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CN116160300B - A collaborative robot grinding and polishing process control method - Google Patents

A collaborative robot grinding and polishing process control method Download PDF

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Publication number
CN116160300B
CN116160300B CN202310197540.2A CN202310197540A CN116160300B CN 116160300 B CN116160300 B CN 116160300B CN 202310197540 A CN202310197540 A CN 202310197540A CN 116160300 B CN116160300 B CN 116160300B
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polishing
grinding
force
coordinate system
robot
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CN116160300A (en
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梁亮
郭东旭
王静
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Northeastern University China
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Northeastern University China
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B24GRINDING; POLISHING
    • B24BMACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B1/00Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B24GRINDING; POLISHING
    • B24BMACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B49/00Measuring or gauging equipment for controlling the feed movement of the grinding tool or work; Arrangements of indicating or measuring equipment, e.g. for indicating the start of the grinding operation
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B24GRINDING; POLISHING
    • B24BMACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B51/00Arrangements for automatic control of a series of individual steps in grinding a workpiece
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J11/00Manipulators not otherwise provided for
    • B25J11/005Manipulators for mechanical processing tasks
    • B25J11/0065Polishing or grinding
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02PCLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Robotics (AREA)
  • Finish Polishing, Edge Sharpening, And Grinding By Specific Grinding Devices (AREA)
  • Manipulator (AREA)

Abstract

The invention discloses a control method of a grinding and polishing process of a cooperative robot, which comprises the following steps: step 1: a six-dimensional force/moment sensor is arranged between the tail end of the robot and the polishing tool, and the initial value of the six-dimensional force/moment sensor and the gravity parameter of the polishing tool are automatically distinguished; step 2: calibrating a user coordinate system of a workpiece to be polished, and recording a polishing track in teaching; step 3: when the polishing operation is executed, the contact force between the polishing tool and the polishing surface and the posture of the polishing tool are regulated according to the feedback force and the force position mixed control acquired by the six-dimensional force/torque sensor, and the polishing operation is completed. The method of the invention uses a force-position mixed control method, realizes the function of finishing grinding and polishing operation by the cooperative robot, replaces manual work by the robot, improves grinding and polishing effect and improves labor environment.

Description

Control method for grinding and polishing process of cooperative robot
Technical Field
The invention belongs to the technical field of polishing processing control, and relates to a polishing process control method of a cooperative robot.
Background
At present, with the rising of new generation industrial robots, cooperative robot control technology is widely paid attention to and widely applied. The polishing and burnishing is the most basic process in the 3C field, automobile parts, hardware, die castings, ceramic products and other traditional manufacturing industries, and the cooperative robot is used for realizing the polishing and burnishing function, so that the cooperative robot polishing and burnishing process with excellent effect, high stability and simple and convenient operation has important significance.
At present, some robot products are divided into two types by using a control interface provided by a force sensor, the first type of robot only needs to move a fixed track, the passive compliance is implemented by a grinding and polishing tool integrating force sensing and hydraulic equipment, and the adaptive workpiece subjected to grinding and polishing is only suitable for workpieces which are produced in a large scale and have a flat surface; the second type can realize active force control, but does not aim at polishing alone, but is a force control related function set, motion in the polishing process teaches polishing tracks by means of joint-like motion or linear motion instructions, operation is complex, teaching effects are difficult to ensure, if offline programming software or a visual sensor is used for generating polishing surface tracks, use cost is greatly increased, and production efficiency is seriously influenced for products (such as molds) which do not need mass production.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a control method of a grinding and polishing process of a cooperative robot, which comprises the steps of carrying a six-dimensional force/moment sensor at the tail end of the cooperative robot to obtain contact force/moment between a grinding and polishing tool and a grinding and polishing surface, and enabling the cooperative robot to keep constant contact force when the grinding and polishing tool is driven to move on the ground and polishing surface through force-position mixed control; if the polished surface is a curved surface, the tool and the curved surface can be always kept attached, so that the polishing operation is completed.
