Hole pose error compensation method and system based on manifold error similarity

Abstract

The application provides a hole pose error compensation method and system based on manifold error similarity, and relates to the technical field of machining, and comprises the following steps: S1, obtaining a target pose of a point to be machined and a theoretical pose of a reference point according to offline programming; S2, positioning an end effector to each reference point in sequence by a robot, and measuring a real pose of the reference point on a curved surface product; S3, calculating a pose error through the theoretical pose and the real pose of the reference point, correcting the target pose of the point to be machined on the curved surface product in combination with a compensation algorithm, and realizing compensation of the pose error of the point to be machined; and S4, further correcting an initial normal of the point to be machined by means of pose data of a machined point. The application can realize correction of the position coordinates and the initial normal of the point to be machined, and greatly improves the positioning and normal precision of the robot system on a workpiece.

Description

Technical Field

[0001] This invention relates to the field of machining technology, and more specifically, to a hole orientation error compensation method and system based on manifold error similarity. Background Technology

[0002] Automated drilling in aerospace applications requires high precision in hole position and perpendicularity. To ensure the final drilling accuracy on the product, it is necessary to use the existing reference hole information on the product to correct the position and orientation, thereby guaranteeing the final drilling accuracy.

[0003] The existing approach involves optimally fitting the theoretical and actual coordinates of the reference hole, followed by pose correction using rigid body transformation. This method is suitable for applications with good product rigidity and very low manufacturing errors in the reference hole position. However, in scenarios where product rigidity is weak or the manufacturing error in the reference hole position cannot be ignored, the compensation effect of this method has certain limitations.

[0004] Patent CN110849267B discloses a method for positioning and coordinate system transformation on a product using a mobile automated system based on local reference holes. First, the mobile automated system is moved or installed to a local hole-making area. A hole position detection device on the equipment detects the reference holes, thus determining their spatial position in the equipment coordinate system. Second, by comparing the spatial position of the reference holes in the product coordinate system, the homogeneous transformation matrix between the current equipment coordinate system and the product coordinate system can be calculated, thereby determining (positioning) the equipment coordinate system in the product coordinate system. Finally, the position of the processing point in the product coordinate system is transformed to the equipment coordinate system using this homogeneous transformation matrix, allowing processing of the local area determined by the reference holes in the equipment coordinate system. The drawback of this invention is that when the reference hole position error is large, the hole spacing and row spacing are prone to exceeding tolerances, and at least three reference holes are required. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a hole pose error compensation method and system based on manifold error similarity.

[0006] According to the present invention, a hole pose error compensation method and system based on manifold error similarity are provided, the scheme of which is as follows:

[0007] Firstly, a hole pose error compensation method based on manifold error similarity is provided, the method comprising:

[0008] Step S1: Obtain the target pose of the point to be processed and the theoretical pose of the reference point based on offline programming;

[0009] Step S2: The robot sequentially positions the end effector to each reference point and measures the actual pose of the reference points on the curved product.

[0010] Step S3: Calculate the pose error using the theoretical and actual poses of the reference points, and combine the compensation algorithm to correct the target pose of the points to be processed on the curved surface product, thereby compensating for the pose error of the points to be processed.

[0011] Step S4: Using the pose data of the processed points, further correct the initial normal of the points to be processed.

[0012] Preferably, the initial pose of the reference point includes:

[0013] ρ=[p T ,q T ] T =[p T ,0,n T ] T

[0014] Where p represents the position vector, n represents the unit normal vector, and q is the unit quaternion;

[0015] The pose error is calculated using the following formula:

[0016]

[0017] Where, ρ t and ρ o These represent the target pose and the initial pose, respectively, where δp is the position error and δ q The unit quaternion representing the normal error, representing n o up to n t The rotational transformation, α = arccos(n) o ·n t ) is n o and n t The included angle, The generalized subtraction represents the hole pose error; correspondingly, the generalized addition for hole pose correction is defined as follows:

[0018]

[0019] in, Represents the multiplication of quaternions.

