Dual-manipulator synchronization correction method based on geometric algebraic gradient

Abstract

The present invention provides a dual-manipulator synchronous calibration method based on geometric algebraic gradient, comprising the following steps: step 1: building a dual-manipulator system; step 2: generating an offline calibration posture according to the initial calibration data of the dual-manipulator system, and obtaining a calibration data set by executing the calibration posture; step 3: correcting the calibration data set sign; step 4: completing the optimization of the target problem based on the geometric algebraic gradient to achieve synchronous calibration of the dual-manipulator system. The present invention can be used for system calibration of a dual-manipulator measurement-processing intelligent processing system, and effectively improve the processing and measurement accuracy of the system.

Description

Technical Field

[0001] The present invention relates to a calibration method for a multi-robot cooperation system, and in particular to a dual-robot synchronization correction method based on geometric algebraic gradient. Background Art

[0002] Nowadays, multi-robot joint processing systems have been widely used in aerospace, energy and other important manufacturing fields that require large-scale parts processing due to their high flexibility, convenient deployment, ability to complete complex tasks and high efficiency. In these processing and manufacturing fields, using one robot to perform real-time measurement of the parts to be processed and another robot to perform precise processing based on the measurement results can significantly improve the efficiency and accuracy of processing.

[0003] After deploying the dual-arm machining system, the system must first be calibrated in advance (such as the transformation relationship between the base coordinate systems of the two robotic arms, the transformation relationship between the coordinate system of the measuring device and the coordinate system of the end of the robotic arm holding it, and the transformation relationship between the tool coordinate system and the coordinate system of the end of the robotic arm holding the tool) to ensure the operating accuracy during the actual machining process. The efficiency and accuracy of the correction algorithm will therefore directly affect the working condition of the system. However, the parameters to be corrected in the dual-arm machining system are significantly increased compared to the traditional single-arm machining device, and there is a nonlinear relationship between the parameters, which puts higher requirements on the correction algorithm.

[0004] After investigating the existing technologies, it was found that most of the current algorithms do not have the characteristics of simultaneous correction and have a slow execution speed. It is urgent to propose an efficient and high-precision correction method that can synchronously correct the dual-arm-hand-eye-tool transformation relationship of the dual-arm machining system. Summary of the invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a dual-manipulator synchronous correction method based on geometric algebraic gradient, which can complete the synchronous correction of the dual-manipulator, hand-eye, and tool coordinate system transformation of the dual-manipulator machining system, and improve the system processing efficiency and accuracy. The present invention is suitable for the calibration of the dual-manipulator collaborative machining system.

[0006] A dual-manipulator synchronous correction method based on geometric algebraic gradient provided by the present invention includes a manipulator with a structured light camera mounted on the end and another manipulator with a calibration target sphere system mounted on the end; and further includes the following steps:

[0007] Step 1: Build a dual-manipulator system; establish a camera coordinate system of a manipulator with a structured light camera at the end and a target sphere coordinate system of another manipulator with a calibration target sphere system at the end; use the manipulator with the structured light camera at the end to shoot the other manipulator with the calibration target sphere system at the end, determine the relative position between the camera coordinate system and the target sphere coordinate system, and obtain initial calibration data;

[0008] Step 2: generating an offline calibration posture according to the initial calibration data of the dual-manipulator system, and obtaining a calibration data set by executing the calibration posture;

[0009] Step 3: Correct the sign of the calibration data set; use a small number of samples to correct the measured data to achieve sign calibration of the calibration data set.

[0010] Step 4: Complete the optimization of the target problem based on the geometric algebraic gradient and realize the synchronous calibration of the dual-arm system.

[0011] Preferably, the target ball coordinate system of the calibration target ball system is composed of three precisely measured ceramic balls, with the origin determined as the center of the short side of the triangle at the center of the three balls, the Z axis pointing to the normal of the plane of the center of the three balls, the X axis along the short side of the triangle, and the Y axis along the short side through the center of the third ball.

[0012] Preferably, the robotic arm with a structured light camera mounted on its end is used to photograph the calibration target sphere system of another robotic arm and the measurement work of the other robotic arm during the calibration process.