The invention provides a control method of a grinding and polishing process of a cooperative robot, which comprises the following steps:
Step 1: a six-dimensional force/moment sensor is arranged between the tail end of the robot and the polishing tool, and the initial value of the six-dimensional force/moment sensor and the gravity parameter of the polishing tool are automatically distinguished;
step 2: calibrating a user coordinate system of a workpiece to be polished, and recording a polishing track in teaching;
Step 3: when the polishing operation is executed, the contact force between the polishing tool and the polishing surface and the posture of the polishing tool are regulated according to the feedback force and the force position mixed control acquired by the six-dimensional force/torque sensor, and the polishing operation is completed.
In the control method of the cooperative robot polishing process of the present invention, the initial values of the six-dimensional force/torque sensor in the step 1 are as follows: force of the sensor in the X-axis, Y-axis and Z-axis directions and moment of the sensor in the X-axis, Y-axis and Z-axis directions; the gravity parameters of the polishing tool are as follows: tool gravity G T and tool centroid coordinate L x Ly Lz.
In the control method of the grinding and polishing process of the cooperative robot, the process of teaching and recording the grinding and polishing track in the step 2 comprises two modes according to actual application scenes:
the first mode aims at the belt-shaped grinding and polishing track, teaching is carried out through a manual dragging robot, and the grinding and polishing track is automatically recorded while dragging;
the second mode aims at the block polishing area, and four vertexes of any trapezoid or three vertexes of a triangle are marked in the polishing area to teach the polishing area.
In the cooperative robot polishing process control method of the invention, the step 3 specifically comprises the following steps:
step 3.1: the feedback force collected by the six-dimensional force/torque sensor is sent to the controller;
Step 3.2: performing gravity compensation and static force conversion on the feedback force to calculate the equivalent contact force between the grinding and polishing tool and the grinding and polishing surface;
step 3.3: acquiring the total speed of the tail end of the robot in the Cartesian space based on the force-position hybrid control;
Step 3.4: based on differential transformation of a Jacobian matrix of the robot, obtaining angular velocities of all joints of the robot in a joint space according to the total velocity of the tail end of the robot in a Karl space;
Step 3.5: and obtaining the target position of each joint in each control period according to the angular speed of each joint of the robot in the joint space, and finishing the polishing operation.
In the control method of the cooperative robot polishing process of the present invention, the feedback force F S in the step 3.1 is in a six-dimensional force/moment form:
FS=(fx fy fz tx ty tz)T
Wherein, f x、fy、fz is the force in the X axis, Y axis and Z axis directions, and t x、ty、tz is the moment in the X axis, Y axis and Z axis directions; the calculating box of the six-dimensional force/moment sensor is connected with the controller through a network cable, data transmission is carried out through a UDP protocol, and the synchronization period is kept consistent with the control period.
In the cooperative robot polishing process control method of the present invention, the step 3.2 specifically includes:
Step 3.2.1: let the position of the sensor coordinate system S in the base coordinate system be described by the rotation matrix R as follows:
Wherein is a unit direction vector of the sensor coordinate system/> axis in the base coordinate system,/> is a unit direction vector of the sensor coordinate system/> axis in the base coordinate system,/> is a unit direction vector of the sensor coordinate system/> axis in the base coordinate system;
Step 3.2.2: the force applied to the sensor due to the gravity of the polishing tool is obtained as follows:
FG=[Gx Gy Gz Mx My Mz]T
wherein the method comprises the steps of ,Gx=axGT、Gy=ayGT、Gz=azGT、Mx=GzLy-GyLz、My=GxLz-GzLx、Mz=GyLx-GxLy;
Step 3.2.3: performing static conversion of a sensor coordinate system S and a tool coordinate system T, and equating the stress of the sensor to an equivalent contact force F T between the grinding and polishing tool and the grinding and polishing surface:
Wherein is the jacobian matrix of the sensor coordinate system S to the tool coordinate system T; the homogeneous transformation matrix/> for the tool coordinate system T with respect to the sensor coordinate system S is as follows:
the concrete form of is obtained as follows:
Wherein is a rotation matrix of the tool coordinate system T with respect to the sensor coordinate system S, and/() is a position coordinate of an origin of the tool coordinate system T in the sensor coordinate system S.