[0020] Preferably, the step S3 of correcting the target pose of the points to be processed on the curved surface product includes: using... <R m ,ρ m The initial correction of the hole pose error is achieved as follows:

[0021]

[0022]

[0023] In the formula, ρ n Represents the nominal aperture pose, ρ m This represents the initial corrected aperture pose, where x, y, and z represent the directions of the linear axes in the Cartesian coordinate system; where x m y m z m α m β m γ m These are the pose parameters, obtained by solving the optimization problem shown in the following equation:

[0024]

[0025] Where W represents the weight matrix, ρ Rri Represents the actual reference point coordinates, ρ Rmi Represents the corrected pose of the reference point, ||·|| 2 Let L2 represent the L2 norm, and i represent the i-th reference point.

[0026] Preferably, step S3 further includes secondary correction. Before performing secondary correction of the hole pose, the surface s(u,v) is reconstructed based on the target coordinates of the hole. For p within the surface region... i The coordinates of a point, [u,v], are obtained by projecting it onto the interpolation surface along the normal. The calculation process is regarded as solving the following optimization problem:

[0027] [u i ,v i ] = arg min u,v (||(s(u,v)-p i )×n i || 2 )

[0028] The target pose ρ after secondary correction is calculated using the following formula. ti And use it as the target pose for locating the point to be processed:

[0029]

[0030] in, Represents the reference point position error matrix, c i =[1-u i -v i +u i v i u i -u i v i v i -ui v i u i v i ] T C is the interpolation coefficient vector. R =[c R1 c R2 c R3 c R4 ] represents the interpolation coefficient matrix for the reference point, ρ mi This represents the initial pose of the point to be processed, ρ. ni This represents the pose of the theoretical point to be processed.

[0031] Preferably, in step S4, for the correction of the normal vector in the hole pose, the initial normal of the point to be processed is corrected using the data of the processed points, and the process is as follows:

[0032] Step S4.1: Set the true pose ρ of the reference point. Rr And the pose ρ after initial correction Rm Store in matrix M done middle;

[0033] Step S4.2: Calculate the location ρ of the point to be processed. i To M done The distance between all the holes in the middle;

[0034] Step S4.3: Select M done The four holes closest to the point to be processed are used as new reference points;

[0035] Step S4.4: Using the new reference point data, calculate the target pose ρ after secondary correction. ti ;

[0036] Step S4.5: ρ ti The normal vector in the image is used as the normal for final positioning. After positioning is completed, the equipment performs online normal measurement and adjustment to obtain the final pose ρ during processing. ri ;

[0037] Step S4.6: If all holes in the area have been machined, then end; otherwise, continue processing. ri and ρ mi Store in M done Then, proceed to step S4.2.

[0038] Preferably, for cases where the points to be processed are arranged in a line and there are only two reference points, they are treated as a scenario where the two boundary curves of the surface coincide.

[0039] Secondly, a hole pose error compensation system based on manifold error similarity is provided, the system comprising:

[0040] Module M1: Obtains the target pose of the point to be processed and the theoretical pose of the reference point based on offline programming;

[0041] Module M2: The robot sequentially positions the end effector to each reference point and measures the actual pose of the reference points on the curved product.

[0042] Module M3: Calculates the pose error using the theoretical and actual poses of the reference points, and combines them with a compensation algorithm to correct the target pose of the points to be processed on the curved surface product, thereby compensating for the pose error of the points to be processed.

[0043] Module M4: Using the pose data of the processed points, further correct the initial normal of the points to be processed.

[0044] Preferably, the initial pose of the reference point includes:

[0045] ρ=[p T ,q T ] T =[p T ,0,n T ] T

[0046] Where p represents the position vector, n represents the unit normal vector, and q is the unit quaternion;

[0047] The pose error is calculated using the following formula:

[0048]

[0049] Where, ρ t and ρ o Let δp be the target pose and δq be the initial pose, respectively. Let δp be the position error and δq be the unit quaternion representing the normal error, where n is the number of quaternions. o up to n t The rotational transformation, α = arccos(n) o ·n t ) is n o and n t The included angle, The generalized subtraction represents the hole pose error; correspondingly, the generalized addition for hole pose correction is defined as follows:

