Constraint relaxation-based kinematics calibration method and device for sub-contained closed-loop robot

Abstract

The invention provides a sub-closed-loop-containing robot kinematics calibration method and device based on constraint relaxation, and relates to the technical field of robot calibration, and the method comprises the steps: carrying out the decomposition of a main kinematic chain under the condition that there are multiple branches in the main kinematic chain of a robot, so as to generate multiple virtual kinematic chains; according to kinematic parameters and closed-loop geometric constraints of virtual joints in each virtual kinematic chain, the theoretical tail end pose of the robot is determined; parameter errors are determined according to the pose deviation between the theoretical tail end pose and the actual tail end pose of the robot; according to the parameter errors and the calibrated kinematics parameters, the corrected pose deviation is determined; and the active joint displacement is updated according to the corrected pose deviation until the corrected pose deviation or the active joint displacement meets the iteration termination condition, the robot is calibrated according to the determined active joint target displacement, and the calibration precision of the robot is improved.

Description

Technical Field

[0001] This application relates to the field of robot calibration technology, and in particular to a kinematic calibration method and apparatus for a closed-loop robot with sub-components based on constraint relaxation. Background Technology

[0002] With the development of technology, the types of robots are increasing, and their utilization rate is also rising. Sub-loop robots refer to a special type of robot whose branches contain closed-loop kinematic sub-chains. By rationally introducing sub-loops to replace some complex kinematic pairs, the difficulty of component processing can be reduced while improving assembly accuracy. Furthermore, the proper layout of the sub-loops can increase the robot's flexibility and rigidity. Therefore, sub-loop robots have a very broad application prospect in work environments requiring high dexterity and high precision. Absolute positioning accuracy is one of the important performance indicators of a robot. Errors caused by assembly, processing, and other factors may affect the absolute positioning accuracy of sub-loop robots. Without changing the structure, the absolute positioning accuracy of the robot can be improved through kinematic calibration.

[0003] In related technologies, existing calibration methods for robots with sub-loops mainly employ the closed-loop vector method or the superposition principle, respectively applying parameter constraints to eliminate unknown passive joint displacements or separate geometric and non-geometric errors. Both of these methods reinforce the restrictive effect of parameter constraints, resulting in limited improvement in accuracy. Researching calibration methods based on constraint relaxation is expected to weaken the effect of parameter constraints, expand the parameter search space, and improve the absolute positioning accuracy of robots with sub-loops. Summary of the Invention

[0004] This application provides a method and apparatus for kinematic calibration of a closed-loop robot with sub-components based on constraint relaxation.

[0005] According to a first aspect of this application, a kinematic calibration method for a closed-loop robot containing cisterns based on constraint relaxation is provided, the method comprising: When there are multiple branches in the main kinematic chain of a robot, the main kinematic chain is decomposed to generate multiple virtual kinematic chains, wherein any virtual kinematic chain has at least one different kinematic parameter from the other virtual kinematic chains. The theoretical end-effector pose of the robot is determined based on the kinematic parameters of the virtual joints and the closed-loop geometric constraints in each virtual kinematic chain. The parameter error is determined based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot, wherein the actual end-effector pose is obtained by means of a measuring device. Based on the parameter error and the calibrated kinematic parameters, the corrected pose deviation is determined; The active joint displacement is updated based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition, and the robot is calibrated based on the determined active joint target displacement.

[0006] Optionally, when there are multiple branches in the robot's main kinematic chain, the main kinematic chain is decomposed to generate multiple virtual kinematic chains, including: Determine each branch point in the main kinematic chain; Virtual links and virtual joints are constructed at each branch point to generate multiple virtual kinematic chains.

[0007] Optionally, determining the theoretical end-effector pose of the robot based on the kinematic parameters of the virtual joints and closed-loop geometric constraints in each virtual kinematic chain includes: Based on the initial pose, rotational motion, and joint displacement in the nominal kinematic parameters, each virtual kinematic chain is subjected to an exponential product to generate a forward kinematic model corresponding to each virtual kinematic chain. Based on the forward kinematics model corresponding to each virtual kinematic chain, determine the theoretical end pose of each virtual kinematic chain; The theoretical end-effector pose of the robot is determined based on the closed-loop geometric constraints and the theoretical end-effector pose of each virtual kinematic chain. The passive joint displacement is partially derived from the positive kinematic model corresponding to each virtual kinematic chain to determine the passive joint Jacobian matrix. The current passive joint displacement is updated based on the deviation between the theoretical end pose of each virtual kinematic chain and the theoretical end pose of the robot, as well as the passive joint Jacobian matrix, to generate the updated passive joint displacement. Based on the updated passive joint displacement, return to the above steps of determining the theoretical end pose of each virtual kinematic chain until the number of iterations is reached or the deviation between the theoretical end pose of the virtual kinematic chain and the theoretical end pose of the robot is less than a first threshold.

[0008] Optionally, the step of performing kinematic modeling on each of the virtual kinematic chains based on the initial pose, rotational motion, and joint displacements in the nominal kinematic parameters to generate a forward kinematic model corresponding to each virtual kinematic chain includes: Assign a local coordinate system to each virtual link in each virtual kinematic chain, and assign a tool coordinate system on the moving platform; Based on the initial pose of the latter coordinate system in the former coordinate system, determine the initial transformation matrix between adjacent virtual links; The rotation of motion of each virtual joint is determined based on the axis coordinates of each virtual joint in the local coordinate system of the next connected virtual link in each virtual kinematic chain. Based on the initial transformation matrix and the motion spinor, kinematic modeling is performed on the virtual joints in each virtual kinematic chain in combination with the joint displacements to generate the forward kinematic model corresponding to each virtual kinematic chain.

[0009] Optionally, determining the parameter error based on the pose deviation between the theoretical and actual end-effector poses of the robot includes: The active joint displacement is input into the robot, and the actual end-effector pose of the robot is obtained through a measuring device; The pose deviation is determined based on the difference between the theoretical end-effector pose and the actual end-effector pose of the robot. The positive kinematic model of each virtual kinematic chain is subjected to partial derivatives with respect to geometric parameters to determine the error Jacobian matrix; The geometric parameter error value is determined based on the error Jacobian matrix and the pose deviation. The current kinematic parameters are updated using the geometric parameter error values ​​to generate updated kinematic parameters; Based on the updated kinematic parameters, return to the steps described above for determining the pose deviation, until the parameter error is determined.