In the cooperative robot polishing process control method of the present invention, the step 3.3 specifically includes:
step 3.3.1: in Cartesian space, translational movements of the grinding and polishing tool end points along the axis, the/> axis and the/> axis of a tool coordinate system are respectively called P x、Py and P z directions, and rotational movements of the grinding and polishing tool end points along the/> axis, the/> axis and the/> axis of the tool coordinate system are respectively called R x、Ry and R z directions; the admittance control theory is selected to control the force in the direction P z/Rx/Ry, the expected contact force between the grinding and polishing tool and the grinding and polishing surface in the grinding and polishing process is f D, and the expected force is 0 around the x axis and the y axis because the grinding and polishing tool and the grinding and polishing surface are always attached, and is:
FD=(00fD 000)T
The robot tip acceleration in cartesian space is obtained from admittance control as follows:
x e is the position, the speed and the acceleration deviation of the tail end of the robot, x e is obtained by taking the difference between the expected position x D and the current actual position x 0 to obtain x e=xD-x0, the same thing/> M, B, K is a 6 x 6 parameter matrix which is respectively called an inertia matrix, a damping matrix and a rigidity matrix, and each value is specified by a developer according to the characteristics of the robot body and the actual debugging effect;
step 3.3.2: the robot tip speed in cartesian space is as follows:
Wherein and/> are the current actual speed and acceleration of the robot tip, respectively;
Step 3.3.3: according to the polishing track recorded in the teaching, the speed of the tail end of the robot in the Cartesian space is obtained through track planning, and the speed obtained by the position control and the force control is not coupled in the Cartesian space, so that the total speed of the tail end of the robot is directly obtained:
In the cooperative robot polishing process control method of the present invention, the step 3.4 specifically includes:
According to the differential motion transformation of the robot, the angular velocity of the robot motion in the joint space is obtained:
wherein J (q) is a robot Jacobian matrix, and is solved by a homogeneous transformation matrix among joints in kinematics by using a differential transformation method; for a robot with n joints, assuming that the homogeneous transformation matrix from the i-1 joint to the i joint is , the homogeneous transformation matrix/> from the i joint to the n joint at the end is:
wherein, the ith column J i of jacobian matrix J (q) is as follows:
The control method of the grinding and polishing process of the cooperative robot has at least the following beneficial effects:
(1) The control method for finishing the polishing operation by the cooperative robot is realized, and the polishing degree is more accurate and the polishing effect is better by taking the quantifiable contact force as feedback;
(2) The robot is used for replacing the manpower, so that the worker is prevented from working in a dust environment, and the labor cost of enterprises is saved;
(3) The operation of the user is simple, no gate is used, and no special training is needed;
(4) And the off-line programming software or a visual sensor is not required to be matched, so that the cost is saved.
Drawings
FIG. 1 is a flow chart of a cooperative robot polishing process control method of the present invention;
FIG. 2 is a graph of a quadrilateral arcuate traversal trajectory;
FIG. 3 is a triangle arch traversal trajectory;
fig. 4 is a quadrilateral co-directional bar track.
Detailed Description
As shown in fig. 1, the control method of the polishing process of the cooperative robot comprises the following steps:
step 1: and installing a six-dimensional force/moment sensor between the tail end of the robot and the polishing tool, and automatically distinguishing the initial value of the six-dimensional force/moment sensor and the gravity parameter of the polishing tool.
The initial values of the six-dimensional force/torque sensor are: force of the sensor in the X-axis, Y-axis and Z-axis directions and moment of the sensor in the X-axis, Y-axis and Z-axis directions.