[0050]

[0051] in, Represents the multiplication of quaternions;

[0052] The target pose of the points to be processed on the surface product in module M3 includes: using... <R m ,ρ mThe initial correction of the hole pose error is achieved as follows:

[0053]

[0054]

[0055] In the formula, ρ n Represents the nominal aperture pose, ρ m This represents the initial corrected aperture pose, where x, y, and z represent the directions of the linear axes in the Cartesian coordinate system; where x m y m z m α m β m γ m These are the pose parameters, obtained by solving the optimization problem shown in the following equation:

[0056]

[0057] Where W represents the weight matrix, ρ Rri Represents the actual reference point coordinates, ρ Rmi Represents the pose of the corrected reference point, ||·|| 2 Let L2 represent the norm, and i represent the i-th reference point.

[0058] The module M3 also includes secondary correction. Before performing secondary correction of the hole pose, the surface s(u,v) is reconstructed based on the target coordinates of the hole. For p within the surface region... i The coordinates of a point, [u,v], are obtained by projecting it onto the interpolation surface along the normal. The calculation process is regarded as solving the following optimization problem:

[0059] [u i ,v i ] = arg min u,v (||(s(u,v)-p i )×n i || 2 )

[0060] The target pose ρ after secondary correction is calculated using the following formula. ti And use it as the target pose for locating the point to be processed:

[0061]

[0062] in, Represents the reference point position error matrix, c i =[1-u i -v i +u i v i ui -u i v i v i -u i v i u i v i ] T C is the interpolation coefficient vector. R =[c R1 c R2 c R3 c R4 ] represents the interpolation coefficient matrix for the reference point, ρ mi This represents the initial pose of the point to be processed, ρ. ni This represents the pose of the theoretical point to be processed.

[0063] In module M4, the normal vector correction in the hole pose is performed by correcting the initial normal vector of the point to be processed using data from the already processed points. The process is as follows:

[0064] Module M4.1: Transmits the true pose ρ of the reference point. Rr And the pose ρ after initial correction Rm Store in matrix M done middle;

[0065] Module M4.2: Calculate the position ρ of the point to be processed. i To M done The distance between all the holes in the middle;

[0066] Module M4.3: Select M done The four holes closest to the point to be processed are used as new reference points;

[0067] Module M4.4: Calculates the target pose ρ after secondary correction using the new reference point data. ti ;

[0068] Module M4.5: will ρ ti The normal vector in the image is used as the normal for final positioning. After positioning is completed, the equipment performs online normal measurement and adjustment to obtain the final pose ρ during processing. ri ;

[0069] Module M4.6: If all holes in the area have been machined, then end; otherwise, ρ ri and ρ mi Store in M done Then, proceed to module M4.2;

[0070] For cases where the points to be processed are arranged in a line and there are only two reference points, they are treated as a scenario where the two boundary curves of the surface coincide.

[0071] Thirdly, a computer-readable storage medium is provided storing a computer program, which, when executed by a processor, implements the steps in the hole pose error compensation method based on manifold error similarity.

[0072] Fourthly, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps in the hole pose error compensation method based on manifold error similarity.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] By fully utilizing the pose data of the reference points and the normal data of the processed points, the position coordinates and initial normals of the points to be processed were corrected, which greatly improved the positioning and normal accuracy of the robot system on the workpiece.

[0075] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0076] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0077] Figure 1 This is an overall flowchart of the present invention;

[0078] Figure 2 This is a schematic diagram of the structure of the present invention;

[0079] Figure 3 This is a schematic diagram of the second correction.

[0080] Figure 4 This is a schematic diagram of the initial normal correction.

