Multi-robot cooperative control method for robot grinding and polishing

Abstract

The invention belongs to the related technical field of calibration and control of machining equipment, and particularly relates to a multi-robot cooperative control method for robot grinding and polishing. The method comprises the following steps: step 1, connecting the tail ends of mechanical arms of two robots through a calibration tool, changing the postures of the two mechanical arms for multiple times, collecting the spatial postures of the two mechanical arms under the postures, deducing closed-loop kinematic chains of the two mechanical arms to obtain a solution model, and calculating a transformation relation between base coordinate systems of the two mechanical arms according to the solution model; secondly, based on the transformation relation between the base coordinate systems of the two mechanical arms, the driving torque of each mechanical arm is determined according to the cooperative motion model of the two mechanical arms, the machining position and the impedance control law; wherein the cooperative motion model is obtained according to a closed kinematic chain formed during grinding and polishing, and the impedance control rate is obtained by setting parameters according to the basic principle of impedance control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of calibration and control of processing equipment, and particularly relates to a multi-robot cooperative control method for robot grinding and polishing. BACKGROUND

[0002] With the continuous development of manufacturing industry, various industrial robots are applied to manufacturing scenes, and production efficiency is greatly improved, so industrial robots play an important role in the development of manufacturing industry and have a wide application range and broad development prospect. However, with the continuous development of manufacturing technology and the increasing demand for production efficiency and production quality, various technical problems are faced, and the work task is more complex. At present, most of the industrial production is carried out by using a single robot, and the single robot is difficult to cope with these complex problems, and the use of multi-robot cooperative task has gradually become a trend.

[0003] In the field of grinding and polishing, compared with worker operation, the robot has higher repeated positioning accuracy and can work continuously for a long time. After force control is added, the workpiece to be polished can also obtain higher quality, so that the grinding and polishing process can better adapt to batch production. At the same time, since grinding and polishing will produce a large amount of dust and debris, it will affect the health of workers for a long time. Therefore, in order to achieve better economic benefits and social benefits, manual operation is replaced by robot operation in more and more grinding and polishing operations. The traditional robot grinding method is to use a mechanical arm loaded with a grinding tool to grind a workpiece fixed on a workbench or to install the workpiece at the end of the mechanical arm close to the abrasive belt for grinding. Since the working space of the robot is limited, there are dead angles for grinding, and for parts with large surface curvature changes, the workpiece pose needs to be adjusted, and the adjusted workpiece needs to be re-calibrated, which will affect the processing efficiency and processing accuracy. The cooperation of multiple robots has greater flexibility and can solve the above problems to some extent.

[0004] In summary, in the field of robot grinding and polishing, there are problems such as poor flexibility of single robot, inability to adapt to complex part processing requirements, and low processing efficiency and processing quality, which need to be solved by introducing multi-robot cooperative operation. SUMMARY

[0005] The application aims to provide a multi-robot cooperative control method for robot grinding and polishing, which aims to solve the flexibility problem and cooperation problem in the field of robot grinding and polishing.

[0006] TECHNICAL SOLUTION A multi-robot cooperative control method for robot grinding and polishing, the method is executed by means of two robots, each robot is respectively provided with a mechanical arm, and the method comprises the following steps: Step one, through the calibration tool, connect the end of the two robot arms, change the posture of the two arms multiple times, collect the spatial pose of the two arms in these postures, derive the solving model through the closed loop kinematic chain of the two arms, calculate the transformation relationship between the base coordinate systems of the two arms according to the solving model; Step two, based on the transformation relationship between the base coordinate systems of the two arms, according to the cooperative motion model of the two arms, the processing position And apply impedance control law, determine the driving torque of each arm ; wherein, the cooperative motion model is derived according to the closed kinematic chain formed during polishing.

[0007] Further, in step one, the solving model is AX=XB, wherein, i.e. , , Wherein, the transformation matrix between the end flange of each arm and the base coordinate system , Is calculated by the arm itself and then obtained by reading the arm state, i and j are the numbers of the two arms respectively, and n represents the measurement times.