The gravity parameters of the polishing tool are as follows: tool gravity G T and tool centroid coordinate L x Ly Lz.
Step 2: calibrating a user coordinate system of a workpiece to be polished, and recording a polishing track in teaching.
In specific implementation, the process of teaching and recording the grinding and polishing track comprises two modes according to actual application scenes:
the first mode aims at the belt-shaped grinding and polishing track, teaching is carried out through a manual dragging robot, and the grinding and polishing track is automatically recorded while dragging;
the second mode aims at the block polishing area, and four vertexes of any trapezoid or three vertexes of a triangle are marked in the polishing area to teach the polishing area.
Step 3: when the polishing operation is executed, the contact force between the polishing tool and the polishing surface and the posture of the polishing tool are regulated according to the feedback force and the force position mixed control acquired by the six-dimensional force/torque sensor, and the polishing operation is completed, wherein the step 3 specifically comprises the following steps:
Step 3.1: and sending the feedback force acquired by the six-dimensional force/torque sensor to the controller.
Feedback force F S is in the form of six-dimensional force/moment:
FS=(fx fy fz tx ty tz)T
Wherein, f x、fy、fz is the force in the X axis, Y axis and Z axis directions, and t x、ty、tz is the moment in the X axis, Y axis and Z axis directions; the calculating box of the six-dimensional force/moment sensor is connected with the controller through a network cable, data transmission is carried out through a UDP protocol, and the synchronization period is kept consistent with the control period, and the period is 16ms in the embodiment.
Step 3.2: and carrying out gravity compensation and static force conversion on the feedback force to calculate the equivalent contact force between the grinding and polishing tool and the grinding and polishing surface.
In specific implementation, the feedback force obtained in step 3.1 is actually the stress of the sensor end element, and needs to be processed to offset the component generated by self gravity of the polishing tool, which needs to use the tool gravity parameters, specifically:
Step 3.2.1: let the position of the sensor coordinate system S in the base coordinate system be described by the rotation matrix R as follows:
Wherein is a unit direction vector of the sensor coordinate system/> axis in the base coordinate system,/> is a unit direction vector of the sensor coordinate system/> axis in the base coordinate system,/> is a unit direction vector of the sensor coordinate system/> axis in the base coordinate system;
Step 3.2.2: the force applied to the sensor due to the gravity of the polishing tool is obtained as follows:
FG=[Gx Gy Gz Mx My Mz]T
wherein the method comprises the steps of ,Gx=axGT、Gy=ayGT、Gz=azGT、Mx=GzLy-GyLz、My=GxLz-GzLx、Mz=GyLx-GxLy;
Step 3.2.3: performing static conversion of a sensor coordinate system S and a tool coordinate system T, and equating the stress of the sensor to an equivalent contact force F T between the grinding and polishing tool and the grinding and polishing surface:
Wherein is the jacobian matrix of the sensor coordinate system S to the tool coordinate system T; the homogeneous transformation matrix/> for the tool coordinate system T with respect to the sensor coordinate system S is as follows:
The concrete form of is obtained as follows:
Wherein is a rotation matrix of the tool coordinate system T with respect to the sensor coordinate system S, and/() is a position coordinate of an origin of the tool coordinate system T in the sensor coordinate system S.