[0010] Optionally, the step of returning to the above-described steps of determining the pose deviation based on the updated kinematic parameters until the parameter error is determined includes: If the geometric parameter error value is less than the second threshold or the pose deviation is less than the third threshold, the parameter error of the current round is determined based on the pose deviation between the theoretical end pose and the actual end pose of the robot. The parameter error of the current round is input into the trained neural network model, and the corrected parameter error is determined after processing by the neural network model.

[0011] Optionally, determining the corrected pose deviation based on the parameter error and the calibrated kinematic parameters includes: The kinematic parameters are updated using the parameter error to generate calibrated kinematic parameters; Based on the calibrated kinematic parameters, the corrected pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot is determined.

[0012] Optionally, updating the active joint displacement based on the corrected pose deviation includes: The positive kinematic model of each virtual kinematic chain is used to perform partial derivative processing on the active joint displacement to determine the active joint Jacobian matrix; The active joint displacement is updated based on the active joint Jacobian matrix and the corrected pose deviation.

[0013] According to a second aspect of this application, a kinematic calibration device for a closed-loop robot containing subatomic components based on constraint relaxation is provided, comprising: The generation module is used to decompose the main kinematic chain of the robot into multiple virtual kinematic chains when there are multiple branches in the main kinematic chain, wherein any virtual kinematic chain has at least one different kinematic parameter from the other virtual kinematic chains. The first determining module is used to determine the theoretical end-effector pose of the robot based on the kinematic parameters of the virtual joints and the closed-loop geometric constraints in each of the virtual kinematic chains. The second determining module is used to determine the parameter error based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot, wherein the actual end-effector pose is obtained by means of a measuring device. The third determining module is used to determine the corrected pose deviation based on the parameter error and the calibrated kinematic parameters. The update module is used to update the active joint displacement based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition, and to calibrate the robot based on the determined active joint target displacement.

[0014] Optionally, the generation module is specifically used for: Determine each branch point in the main kinematic chain; Virtual links and virtual joints are constructed at each branch point to generate multiple virtual kinematic chains.

[0015] Optionally, the first determining module includes: The generation unit is used to perform exponential product processing on each of the virtual kinematic chains based on the initial pose, rotational motion and joint displacement in the nominal kinematic parameters, so as to generate the forward kinematic model corresponding to each of the virtual kinematic chains. The first determining unit is used to determine the theoretical end pose of each virtual kinematic chain based on the forward kinematic model corresponding to each virtual kinematic chain. The second determining unit is used to determine the theoretical end pose of the robot based on the closed-loop geometric constraints and the theoretical end pose of each virtual kinematic chain. The first processing unit is used to perform partial derivative processing on the passive joint displacement of the positive kinematic model corresponding to each virtual kinematic chain to determine the passive joint Jacobian matrix. The first update unit is used to update the current passive joint displacement based on the deviation between the theoretical end pose of each virtual kinematic chain and the theoretical end pose of the robot and the passive joint Jacobian matrix, so as to generate the updated passive joint displacement. The third determining unit is used to return to the above steps of determining the theoretical end pose of each virtual kinematic chain based on the updated passive joint displacement, until the number of iterations is reached or the deviation between the theoretical end pose of the virtual kinematic chain and the theoretical end pose of the robot is less than a first threshold.

[0016] Optionally, the generation unit is specifically used for: Assign a local coordinate system to each virtual link in each virtual kinematic chain, and assign a tool coordinate system on the moving platform; Based on the initial pose of the latter coordinate system in the former coordinate system, determine the initial transformation matrix between adjacent virtual links; The rotation of motion of each virtual joint is determined based on the axis coordinates of each virtual joint in the local coordinate system of the next connected virtual link in each virtual kinematic chain. Based on the initial transformation matrix and the motion spinor, kinematic modeling is performed on the virtual joints in each virtual kinematic chain in combination with the joint displacements to generate the forward kinematic model corresponding to each virtual kinematic chain.

[0017] Optionally, the second determining module includes: The acquisition unit is used to input the active joint displacement into the robot and acquire the actual end-effector pose of the robot through a measuring device. The fourth determining unit is used to determine the pose deviation based on the difference between the theoretical end-effector pose and the actual end-effector pose of the robot. The second processing unit is used to perform partial derivative processing on the geometric parameters of the forward kinematic model of each virtual kinematic chain to determine the error Jacobian matrix; The fifth determining unit is used to determine the geometric parameter error value based on the error Jacobian matrix and the pose deviation; The second update unit is used to update the current kinematic parameters using the geometric parameter error value to generate updated kinematic parameters. The sixth determining unit is used to return to the above-mentioned steps of determining the pose deviation based on the updated kinematic parameters, until the parameter error is determined.

[0018] Optionally, the sixth determining unit is specifically used for: If the geometric parameter error value is less than the second threshold or the pose deviation is less than the third threshold, the parameter error of the current round is determined based on the pose deviation between the theoretical end pose and the actual end pose of the robot. The parameter error of the current round is input into the trained neural network model, and the corrected parameter error is determined after processing by the neural network model.

[0019] Optionally, the third determining module is specifically used for: The kinematic parameters are updated using the parameter error to generate calibrated kinematic parameters; Based on the calibrated kinematic parameters, the corrected pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot is determined.

[0020] Optionally, the update module is specifically used for: The positive kinematic model of each virtual kinematic chain is used to perform partial derivative processing on the active joint displacement to determine the active joint Jacobian matrix; The active joint displacement is updated based on the active joint Jacobian matrix and the corrected pose deviation.

[0021] According to a third aspect of this application, an electronic device is provided, comprising: a processor and a memory storing computer program instructions; the processor, when executing the computer program instructions, implements any of the above-described constraint relaxation-based kinematic calibration methods for a closed-loop robot containing subatomic components.

[0022] According to a fourth aspect of this application, a computer-readable storage medium is provided, on which computer program instructions are stored, which, when executed by a processor, implement any of the above-described constraint relaxation-based kinematic calibration methods for a closed-loop robot containing sub-loops.