[0013] Preferably, the calibration posture needs to meet the following conditions: the dual robotic arms do not collide with the environment, the dual robotic arms do not collide with each other, and the measurement and calibration target sphere system is within the field of view of the structured light camera.

[0014] Preferably, the process of executing the calibration posture needs to meet the following conditions: the robotic arms do not collide with the environment during operation, and do not collide with each other; during each shooting in the process of executing the calibration posture, the joint angles and end postures of the two robotic arms and the point cloud data generated by the current shooting are obtained at the same time. The three together constitute a calibration data point, and the calibration data points under all calibration postures are used to obtain the calibration data set.

[0015] Preferably, the specific method of correcting the measurement data using a small amount of samples in step 3 is:

[0016] S1: Using geometric algebraic manipulator forward kinematics, obtain kinematic elements with correct signs that represent the transformation relationship between the two manipulator ends and their respective base coordinate systems;

[0017] S2: Using a small number of calibration data points in the calibration data set, traverse the symbol combination of the kinematic element used to represent the transformation relationship from the camera coordinate system to the target sphere coordinate system, and generate the optimal rough estimate solution;

[0018] S3: Using the optimal rough estimate solution, correct the remaining symbols of all kinematic elements used to represent the transformation relationship from the camera coordinate system to the target sphere coordinate system.

[0019] Preferably, in step 4, the optimization of the target problem is completed based on the geometric algebraic gradient, and the specific method is:

[0020] Step 1: Construct the objective function of the optimization problem. The objective function of the optimization problem aims to minimize the least squares residual and uses Lagrange relaxation multipliers to take into account the constraints of the optimization variables in the motion submanifold. The specific form is:

[0021]

[0022] Among them, A is a motor used to represent the transformation relationship between the end of the manipulator loaded with the structured light camera and its base coordinate system, B is a motor used to represent the position of the calibration target ball system in the camera coordinate system, C is a motor used to represent the transformation relationship between the end of the manipulator holding the target ball system and its base coordinate system, X is a motor used to represent the transformation relationship between the end of the manipulator loaded with the structured light camera and the structured light camera coordinate system, Y is a motor used to represent the base of the manipulator loaded with the structured light camera to the base of the manipulator holding the calibration target ball system, and Z is a motor used to represent the relative relationship between the coordinate system formed by the calibration target ball system and the end of the manipulator holding it. A, B, C, X, Y, and Z are all represented by motors, and all operations except addition and subtraction are geometric products. It is the reverse operation in geometric algebra; Step 2: Use the descent method of the stochastic gradient algorithm and the geometric algebra gradient to optimize the target problem.

[0023] Preferably, the stochastic gradient algorithm uses a momentum-based KatyushaX algorithm.

[0024] Preferably, the geometric algebraic gradient is as follows: for the least squares residual term f(X,Y,Z)=||BXA-ZCY|| 2 , whose derivative is:

[0025]

[0026] Wherein E = BXA-ZCY.

[0027] For the Lagrangian relaxation term Its geometric algebraic gradient is:

[0028]

[0029] In the formula

[0030] Preferably, the step one also includes establishing an end coordinate system of another robotic arm that loads the calibration target ball system at the end, and a base coordinate system of the two robotic arm bases; the transformation relationship between the end coordinate systems of the two robotic arms and the base coordinate system, and the transformation relationship between the target ball coordinate system in the camera coordinate system can be expressed in the form of Euler angles or homogeneous transformation matrices.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] 1. The present invention can complete the synchronous correction of the dual-arm, hand-eye and tool coordinate system transformation of the dual-arm machining system, thereby improving the system machining efficiency and accuracy.

[0033] 2. The present invention can be used for system calibration of a dual-manipulator measurement-processing intelligent processing system, and can improve the processing and measurement accuracy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0035] Figure 1 A schematic diagram of a logic flow of a dual-manipulator synchronous correction method based on geometric algebraic gradient according to the present invention;

[0036] Figure 2 It is a schematic diagram of the structure of the dual-manipulator calibration system of the present invention;

[0037] Figure 3 It is a schematic diagram of the structure of the target sphere calibration system of the present invention;

[0038] Figure 4 A schematic diagram of symbol definition of calibration data of the present invention;

[0039] Figure 5 A flow chart is generated for the calibration posture of the present invention. DETAILED DESCRIPTION