[0008] Further, in step one, the spatial pose of the two arms is the spatial coordinates of each arm respectively.

[0009] Further, in step one, the transformation relationship between the base coordinate systems of the two arms is calculated according to the solving model, which is specifically: Let , , Be expressed in the form of homogeneous matrix: , , Substitute into equation For calculation, we get: (1) (2) Wherein , Is the rotation matrix part, , Is the position vector part, first use the least square method to solve the rotation matrix According to formula (1), substitute the calculated Into formula (2) for calculation, get , that is, the required solution .

[0010] Further, the cooperative motion model of the two arms is: Wherein, Workpiece coordinate system Relative to the robot End flange coordinate system Homogeneous transformation matrix of the machining point Tool coordinate system To the robot arm End coordinate system Homogeneous transformation matrix between the end coordinate system and the tool coordinate system .

[0011] Further, the impedance control law is: Wherein, the actual position, velocity and acceleration quantities of the robot arm end contact force are , , The desired position, velocity and acceleration quantities of the robot arm end contact force are , , The reference output force Fext, , , The desired impedance model coefficient.

[0012] Further, the driving torque Is: Wherein, , , The position, velocity and acceleration vectors of m joints are respectively, The inertia matrix is, The Coriolis force and centrifugal force are represented, The gravity vector is, The friction and other interference terms are, The joint driving torque is represented The transpose of the robot arm Jacobian matrix is.

[0013] Further, the driving torque Is simplified as: Ignoring the joint acceleration Ignoring Calculated by the velocity in the Cartesian space, Ignoring Get: .

[0014] Beneficial effects: 1. For the base coordinate system calibration problem in multi-robot cooperation, the commonly used laser instruments, visual equipment, etc. are expensive, complex to operate, and not easy to execute, while using a simple calibration tool to connect the two robot arms is cheap and only needs to change the pose of the two robots and record the pose data of the robots.

[0015] 2. The mechanical arms are reasonably assigned tasks, one mechanical arm clamps the workpiece, and the other executes the polishing task, and the two relative movements; the impedance control law is applied to ensure that the robot can move according to the preset trajectory while ensuring a certain compliance, and ensure the quality of the collaborative task.

[0016] The application solves the problem of poor flexibility of single robot, which cannot adapt to the processing needs of complex parts, resulting in low processing efficiency and processing quality. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flow chart of a multi-robot cooperative control method for robot polishing provided by the application; Figure 2 is Figure 1 the schematic diagram of the motion chain transmission modeling involved in the multi-robot cooperative control method for robot polishing in Figure 3 is Figure 1 the schematic diagram of a simple calibration tool involved in the multi-robot cooperative control method for robot polishing in Figure 4 is Figure 1 the schematic diagram of the trajectory tracking method based on impedance control involved in the multi-robot cooperative control method for robot polishing in DETAILED DESCRIPTION

[0018] In order to make the purpose, technical scheme and advantages of the application clearer, the technical scheme in the application embodiment will be described in more detail below in combination with the drawings in the application embodiment. In the drawings, the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The described embodiments are part of the embodiments of the application, not all embodiments. The embodiments described below by reference to the drawings are exemplary and are intended to explain the application, and cannot be understood as limiting the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application. The embodiments of the application will be described in detail below in combination with the drawings.

[0019] In the description of the present application, it should be understood that the terms "center", "axial", "vertical", "upper", "lower", "upper end", "bottom end", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the scope of protection of the present application.

[0020] The present application provides a multi-robot collaborative control method for robot grinding and polishing, which comprises the following steps: Step one, by calibrating the tool, the end of the two robot arms is connected, the posture of the two arms is changed many times, the space posture of the two arms under these postures is collected, the solving model is derived through the closed loop kinematic chain of the two arms, and the transformation relationship between the base coordinate systems of the two arms is calculated according to the solving model; Step two, based on the relationship between the two arms, the motion trajectory of the two arms is designed according to the collaborative motion model of the two arms, and the impedance control law is applied to complete the collaborative grinding and polishing motion; wherein the collaborative motion model is derived according to the closed kinematic chain formed during grinding and polishing, and the impedance control rate is derived according to the basic principle of impedance control.