[0081] Reference numerals: 1. Robot; 2. End effector; 3. Reference point; 4. Point to be processed; 5. Curved surface product. Detailed Implementation

[0082] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0083] This invention provides a hole pose error compensation method based on manifold error similarity, referring to... Figure 1 As shown, the robot 1 integrates a multi-functional end effector 2, forming an automatic hole-making system. The end effector 2 has functions such as hole making, normal measurement, and spatial coordinate measurement of reference points. Several reference points 3 are arranged on the curved surface product 5. The automatic hole-making system measures the position and normal deviation of the reference points and, combined with a compensation algorithm, corrects the theoretical pose of the points 4 to be processed on the curved surface product 5, i.e., compensates for their position and normal coordinates. In this embodiment, the points to be processed include, but are not limited to, holes to be processed, and the reference points include, but are not limited to, reference holes / pins. The specific details of the invention are as follows:

[0084] Step S1: Obtain the target pose of the point to be processed 4 and the theoretical pose of the reference point based on offline programming.

[0085] Step S2: The robot 1 positions the end effector 2 sequentially to each reference point 3, and measures the actual pose of the reference point 3 on the curved product 5.

[0086] Step S3: Calculate the pose error using the theoretical and actual poses of the reference point 3, and combine it with the compensation algorithm to correct the target pose of the point 4 to be processed on the curved surface product 5, thereby compensating for the pose error of the point 4 to be processed.

[0087] Step S4: Using the pose data of the processed points, further correct the initial normal of the point 4 to be processed.

[0088] The initial pose of the reference point includes:

[0089] ρ=[p T ,q T ] T =[p T ,0,n T ] T

[0090] Where p represents the position vector, n represents the unit normal vector, and q is the unit quaternion;

[0091] The pose error is calculated using the following formula:

[0092]

[0093] Where, ρ t and ρ o Let δp be the target pose and δq be the initial pose, respectively. Let δp be the position error and δq be the unit quaternion representing the normal error, where n is the number of quaternions. o up to n t The rotational transformation, α = arccos(n) o ·nt ) is n o and n t The included angle, The generalized subtraction represents the hole pose error; correspondingly, the generalized addition for hole pose correction is defined as follows:

[0094]

[0095] in, Represents the multiplication of quaternions.

[0096] Specifically, step S3, correcting the target pose of the points to be processed on the curved surface product, includes: using... <R m ,ρ m The initial correction of the hole pose error is achieved as follows:

[0097]

[0098]

[0099] In the formula, ρ n Represents the nominal aperture pose, ρ m This represents the initial corrected aperture pose, where x, y, and z represent the directions of the linear axes in the Cartesian coordinate system; where x m y m z m α m β m γ m These are the pose parameters, obtained by solving the optimization problem shown in the following equation:

[0100]

[0101] Where W represents the weight matrix, ρ Rri Represents the actual reference point coordinates, ρ Rmi Represents the pose of the corrected reference point, ||·|| 2 Let L2 represent the L2 norm, and i represent the i-th reference point.

[0102] Before performing secondary correction of the hole pose, the surface s(u,v) is reconstructed based on the target coordinates of the hole. For p within the surface region... i A point, whose manifold coordinates [u,v] are obtained by projection along the normal onto the interpolation surface, such as... Figure 2 As shown. The calculation process is considered as solving the following optimization problem:

[0103] [u i ,v i ] = arg min u,v (||(s(u,v)-p i )×ni || 2 )

[0104] Reference Figure 3 As shown, the target pose ρ after secondary correction is calculated using the following formula. ti And use it as the target pose for locating the point to be processed:

[0105]

[0106] in, Represents the reference point position error matrix, c i =[1-u i -v i +u i v i u i -u i v i v i -u i v i u i v i ] T C is the interpolation coefficient vector. R =[c R1 c R2 c R3 c R4 ] represents the interpolation coefficient matrix for the reference point, ρ mi This represents the initial pose of the point to be processed, ρ. ni This represents the pose of the theoretical point to be processed.

[0107] Reference Figure 4 As shown, in step S4, the normal vector correction in the hole pose is performed by using the data of the already machined points to correct the initial normal vector of the point to be machined. The process is as follows:

[0108] Step S4.1: Set the true pose ρ of the reference point. Rr And the pose ρ after initial correction Rm Store in matrix M done middle;

[0109] Step S4.2: Calculate the location ρ of the point to be processed. i To M done The distance between all the holes in the middle;

[0110] Step S4.3: Select M done The four holes closest to the point to be processed are used as new reference points;

[0111] Step S4.4: Using the new reference point data, calculate the target pose ρ after secondary correction. ti ;

[0112] Step S4.5: ρ ti The normal vector in the image is used as the normal for final positioning. After positioning is completed, the equipment performs online normal measurement and adjustment to obtain the final pose ρ during processing. ri ;

[0113] Step S4.6: If all holes in the area have been machined, then end; otherwise, continue processing. ri and ρ mi Store in M done Then, proceed to step S4.2.

