A dual hybrid robot mirror image processing equipment trajectory planning method

Abstract

The application discloses a kind of double hybrid robot mirror image processing equipment trajectory planning methods, steps are as follows, double machine tool tip point position path, same point position path on tool shaft is defined in Cartesian coordinate system;Double hybrid robot double tool tip point and double tool shaft point path, four tool tip point paths and same point paths on tool shaft are all fitted fair with spline curve, introduce fitting error evaluation method, reduce fitting error by adjusting control point, determine final double robot four Nurbs curve;Adopt cubic B spline to express double machine speed curve, introduce synchronous coordination processing constraint, joint constraint, tool shaft constraint and tool tip point speed, acceleration, jerk threshold value, obtain double machine speed curve control point using improved iterative optimization algorithm, ensure that speed curve satisfies multiple constraints.The application realizes the trajectory planning process of double hybrid robot mirror image processing equipment, takes time optimization as objective function, greatly improves processing efficiency, and meets accuracy requirement.

Description

Technical Field

[0001] This invention relates to the field of robotic machining, and in particular to a trajectory planning method for a dual-hybrid robot mirror machining equipment. Background Technology

[0002] Variable wall thickness parts (such as engine blades) are widely used in aerospace and energy equipment, and are key components for improving equipment performance and efficiency. These parts typically have complex spatial curved surfaces and varied wall thickness distributions, placing extremely high demands on their machining. They must not only meet stringent geometric accuracy requirements but also ensure a smooth surface finish. To address this issue, two industrial robots and a dual-tool system are integrated into a single machining platform to achieve simultaneous machining of the part's internal and external contour surfaces. This machining mode offers the following significant advantages: First, it eliminates the secondary flipping step in traditional machining, effectively reducing positioning errors; second, the collaborative cutting by the dual tools significantly improves machining efficiency and shortens the production cycle.

[0003] The research on trajectory planning for dual-hybrid robot mirror machining equipment needs to solve two types of problems: (1) path planning for dual-hybrid robot mirror machining equipment; (2) speed planning for dual-hybrid robot mirror machining equipment. In terms of path planning for dual-hybrid robot mirror machining, existing methods are divided into two categories. One type uses the same point on a rigid iron bar to represent the path between the tool position point and the tool axis point of the dual-hybrid robot, and then generates four path curves from one path curve according to the equidistant condition, but it is only applicable to the machining of curved surfaces with equal wall thickness; the other type uses the redundant degrees of freedom of the robot to balance the stiffness requirements of the robot during machining, but since the application object of the robot has changed, it is not applicable to this dual-hybrid robot mirror machining equipment. Therefore, there is an urgent need for a path planning method that can improve computational efficiency and meet the requirements of collaborative machining.

[0004] In terms of speed planning, there are two solutions: one is to achieve coordinated processing through iterative optimization algorithms, but the amount of computation increases significantly; the other is to only consider synchronization constraints, which does not meet the goal of time optimization. Therefore, there is an urgent need for an iterative method that can meet the time optimization of dual-machine coordinated processing speed planning and reduce the amount of computation generated by iteration. Summary of the Invention

[0005] To address the above problems, this invention provides a trajectory planning method for a dual-hybrid robot mirror processing equipment, solving the problem of processing path planning for mirror structures.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A trajectory planning method for a dual-hybrid robot mirror processing equipment, characterized in that the method includes the following steps:

[0008] 1) Let the endpoint trajectory of the unit vector of the tool axis be the tool axis direction path, and the tool tip position trajectory be the tool tip position path. Both are defined in the Cartesian coordinate system and smoothed by NURBS curve fitting. The arc length parameter method is used to determine the node vector, a fitting error evaluation standard is introduced, a fitting error limit is set, the fitting error is reduced by adjusting the spline control points, and finally the tool tip and tool axis position paths of the dual hybrid robot are determined by combining the constraints introduced by synchronous cooperation.

[0009] 2) Next, it is necessary to determine the speed curve of the two machines. The speed curve is a cubic B-spline. Establish joint constraints, tool axis speed, acceleration, and jump constraints, as well as tool tip speed, acceleration, and jump constraints. With time optimization as the objective function, first generate the single-machine time-optimal speed curve, and then combine the synchronization constraints to generate the final dual-machine time-optimal speed curve control points.