[0021] Step one, specifically includes: constructing a calibration equation under the calibration scene for two arms, for the system composed of arm i and arm j, the coordinate system contained has: Establish , , respectively, the base coordinate system of the arm and the arm , located in the center of the installation base plane; establish , , respectively, the end flange coordinate system of the arm and the arm , located in the center of the arm end flange surface. The transformation matrix , between is required to be solved.

[0022] The transformation matrix between the end flange and the base coordinate system of each arm is , , this transformation matrix can be obtained by reading the current position and posture of the arm end in real time. After the ends of the two arms are connected, the transformation relationship between the end flange coordinate systems of the two arms is , and this transformation relationship is fixed and unchanged. Then after forming a closed loop system, the entire kinematic chain can be represented as: (1) The invariant , and use this invariant term to construct a system of equations.

[0023] At the nth measurement: (2) Express this formula as AX=XB: (3) Right now , , , where the transformation matrix between each robot end flange and the base coordinate system is , It can be calculated by the robot itself and then obtained by reading the robot state.

[0024] Furthermore, a simple calibration tool is used to connect the two robotic arms, change their positions, collect data, and solve equations. The tool is installed between the two robotic arms, maintaining a fixed relationship between them. Simultaneously changing the spatial positions of the two robotic arms requires ensuring that each arm's motion position avoids confining to a single plane, and that the variation between the arm's positions is as large as possible.

[0025] In order to obtain the most accurate solution for X, it is necessary to collect a reasonable amount of robot arm posture data. Considering the practical operation, a total of 15-20 sets of robot arm posture data are collected. After listing a series of calibration equations, the two-step method proposed by Shiu is used to solve the problem. First, , , Expressed as a homogeneous matrix: , , (4) Substituting into the equation Calculate in and express the original equation as: (5) (6) in , is the rotation matrix part, , For the position vector part, first use the least squares method to calculate the rotation matrix according to formula (5) , the calculated Substituting into formula (6), we get , you can get the required solution .

[0026] Step 2 specifically includes: establishing a robot arm collaborative grinding and polishing model according to the characteristics of the grinding and polishing task, setting one robot arm to install a clamping tool, the clamping tool clamps the workpiece, and the other to install the grinding and polishing tool. Set the robot arm that clamps the workpiece as the robot arm , the grinding and polishing robot arm is a robot arm , and establish the clamping tool coordinate system ;Workpiece coordinate system , grinding and polishing tool coordinate system .

[0027] For robot arm i, the workpiece coordinate system It is established at a certain position of the workpiece. In this coordinate system, the position of each point on the workpiece surface can be expressed. According to the part of the workpiece that needs to be processed, the processing trajectory along the surface can be planned. The coordinates of a series of planned processing trajectory points are marked as .

[0028] In the coordinate system expressing the clamping tool For the convenience of representation, the coordinate system is combined with the robot arm End flange coordinate system Overlap, that is ; Determine the workpiece coordinate system Relative to the fixture coordinate system The transformation relationship between them is equivalent to obtaining the workpiece coordinate system Compared to robots End flange coordinate system The homogeneous transformation matrix ; Select the appropriate processing position on the workpiece surface and plan a series of processing points , the expression of the planned processing points on the workpiece surface in the world coordinate system satisfies the following relationship: (7) robotic arm The end of the grinding and polishing tool needs to be installed. The grinding and polishing tool is equipped with a tangential grinding head, which contacts the workpiece in the tangential direction and moves along the surface wire for grinding and polishing. The tool coordinate system of the grinding and polishing tool is Set in the front center of the grinding head. Install the tool on the grinding and polishing robot arm At the end, the tool coordinate system is measured To the robotic arm End coordinate system The homogeneous transformation matrix between , we can get the coordinate system of the grinding and polishing tool on the robot arm The following expression ; The end of the two mechanical arms needs to maintain a certain constraint relationship, and when performing polishing tasks, the tool coordinate system origin needs to maintain contact with the planned trajectory point. The polishing tool coordinate system is also transformed into the world coordinate system: (8) When performing polishing tasks, the relationship between the polishing tool coordinate system and each processing trajectory point does not need to concern the change in attitude, only the coincidence of their respective origins is needed, and the following can be obtained: (9) Further, the impedance control of multi-robot cooperation is designed: first, the contact force at the end of the mechanical arm and the actual position, velocity and acceleration quantity are obtained, and then the actual quantity (the actual position of the end of the mechanical arm), , is taken as the deviation between the set expected quantity , , and the reference output force Fext is obtained according to the impedance relationship (formula 10). Since the expected impedance model coefficients , , are generally inaccurate or even unknown, the self-defined , , is used instead of the expected model coefficient, that is (10) For any mechanical arm, the dynamics is described as follows: (11) wherein, , , are the position, velocity and acceleration vectors of m joints respectively. is the inertia matrix. represents the Coriolis force and centrifugal force. is the gravity vector. is the interference term such as friction. represents the joint driving torque. is an n-dimensional external force vector, is the transpose of the Jacobian matrix of the mechanical arm.