[0023] In summary, the constraint-relaxed closed-loop robot kinematic calibration method and apparatus provided in this application have at least the following beneficial effects: When there are multiple branches in the robot's main kinematic chain, the main kinematic chain can be decomposed to generate multiple virtual kinematic chains. Each virtual kinematic chain has at least one different kinematic parameter from the others. Then, based on the kinematic parameters of the virtual joints in each virtual kinematic chain and the closed-loop geometric constraints, the theoretical end-effector pose of the robot can be determined. The parameter error is determined based on the pose deviation between the theoretical and actual end-effector poses, where the actual end-effector pose is obtained using a measuring device. Then, based on the parameter error and the calibrated kinematic parameters, the corrected pose deviation is determined. The active joint displacements are updated based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition. Finally, the robot is calibrated based on the determined target displacement of the active joints. Therefore, by decomposing the virtual kinematic chain, the complex structure can be transformed into a parallel model. Then, the geometric parameter error is solved iteratively through parameter identification, and the active joint target displacement is generated iteratively by combining error compensation. The robot is then calibrated based on the active joint target displacement, thereby effectively improving the robot's calibration accuracy. Attached Figure Description

[0024] To more clearly illustrate the specific embodiments of this application or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A flowchart illustrating a kinematic calibration method for a closed-loop robot with a calculus based on constraint relaxation, provided for embodiments of this application; Figure 2 A schematic diagram of virtual kinematic chain generation provided for an embodiment of this application; Figure 3 A schematic diagram illustrating another virtual kinematic chain generation provided for embodiments of this application; Figure 4 A structural diagram of a kinematic calibration device for a closed-loop robot with a child based on constraint relaxation, provided for an embodiment of this application; Figure 5 This is a structural diagram of an electronic device provided as an embodiment of the present application. Detailed Implementation

[0026] To make the above and other features and advantages of this application clearer, the application is further described below with reference to the accompanying drawings. It should be understood that the specific embodiments given herein are for the purpose of explanation to those skilled in the art, and are exemplary only, not restrictive.

[0027] In the following description, numerous specific details are set forth to provide a thorough understanding of this application. However, it will be apparent to those skilled in the art that the specific details are not required to practice this application. In other instances, well-known steps or operations have not been described in detail to avoid obscuring this application.

[0028] The constraint-relaxed closed-loop robot kinematic calibration method based on constraint relaxation provided in this application embodiment can be executed by the constraint-relaxed closed-loop robot kinematic calibration device based on constraint relaxation provided in this application embodiment, which can be configured in an electronic device.

[0029] refer to Figure 1 This application provides a kinematic calibration method for a closed-loop robot with numerators based on constraint relaxation, the method comprising: Step 101: If there are multiple branches in the main motion chain of the robot, the main motion chain is decomposed to generate multiple virtual motion chains, wherein any virtual motion chain has at least one different kinematic parameter from the other virtual motion chains.

[0030] The kinematic parameters may include initial pose, joint displacement, rotation, etc., which are not limited in this application.

[0031] Optionally, each branch point in the main kinematic chain can be determined first, and virtual links and virtual joints can be constructed at each branch point to generate multiple virtual kinematic chains.

[0032] For example, in such Figure 2 The main kinematic chain shown includes link 1{1}, joint 1, link 2{2}, and branch 1 (also called sub-chain 1) formed by joint 2 and link 3{3}, and branch 2 (also called sub-chain 2) formed by joint 3 and link 4{4}. The rotational motion of joint 1 is s1, and its displacement is q1; the rotational motion of joint 2 is s2, and its displacement is q2; the rotational motion of joint 3 is s3, and its displacement is q3. Figure 2It can be seen that the branch point is link 2{2}. Virtual links and virtual joints can then be constructed at link 2{2} to generate virtual kinematic chains 1 and 2. For example, virtual link 1,1{1,1}, virtual joint 2,1, virtual link 2,1{2,1}, virtual joint 3,1, and virtual link 3,1{3,1} constitute virtual kinematic chain 1; virtual link 1,2{1,2}, virtual joint 2,2, virtual link 2,2{2,2}, virtual joint 3,2, and virtual link 3,2{3,2} constitute virtual kinematic chain 2. The spin of virtual joint 2,1 can be expressed as s. 2,1 The displacement can be expressed as q 2,1 The rotational motion of the virtual joint 3,1 is s. 3,1 The displacement is q 3,1 The rotational motion of virtual joint 2,2 is s 2,2 The displacement is q 2,2 The rotational motion of the virtual joint 3,2 is s. 3,2 The displacement is q 3,2 Among them, for joint displacement, q 2,1 With q 2,2 Under the same conditions, q 3,1 With q 3,2 Different; or, q 3,1 With q 3,2 Under the same conditions, q 2,1 With q 2,2 Different; or, q 2,1 With q 2,2 Different, and q 3,1 With q 3,2 They are also different, which means that any virtual kinematic chain has at least one different kinematic parameter from the rest of the virtual kinematic chains.

[0033] Or, in such Figure 3 The main kinematic chain shown includes link 1{1}, joint 1, link 2{2}, joint 2, link 3{3}, joint 3, link 4{4}, joint 4, link 5{5}, joint 5, link 6{6}, joint 6, and link 7{7}. The rotational force of joint 1 is s1, and its displacement is q1; the rotational force of joint 2 is s2, and its displacement is q2; the rotational force of joint 3 is s3, and its displacement is q3; the rotational force of joint 4 is s4, and its displacement is q4; the rotational force of joint 5 is s5, and its displacement is q5; and the rotational force of joint 6 is s6, and its displacement is q6. Figure 3It can be seen that the branch points are links 2{2}, 4{4}, and 6{6}. Virtual links and virtual joints can then be constructed at links 2{2}, 4{4}, and 6{6} to generate virtual kinematic chain 1 and virtual kinematic chain 2, such as virtual link 1,1{1,1}, virtual joint 2,1, virtual link 2,1{2,1}, virtual joint 3,1, virtual link 3,1{3,1}, and virtual joint 4,1. Virtual links 4,1{4,1}, virtual joints 5,1, and 5,1{5,1} constitute virtual kinematic chain 1; virtual links 1,2{1,2}, virtual joints 2,2, 2,2{2,2}, 3,2, 3,2{3,2}, 4,2, 4,2{4,2}, 5,2, and 5,2{5,2} constitute virtual kinematic chain 2. The rotation of each virtual joint is... And the displacement q can be expressed as: virtual joint 2,1 is s 2,1 q 2,1 Virtual joint 3,1 is s 3,1 q 3,1 Virtual joint 4,1 is s 4,1 q 4,1 Virtual joint 5,1 is s 5,1 q 5,1 Virtual joint 2,2 is s 2,2 q 2,2 Virtual joints 3 and 2 are s 3,2 q 3,2 Virtual joints 4 and 2 are s 4,2 q 4,2 Virtual joints 5 and 2 are s 5,2 q 5,2 Among them, for joint displacement, q 2,1 With q 2,2 q 3,1 With q 3,2 q 4,1 With q 4,2 q 5,1 With q 5,2 At least one set of displacement values ​​are different, so that any virtual kinematic chain has at least one different kinematic parameter from the other virtual kinematic chains.