Step 3.3: the total speed of the tail end of the robot in the Cartesian space is obtained based on force-position hybrid control, and the method specifically comprises the following steps:
Step 3.3.1: in Cartesian space, translational movements of the polishing tool tip along the axis,/> axis and/> axis of the tool coordinate system are referred to as P x、Py and P z directions, respectively, and rotational movements of the polishing tool tip along the/> axis,/> axis and/> axis of the tool coordinate system are referred to as R x、Ry and R z directions, respectively. The admittance control theory is selected to control the force in the direction P z/Rx/Ry, the expected contact force between the grinding and polishing tool and the grinding and polishing surface in the grinding and polishing process is f D, and the expected force is 0 around the x axis and the y axis because the grinding and polishing tool and the grinding and polishing surface are always attached, and is:
FD=(00fD 000)T
The robot tip acceleration in cartesian space is obtained from admittance control as follows:
X e is the position, the speed and the acceleration deviation of the tail end of the robot, x e is obtained by taking the difference between the expected position x D and the current actual position x 0 to obtain x e=xD-x0, the same thing/> M, B, K is a 6 x 6 parameter matrix which is respectively called an inertia matrix, a damping matrix and a rigidity matrix, and each value is specified by a developer according to the characteristics of the robot body and the actual debugging effect;
step 3.3.2: the robot tip speed in cartesian space is as follows:
Wherein and/> are the current actual speed and acceleration of the robot tip, respectively;
Step 3.3.3: according to the polishing track recorded in the teaching, the speed of the tail end of the robot in the Cartesian space is obtained through track planning, and the speed obtained by the position control and the force control is not coupled in the Cartesian space, so that the total speed of the tail end of the robot is directly obtained:
Step 3.4: based on differential transformation of a jacobian matrix of the robot, according to the total terminal speed of the robot in the Karl space, the angular speed of each joint of the robot in the joint space is obtained, specifically:
According to the differential motion transformation of the robot, the angular velocity of the robot motion in the joint space is obtained:
Wherein J (q) is a robot Jacobian matrix, and is solved by a homogeneous transformation matrix among joints in kinematics by using a differential transformation method; for a robot with n joints, assuming that the homogeneous transformation matrix from the i-1 joint to the i joint is , the homogeneous transformation matrix/> from the i joint to the n joint at the end is:
wherein, the ith column J i of jacobian matrix J (q) is as follows:
Step 3.5: and according to the angular velocity of each joint of the robot in the joint space, obtaining the target position of each joint in each control period, and controlling the motion of the robot body to finish the polishing task operation through each joint driver issued by the CANOpen bus.
The invention develops a cooperative robot polishing process instruction packet based on a cooperative robot polishing process control method. The provided polishing process instruction packet can lead an operator to finish polishing tasks only through simple operation while supporting the polishing function, does not need professional training and additional software and hardware equipment, and saves time and cost.
The initial value of the six-dimensional force/moment sensor in step 1 and the gravity parameter of the polishing tool can be automatically distinguished by using the instruction FTMLU.
Since the collaborative robot itself has a drag teaching function, a robot end button can be used to automatically insert drag teaching instructions FTMLU during drag, record a drag trajectory, and automatically smooth the recorded trajectory using a spline interpolation function when performing a grinding and polishing motion.
In addition, three to four vertexes under the XOY plane of the user coordinate system can be calibrated, a triangle or quadrilateral region can be calibrated, and a FTQUA/FTTRI/FTQUM instruction is used in a matched manner, so that a quadrilateral bow-shaped traversing track, a triangle bow-shaped traversing track and a quadrilateral same-direction bar track shown in figures 2-4 can be automatically generated.
As shown in fig. 2, FTQUA instructs to perform arcuate traversal polishing on the quadrangular region, i.e., to automatically split the massive quadrangular region into arcuate strip-shaped trajectories. As shown in fig. 3, FTTRI instructs to perform a bowing-like traversal polish on the triangle polish area. As shown in fig. 4, FTQUM is similar to FTQUA except that each of the split polishing strips is polished in the same direction.
By using the two track generation modes aiming at the practical application scene, the track teaching process is simplified, and the cost caused by using additional software and hardware is avoided.
The invention theoretically uses a force-position mixed control method, realizes the function of finishing grinding and polishing operation by the cooperative robot, replaces manual work by the robot, improves grinding and polishing effect and improves labor environment. The special process instruction packet developed in the application is more targeted to the actual scene, the requirements are effectively attached through simple operation, the production time is saved, and the production cost is reduced.