[0029] The driving torque input to the mechanical arm can be divided into the torque generated by the interaction between the mechanical arm and the environment and the torque generated by the motion of the mechanical arm itself. According to the impedance control model, the end of the mechanical arm is equivalent to a second-order impedance model, and the external force received is At this time, for the whole robot system, formula (10) is substituted into formula (11) to obtain the driving torque needed to be input is: (12) According to different actual application scenarios, different effects can be designed. When performing a trajectory tracking task, the expected force is set to 0, and the actual effect is to track the expected trajectory.

[0030] Generally, for safety considerations, when planning a trajectory for a robot, a small acceleration is usually set, or the acceleration change is as smooth as possible, that is, the joint speed changes slowly, in order to simplify the calculation difficulty, the joint acceleration is ignored. Similarly, the acceleration in the Cartesian space is also not too large, and the calculated by the speed in the Cartesian space can also be ignored, so the term in the impedance control model can also be ignored, and the following can be obtained: (13) The Coriolis force term, the gravity term and the friction term of the robot can be calculated from the robot parameters. It should be noted that after the tool and the workpiece are installed at the end of the robot, gravity compensation operation is needed, and after the mass and the center of gravity position of the object installed at the end are recorded, the gravity of the tool and the workpiece is calculated into the model.

[0031] Further, according to the actual task requirements, multiple robots are installed, the base coordinate system of the multiple robots is calibrated, the robot clamping the workpiece and the robot installing the tool are set according to the size and shape of the workpiece, the motion trajectory of each robot is set according to the machining trajectory planning, and finally the appropriate impedance parameters are set. Impedance control is applied to perform a collaborative polishing task.

[0032] Embodiment: The application provides a multi-robot collaborative control method for robot polishing, the calibration method uses a simple calibration tool, which is more economical than the equipment used in the prior art calibration, and is easier to operate, thereby saving calibration costs and simplifying the operation process; the trajectory planning method according to the collaborative motion model and the motion control method based on impedance control can ensure the quality of collaborative polishing.