[0010] 3) Verify whether the generated speed curve of the driven robot meets the single-machine motion constraints, adjust the over-limit control points to meet the constraints, and determine the final speed curve;

[0011] 4) Finally, using the parameter interpolation algorithm, the interpolation points of the tool tip and tool axis of the dual-machine are generated to realize the collaborative processing of the dual hybrid robots.

[0012] According to the aforementioned trajectory planning method for dual-hybrid robot mirror machining equipment, step 1) of the method further includes the following steps: a method for determining four sets of control points for the dual-machine tool tip path and the path to the same point on the tool axis, based on coaxial constraints, wherein the active robot tool tip path and the same point on the tool axis are respectively derived directly from the CNC software as five-dimensional arrays. The control points are calculated separately, including the tool tip control point and the same control point on the tool axis. It can be calculated by the following formula

[0013] ,

[0014] The rotation angles are A and B axes, respectively. For the first The coordinates of the blade tip;

[0015] To determine the control points of the driven robot's tool tip and tool axis, a surface fitting is required for the driven tool measurement point. Then, the intersection points of the straight line constructed from the active robot's tool tip and tool axis points and the constructed curve, along with the inverse of the tool axis vector, are used to construct the control points, as shown in the following formula. Assuming the mathematical equation of the driven side surface is known... express,

[0016] ,

[0017] in For linear parameters, For the first active robot The equation of the straight line formed by the control points.

[0018] The control point of the driven robot can be obtained by solving the above equation. As shown in the following formula:

[0019] ,

[0020] The parametric solution matrix represents the intersection of the constructed straight line equation and the surface. Note that the offset direction of the control point of the tool axis point of the driven robot relative to the tool tip point is opposite to that of the active robot.

[0021] The trajectory planning method for the dual-hybrid robot mirror processing equipment is characterized by the following step: determining the node vector using the chord length method. For any m control points First, calculate the chord length between adjacent control points. chord length cumulative value Corresponding parameter value Finally, node vectors are constructed. as follows:

[0022] .

[0023] According to the trajectory planning method for the dual-hybrid robot mirror machining equipment, the method is characterized by further including the following steps: an evaluation method for fitting error: Fitting error refers to the difference between the fitted curve and the target curve. For the dual-hybrid robot, the fitting error is divided into the fitting error of the tool tip point and the fitting error of the tool axis vector. The calculation method is as follows:

[0024] ,

[0025] in This indicates the fitting error at the knife tip. This indicates the tool axis vector fitting error; These represent the control points at the tool tip and the same point on the tool axis, respectively. These represent the fitting curves for the tool tip point and the tool axis vector, respectively.

[0026] According to the trajectory planning method for the dual-hybrid robot mirror processing equipment, the method is characterized by further including the following steps: introducing a fitting error evaluation standard and iteratively adjusting the speed control point; the specific steps include:

[0027] Step A1: Use the arc length nodal vector method and the calculated control points to initially fit the curve, and calculate the interval. Fitting error within ,

[0028] Step A2: Verify the fitting error Does it exceed the limit? ,

[0029] Step A3: If the fitting error limit is not met, insert a node. ,

[0030] Step A4: Iteratively insert nodes when the fitting error of all intervals is less than the threshold value. The iteration process terminates.

[0031] The trajectory planning method for the dual-hybrid robot mirror processing equipment is characterized by the following steps: considering that the coordinated synchronous motion of the two robots needs to satisfy synchronization constraints, the construction method is based on the generated four NURBS curves. , , , For any parameter It should satisfy the following equation:

[0032] ,

[0033] Let be a certain constant.

[0034] According to the trajectory planning method for dual-hybrid robot mirror machining equipment, the method further includes the following steps: to ensure that both robots simultaneously reach the synchronization point set that satisfies the synchronization constraint along the entire toolpath, based on the principle that the path ratio equals the speed ratio, two cubic B-spline curves are used to describe the motion law of the two robots respectively. The feed rate curves of the two robots are shown in the following formulas.