The foregoing description of the preferred embodiments of the invention is not intended to limit the scope of the invention, but rather to enable any modification, equivalent replacement, improvement or the like to be made without departing from the spirit and principles of the invention.

Claims (1)

1.一种协作机器人磨抛工艺控制方法,其特征在于,包括如下步骤:1. A collaborative robot grinding and polishing process control method, characterized in that it includes the following steps: 步骤1:在机器人末端和磨抛工具之间安装六维力/力矩传感器,并自动辨别六维力/力矩传感器的初始值和磨抛工具的重力参数;Step 1: Install a six-dimensional force/torque sensor between the robot end and the grinding and polishing tool, and automatically identify the initial value of the six-dimensional force/torque sensor and the gravity parameter of the grinding and polishing tool; 步骤2:标定待磨抛工件的用户坐标系,在示教中记录磨抛轨迹;Step 2: Calibrate the user coordinate system of the workpiece to be ground and polished, and record the grinding and polishing trajectory during teaching; 步骤3:执行磨抛作业时,根据六维力/力矩传感器采集的反馈力和力位混合控制调整磨抛工具与磨抛面间的接触力和磨抛工具姿态,完成磨抛作业;Step 3: When performing the grinding and polishing operation, the contact force between the grinding and polishing tool and the grinding and polishing surface and the posture of the grinding and polishing tool are adjusted according to the feedback force and force-position hybrid control collected by the six-dimensional force/torque sensor to complete the grinding and polishing operation; 所述步骤1中六维力/力矩传感器的初始值为:传感器在X轴、Y轴、Z轴方向的力和传感器在X轴、Y轴、Z轴方向的力矩;所述磨抛工具的重力参数为:工具重力GT和工具质心坐标LxLy LzThe initial values of the six-dimensional force/torque sensor in step 1 are: the force of the sensor in the X-axis, Y-axis, and Z-axis directions and the torque of the sensor in the X-axis, Y-axis, and Z - axis directions; the gravity parameters of the polishing tool are: tool gravity GT and tool center of mass coordinates LxLyLz ; 所述步骤2中示教记录磨抛轨迹的过程根据实际应用场景包括两种方式:The process of teaching and recording the grinding and polishing trajectory in step 2 includes two methods according to the actual application scenario: 第一种方式针对带状磨抛轨迹,通过手动拖拽机器人进行示教,在拖拽同时自动记录磨抛轨迹;The first method is to teach the belt-shaped grinding and polishing track by manually dragging the robot, and automatically record the grinding and polishing track while dragging; 第二种方式针对块状磨抛区域,通过在磨抛区域标定任意凸四边形的四个顶点或三角形的三个顶点对磨抛区域进行示教;The second method is for block-shaped grinding and polishing areas, and the grinding and polishing area is taught by marking the four vertices of any convex quadrilateral or the three vertices of a triangle in the grinding and polishing area; 所述步骤3具体为:The step 3 is specifically as follows: 步骤3.1:将六维力/力矩传感器采集的反馈力发送给控制器;Step 3.1: Send the feedback force collected by the six-dimensional force/torque sensor to the controller; 步骤3.2:对反馈力进行重力补偿和静力变换计算磨抛工具和磨抛面间的等效接触力;Step 3.2: Perform gravity compensation and static transformation on the feedback force to calculate the equivalent contact force between the grinding and polishing tool and the grinding and polishing surface; 步骤3.3:基于力位混合控制获得笛卡尔空间下机器人末端总体速度;Step 3.3: Obtain the overall velocity of the robot end in Cartesian space based on force-position hybrid control; 步骤3.4:基于机器人雅克比矩阵的微分变换,根据卡尔空间下机器人末端总体速度,得到关节空间下机器人各关节的角速度;Step 3.4: Based on