[0033] Please refer to Figures 1 to 4 , the calibration method mainly includes the following steps: Step one, through the calibration tool, connect the two mechanical arm ends, change the pose of the two mechanical arms, execute a certain group, through the acquisition of the spatial pose of the two mechanical arms in these cases, calculate the transformation relationship between the base coordinate systems of the two fixed installation mechanical arms; wherein the model is derived by deducing the closed loop kinematic chain of the double mechanical arm; Step two, based on the relationship between the two mechanical arms obtained, according to the cooperative motion model of the two mechanical arms, design the motion trajectory of the two mechanical arms respectively, and apply impedance control law to complete the cooperative grinding and polishing motion; wherein, the cooperative motion model is derived according to the closed kinematic chain formed during grinding and polishing, and the impedance control rate is derived according to the basic principle of impedance control and parameter setting; The calibration of the base coordinate system of the mechanical arm includes the following steps: S1, constructing calibration equations in calibration scenarios for two mechanical arms For the calibration of a multi-robot system, it can be simplified into pairwise calibration between robots, so in this invention, only the base coordinate system calibration of the double mechanical arm system is introduced. For the system composed of mechanical arm i and mechanical arm j, the coordinate systems contained are: Establishment , , respectively, the base coordinate system of the mechanical arm and the base coordinate system of the mechanical arm , located at the center of the installation base plane; establishment , , respectively, the end flange coordinate system of the mechanical arm and the end flange coordinate system of the mechanical arm , located at the center of the mechanical arm end flange surface. The transformation matrix , between is required to be solved. The transformation matrix between the end flange and the base coordinate system of each mechanical arm is , , this transformation matrix can be obtained by real-time reading the current position and attitude of the mechanical arm end. After the ends of the two mechanical arms are connected, the transformation relationship between them is , and this transformation relationship is fixed and unchanged. Then after forming a closed loop system, the entire kinematic chain can be represented as: (1) The invariant term is used to construct the equation group. At the nth measurement: (2) Express this formula as AX=XB: (3) That is , , , where the transformation matrix between each robot end flange and the base coordinate system is , It can be calculated by the robot itself and then obtained by reading the robot state.

[0034] S2, using a simple calibration tool, connects the ends of the two robotic arms, changes the posture of the two robotic arms, collects data and solves the equations.

[0035] The simple calibration tool has flanges at both ends that can be connected and fixed to the end of the robotic arm. The tool itself has a simple structure, is easy to process, and has low manufacturing cost. The required design length of the calibration tool can be roughly estimated based on the installation distance between the two robotic arms and the arm span of the robotic arms. The tool is installed between the ends of the two robotic arms, so that the ends of the two robotic arms maintain a fixed relationship. To change the spatial position of the ends of the two robotic arms simultaneously, it is necessary to ensure that the movement position of each robotic arm does not remain in the same plane, and the change between the robotic arm positions should be as large as possible.

[0036] In order to obtain the most accurate solution for X, it is necessary to collect a reasonable amount of robot arm posture data. Considering the practical operation, a total of 15-20 sets of robot arm posture data are collected. After listing a series of calibration equations, the two-step method proposed by Shiu is used to solve the problem. First, , , Expressed as a homogeneous matrix: , , (4) Substituting into the equation Calculate in and express the original equation as: (5) (6) in , is the rotation matrix part, , For the position vector part, first use the least squares method to calculate the rotation matrix according to formula (5) , the calculated Substituting into formula (6), we get , you can get the required solution .

[0037] S3, establishes a robot arm collaborative grinding and polishing model based on the characteristics of the grinding and polishing task, which specifically includes the following steps: For dual-arm systems, in the application scenario of performing grinding and polishing tasks, one robot arm is set to hold the workpiece and the other is set to hold the grinding and polishing tools. Set the robot arm holding the workpiece as the robot arm , the grinding and polishing robot arm is a robot arm , and establish the clamping tool coordinate system , clamping tool; workpiece coordinate system , grinding and polishing tool coordinate system .