[0040] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0041] In order to realize the synchronous correction of the dual-arm, hand-eye, and tool coordinate system transformation of the dual-arm machining system and improve the system machining efficiency and accuracy, the present invention provides a dual-arm synchronous correction method based on geometric algebraic gradient, including a mechanical arm with a structured light camera at the end and another mechanical arm with a calibration target sphere system at the end; and also includes the following steps:

[0042] Step 1: Build a dual-manipulator system; establish a camera coordinate system of a manipulator with a structured light camera at the end and a target sphere coordinate system of another manipulator with a calibration target sphere system at the end; use the manipulator with the structured light camera at the end to shoot the other manipulator with the calibration target sphere system at the end, determine the relative position between the camera coordinate system and the target sphere coordinate system, and obtain initial calibration data;

[0043] Step 2: generating an offline calibration posture according to the initial calibration data of the dual-manipulator system, and obtaining a calibration data set by executing the calibration posture;

[0044] Step 3: Correct the sign of the calibration data set; use a small number of samples to correct the measured data to achieve sign calibration of the calibration data set.

[0045] Step 4: Based on the geometric algebraic gradient, the optimization of the target problem is completed to achieve the synchronous calibration of the dual-manipulator system. This method can be used for the system calibration of the dual-manipulator measurement-processing intelligent processing system to improve the processing and measurement accuracy of the system.

[0046] like Figure 1 As shown, the specific process of this embodiment includes: first, building a dual-manipulator system, and generating a calibration posture that satisfies the field of view constraint, joint limit constraint, environmental collision constraint and self-collision constraint according to the built system; then, controlling the manipulator to run to the generated calibration posture and perform the shooting task to generate a calibration data set; since the method used in the present invention has strict constraints on the signs of each data point in the data set, it is necessary to calibrate the signs of the calibration data set before using the calibration data set; finally, defining an optimization problem on the motion submanifold that minimizes the loss function of the least squares problem and takes into account the constraints of the optimization variables using the Lagrangian operator, and using the stochastic gradient descent method based on the geometric algebraic gradient to complete the calibration of the entire system.

[0047] In this embodiment, Figure 2 Taking the dual mechanical system shown in the figure as an example, the method proposed in the present invention is used to calibrate the transformation relationship between the hand-eye, dual mechanical arm, and tool (calibration target ball system) of the dual mechanical arm system. The specific steps are as follows:

[0048] Step 1: Construct a dual-arm calibration system; the dual-arm calibration system specifically includes: two robotic arms, one of which is equipped with a structured light camera at the end to complete the scanning and shooting of the calibration object; the other robotic arm is equipped with a calibration target ball system at the end, and the relative position between the camera coordinate system and the target ball (tool) coordinate system can be determined by shooting the calibration target ball system. The dual-arm calibration system includes two robotic arms, one of which is equipped with a structured light camera at the end to shoot the calibration target ball system clamped at the end of the other robotic arm and perform measurement work during the processing process.

[0049] The calibration target system consists of three precisely measured ceramic balls (such as Figure 3 ), a coordinate system can be determined through the centers of the three balls, with the origin located at the center of the short side of the triangle at the center of the three balls, the Z axis pointing to the normal of the plane of the three balls' centers, the X axis along the short side of the triangle, and the Y axis along the short side passing through the center of the third ball.

[0050] In addition, during the calibration process, the definitions of the symbols are as follows (see Figure 4 ): Define A as a motor used to represent the transformation relationship between the end of the manipulator loaded with the structured light camera and its base coordinate system, B as a motor used to represent the position of the calibration target ball system in the camera coordinate system, C as a motor used to represent the transformation relationship between the end of the manipulator holding the target ball system and its base coordinate system, X as a motor used to represent the transformation relationship between the end of the manipulator loaded with the structured light camera and the structured light camera coordinate system, Y as a motor used to represent the base of the manipulator loaded with the structured light camera to the base of the manipulator holding the calibration target ball system, and Z as a motor used to represent the relative relationship between the coordinate system formed by the calibration target ball system and the end of the manipulator holding it. It should be noted that A, B, C, X, Y, and Z are all represented by the element motor (Motor) in geometric algebra, and the data obtained under the i-th measurement posture are respectively recorded as A i ,B i ,C i ; A, B, C are known in each measurement posture, and X, Y, Z are parameters to be calibrated.