the differential transformation of the robot Jacobian matrix, the angular velocity of each joint of the robot in the joint space is obtained according to the overall velocity of the robot end in the Carr space; 步骤3.5:根据关节空间下机器人各关节的角速度,在每个控制周期得到各关节的目标位置,完成磨抛作业;Step 3.5: According to the angular velocity of each joint of the robot in the joint space, the target position of each joint is obtained in each control cycle to complete the grinding and polishing operation; 所述步骤3.1中反馈力FS为六维力/力矩形式:The feedback force FS in step 3.1 is in the six-dimensional force/rectangular form: FS=(fx fy fz tx ty tz)T F S =(f x f y f z t x t y t z ) T 其中,fx、fy、fz分别为X轴、Y轴、Z轴方向的力,tx、ty、tz分别为X轴、Y轴、Z轴方向的力矩;六维力/力矩传感器的计算盒和控制器通过网线相连,通过UDP协议进行数据传输,同步周期与控制周期保持一致;Among them, fx , fy , and fz are the forces in the directions of the X-axis, Y-axis, and Z-axis respectively, and tx , ty , and tz are the moments in the directions of the X-axis, Y-axis, and Z-axis respectively; the calculation box and the controller of the six-dimensional force/torque sensor are connected through a network cable, and data is transmitted through the UDP protocol, and the synchronization cycle is consistent with the control cycle; 所述步骤3.2具体为:The step 3.2 is specifically as follows: 步骤3.2.1:设传感器坐标系S在基坐标系中的方位通过如下的旋转矩阵R来描述:Step 3.2.1: Assume that the orientation of the sensor coordinate system S in the base coordinate system is described by the following rotation matrix R: 其中,为传感器坐标系/>轴在基坐标系中的单位方向向量,/>为传感器坐标系/>轴在基坐标系中的单位方向向量,/>为传感器坐标系/>轴在基坐标系中的单位方向向量;in, is the sensor coordinate system/> The unit direction vector of the axis in the base coordinate system, /> is the sensor coordinate system/> The unit direction vector of the axis in the base coordinate system, /> is the sensor coordinate system/> The unit direction vector of the axis in the base coordinate system; 步骤3.2.2:得到由于磨抛工具重力使传感器受到的力为:Step 3.2.2: The force on the sensor due to the gravity of the grinding and polishing tool is: FG=[Gx Gy Gz Mx My Mz]T F G = [G x G y G z M x M y M z ] T 其中,Gx=axGT、Gy=ayGT、Gz=azGT、Mx=GzLy-GyLz、My=GxLz-GzLx、Mz=GyLx-GxLyAmong them , Gx axGT , Gy ayGT , Gz azGT, MxGzLy - GyLz , My GxLz - GzLx , Mz GyLx - GxLy ; 步骤3.2.3:进行传感器坐标系S和工具坐标系T的静力变换,将传感器受力等效为磨抛工具和磨抛面之间的等效接触力FTStep 3.2.3: Perform static transformation between the sensor coordinate system S and the tool coordinate system T, and convert the sensor force into the equivalent contact force F T between the polishing tool and the polishing surface: 其中,为传感器坐标系S到工具坐标系T的雅克比矩阵;当工具坐标系T相对于传感器坐标系S的齐次变换矩阵/>如下时:in, is the Jacobian matrix from the sensor coordinate system S to the tool coordinate system T; when the tool coordinate system T is the homogeneous transformation matrix relative to the sensor coordinate system S/> As follows: 得到具体形式如下:get The specific form is as follows: 其中,为工具坐标系T相对于传感器坐标系S的旋转矩阵,/>为工具坐标系T的原点在传感器坐标系S中的位置坐标;in, is the rotation matrix of the tool coordinate system T relative to the sensor coordinate system S,/> is the position coordinate of the origin of the tool coordinate system T in the sensor coordinate system S; 所述步骤3.3具体为:The step 3.3 is specifically as follows: 