[0038] Step S3.1: For robot arm i, set the workpiece coordinate system It is established at a certain position of the workpiece. In this coordinate system, the position of each point on the surface can be expressed. According to the part of the workpiece that needs to be processed, the processing trajectory along the surface can be planned. The coordinates of a series of planned processing trajectory points are marked as In the coordinate system expressing the clamping tool For the convenience of representation, the coordinate system is combined with the robot arm End flange coordinate system Overlap, that is ; Step S3.2, determine the workpiece coordinate system Relative to the fixture coordinate system The transformation relationship between them is equivalent to obtaining the workpiece coordinate system Compared to robots End flange coordinate system The homogeneous transformation matrix ; Step S3.3, select the appropriate processing position on the workpiece surface and plan a series of processing points , the expression of the planned processing points on the workpiece surface in the world coordinate system satisfies the following relationship: (7) Step S3.4, robotic arm The end of the grinding and polishing tool needs to be installed. The grinding and polishing tool is equipped with a tangential grinding head, which contacts the workpiece in the tangential direction and moves along the surface wire for grinding and polishing. The tool coordinate system of the grinding and polishing tool is Set in the front center of the grinding head. Install the tool on the grinding and polishing robot arm At the end, the tool coordinate system is measured To the robotic arm End coordinate system The homogeneous transformation matrix between , we can get the coordinate system of the grinding and polishing tool on the robot arm The following expression ; Step S3.5, the end of the two mechanical arms needs to keep a certain constraint relationship, when performing the polishing task, the tool coordinate system origin needs to keep contact with the planned trajectory point. The polishing tool coordinate system is also transformed to the world coordinate system: (8) When performing the polishing task, the relationship between the polishing tool coordinate system and each machining trajectory point does not need to care about the change of the attitude, only the coincidence of the origins can be obtained: (9) The steps of designing the impedance control of the multi-robot cooperation correspond to S4, which specifically includes the following sub-steps: Step S4.1, in the implementation process of the impedance control, the contact force of the end of the mechanical arm and the actual position, velocity and acceleration quantity are obtained first, and then the deviation between the actual quantity , , and the set expected quantity , , is input into the position outer ring, and the reference output force is obtained according to the impedance relationship . Since the expected impedance model coefficients , , are generally inaccurate or even unknown, the self-defined , , is used to replace the expected model coefficient, that is (10) For any one mechanical arm, the dynamics description is as follows: (11) Wherein, , , are the position, velocity and acceleration vectors of m joints respectively. is the inertia matrix. represents the Coriolis force and centrifugal force. is the gravity vector. is the interference term such as friction. represents the joint driving torque. is an n-dimensional external force vector, is the transpose of the Jacobian matrix of the mechanical arm.

[0039] As can be seen from the dynamics description equation, the driving torque input to the mechanical arm can be divided into the torque generated by the interaction between the mechanical arm and the environment and the torque that generates the motion of the manipulator itself. According to the impedance control model, the end of the manipulator is equivalent to a second-order impedance model, and the external force received is When, for the entire manipulator system, formula (10) is substituted into formula (11), the driving torque required to be input is (12) According to different actual application scenarios, different effects can be designed. When performing a trajectory tracking task, the expected force is set to 0, and the actual effect exhibited is the effect of tracking the expected trajectory.

[0040] Step S4.2, when actually moving, the joint acceleration is calculated after the joint angular velocity undergoes differentiation, and the calculation error is large. Moreover, in actual experimental operations, generally, in order to ensure safety, a small acceleration is set in the process of trajectory planning of the manipulator, or the acceleration change is made as gentle as possible, that is, the joint speed changes slowly. In order to simplify the calculation difficulty, the joint acceleration is ignored. Similarly, the acceleration in the Cartesian space is also not large, and the calculated through the speed in the Cartesian space can also be ignored, so the term in the impedance control model can also be ignored, and the following can be obtained: (13) The Coriolis force term, the gravity term, and the friction force term of the robot can be calculated from the robot parameters. It should be noted that after the tool and the workpiece are installed at the end of the manipulator, gravity compensation operation needs to be performed. After the mass and the center of gravity position of the object installed at the end are recorded, the gravity of the tool and the workpiece is calculated into the model.

[0041] Step S4.3, since the impedance model is a second-order system, the Laplace transform is performed on the model, the input of the system is , and the output of the system is , so the second-order system can be expressed as: (14) Since it is hoped that the manipulator can exhibit the desired characteristics in each direction in the Cartesian space and the directions are not coupled with each other, so that control can be performed on the directions of interest respectively, the , , are designed as diagonal matrices to realize decoupling of control in each direction.

[0042] For the system, generally, , for the impedance controller, the transfer function, that is, the system impedance is: ​ (15) Among them, the damping ratio and natural frequency of the system are expressed as: , (16) According to the Routh-Hurwitz criterion, for a second-order system, when the coefficients of its characteristic polynomial are all positive, the system with second-order polynomial characteristics is stable. Moreover, for a second-order system, the two most important parameters that determine the system performance are the damping ratio and the natural frequency. When the damping ratio is constant, the larger the natural frequency, the faster the response speed and the larger the overshoot; when the natural frequency is constant, the larger the damping ratio, the slower the response and the smaller the overshoot. When , it is underdamped and the system is prone to oscillation; When , it is an over-damped situation and the system responds slowly. Therefore, in order to make the impedance controller produce the fastest possible non-oscillatory response, the damping ratio is taken here. , that is, take: (17) When designing the impedance parameters in various directions, the selected stiffness and damping parameters satisfy the above relationship.