[0051] Step 2: Control the robotic arm to run to the generated calibration posture and perform the shooting task, generate a calibration data set, generate the calibration posture offline and perform calibration to obtain the calibration data set; the calibration posture requires: the robotic arm does not collide with the environment, the two robotic arms do not collide with each other, and the measurement target ball system is within the field of view of the structured light camera.

[0052] The process of executing the calibration posture requires that: the robotic arms do not collide with the environment or with each other during operation; when executing each shot, the joint angles and end postures of the two robotic arms and the point cloud data generated by the current shot are obtained at the same time. The three together constitute a calibration data point, and the data points under all calibration postures together constitute the calibration data set.

[0053] Specifically, the process of generating calibration poses offline is as follows: Figure 5 shown.

[0054] First, the undetermined parameters X, Y, and Z can be estimated based on the environment. Using the estimated transformation relationships between the dual robotic arms, hand-eye, and tool, random calibration posture actions are generated in the simulation environment according to certain rules. For the calibration posture action, the following judgments are required: if the action does not meet the joint constraints of the robotic arm, it is regenerated; if the action causes the robotic arm to collide with the working environment, the action is regenerated; if the action causes a collision between the two robotic arms, the action is regenerated; if the action cannot ensure that the target ball falls within the field of view of the structured light camera, the action is regenerated.

[0055] The loop is executed until the specified number of calibration postures n is generated, and then the dual-arm calibration posture loop stops.

[0056] Execute calibration actions and collect calibration data sets;

[0057] In order to complete the calibration work automatically, safely and efficiently, in actual implementation, it is first necessary to model the working environment and use the random tree algorithm to generate the calibration path to ensure that during the execution process, the dual robotic arms will neither collide with themselves nor with obstacles in the environment.

[0058] Step 3: Correct the sign of the calibration dataset; use a small number of samples to correct the measured data to achieve sign calibration of the calibration dataset. Since this method has strict constraints on the sign of each data point in the dataset, it is necessary to calibrate the sign of the dataset before using the calibration dataset. Among them, the specific method of using a small number of samples to correct the measured data is:

[0059] S1: Use geometric algebraic robot forward kinematics to obtain the correct-signed motor that represents the transformation relationship between the two robot ends and their respective base coordinate systems;

[0060] S2: Using a small number of calibration data points in the calibration data set, traverse the symbol combination of the kinematic element used to represent the transformation relationship from the camera coordinate system to the target sphere coordinate system, and generate the optimal rough estimate solution;

[0061] S3: Using the optimal rough estimate solution, correct all remaining symbols of the kinematic elements used to represent the transformation relationship from the camera coordinate system to the target sphere (tool) coordinate system.

[0062] In the original data of the calibration data set, whether it is the transformation relationship between the end of the robot arm and the base (A, C), or the representation of the target sphere coordinate system in the structured light camera coordinate system (B), Euler angles or homogeneous transformation matrices can be used. Since these representations are one-to-two with the geometric algebraic motion sub-conversion used in the present invention—the positive and negative motion sub-conversions correspond to the same homogeneous transformation matrix, and the optimization algorithm used in the present invention is very sensitive to the sign of the motion sub-conversion, it is necessary to correct the sign of the data set before executing the optimization algorithm. Taking the transformation from the homogeneous transformation matrix to the motion sub-conversion as an example, the correction process is as follows:

[0063] First, the homogeneous transformation matrix from the end of the robot to the base is converted. Since the joint angles of the robot are known during the measurement process, the nominal kinematics of the robot based on geometric algebra can be used to combine the nominal robot geometric parameters to solve the nominal kinematics. Then the actual transformation matrix A of the robot arm i ,C i Transform into a motion (The rotation quaternion part is ) and with the nominal motion factor Compare the signs and make corrections according to the signs of the nominal kinematic components to complete the (The rotation quaternion part is ) sign correction.