[0035] ,

[0036] In the formula For the speed control point of the active robot, parameters The parameters are consistent with those of the NURBS toolpath. , Four NURBS curves , , , For parameters The first derivative, It is a cubic B-spline basis function.

[0037] According to the trajectory planning method for dual-hybrid robot mirror processing equipment, the specific steps for obtaining the optimal speed curve of the two machines in time include:

[0038] Step B1: Assume that the speed curves of both machines are cubic B-splines, and the initial speed curve is composed of a set of control points that are zero at the beginning and end but have the maximum value at the rest.

[0039] Step B2: Based on time optimization, optimize the control points of the active robot's velocity curve. The optimized parameter settings are as follows:

[0040] ,

[0041] ,

[0042] In the formula The feed rate along the tool path, For the trajectory of the blade tip of the active robot The first derivative;

[0043] Step B3: By calculating the ratio of the first derivative of the dual-machine tool tip trajectory to the parameter, the speed ratio curve of the dual-machine is obtained, as shown in the following formula:

[0044] ,

[0045] In the formula These are the first derivatives of the tool tip trajectory of the dual-machine path;

[0046] Step B4: The speed curve of the driven robot can be obtained by dividing the optimal speed curve of the active robot by the speed ratio curve of the two robots, as shown in the following formula:

[0047] ,

[0048] In the formula This refers to the speed control point for the active robot.

[0049] According to the trajectory planning method for the dual-machine hybrid robot mirror processing equipment, after determining the optimal speed curve of the two machines, the control points of the dual-machine speed curve need to be adjusted point by point according to the situation of exceeding the limit of the obtained dual-machine speed curve. The specific steps are as follows:

[0050] Step C1: Solve for the over-limit situation of the slave robot's speed curve based on the calculated dual-machine speed curve;

[0051] Step C2: Adjust the speed control points of the relevant slave robots according to the over-limit situation, and proportionally reduce the speed control points of the active robot according to the synchronization constraints;

[0052] Step C3: Verify the speed constraint of the adjusted dual-machine speed curve and output the control points of the dual-machine speed curve that satisfy the constraints.

[0053] The advantages and positive effects of this invention are:

[0054] 1. Based on the constraints of collaborative processing, this invention proposes a method for determining the path control points of a dual-hybrid robot mirror processing equipment.

[0055] 2. Based on the constraints of the fitting error, this invention obtains four path curves that satisfy the error constraints by iteratively adjusting the control points.

[0056] 3. This invention proposes an improved iterative adjustment method for speed control points, which satisfies the single-machine processing constraints while achieving maximum processing efficiency and reducing the computational load generated by iterative calculations. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method of the present invention.

[0058] Figure 2 This is a diagram of the dual-hybrid robot mirror processing system of the present invention.

[0059] Figure 3 This is a flowchart illustrating the path parameterization process of the present invention.

[0060] Figure 4 This is a flowchart illustrating the time-optimal speed curve of the dual-robot method of the present invention.

[0061] Figure 5 This is a flowchart illustrating the time-optimal speed curve of the dual robots satisfying the constraints of the method of this invention. Detailed Implementation

[0062] To further understand the invention's content, features, and effects, the following embodiments are provided, along with detailed descriptions in conjunction with the accompanying drawings:

[0063] See Figures 1 to 5 The present invention provides a trajectory planning method for a dual-hybrid robot mirror processing equipment, comprising the following steps:

[0064] 1) Let the endpoint trajectory of the unit vector of the tool axis be the tool axis direction path; let the tool tip position trajectory be the tool tip position path. Both are defined in the Cartesian coordinate system and smoothed by NURBS curve fitting. The arc length parameter method is used to determine the node vector, a fitting error evaluation standard is introduced, a fitting error limit is set, the fitting error is reduced by adjusting the spline control points, and finally, the tool tip and tool axis position paths of the dual hybrid robot can be determined by combining the constraints introduced by synchronous cooperation.