[0043] S5, combined with the previous steps, performs multi-machine collaborative grinding and polishing tasks: According to the actual task requirements, multiple robotic arms are installed and the base coordinate system of the multiple robotic arms is calibrated. According to the size and shape of the workpiece, the robotic arms for clamping the workpiece and the robotic arms for installing the tools are set. According to the processing trajectory planning, the motion trajectory of each robotic arm is set. Finally, the appropriate impedance parameters are set, and the impedance control rate is applied to perform collaborative grinding and polishing tasks.

[0044] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-robot collaborative control method for robot grinding and polishing, characterized in that: The method is performed by means of two robots, each of which is provided with a robotic arm, and comprises: Step 1: Use a calibration tool to connect the ends of the two robotic arms, change the postures of the two robotic arms multiple times, collect the spatial positions of the two robotic arms under these postures, derive a solution model by deriving the closed-loop kinematic chain of the two robotic arms, and calculate the transformation relationship between the base coordinate systems of the two robotic arms based on the solution model; Step 2: Based on the transformation relationship between the base coordinate systems of the two robotic arms, according to the collaborative motion model of the two robotic arms and the processing position And apply the impedance control law to determine the driving torque of each manipulator ; Wherein, the collaborative motion model is derived based on the closed motion chain formed during grinding and polishing.

2. The multi-robot collaborative control method for robot grinding and polishing according to claim 1 is characterized in that: In step 1, the solution model is: AX=XB, where , , , where the transformation matrix between each robot end flange and the base coordinate system is , It is calculated by the robot arm itself and then obtained by reading the robot arm status. i and j are the numbers of the two robot arms respectively, and n represents the number of measurements.

3. The multi-robot collaborative control method for robot grinding and polishing according to claim 2 is characterized in that: In step 1, the spatial poses of the two robotic arms are the spatial coordinates of each robotic arm.

4. The multi-robot collaborative control method for robot grinding and polishing according to claim 3 is characterized in that: In step 1, the transformation relationship between the base coordinate systems of the two robotic arms is calculated based on the solution model, specifically: Will , , Expressed as a homogeneous matrix: , , , substitute into the equation Calculate in and get: （1） （2） in , is the rotation matrix part, , For the position vector part, first use the least squares method to calculate the rotation matrix according to formula (1) , the calculated Substituting into formula (2), we get , you can get the required solution .

5. The multi-robot collaborative control method for robot grinding and polishing according to claim 4 is characterized in that: The collaborative motion model of the two robotic arms is: ,in, is the workpiece coordinate system Compared to robots End flange coordinate system The homogeneous transformation matrix of the processing point , tool coordinate system To the robotic arm End coordinate system The homogeneous transformation matrix between .

6. The multi-robot collaborative control method for robot grinding and polishing according to claim 5, characterized in that: The impedance control law is: , where the contact force and actual position, velocity and acceleration of the end of the manipulator are 、 、 The expected quantities of contact force and actual position, velocity and acceleration at the end of the manipulator are , , , reference output force Fext, 、 、 is the desired impedance model coefficient.

7. The multi-robot collaborative control method for robot grinding and polishing according to claim 6, characterized in that: Driving torque for: ,in, , , are the position, velocity and acceleration vectors of m joints respectively, is the inertia matrix, represents the Coriolis force and centrifugal force, is the gravity vector, is the interference term such as friction, Represents the joint driving torque is the transpose of the manipulator Jacobian matrix.

8. The multi-robot collaborative control method for robot grinding and polishing according to claim 7, characterized in that: Also includes the driving torque Simplified to: Ignore joint acceleration , ignoring the velocity calculation in Cartesian space ,neglect ,get: 。

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