[0114] For cases where the points to be processed are arranged in a line and there are only two reference points, they are treated as a scenario where the two boundary curves of the surface coincide.

[0115] The present invention also provides a hole pose error compensation system based on manifold error similarity. The hole pose error compensation system based on manifold error similarity can be implemented by executing the process steps of the hole pose error compensation method based on manifold error similarity. That is, those skilled in the art can understand the hole pose error compensation method based on manifold error similarity as a preferred embodiment of the hole pose error compensation system based on manifold error similarity.

[0116] Based on the theoretical pose obtained through offline programming, the system positions the robot's end effector sequentially to each reference point and measures the actual pose of each reference point. Then, it compensates for the pose error of the point to be processed through the following two corrections:

[0117] Module M1: Obtains the target pose of the point to be processed and the theoretical pose of the reference point based on offline programming;

[0118] Module M2: The robot sequentially positions the end effector to each reference point and measures the actual pose of the reference points on the curved product.

[0119] Module M3: Calculates the pose error using the theoretical and actual poses of the reference points, and combines them with a compensation algorithm to correct the target pose of the points to be processed on the curved surface product, thereby compensating for the pose error of the points to be processed.

[0120] Module M4: Using the pose data of the processed points, further correct the initial normal of the points to be processed.

[0121] The initial pose of the reference point includes:

[0122] ρ=[p T ,q T ] T =[p T ,0,nT ] T

[0123] Where p represents the position vector, n represents the unit normal vector, and q is the unit quaternion;

[0124] The pose error is calculated using the following formula:

[0125]

[0126] Where, ρ t and ρ o Let δp be the target pose and δq be the initial pose, respectively. Let δp be the position error and δq be the unit quaternion representing the normal error, where n is the number of quaternions. o up to n t The rotational transformation, α = arccos(n) o ·n t ) is n o and n t The included angle, The generalized subtraction represents the hole pose error; correspondingly, the generalized addition for hole pose correction is defined as follows:

[0127]

[0128] in, Represents the multiplication of quaternions.

[0129] Specifically, the target pose of the points to be processed on the surface product in module M3 includes: using... <R m ,ρ m The initial correction of the hole pose error is achieved as follows:

[0130]

[0131]

[0132] In the formula, ρ n Represents the nominal aperture pose, ρ m This represents the initial corrected aperture pose, where x, y, and z represent the directions of the linear axes in the Cartesian coordinate system; where x m y m z m α m β m γ m These are the pose parameters, obtained by solving the optimization problem shown in the following equation:

[0133]

[0134] Where W represents the weight matrix, ρ Rri Represents the actual reference point coordinates, ρRmi Represents the pose of the corrected reference point, ||·|| 2 Let L2 represent the L2 norm, and i represent the i-th reference point.

[0135] Before performing secondary correction of the hole pose, the surface s(u,v) is reconstructed based on the target coordinates of the hole. For p within the surface region... i A point, whose manifold coordinates [u,v] are obtained by projection along the normal onto the interpolation surface, such as... Figure 2 As shown. The calculation process is considered as solving the following optimization problem:

[0136] [u i ,v i ] = arg min u,v (||(s(u,v)-p i )×n i || 2 )

[0137] Reference Figure 3 As shown, the target pose ρ after secondary correction is calculated using the following formula. ti And use it as the target pose for locating the point to be processed:

[0138]

[0139] in, Represents the reference point position error matrix, c i =[1-u i -v i +u i v i u i -u i v i v i -u i v i u i v i ] T C is the interpolation coefficient vector. R =[c R1 c R2 c R3 c R4 ] represents the interpolation coefficient matrix for the reference point, ρ mi This represents the initial pose of the point to be processed, ρ. ni This represents the pose of the theoretical point to be processed.