[0034] It should be noted that the above examples are merely illustrative and should not be construed as limiting the number of virtual joints and virtual links, the values ​​of joint displacement and rotation in the embodiments of this application.

[0035] Step 102: Determine the theoretical end-effector pose of the robot based on the kinematic parameters of the virtual joints in each virtual kinematic chain and the closed-loop geometric constraints.

[0036] In this context, the closed-loop geometric constraint can be understood as the end poses of multiple virtual kinematic chains obtained by decomposing the same master kinematic chain being the same, or it can also be understood as, in the closed-loop kinematic chain, there can be multiple different paths from the same starting point to the same ending point, but the final destination is the same, etc. This application does not limit this.

[0037] Optionally, kinematic modeling can be performed on each virtual kinematic chain based on the initial pose, rotational motion, and joint displacement in the nominal kinematic parameters to generate the corresponding forward kinematic model for each virtual kinematic chain.

[0038] The nominal kinematic parameters, also known as theoretical kinematic parameters, are usually the starting point and benchmark of the robot calibration process. They include all the geometric and motion variables required to construct the idealized or nominal kinematic model of the robot, and this application does not limit them.

[0039] Optionally, a local coordinate system can be assigned to each virtual link in each virtual kinematic chain, and a tool coordinate system can be assigned on the moving platform. Then, based on the initial pose of the latter coordinate system in the former coordinate system, the initial transformation matrix between adjacent virtual links can be determined. Then, based on the axis coordinates of each virtual joint in each virtual kinematic chain in the local coordinate system of the connected latter virtual link, the motion screw of each virtual joint can be determined. Finally, based on the initial transformation matrix and motion screw, combined with the joint displacement, kinematic modeling of the virtual joints in each virtual kinematic chain can be performed to generate the forward kinematic model corresponding to each virtual kinematic chain.

[0040] The moving platform, also known as the robot's end effector, can be assigned a local coordinate system along each virtual link, starting from the base coordinate system, until the moving platform is assigned a tool coordinate system. The local and tool coordinate systems can be assigned using various rules, such as the DH parameter method or any other feasible coordinate system assignment rules; this application does not limit the specific rules.

[0041] Subsequently, when the robot is in its initial state with all joint displacements at zero, nominal kinematic parameters can be obtained through measurement or CAD model analysis, i.e., the initial transformation matrix between adjacent virtual links can be obtained. For each virtual joint in the virtual kinematic chain, its motion screw at zero position can be calculated based on its axis coordinates in the local coordinate system. Furthermore, for rotary joints, the motion screw can be determined by processing the unit direction vector of its joint axis in the local coordinate system and the position vector of any point on the joint axis; for translating joints, the motion screw can be determined by processing the unit direction vector of its translation direction in the local coordinate system. In this case, the motion screw is used to characterize translational motion, etc., and this application does not limit this.

[0042] In addition, the initial transformation matrices between all adjacent links and the tool coordinate system can be multiplied sequentially to obtain the total initial transformation matrix, which can be used to characterize the overall pose of the end-effector tool coordinate system relative to the robot base coordinate system. Then, the motion screw of each virtual joint and its displacement can be combined into an exponential transformation operator. Starting from the total initial transformation matrix, all exponential transformation operators are multiplied sequentially from the base to the end-effector to generate the forward kinematic model corresponding to each virtual kinematic chain through kinematic modeling.

[0043] Then, based on the forward kinematics model corresponding to each virtual kinematic chain, the theoretical end-effector pose of each virtual kinematic chain can be determined. Based on the closed-loop geometric constraints and the theoretical end-effector pose of each virtual kinematic chain, the theoretical end-effector pose deviation of the robot can be determined. The passive joint displacements are then partially derived from the forward kinematics model corresponding to each virtual kinematic chain to determine the passive joint Jacobian matrix. Next, based on the deviation between the theoretical end-effector pose of each virtual kinematic chain and the theoretical end-effector pose of the robot, and the passive joint Jacobian matrix, the current passive joint displacements are updated to generate updated passive joint displacements. Then, based on the updated passive joint displacements, the process of determining the theoretical end-effector pose of each virtual kinematic chain can be repeated until the required number of iterations is reached or the deviation between the theoretical end-effector pose of the virtual kinematic chain and the theoretical end-effector pose of the robot is less than a first threshold.

[0044] In this process, joint displacements can be used as input data for the forward kinematics model. After processing by the forward kinematics model, the theoretical end-effector pose of each virtual kinematic chain can be determined. Based on the closed-loop geometric constraint that the end-effector poses of multiple virtual kinematic chains obtained from the decomposition of the same master kinematic chain are equal, and combined with the theoretical end-effector pose of each virtual kinematic chain, the theoretical end-effector pose of the robot can be further determined.

[0045] It is understandable that in robots with sub-loops, passive joints refer to joints whose displacements cannot be directly given by the controller, but can only be determined by the robot's mechanical structure and geometric closed-loop constraints. Therefore, in this embodiment, the theoretical end-effector pose of each virtual kinematic chain can be calculated using a forward kinematics model based on the initial pose, kinematic spinor, known active joint displacements, and currently estimated passive joint displacements from the current nominal kinematic parameters. Then, based on the closed-loop geometric constraint that the end-effector poses of all virtual kinematic chains are equal, the theoretical end-effector pose of the robot is determined. Subsequently, the partial derivative of the forward kinematics model of each virtual kinematic chain with respect to the passive joint displacements can be obtained to obtain the passive joint Jacobian matrix. This passive joint Jacobian matrix reflects the relationship between the small movements of the passive joint and the small changes in the end-effector pose; that is, the passive joint Jacobian matrix indicates in which direction and by how much the passive joint should move to reduce pose deviation. Then, based on the deviation between the theoretical end pose of the current robot and the theoretical end pose of the virtual kinematic chain, as well as the Jacobian matrix of the passive joints, the passive joint displacement correction amount required to eliminate the deviation can be solved in reverse. The calculated correction amount is then applied to the currently estimated passive joint displacement to generate the updated passive joint displacement.