[0064] Secondly, it is necessary to transform and check the homogeneous transformation matrix of the target ball system in the structured light camera coordinate system. The process is as follows: first select a small amount of calibration data (m, m is not less than 5), traverse all the motion sub-symbol combinations of B (2 m combinations), and the corresponding A and C with corrected signs form a set of temporary data sets. For each temporary data set, extract the rotation part (quaternion part) in the temporary data set, and use the matrix representation of the rotation part and the quaternion to write the least squares problem for solving the X, Y, and Z rotation parts; perform singular value decomposition on the normal equation matrix of the least squares problem, find the smallest one among all the singular values ​​generated by the temporary data sets, and the symbol combination of the normal equation corresponding to the singular value is the optimal symbol combination. The X, Y, and Z rotation parts calculated using this set of temporary data sets can be used as initial values ​​to correct the signs of other B movers.

[0065] Finally, the remaining B motions with undetermined symbols need to be adjusted. First, the remaining homogeneous transformation matrix B i Transformed into a moving unit whose sign is yet to be determined The rotating part is The correct sign of the motion element B can be determined according to the following formula:

[0066]

[0067] The above method can realize the conversion of A, B, C homogeneous transformation matrix to motor and the symbol calibration.

[0068] Step 4: Complete the optimization of the target problem based on the geometric algebraic gradient and realize the synchronous calibration of the dual-manipulator system. Specifically, define the optimization problem of minimizing the least squares problem loss function and taking into account the constraints of the optimization variables on the motion submanifold using the Lagrangian operator, and use the stochastic gradient descent method based on the geometric algebraic gradient to complete the calibration of the system. The specific method for completing the optimization of the target problem based on the geometric algebraic gradient is as follows:

[0069] Step 1: construct an optimization problem objective function, wherein the optimization problem objective function is to minimize the least squares residual, and use Lagrange relaxation multipliers to take into account the constraints of the optimization variables within the motion submanifold;

[0070] Specifically, the least squares problem loss function is expressed as follows:

[0071]

[0072] Among them, A is a motor used to represent the transformation relationship between the end of the manipulator loaded with structured light camera and its base coordinate system, B is a motor used to represent the position of the calibration target ball system in the camera coordinate system, C is a motor used to represent the transformation relationship between the end of the manipulator holding the target ball system and its base coordinate system, X is a motor used to represent the transformation relationship between the end of the manipulator loaded with structured light camera and the structured light camera coordinate system, Y is a motor used to represent the base of the manipulator loaded with structured light camera to the base of the manipulator holding the calibration target ball system, and Z is a motor used to represent the relative relationship between the coordinate system formed by the calibration target ball system and the end of the manipulator holding it. A, B, C, X, Y, and Z are all represented by motors. Except for addition and subtraction, all other operations are geometric products. ||■|| is the geometric algebraic norm. n is the number of calibration postures.

[0073] The Lagrange multiplier term expression used to constrain the optimization variables on the motor manifold is as follows:

[0074]

[0075] In the formula, It is the reverse operation in geometric algebra, and ■ can be X, Y, or Z.

[0076] The objective function combined with this Lagrangian relaxation term is as follows:

[0077]

[0078] Where γ1,γ2,γ3 are Lagrange relaxation multipliers. So the optimization problem can be defined as:

[0079]

[0080] Step 2: Use the descent method of the stochastic gradient algorithm and the geometric algebraic gradient to optimize the target problem.

[0081] Specifically, the geometric algebraic gradient is as follows, for f(X,Y,Z) = ||BXA-ZCY|| 2 , whose derivative is:

[0082]

[0083] Wherein E = BXA-ZCY.

[0084] for Its geometric algebraic gradient is:

[0085]

[0086] In the formula

[0087] The stochastic gradient algorithm is the momentum-based KatyushaX algorithm.

[0088] Further, as shown in the following table,

[0089]

[0090] Table To optimize variables , vec(■) refers to the gradient of the optimization variable Transform to vector.

[0091] The above method can be used to complete the calibration of the dual robot arm system, which can effectively improve the system processing efficiency and accuracy.