[0140] Reference Figure 4 As shown, in module M4, the normal vector correction in the hole pose is performed by using the data of the already machined points to correct the initial normal vector of the point to be machined. The process is as follows:

[0141] Module M4.1: Transmits the true pose ρ of the reference point. Rr And the pose ρ after initial correction Rm Store in matrix M done middle;

[0142] Module M4.2: Calculate the position ρ of the point to be processed. i To M done The distance between all the holes in the middle;

[0143] Module M4.3: Select M done The four holes closest to the point to be processed are used as new reference points;

[0144] Module M4.4: Calculates the target pose ρ after secondary correction using the new reference point data. ti ;

[0145] Module M4.5: will ρ ti The normal vector in the image is used as the normal for final positioning. After positioning is completed, the equipment performs online normal measurement and adjustment to obtain the final pose ρ during processing. ri ;

[0146] Module M4.6: If all holes in the area have been machined, then end; otherwise, ρ ri and ρ mi Store in M done Then, proceed to module M4.2;

[0147] For cases where the points to be processed are arranged in a line and there are only two reference points, they are treated as a scenario where the two boundary curves of the surface coincide.

[0148] This invention provides a hole pose error compensation method and system based on manifold error similarity. By making full use of the pose data of the reference point and the normal data of the processed point, the position coordinates and initial normal of the point to be processed are corrected, which greatly improves the positioning and normal accuracy of the robot system on the workpiece.

[0149] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0150] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A hole pose error compensation method based on manifold error similarity, characterized in that, include: Step S1: Obtain the target pose of the point to be processed and the theoretical pose of the reference point based on offline programming; Step S2: The robot sequentially positions the end effector to each reference point and measures the actual pose of the reference points on the curved product. Step S3: Calculate the pose error using the theoretical and actual poses of the reference points, and combine the compensation algorithm to correct the target pose of the points to be processed on the curved surface product, thereby compensating for the pose error of the points to be processed. Step S4: Using the pose data of the processed points, further correct the initial normal of the points to be processed; The step S3 of correcting the target pose of the points to be processed on the curved surface product includes: using < , The initial correction of the hole pose error is achieved as follows: In the formula, Indicates the nominal hole position. This indicates the hole pose after the initial correction. , , They represent the directions of the linear axes in the Cartesian coordinate system; where , , , , , These are the pose parameters, obtained by solving the optimization problem shown in the following equation: in, W Represents the weight matrix. Represents the actual coordinates of the reference point. This represents the pose of the corrected reference point. Represents the L2 norm, i This represents the position of the i-th reference point; Step S3 also includes a secondary correction. Before performing the secondary correction of the hole pose, the surface is reconstructed based on the target coordinates of the hole. For the curved surface region Point, its manifold coordinates [ u , v The result is obtained by projecting the curve along the normal onto the interpolation surface. The calculation process is regarded as solving the following optimization problem: The target pose after secondary correction is calculated using the following formula. And use it as the target pose for locating the point to be processed: in, Represents the reference point position error matrix. The interpolation coefficient vector, The interpolation coefficient matrix for the reference points. This indicates the pose of the point to be added after the initial correction. This represents the pose of the theoretical point to be processed. In step S4, the normal vector correction in the hole pose is performed by using the data of the already machined points to correct the initial normal vector of the point to be machined. The process is as follows: Step S4.1: Set the true pose of the reference point. and the initial corrected pose Store in matrix M done middle; Step S4.2: Calculate the points to be processed arrive M done The distance between all the holes in the middle; Step S4.3: Select M done The four holes closest to the point to be processed are used as new reference points; Step S4.4: Using the new reference point data, calculate the target pose after secondary correction. ; Step S4.5: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The normal vector in the image is used as the normal for final positioning. After positioning is completed, the equipment performs online normal measurement and adjustment to obtain the final pose for processing. ; Step S4.6: If all holes in the area have been machined, then the process ends; otherwise, continue. and deposit M done Then, proceed to step S4.

2.