[0046] In addition, the first threshold can be a pre-set value, or it can be adjusted as needed, etc., and this application does not limit it in this regard.

[0047] Understandably, the termination condition can be determined by whether the number of iterations reaches the upper limit, or whether the deviation between the robot's theoretical end-effector pose and the theoretical end-effector pose of the virtual kinematic chain is less than a first threshold. If the termination condition is met, the loop exits, and the passive joint displacement at this point becomes the final solution, determining the robot's current theoretical end-effector pose. If the termination condition is not met, the updated passive joint displacement can be used to return to the steps of determining the theoretical end-effector pose of each virtual kinematic chain, recalculating until the termination condition is met.

[0048] Step 103: Determine the parameter error based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot. The actual end-effector pose is obtained using a measuring device.

[0049] The measuring equipment can be a laser tracker, a vision system, etc., and this application does not limit it.

[0050] Understandably, for a given set of active joint displacements, the theoretical end-effector pose of the robot can be determined using the current forward kinematics model and iterative algorithm. Then, the active joint displacements are input into the robot, and the actual end-effector pose of the robot under the same set of active joint displacements is obtained using measurement equipment. The difference between the theoretical end-effector pose and the actual end-effector pose is then calculated to obtain the pose deviation. This pose deviation is then analyzed to determine the parameter error.

[0051] Optionally, the active joint displacement can be input into the robot first, and the actual end-effector pose of the robot can be obtained through a measuring device. Then, the pose deviation can be determined based on the difference between the theoretical end-effector pose and the actual end-effector pose. The forward kinematics model of each virtual kinematic chain is then processed with partial derivatives of the geometric parameters to determine the error Jacobian matrix. Then, the geometric parameter error value is determined based on the error Jacobian matrix and the pose deviation. The current kinematic parameters can then be updated using the geometric parameter error value to generate updated kinematic parameters. Based on the updated kinematic parameters, the steps to determine the pose deviation described above are returned until the parameter error is determined.

[0052] The geometric parameters may include, for example, link length, link torsion angle, and joint zero position, but this application does not limit them.

[0053] Understandably, all the geometric parameters to be identified, such as link length, link twist angle, and joint zero position, can be arranged into a geometric parameter vector. Then, the partial derivative of this geometric parameter vector can be obtained using a forward kinematics model to yield the error Jacobian matrix. This matrix characterizes the sensitivity of small changes in geometric parameters to the end effector pose. Next, based on the currently calculated pose deviation and error Jacobian matrix, the geometric parameter error values ​​can be solved using the least squares method or the Levenberg-Marquardt algorithm. In other words, a set of parameter corrections that optimally reduces the current pose deviation can be obtained through inversion calculation. Then, the currently used kinematic parameters are updated using the obtained geometric parameter error values ​​to generate updated kinematic parameters. Finally, based on the updated kinematic parameters, a new theoretical end effector pose can be recalculated. The difference between the new theoretical end effector pose and the actual end effector pose is used to determine the pose deviation, starting a new round of iterative calculations until a termination condition is met to determine the parameter error at this point.

[0054] Optionally, if the geometric parameter error is less than the second threshold or the pose deviation is less than the third threshold, the parameter error for the current round can be determined based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose. Then, the parameter error for the current round can be input into the trained neural network model, and the corrected parameter error can be determined after processing by the neural network model.

[0055] The second and third thresholds can be pre-set values ​​or can be adjusted as needed; this application does not limit this.

[0056] In addition, the neural network model can be any model that can perform regression processing, such as random forest (RM), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), residual network (ResNet-1D), long short-term memory network (LSTM), or other machine learning models that can perform regression processing, etc., and this application does not limit it in this regard.

[0057] Furthermore, if the geometric parameter error value is less than the second threshold or the pose deviation is less than the third threshold, it indicates that convergence is near. The neural network model can then be used to further process difficult-to-model geometric parameter errors such as thermal drift, joint flexibility, friction, reducer backlash, and measurement noise. At this point, the geometric parameter error value calculated in the current iteration can be used as an input vector into the trained neural network model. After nonlinear transformations and processing within the neural network's internal layers, a corrected parameter error can be output. This corrected parameter error fully considers error components that were not captured in previous iterations, such as higher-order nonlinearities and coupling effects, thereby improving the comprehensiveness of the parameter error.

[0058] Understandably, given the numerous factors influencing parameter errors, a neural network model can be used for fitting and estimation. For instance, introducing a skip connection architecture in the neural network model can effectively avoid the vanishing and exploding gradient problems that occur with excessive network layers, and shorten the gradient accumulation during backpropagation for updating the weights of neurons near the input layer. Therefore, by training the network parameters using error backpropagation, a trained neural network model can be generated, enabling the identification of error parameters in a closed-loop robot.

[0059] Therefore, in the embodiments of this application, during the process of determining parameter errors, all geometric parameter errors, including virtual joints and virtual links, such as link length, joint zero position, and axial direction, are fully identified, thereby effectively improving the completeness and comprehensiveness of parameter identification and providing a solid data foundation for subsequent robot calibration based on the determined parameter errors.

[0060] Step 104: Determine the corrected pose deviation based on the parameter error and the calibrated kinematic parameters.

[0061] Among them, calibrated kinematic parameters can be understood as kinematic parameters that, after being corrected from the nominal kinematic parameters, can more accurately describe the robot's motion characteristics.

[0062] Optionally, after determining the parameter error, the current kinematic parameters can be corrected and updated based on the parameter error to generate calibrated kinematic parameters. Then, based on the calibrated kinematic parameters, the theoretical end-effector pose and the actual end-effector pose of the robot can be recalculated, and the corrected pose deviation between the theoretical end-effector pose and the actual end-effector pose can be determined based on the difference between the two.