[0092] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0093] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A dual-manipulator synchronization correction method based on geometric algebraic gradient, characterized in that: The method comprises a mechanical arm with a structured light camera mounted on the end and another mechanical arm with a calibration target sphere system mounted on the end; and further comprises the following steps: Step 1: Build a dual-manipulator system; establish a camera coordinate system of a manipulator with a structured light camera at the end and a target sphere coordinate system of another manipulator with a calibration target sphere system at the end; determine the relative position between the camera coordinate system and the target sphere coordinate system by shooting the calibration target sphere system through the manipulator with the structured light camera at the end, and obtain initial calibration data; Step 2: Generate an offline calibration posture according to the initial calibration data of the dual-manipulator system, and obtain a calibration data set by executing the calibration posture. The calibration posture must meet the following conditions: the dual-manipulators do not collide with the environment, the dual-manipulators do not collide with each other, and the measurement calibration target ball system is within the field of view of the structured light camera. The process of executing the calibration posture must meet the following conditions: the robotic arms do not collide with the environment during operation, and the robotic arms do not collide with each other; in each shot during the execution of the calibration posture, the joint angles and end postures of the two robotic arms and the point cloud data generated by the current shot are simultaneously obtained. The three together constitute a calibration data point, and the calibration data points under all calibration postures are used to obtain the calibration data set; Step 3: Correct the sign of the calibration data set; use a small number of samples to correct the measured data to achieve sign calibration of the calibration data set. The specific method of correcting the measured data with a small number of samples is as follows: S1: Using geometric algebraic manipulator forward kinematics, obtain kinematic elements with correct signs that represent the transformation relationship between the two manipulator ends and their respective base coordinate systems; S2: Using a small number of calibration data points in the calibration data set, traverse the symbol combination of the kinematic element used to represent the transformation relationship from the camera coordinate system to the target sphere coordinate system, and generate the optimal rough estimate solution; S3: Using the optimal rough estimate solution, correct the remaining symbols of all kinematic elements used to represent the transformation relationship from the camera coordinate system to the target sphere coordinate system; Step 4: Optimize the target problem based on the geometric algebraic gradient, realize the synchronous calibration of the dual-manipulator system, and optimize the target problem based on the geometric algebraic gradient. The specific method is as follows: Step 1: construct an optimization problem objective function, wherein the optimization problem objective function is to minimize the least squares residual, and use Lagrange relaxation multipliers to take into account the constraints of the optimization variables within the motion submanifold; Step 2: Use the descent method of the stochastic gradient algorithm and the geometric algebraic gradient to optimize the target problem; The objective function of the optimization problem is: Among them, A is a kinematic unit used to represent the transformation relationship between the end of the manipulator loaded with the structured light camera and its base coordinate system, B is a kinematic unit used to represent the position of the calibration target ball system in the camera coordinate system, C is a kinematic unit used to represent the transformation relationship between the end of the manipulator holding the target ball system and its base coordinate system, X is a kinematic unit used to represent the transformation relationship between the end of the manipulator loaded with the structured light camera and the structured light camera coordinate system, Y is a kinematic unit used to represent the base of the manipulator loaded with the structured light camera to the base of the manipulator holding the calibration target ball system, and Z is a kinematic unit used to represent the relative relationship between the coordinate system formed by the calibration target ball system and the end of the manipulator holding it; A, B, C, x, Y, and Z are all represented by kinematic units, and all operations except addition and subtraction are geometric products, and ||■|| is the geometric algebraic norm; n is the number of calibration postures; Used to constrain optimization variables on the motion submanifold; γ1, γ2, γ3 are Lagrange relaxation multipliers; The geometric algebraic gradient is as follows: for f(X,Y,Z)=||BXA-ZCY|| 2 , whose derivative is: Wherein E = BXA-ZCY; for Its geometric algebraic gradient is: In the formula 2. The dual-manipulator synchronization correction method based on geometric algebraic gradient according to claim 1 is characterized in that: The target ball coordinate system of the calibration target ball system is composed of three precisely measured ceramic balls. The origin is determined as the center of the short side of the triangle at the center of the three balls, the Z axis points to the normal of the plane of the center of the three balls, the X axis is along the short side of the triangle, and the Y axis is along the short side through the center of the third ball.

3. The dual-manipulator synchronization correction method based on geometric algebraic gradient according to claim 1 is characterized in that: The mechanical arm with a structured light camera mounted on the end is used to photograph the calibration target sphere system of the other mechanical arm and the measurement work of the other mechanical arm during the calibration process.

4. The dual-manipulator synchronization correction method based on geometric algebraic gradient according to claim 1 is characterized in that: The stochastic gradient algorithm is the KatyushaX algorithm.

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