2. The hole pose error compensation method based on manifold error similarity according to claim 1, characterized in that, The initial pose of the reference point includes: in, p Represents the position vector. n Represents the unit normal vector. q It is a unit quaternion; The pose error is calculated using the following formula: in, and These are the target pose and the initial pose, respectively. For positional error, The unit quaternion representing the normal error, representing to Rotational transformation, yes and The included angle, "This represents the generalized subtraction of the hole pose error; correspondingly, the generalized addition of the hole pose correction is defined as follows:" in," "Represents the multiplication of quaternions." 3. The hole pose error compensation method based on manifold error similarity according to claim 1, characterized in that, For cases where the points to be processed are arranged in a line and there are only two reference points, they are treated as a scenario where the two boundary curves of the surface coincide.

4. A hole pose error compensation system based on manifold error similarity, characterized in that, include: Module M1: Obtains the target pose of the point to be processed and the theoretical pose of the reference point based on offline programming; Module M2: The robot sequentially positions the end effector to each reference point and measures the actual pose of the reference points on the curved product. Module M3: Calculates the pose error using the theoretical and actual poses of the reference points, and combines them with a compensation algorithm to correct the target pose of the points to be processed on the curved surface product, thereby compensating for the pose error of the points to be processed. Module M4: Using the pose data of the processed points, further correct the initial normal of the points to be processed; The target pose of the points to be processed on the surface product in module M3 includes: using < , The initial correction of the hole pose error is achieved as follows: In the formula, Indicates the nominal hole position. This indicates the hole pose after the initial correction. , , They represent the directions of the linear axes in the Cartesian coordinate system; where , , , , , These are the pose parameters, obtained by solving the optimization problem shown in the following equation: in, W Represents the weight matrix. Represents the actual coordinates of the reference point. This represents the pose of the corrected reference point. Represents the L2 norm, i This represents the position of the i-th reference point; The module M3 also includes a secondary correction. Before performing the secondary correction of the hole pose, the surface is reconstructed based on the target coordinates of the hole. For the curved surface region Point, its manifold coordinates [ u , v The result is obtained by projecting the curve along the normal onto the interpolation surface. The calculation process is regarded as solving the following optimization problem: The target pose after secondary correction is calculated using the following formula. And use it as the target pose for locating the point to be processed: in, Represents the reference point position error matrix. The interpolation coefficient vector, The interpolation coefficient matrix for the reference points. This indicates the pose of the point to be added after the initial correction. This represents the pose of the theoretical point to be processed. In module M4, the normal vector correction in the hole pose is performed by correcting the initial normal vector of the point to be processed using data from the already processed points. The process is as follows: Module M4.1: Transmits the true pose of the reference point. and the initial corrected pose Store in matrix M done middle; Module M4.2: Calculate the location of the point to be processed arrive M done The distance between all the holes in the middle; Module M4.3: Selection M done The four holes closest to the point to be processed are used as new reference points; Module M4.4: Calculates the target pose after secondary correction using the new reference point data. ; Module M4.5: will The normal vector in the image is used as the normal for final positioning. After positioning is completed, the equipment performs online normal measurement and adjustment to obtain the final pose for processing. ; Module M4.6: If all holes in the area have been machined, then end; otherwise, continue. and deposit M done Then, proceed to module M4.

2.

5. The hole pose error compensation system based on manifold error similarity according to claim 4, characterized in that, The initial pose of the reference point includes: in, p Represents the position vector. n Represents the unit normal vector. q It is a unit quaternion; The pose error is calculated using the following formula: in, and These are the target pose and the initial pose, respectively. For positional error, The unit quaternion representing the normal error, representing to Rotational transformation, yes and The included angle, "This represents the generalized subtraction of the hole pose error; correspondingly, the generalized addition of the hole pose correction is defined as follows:" in," "Represents quaternion multiplication; For cases where the points to be processed are arranged in a line and there are only two reference points, they are treated as a scenario where the two boundary curves of the surface coincide.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the hole pose error compensation method based on manifold error similarity as described in any one of claims 1 to 3.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of the hole pose error compensation method based on manifold error similarity as described in any one of claims 1 to 3.

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