[0063] For example, after determining the parameter error, it can be summed or weighted and fused with the kinematic parameters from the previous iteration or the initial kinematic parameters to obtain the calibration kinematic parameters. Then, the active joint displacements and calibration kinematic parameters can be input into the forward kinematics model to recalculate the robot's theoretical end-effector pose. This process can simultaneously solve for any possible passive joint displacements to ensure the model satisfies all closed-loop constraints. Afterward, the actual end-effector pose of the robot, acquired by the laser tracker in the current pose, can be read or retrieved, and the difference between the corrected theoretical end-effector pose and the actual end-effector pose can be calculated, which is used as the corrected pose deviation, etc. This application does not limit this process.

[0064] Step 105: Update the active joint displacement based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition, and calibrate the robot based on the determined active joint target displacement.

[0065] The iteration termination condition can be that the corrected pose deviation is less than a certain value, the active joint displacement update is less than a certain value, or the iteration cycle is reached, etc., or it can be adjusted according to actual needs. This application does not limit this.

[0066] Understandably, after determining the corrected pose deviation, the active joint displacements can be updated. Using these updated displacements, the theoretical end-effector pose of the robot is recalculated, and the updated displacements are input into the robot to obtain its actual end-effector pose via measurement equipment. The parameter error is determined based on the pose deviation between the theoretical and actual end-effector poses. This parameter error, along with the calibrated kinematic parameters, is then used to determine the corrected pose deviation. Next, it is determined whether the corrected pose deviation or active joint displacements meet the iteration termination condition. If the condition is met, the robot is calibrated based on the target displacements of the active joints determined in the current iteration. If the termination condition is not met, the active joint displacements are updated again based on the corrected pose deviation. This process is repeated iteratively until the termination condition is met, thus achieving robot calibration.

[0067] Therefore, in this embodiment of the application, by iterating multiple times and gradually approximating the values, the target displacement of the active joint that accurately reaches the desired pose can be obtained. Then, the target displacement value of the active joint is input into the robot controller, which can improve the absolute positioning accuracy of the end effector and thus achieve the purpose of calibration.

[0068] Optionally, in the process of updating the active joint displacement based on the corrected pose deviation, the positive kinematic model of each virtual kinematic chain can be used to perform partial derivative processing on the active joint displacement to determine the active joint Jacobian matrix, and then the active joint displacement can be updated based on the active joint Jacobian matrix and the corrected pose deviation.

[0069] Specifically, the robot's differential kinematics formula can be used to process the partial derivatives of the active joint displacements through a forward kinematics model to determine the active joint Jacobian matrix. Then, the corrected pose deviation and the active joint Jacobian matrix can be solved to determine the adjustment amount of the active joint displacement. This ensures that after executing this displacement, the robot's end effector pose can eliminate the current deviation. Subsequently, this active joint displacement adjustment amount can be summed or weighted and fused with the current active joint displacement to generate a new set of joint commands that theoretically bring the robot's end effector closer to the desired pose, thus updating the active joint displacements.

[0070] Optionally, the identified error parameters can be substituted into the forward kinematics model to obtain a calibrated forward kinematics model. This calibrated model can then be used to perform partial differential processing on the active joint displacements to establish a differential error compensation model. Following this, based on the kinematic characteristics of the unibody closed-loop robot, the displacement constraints between each active joint in each virtual kinematic chain can be listed, and active joint displacement constraint equations can be established. These equations are then combined with the differential error compensation model to establish an error compensation model for the unibody closed-loop robot. Subsequently, the augmented matrix method is used to transform the constrained error compensation model into an unconstrained optimization problem, thereby achieving error compensation for the unibody closed-loop robot. This application does not limit the scope of this application.

[0071] Therefore, in this embodiment of the application, by constructing a virtual kinematic chain, the complex closed-loop robot with sub-loops is transformed into a common parallel robot, which can eliminate joint displacement constraints and link initial pose constraints in the calibration process, thereby effectively improving the calibration accuracy and absolute positioning accuracy of the robot.

[0072] In this embodiment, when the main kinematic chain of a robot has multiple branches, it can be decomposed to generate multiple virtual kinematic chains. Each virtual kinematic chain has at least one different kinematic parameter from the others. Then, based on the kinematic parameters of the virtual joints in each virtual kinematic chain and the closed-loop geometric constraints, the theoretical end-effector pose of the robot is determined. The parameter error is determined based on the pose deviation between the theoretical and actual end-effector poses (the actual end-effector pose is obtained using a measuring device). Then, based on the parameter error and the calibration kinematic parameters, a corrected pose deviation is determined. The active joint displacements are updated based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition. The robot is then calibrated based on the determined active joint target displacements. Thus, by decomposing the virtual kinematic chain, a complex structure can be transformed into a parallel model. Then, geometric parameter errors are solved iteratively through parameter identification, and active joint target displacements are generated iteratively with error compensation. Finally, robot calibration is performed based on the active joint target displacements, thereby improving the robot's calibration accuracy.

[0073] This application provides a kinematic calibration device 400 for a closed-loop robot containing subatomic components based on constraint relaxation, such as... Figure 4 As shown, the device includes a generation module 410, a first determination module 420, a second determination module 430, a third determination module 440, and an update module 450.

[0074] The generation module 410 is used to decompose the main motion chain of the robot into multiple virtual motion chains when there are multiple branches in the main motion chain, wherein any virtual motion chain has at least one different kinematic parameter from the other virtual motion chains.

[0075] The first determining module 420 is used to determine the theoretical end-effector pose of the robot based on the kinematic parameters of the virtual joints and the closed-loop geometric constraints in each of the virtual kinematic chains.

[0076] The second determining module 430 is used to determine the parameter error based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot, wherein the actual end-effector pose is obtained by means of a measuring device.

[0077] The third determining module 440 is used to determine the corrected pose deviation based on the parameter error and the calibrated kinematic parameters.

[0078] The update module 450 is used to update the active joint displacement according to the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition, and to calibrate the robot according to the determined active joint target displacement.

[0079] Optionally, the generation module 410 is specifically used for: Determine each branch point in the main kinematic chain; Virtual links and virtual joints are constructed at each branch point to generate multiple virtual kinematic chains.

