greater the weight, the smoother the curve, and the iteration is terminated when the final fitting error is lower than the predefined tolerance. 8.A robot polishing trajectory optimization system based on macro-micro force control redundancy constraint, characterized in that, It comprises: a CAD modeling module, a curvature estimation module, a nonlinear path optimization module, a dominant point selection module and a spline fitting module; wherein the modules are connected in sequence, the CAD modeling module is used to generate an initial path, the curvature estimation module is used to calculate the discrete point curvature, the nonlinear path optimization module is used to optimize the path under the redundant constraint, the dominant point selection module is used to select the dominant points, and the spline fitting module is used to generate the final smooth polishing path.

9. The system of claim 8, wherein, The nonlinear path optimization module uses a nonlinear programming algorithm, constructs a hybrid optimization objective function according to the discrete curvature, and solves to obtain the optimized path points under the conditions of satisfying the normal, arc length and boundary constraints.

10. A computer readable storage medium storing a computer executable program, wherein the program comprises the steps of: When the program is executed by the processor, the trajectory optimization method considering the redundant characteristics of the robot macro-micro force control polishing system is realized.

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