[0065] 2) Next, it is necessary to determine the speed curve of the two machines. The speed curve is a cubic B-spline. Establish joint constraints, tool axis speed, acceleration, and jump constraints, as well as tool tip speed, acceleration, and jump constraints. With time optimization as the objective function, first generate the single-machine time-optimal speed curve, and then combine the synchronization constraints to generate the final dual-machine time-optimal speed curve control points.

[0066] 3) Verify whether the generated speed curve of the driven robot meets the single-machine motion constraints, adjust the over-limit control points to meet the constraints, and determine the final speed curve;

[0067] 4) Finally, the parameter interpolation algorithm is used to generate the interpolation points of the tool tip and tool axis of the dual machine to realize the dual machine collaborative processing.

[0068] Specifically, in step 1), the discrete points of the tool tip and tool axis positions of the dual hybrid robot should satisfy the coaxial constraint, i.e.

[0069] ,

[0070] In the formula , , , These represent the path fitting curves for the tool tip and tool axis points of the dual-robot system, respectively. Let be a certain constant.

[0071] The starting point of the tool axis fixed point path is the ending point of the tool tip position along the tool axis vector. The tool tip fitting error refers to the error in the discrete data points along the path. Parameters of the fitted curve to the tip of the blade The distance. The tool axis point fitting error refers to the error caused by discrete data points. The constructed tool axis vector and The included angle.

[0072] Preferably, the method further includes the following step: iteratively adjusting the path control points until the fitting error within the parameter range meets the error requirement, specifically including:

[0073] Step A1: Use the arc length nodal vector method and the calculated control points to initially fit the curve, and calculate the interval. Fitting error within .

[0074] Step A2: Verify the fitting error Does it exceed the limit? .

[0075] Step A3: If the fitting error limit is not met, insert a node. .

[0076] Step A4: Iteratively insert nodes when the fitting error of all intervals is less than the threshold value. The iteration process terminates.

[0077] Preferably, the specific steps for obtaining the optimal speed curve of the two machines over time include:

[0078] Step B1: Assume that the speed curves of both machines are cubic B-splines, and the initial speed curve is composed of a set of control points that are zero at the beginning and end but have the maximum value for the rest.

[0079] Step B2: Based on time optimization, optimize the control points of the active robot's velocity curve. The optimized parameter settings are as follows:

[0080] ,

[0081] ,

[0082] In the formula The feed rate along the tool path, For the trajectory of the blade tip of the active robot The first derivative.

[0083] Step B3: By calculating the ratio of the first derivative of the dual-machine tool tip trajectory to the parameter, the speed ratio curve of the dual-machine is obtained, as shown in the following formula:

[0084] ,

[0085] In the formula These are the first derivatives of the trajectory of the blade tip point on the dual-machine path.

[0086] Step B4: The speed curve of the driven robot can be obtained by dividing the optimal speed curve of the active robot by the speed ratio curve of the two robots. However, it is still necessary to check whether the speed curve of the driven robot exceeds the limit, as shown in the following formula:

[0087] ,

[0088] In the formula For the speed control point of the active robot, They are respectively , , , For parameters The first derivative. It is a cubic B-spline basis function.

[0089] Preferably, after determining the optimal speed curve for the two machines, the control points of the speed curve need to be adjusted point by point according to the extent of exceeding the limits. The specific steps are as follows:

[0090] Step C1: Solve for the over-limit situation of the slave robot's speed curve based on the calculated dual-machine speed curve.

[0091] Step C2: Adjust the speed control points of the relevant slave robot according to the over-limit situation, and proportionally reduce the speed curve control points of the active robot according to the synchronization constraints.

[0092] Step C3: Verify the speed constraint of the adjusted dual-machine speed curve and output the control points of the dual-machine speed curve that satisfy the constraints.

[0093] Preferably, after obtaining the dual-robot speed curves that satisfy the constraints, the path spline points of the tool tip and tool axis points of the dual robots are obtained through parameter interpolation. The tool axis vector is then calculated using the tool axis points and tool tip points, and the A / B rotation angle is calculated and input into the CNC machining system.

[0094] The workflow and principle of the present invention will be further illustrated below with a preferred embodiment.