步骤3.3.1:在笛卡尔空间中,将磨抛工具末端点沿工具坐标系的轴、/>轴和/>轴平移运动分别称为Px、Py和Pz方向运动,磨抛工具末端点绕工具坐标系的/>轴、/>轴和/>轴旋转运动分别称为Rx、Ry和Rz方向运动;选择导纳控制理论做Pz/Rx/Ry方向力控制,设在磨抛过程中磨抛工具和磨抛面间的期望接触力为fD,由于想要保证磨抛工具和磨抛面始终贴合,所以绕x轴和y轴方向的期望力矩为0,则期望力为:Step 3.3.1: In Cartesian space, move the end point of the polishing tool along the tool coordinate system. Axis, /> Axis and /> The axial translation motions are called P x , P y and P z directional motions respectively. The end point of the polishing tool moves around the tool coordinate system. Axis, /> Axis and /> The axis rotation motion is called Rx , Ry and Rz direction motion respectively; the admittance control theory is selected to perform Pz / Rx / Ry direction force control. Assume that the expected contact force between the polishing tool and the polishing surface during the polishing process is fD . Since we want to ensure that the polishing tool and the polishing surface always fit together, the expected moment around the x-axis and y-axis is 0, and the expected force is: FD=(00fD 000)T F D =(00f D 000) T 则根据导纳控制得到笛卡尔空间中机器人末端加速度如下:According to the admittance control, the acceleration of the robot end in Cartesian space is as follows: 其中,xe分别为机器人末端位置、速度、加速度偏差,xe由期望位置xD和当前实际位置x0作差得到xe=xD-x0,同理/>M、B、K为6×6参数矩阵,分别称为惯性矩阵、阻尼矩阵和刚度矩阵,其中各项值由开发者根据机器人本体特性和实际调试效果指定;Among them, x e , are the robot end position, velocity, and acceleration deviations respectively. xe is obtained by subtracting the desired position xD from the current actual position x0 to obtain xe = xD - x0 . Similarly, M, B, and K are 6×6 parameter matrices, respectively called inertia matrix, damping matrix, and stiffness matrix. The values of each matrix are specified by the developer based on the robot's characteristics and actual debugging results. 步骤3.3.2:则笛卡尔空间中机器人末端速度如下:Step 3.3.2: The robot terminal velocity in Cartesian space is as follows: 其中,和/>分别为机器人末端当前实际速度和加速度;in, and/> They are the actual current speed and acceleration of the robot end respectively; 步骤3.3.3:在Px/Py方向按位置控制,根据示教中记录的磨抛轨迹,通过轨迹规划得到其笛卡尔空间中机器人末端速度由于位置控制和力控制得到的速度在笛卡尔空间下并不耦合,直接得机器人末端总体速度:Step 3.3.3: According to the position control in the P x /P y direction, according to the polishing trajectory recorded in the teaching, the robot terminal speed in the Cartesian space is obtained through trajectory planning Since the velocities obtained by position control and force control are not coupled in Cartesian space, the overall velocity of the robot end can be directly obtained: 所述步骤3.4具体为:The step 3.4 is specifically as follows: 按机器人微分运动变换,得到关节空间下机器人运动角速度:According to the robot differential motion transformation, the robot motion angular velocity in the joint space is obtained: 其中,J(q)是机器人雅克比矩阵,使用微分变换法,由运动学中各关节之间的齐次变换矩阵求解;对于n个关节的机器人,设第i-1个关节到第i个关节的齐次变换矩阵为则从第i个关节到末端第n个关节的齐次变换矩阵/>为:Where J(q) is the Jacobian matrix of the robot, which is solved by the homogeneous transformation matrix between the joints in kinematics using the differential transformation method; for a robot with n joints, the homogeneous transformation matrix from the i-1th joint to the ith joint is Then the homogeneous transformation matrix from the i-th joint to the n-th joint at the end/> for: 其中,则雅克比矩阵J(q)的第i列Ji如下:Among them, the i-th column Ji of the Jacobian matrix J(q) is as follows:
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