[0080] Optionally, the first determining module 420 includes: The generation unit is used to perform exponential product processing on each of the virtual kinematic chains based on the initial pose, rotational motion and joint displacement in the nominal kinematic parameters, so as to generate the forward kinematic model corresponding to each of the virtual kinematic chains. The first determining unit is used to determine the theoretical end pose of each virtual kinematic chain based on the forward kinematic model corresponding to each virtual kinematic chain. The second determining unit is used to determine the theoretical end pose of the robot based on the closed-loop geometric constraints and the theoretical end pose of each virtual kinematic chain. The first processing unit is used to perform partial derivative processing on the passive joint displacement of the positive kinematic model corresponding to each virtual kinematic chain to determine the passive joint Jacobian matrix. The first update unit is used to update the current passive joint displacement based on the deviation between the theoretical end pose of each virtual kinematic chain and the theoretical end pose of the robot and the passive joint Jacobian matrix, so as to generate the updated passive joint displacement. The third determining unit is used to return to the above steps of determining the theoretical end pose of each virtual kinematic chain based on the updated passive joint displacement, until the number of iterations is reached or the deviation between the theoretical end pose of the virtual kinematic chain and the theoretical end pose of the robot is less than a first threshold.

[0081] Optionally, the generation unit is specifically used for: Assign a local coordinate system to each virtual link in each virtual kinematic chain, and assign a tool coordinate system on the moving platform; Based on the initial pose of the latter coordinate system in the former coordinate system, determine the initial transformation matrix between adjacent virtual links; The rotation of motion of each virtual joint is determined based on the axis coordinates of each virtual joint in the local coordinate system of the next connected virtual link in each virtual kinematic chain. Based on the initial transformation matrix and the motion spinor, kinematic modeling is performed on the virtual joints in each virtual kinematic chain in combination with the joint displacements to generate the forward kinematic model corresponding to each virtual kinematic chain.

[0082] Optionally, the second determining module 430 includes: The acquisition unit is used to input the active joint displacement into the robot and acquire the actual end-effector pose of the robot through a measuring device. The fourth determining unit is used to determine the pose deviation based on the difference between the theoretical end-effector pose and the actual end-effector pose of the robot. The second processing unit is used to perform partial derivative processing on the geometric parameters of the forward kinematic model of each virtual kinematic chain to determine the error Jacobian matrix; The fifth determining unit is used to determine the geometric parameter error value based on the error Jacobian matrix and the pose deviation; The second update unit is used to update the current kinematic parameters using the geometric parameter error value to generate updated kinematic parameters. The sixth determining unit is used to return to the above-mentioned steps of determining the pose deviation based on the updated kinematic parameters, until the parameter error is determined.

[0083] Optionally, the sixth determining unit is specifically used for: If the geometric parameter error value is less than the second threshold or the pose deviation is less than the third threshold, the parameter error of the current round is determined based on the pose deviation between the theoretical end pose and the actual end pose of the robot. The parameter error of the current round is input into the trained neural network model, and the corrected parameter error is determined after processing by the neural network model.

[0084] Optionally, the third determining module 440 is specifically used for: The kinematic parameters are updated using the parameter error to generate calibrated kinematic parameters; Based on the calibrated kinematic parameters, the corrected pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot is determined.

[0085] Optionally, the update module 450 is specifically used for: The positive kinematic model of each virtual kinematic chain is used to perform partial derivative processing on the active joint displacement to determine the active joint Jacobian matrix; The active joint displacement is updated based on the active joint Jacobian matrix and the corrected pose deviation.

[0086] The constraint-relaxed closed-loop robot kinematic calibration device provided in this application can decompose the main kinematic chain of a robot with multiple branches to generate multiple virtual kinematic chains. Each virtual kinematic chain has at least one different kinematic parameter from the others. Then, based on the kinematic parameters of the virtual joints in each virtual kinematic chain and the closed-loop geometric constraints, the theoretical end-effector pose of the robot is determined. The parameter error is determined based on the pose deviation between the theoretical and actual end-effector poses (the actual end-effector pose is obtained using a measuring device). The corrected pose deviation is then determined based on the parameter error and the calibrated kinematic parameters. The active joint displacements are updated based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition. The robot is then calibrated based on the determined active joint target displacements. Thus, by decomposing the virtual kinematic chain, complex structures can be transformed into parallel models. Then, geometric parameter errors are solved iteratively through parameter identification, and active joint target displacements are generated iteratively with error compensation. Finally, robot calibration is performed based on the active joint target displacements, thereby improving the robot's calibration accuracy.

[0087] It should be understood that the specific features, operations, and details described herein with respect to the methods of this application can also be similarly applied to the apparatus and system of this application, or vice versa. Furthermore, each step of the methods of this application described above can be performed by a corresponding component or unit of the apparatus or system of this application.

[0088] It should be understood that the various modules / units of the device of this application can be implemented wholly or partially through software, hardware, firmware, or a combination thereof. Each module / unit can be embedded in the processor of the electronic device in hardware or firmware form or independent of the processor, or it can be stored in the memory of the electronic device in software form for the processor to call to execute the operation of each module / unit. Each module / unit can be implemented as an independent component or module, or two or more modules / units can be implemented as a single component or module.

[0089] like Figure 5 As shown, this application provides an electronic device 500, which includes a processor 501 and a memory 502 storing computer program instructions. When the processor 501 executes the computer program instructions, it implements the steps of the aforementioned constraint relaxation-based kinematic calibration method for a closed-loop robot with sub-loops. This electronic device 500 can be broadly categorized as a server, terminal, or any other electronic device with the necessary computing and / or processing capabilities.

[0090] In one embodiment, the electronic device 500 may include a processor, memory, network interface, communication interface, etc., connected via a system bus. The processor of the electronic device 500 can be used to provide necessary computing, processing, and / or control capabilities. The memory of the electronic device 500 may include non-volatile storage media and internal memory. The non-volatile storage media may store an operating system, computer programs, etc. The internal memory can provide an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface and communication interface of the electronic device 500 can be used to connect and communicate with external devices via a network. When the computer program is executed by the processor, it performs the steps of the method of this application.

[0091] This application provides a computer-readable storage medium storing computer program instructions, which, when executed by a processor, implement the aforementioned constraint relaxation-based kinematic calibration method for a closed-loop robot containing sub-subjects.

[0092] Those skilled in the art will understand that the method steps of this application can be performed by a computer program instructing related hardware, such as electronic device 500 or a processor. The computer program can be stored in a non-transitory computer-readable storage medium, and its execution causes the steps of this application to be performed. Depending on the context, any reference herein to memory, storage, or other media may include non-volatile or volatile memory. Examples of non-volatile memory include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, magnetic tape, floppy disk, magneto-optical data storage device, optical data storage device, hard disk, solid-state drive, etc. Examples of volatile memory include random access memory (RAM), external cache memory, etc.