[0095] Step 1: Obtain the original pose information of the two robots from the discrete tool position points exported from the UG software. This includes the tool tip position, tool axis position, and slave robot tool tip position, all defined in the Cartesian coordinate system. Fit the slave side surface to be machined using the slave robot tool tip position. Construct the corresponding straight line equation using the control points of the active robot tool tip and tool axis. Solve for the intersection of the straight line and the slave side surface to be machined to find the path control point of the slave robot tool tip. Calculate the corresponding tool axis control point of the slave robot using the tool tip control point and the active robot tool axis vector.

[0096] Step 1.1: The five-dimensional arrays of the active robot's tool tip path and the same point on the tool axis are directly exported from the CNC software. The control points are calculated separately, including the tool tip control point and the same control point on the tool axis. It can be calculated by the following formula

[0097] ,

[0098] The rotation angles are A and B axes, respectively. For the first The coordinates of the blade tip.

[0099] Step 1.2: To determine the control points of the driven robot's tool tip and tool axis, a surface fitting is required for the driven tool measurement point. Then, the intersection points of the straight line constructed from the active robot's tool tip and tool axis points and the constructed curve, along with the reverse direction of the tool axis vector, are used to construct the control points, as shown in the following formula. Assume the mathematical equation of the driven side surface is known. express.

[0100] ,

[0101] in For linear parameters, For the first active robot The equation of the straight line formed by the control points.

[0102] Step 1.3: By solving the above equation, the control point of the driven robot can be obtained. As shown in the following formula:

[0103] ,

[0104] The parametric solution matrix represents the intersection of the constructed straight line equation and the surface. Note that the offset direction of the control point of the tool axis point of the driven robot relative to the tool tip point is opposite to that of the active robot.

[0105] Step 2: After determining the path control points for the two robots, consider using the chord length method to determine the node vectors. For any m control points First, calculate the chord length between adjacent control points. chord length cumulative value Corresponding parameter value Finally, node vectors are constructed. as follows:

[0106] ,

[0107] Step 3, introducing a method for evaluating fitting error: Fitting error refers to the difference between the fitted curve and the target curve. For dual-parallel hybrid robots, the fitting error is divided into the fitting error at the tool tip and the fitting error of the tool axis vector. The calculation method is as follows:

[0108] ,

[0109] in This indicates the fitting error at the knife tip. This indicates the tool axis vector fitting error; These represent the control points at the tool tip and the same point on the tool axis, respectively. These represent the fitting curves for the tool tip point and the tool axis vector, respectively.

[0110] Step 4: Introduce a fitting error evaluation criterion and iteratively adjust the velocity control point. Specific steps include:

[0111] Step 4.1: Use the arc length nodal vector method and the calculated control points to initially fit the curve, and calculate the interval. Fitting error within .

[0112] Step 4.2: Verify the fitting error Does it exceed the limit? .

[0113] Step 4.3: If the fitting error limit is not met, insert a node. .

[0114] Step 4.4: Iteratively insert nodes when the fitting error of all intervals is less than the threshold value. The iteration process terminates.

[0115] Step 5: Considering that the coordinated synchronous motion of the two machines must satisfy synchronization constraints, the construction method is based on the generated four NURBS curves. , , , For a certain parameter It should satisfy the following equation:

[0116] ,

[0117] Let be a certain constant.

[0118] Step 6: In order to ensure that both robots reach the synchronization point (the set of synchronization points that satisfy the synchronization constraints) simultaneously on the entire toolpath, based on the principle that the path ratio equals the speed ratio, two cubic B-spline curves are used to describe the motion law of the four NURBS curves. , , Let represent the feed rate, acceleration, and jump of the two robots, respectively. As shown in the following equation...

[0119] ,

[0120] In the formula For the speed control point of the active robot, parameters The parameters are consistent with those of the NURBS toolpath. , They are respectively , , , For parameters The first derivative. It is a cubic B-spline basis function.

[0121] Step 7, the specific steps for obtaining the optimal speed curve for the two machines include:

[0122] Step 7.1: Assume that the speed curves of both machines are cubic B-splines, and the initial speed curve is composed of a set of control points that are zero at the beginning and end but have the maximum value for the rest.