[0093] The technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification, provided that such combination does not contain contradictions.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A kinematic calibration method for a closed-loop robot with numerators based on constraint relaxation, characterized in that, include: When there are multiple branches in the main kinematic chain of a robot, the main kinematic chain is decomposed to generate multiple virtual kinematic chains, wherein any virtual kinematic chain has at least one different kinematic parameter from the other virtual kinematic chains. The theoretical end-effector pose of the robot is determined based on the kinematic parameters of the virtual joints and the closed-loop geometric constraints in each virtual kinematic chain. The parameter error is determined based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot, wherein the actual end-effector pose is obtained by means of a measuring device. Based on the parameter error and the calibrated kinematic parameters, the corrected pose deviation is determined; The active joint displacement is updated based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition, and the robot is calibrated based on the determined active joint target displacement.

2. The method as described in claim 1, characterized in that, When there are multiple branches in the robot's main kinematic chain, the main kinematic chain is decomposed to generate multiple virtual kinematic chains, including: Determine each branch point in the main kinematic chain; Virtual links and virtual joints are constructed at each branch point to generate multiple virtual kinematic chains.

3. The method as described in claim 1, characterized in that, The step of determining the theoretical end-effector pose of the robot based on the kinematic parameters of the virtual joints and closed-loop geometric constraints in each virtual kinematic chain includes: Based on the initial pose, rotational motion, and joint displacement in the nominal kinematic parameters, kinematic modeling is performed on each virtual kinematic chain to generate a corresponding forward kinematic model for each virtual kinematic chain. Based on the forward kinematics model corresponding to each virtual kinematic chain, determine the theoretical end pose of each virtual kinematic chain; The theoretical end-effector pose of the robot is determined based on the closed-loop geometric constraints and the theoretical end-effector pose of each virtual kinematic chain. The passive joint displacement is partially derived from the positive kinematic model corresponding to each virtual kinematic chain to determine the passive joint Jacobian matrix. The current passive joint displacement is updated based on the deviation between the theoretical end pose of each virtual kinematic chain and the theoretical end pose of the robot, as well as the passive joint Jacobian matrix, to generate the updated passive joint displacement. Based on the updated passive joint displacement, return to the above steps of determining the theoretical end pose of each virtual kinematic chain until the number of iterations is reached or the deviation between the theoretical end pose of the virtual kinematic chain and the theoretical end pose of the robot is less than a first threshold.

4. The method as described in claim 3, characterized in that, The step of performing kinematic modeling on each virtual kinematic chain based on the initial pose, rotational motion, and joint displacement in the nominal kinematic parameters to generate a corresponding forward kinematic model for each virtual kinematic chain includes: Assign a local coordinate system to each virtual link in each virtual kinematic chain, and assign a tool coordinate system on the moving platform; Based on the initial pose of the latter coordinate system in the former coordinate system, determine the initial transformation matrix between adjacent virtual links; The rotation of motion of each virtual joint is determined based on the axis coordinates of each virtual joint in the local coordinate system of the next connected virtual link in each virtual kinematic chain. Based on the initial transformation matrix and the motion spinor, kinematic modeling is performed on the virtual joints in each virtual kinematic chain in combination with the joint displacements to generate the forward kinematic model corresponding to each virtual kinematic chain.

5. The method as described in claim 3, characterized in that, The step of determining the parameter error based on the pose deviation between the theoretical and actual end-effector poses of the robot includes: The active joint displacement is input into the robot, and the actual end-effector pose of the robot is obtained through a measuring device; The pose deviation is determined based on the difference between the theoretical end-effector pose and the actual end-effector pose of the robot. The positive kinematic model of each virtual kinematic chain is subjected to partial derivatives with respect to geometric parameters to determine the error Jacobian matrix; The geometric parameter error value is determined based on the error Jacobian matrix and the pose deviation. The current kinematic parameters are updated using the geometric parameter error values ​​to generate updated kinematic parameters; Based on the updated kinematic parameters, return to the steps described above for determining the pose deviation, until the parameter error is determined.

6. The method as described in claim 5, characterized in that, The step of returning to the above-mentioned step of determining the pose deviation based on the updated kinematic parameters until the parameter error is determined includes: If the geometric parameter error value is less than the second threshold or the pose deviation is less than the third threshold, the parameter error of the current round is determined based on the pose deviation between the theoretical end pose and the actual end pose of the robot. The parameter error of the current round is input into the trained neural network model, and the corrected parameter error is determined after processing by the neural network model.

7. The method as described in claim 3, characterized in that, The step of determining the corrected pose deviation based on the parameter error and the calibrated kinematic parameters includes: The kinematic parameters are updated using the parameter error to generate calibrated kinematic parameters; Based on the calibrated kinematic parameters, the corrected pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot is determined.

8. The method as described in claim 7, characterized in that, The step of updating the active joint displacement based on the corrected pose deviation includes: The positive kinematic model of each virtual kinematic chain is used to perform partial derivative processing on the active joint displacement to determine the active joint Jacobian matrix; The active joint displacement is updated based on the active joint Jacobian matrix and the corrected pose deviation.

9. A kinematic calibration device for a closed-loop robot with numerators based on constraint relaxation, characterized in that, include: The generation module is used to decompose the main kinematic chain of the robot into multiple virtual kinematic chains when there are multiple branches in the main kinematic chain, wherein any virtual kinematic chain has at least one different kinematic parameter from the other virtual kinematic chains. The first determining module is used to determine the theoretical end-effector pose of the robot based on the kinematic parameters of the virtual joints and the closed-loop geometric constraints in each of the virtual kinematic chains. The second determining module is used to determine the parameter error based on the pose deviation between the theoretical end-effector pose and the actual end-effector pose of the robot, wherein the actual end-effector pose is obtained by means of a measuring device. The third determining module is used to determine the corrected pose deviation based on the parameter error and the calibrated kinematic parameters. The update module is used to update the active joint displacement based on the corrected pose deviation until the corrected pose deviation or active joint displacement meets the iteration termination condition, and to calibrate the robot based on the determined active joint target displacement.

10. An electronic device, characterized in that, The electronic device includes: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the kinematic calibration method for a closed-loop robot with sub-subjects based on constraint relaxation as described in any one of claims 1-8.

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