[0123] Step 7.2: Based on time optimization, optimize the control points of the active robot's velocity curve. The optimized parameter settings are as follows:

[0124] ,

[0125] ,

[0126] In the formula The feed rate along the tool path, For the trajectory of the blade tip of the active robot The first derivative.

[0127] Step 7.3: By calculating the ratio of the first derivative of the dual-machine tool tip trajectory to the parameter, the speed ratio curve of the dual-machine is obtained, as shown in the following formula:

[0128] ,

[0129] In the formula These are the first derivatives of the trajectory of the blade tip point on the dual-machine path.

[0130] Step 7.4: The speed curve of the driven robot can be obtained by dividing the optimal speed curve of the active robot by the speed ratio curve of the two robots. However, it is still necessary to check whether the speed curve of the driven robot exceeds the limit, as shown in the following formula:

[0131] ,

[0132] In the formula For the speed control point of the active robot, They are respectively , , , For parameters The first derivative. It is a cubic B-spline basis function.

[0133] Step 8: After determining the optimal speed curve for the two machines, the control points of the speed curve need to be adjusted point by point according to the extent of exceeding the limits. The specific steps are as follows:

[0134] Step 8.1: Solve for the over-limit situation of the slave robot's speed curve based on the calculated dual-machine speed curve.

[0135] Step 8.2: Adjust the speed control points of the relevant slave robot according to the over-limit situation, and proportionally reduce the speed curve control points of the active robot according to the synchronization constraints.

[0136] Step 8.3: Verify the speed constraint of the adjusted dual-machine speed curve and output the control points of the dual-machine speed curve that satisfy the constraints.

[0137] Step 9: Use the dual-machine speed curve that satisfies the constraints. and the path of the dual-machine tool tip , and tool axis path , Perform parameter interpolation to generate interpolation spline points, calculate the A / B rotation angle using MATLAB, and input the results into the CNC system for machining using the spline function.

[0138] The above embodiments of trajectory planning methods are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The patent scope of the present invention should not be limited by these embodiments. That is, all equivalent changes or modifications made to the spirit disclosed in the present invention still fall within the patent scope of the present invention.

Claims

1. A method for trajectory planning of a dual-parallel robot mirror machining equipment, characterized in that, The method includes the following steps: 1) Let the endpoint trajectory of the unit vector of the tool axis be the tool axis direction path, and the tool tip position trajectory be the tool tip position path. Both are defined in the Cartesian coordinate system and smoothed by NURBS curve fitting. The arc length parameter method is used to determine the node vector, a fitting error evaluation standard is introduced, a fitting error limit is set, the fitting error is reduced by adjusting the spline control points, and finally the tool tip and tool axis position paths of the dual hybrid robot are determined by combining the constraints introduced by synchronous cooperation. 2) Next, it is necessary to determine the speed curve of the two machines. The speed curve is a cubic B-spline. Establish joint constraints, tool axis speed, acceleration, and jump constraints, as well as tool tip speed, acceleration, and jump constraints. With time optimization as the objective function, first generate the single-machine time-optimal speed curve, and then combine the synchronization constraints to generate the final dual-machine time-optimal speed curve control points. 3) Verify whether the generated speed curve of the driven robot meets the single-machine motion constraints, adjust the over-limit control points to meet the constraints, and determine the final speed curve; 4) Finally, using the parameter interpolation algorithm, the interpolation points of the tool tip and tool axis of the dual-machine are generated to realize the collaborative processing of the dual hybrid robots; Step 1) further comprises the following steps, the determination method of four groups of control points of the double-machine tool tip point path and the same point path on the tool shaft, based on the coaxial constraint, the five-dimensional arrays of the active robot tool tip point path and the same point on the tool shaft are directly derived by numerical control software respectively, wherein the tool tip control point and the same point control point on the tool shaft are calculated can be calculated by the following formula ， A, B axis rotation angles is the first is the first tool tip coordinate To determine the control points of the driven robot's tool tip and tool axis, a surface fitting is required for the driven tool measurement point. Then, the intersection points of the straight line constructed from the active robot's tool tip and tool axis points and the constructed curve, along with the inverse of the tool axis vector, are used to construct the control points, as shown in the following formula. Assuming the mathematical equation of the driven side surface is known... express, ， in For linear parameters, For the first active robot The equation of the straight line formed by the control points. The control point of the driven robot can be obtained by solving the above equation. As shown in the following formula: ， The parametric solution matrix represents the intersection of the constructed straight line equation and the surface. Note that the offset direction of the control point of the tool axis point of the driven robot relative to the tool tip point is opposite to that of the active robot.

2. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 1, characterized in that, The method also includes the following step: determining the node vector using the chord length method. For any m control points First, calculate the chord length between adjacent control points. chord length cumulative value Corresponding parameter value Finally, node vectors are constructed. as follows: 。 3. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 2, characterized in that, The method also includes the following steps: Evaluation of fitting error: Fitting error refers to the difference between the fitted curve and the target curve. For dual-parallel hybrid robots, the fitting error is divided into the fitting error at the tool tip and the fitting error of the tool axis vector. The calculation method is as follows: ， in This indicates the fitting error at the knife tip. This indicates the tool axis vector fitting error; These represent the control points at the tool tip and the same point on the tool axis, respectively. These represent the fitting curves for the tool tip point and the tool axis vector, respectively.

4. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 3, characterized in that, The method also includes the following steps: introducing a fitting error evaluation criterion and iteratively adjusting the velocity control point. Specific steps include: Step A1: Use the arc length nodal vector method and the calculated control points to initially fit the curve, and calculate the interval. Fitting error within , Step A2: Verify the fitting error Does it exceed the limit? , Step A3: If the fitting error limit is not met, insert a node. , Step A4: Iteratively insert nodes when the fitting error of all intervals is less than the threshold value. The iteration process terminates.

5. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 4, characterized in that, The method also includes the following steps: considering that the coordinated synchronous motion of the two machines must satisfy synchronization constraints, the construction method is based on the generated four NURBS curves. , , , For any parameter It should satisfy the following equation: ， Let be a certain constant.

6. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 5, characterized in that, The method also includes the following steps: to ensure that both robots simultaneously reach the synchronization point set that satisfies the synchronization constraint along the entire toolpath, based on the principle that the path ratio equals the speed ratio, two cubic B-spline curves are used to describe the motion law of the two robots respectively. The feed rate curves of the two robots are shown in the following formulas. ， In the formula For the speed control point of the active robot, parameters The parameters are consistent with those of the NURBS toolpath. , Four NURBS curves , , , For parameters The first derivative, It is a cubic B-spline basis function.

7. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 6, characterized in that, The specific steps for obtaining the optimal speed curve for a dual-machine system include: Step B1: Assume that the speed curves of both machines are cubic B-splines, and the initial speed curve is composed of a set of control points that are zero at the beginning and end but have the maximum value at the rest. Step B2: Based on time optimization, optimize the control points of the active robot's velocity curve. The optimized parameter settings are as follows: ， ， In the formula The feed rate along the tool path, For the trajectory of the blade tip of the active robot The first derivative; Step B3: By calculating the ratio of the first derivative of the dual-machine tool tip trajectory to the parameter, the speed ratio curve of the dual-machine is obtained, as shown in the following formula: ， In the formula These are the first derivatives of the tool tip trajectory of the dual-machine path; Step B4: The speed curve of the driven robot can be obtained by dividing the optimal speed curve of the active robot by the speed ratio curve of the two robots, as shown in the following formula: ， In the formula This refers to the speed control point for the active robot.

8. The trajectory planning method for dual-hybrid robot mirror processing equipment according to claim 7, characterized in that, After determining the optimal speed curve for the dual-machine system, the control points of the dual-machine speed curve need to be adjusted point by point according to the extent of exceeding the limits. The specific steps are as follows: Step C1: Solve for the over-limit situation of the slave robot's speed curve based on the calculated dual-machine speed curve; Step C2: Adjust the speed control points of the relevant slave robots according to the over-limit situation, and proportionally reduce the speed control points of the active robot according to the synchronization constraints; Step C3: Verify the speed constraint of the adjusted dual-machine speed curve and output the control points of the dual-machine speed curve that satisfy the constraints.

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