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CN109382828B - A robot shaft hole assembly system and method based on teaching and learning - Google Patents

A robot shaft hole assembly system and method based on teaching and learning Download PDF

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CN109382828B
CN109382828B CN201811275792.8A CN201811275792A CN109382828B CN 109382828 B CN109382828 B CN 109382828B CN 201811275792 A CN201811275792 A CN 201811275792A CN 109382828 B CN109382828 B CN 109382828B
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shaft hole
force
robot
torque
teaching
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CN109382828A (en
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高霄
李淼
简磊
肖晓晖
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Wuhan Cobot Technology Co ltd
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Wuhan University WHU
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/0081Programme-controlled manipulators with leader teach-in means
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B23MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23PMETAL-WORKING NOT OTHERWISE PROVIDED FOR; COMBINED OPERATIONS; UNIVERSAL MACHINE TOOLS
    • B23P19/00Machines for simply fitting together or separating metal parts or objects, or metal and non-metal parts, whether or not involving some deformation; Tools or devices therefor so far as not provided for in other classes
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators

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Abstract

本发明公开了一种基于示教学习的机器人轴孔装配系统及方法,系统包括机械臂、六维力/力矩传感器、被动柔性RCC装置以及PC上位机,机械臂为多轴机械臂,六维力/力矩传感器安装在机械臂末端,被动柔性RCC装置安装在六维力/力矩传感器上,被动柔性RCC装置上安装有用于夹持待装配部件的夹持工具,PC上位机与机械臂和六维力/力矩传感器可进行实时通信。首先人工示教记录人完成装配任务数据,采用学习算法训练装配技能模型,然后机械臂在PC上位机的控制指令下,携带销零件进行轴孔装配,PC上位机搭建的控制系统基于ROS平台。本发明结合示教学习模仿人完成装配任务时的柔性行为,实现机器人自主柔性装配作业,可以很好地满足作业要求。

Figure 201811275792

The invention discloses a robot shaft hole assembly system and method based on teaching and learning. The system includes a mechanical arm, a six-dimensional force/torque sensor, a passive flexible RCC device and a PC upper computer. The force/torque sensor is installed at the end of the robot arm, the passive flexible RCC device is installed on the six-dimensional force/torque sensor, the passive flexible RCC device is installed with a clamping tool for clamping the parts to be assembled, the PC host computer and the robot arm and the six-dimensional force/torque sensor are installed on the passive flexible RCC device. The force/torque sensor can communicate in real time. Firstly, manual teaching and recording of the data of the person completing the assembly task, using the learning algorithm to train the assembly skill model, and then under the control command of the PC host computer, the robotic arm carries the pin parts for shaft hole assembly, and the control system built by the PC host computer is based on the ROS platform. The invention combines teaching and learning to imitate the flexible behavior of humans when completing the assembly task, realizes the autonomous flexible assembly operation of the robot, and can well meet the operation requirements.

Figure 201811275792

Description

Robot shaft hole assembling system and method based on teaching learning
Technical Field
The invention belongs to the field of intelligent manufacturing, relates to a teaching robot, and particularly relates to a robot shaft hole assembling system and method based on teaching learning.
Background
The manufacturing technology is the core of economic competition, and the automation degree of manufacturing and processing is higher and higher. Industrial robots are widely used in the manufacturing field for improving production efficiency and product quality. At present, the industrial robot is mainly used for carrying, painting and other unconstrained operations, and the motion of a tool at the tail end of the robot is not limited. Aiming at constrained tasks such as assembly and other tasks contacting with workpieces, common precision assembly tasks have certain tolerance fit precision requirements, the assembly clearance is small, and the assembly is extremely easy to cause assembly blocking. The industrial robot based on position or speed control has large contact rigidity, and a large contact force is easily generated in the contact process, so that a workpiece or a tool is damaged, and a precision assembly task can not be basically completed. When a traditional industrial robot finishes a constrained task, a teaching point is generally adopted to be changed into off-line programming, and the defects are that the deployment time is long, the algorithm and the programming are complex, the requirement on an operator is high, the traditional industrial robot is only used for a structured environment, the environment adaptability is poor and the like. Therefore, at present, the assembly task is mainly performed manually, the manual operation efficiency is low, the cost is high, the manufacturing environment seriously influences the physical health of workers, the product uniformity is poor, and the defective rate is high. Therefore, aiming at the constrained assembly operation, in order to realize automatic assembly, the real-time measurement and feedback control of the contact force are required to be introduced, the assembly contact force is reduced, the assembly state is estimated based on the contact force, the assembly motion strategy is adjusted, and the flexible assembly operation is realized.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide an assembly robot based on teaching learning and a control system thereof.
In order to solve the technical problems, the invention adopts the technical scheme that:
the utility model provides a robot shaft hole assembly system based on teaching learning which characterized in that: the device comprises a mechanical arm, a six-dimensional force/torque sensor, a passive flexible RCC (remote Center company) device and a PC (personal computer) upper computer, wherein the six-dimensional force/torque sensor is used for measuring contact force, the mechanical arm is a multi-axis mechanical arm with a motion control function, the six-dimensional force/torque sensor is installed at the tail end of the mechanical arm, the passive flexible RCC device is installed on the six-dimensional force/torque sensor, the PC upper computer is in communication connection with the mechanical arm and the six-dimensional force/torque sensor, in the operation process, the mechanical arm carries a clamping pin part of the passive flexible RCC device to carry out shaft hole assembly under the control instruction of the PC upper computer, and a control system built by the PC upper computer is based on an ROS (reactive oxygen species) platform.
As an improvement, the six-dimensional force/torque sensor monitors the stress state between a clamped workpiece and a shaft hole on the passive flexible RCC device in real time through force feedback, and the posture of the workpiece is adjusted in time through the mechanical arm.
A robot shaft hole assembling method based on teaching learning is characterized by comprising the following steps of:
step one, manual teaching, wherein a mechanical arm drives a pin part to move towards a shaft hole part, a pin is controlled to be in contact with a hole plane and keep constant contact force, the mechanical arm drives the pin part to move on the hole plane and search for the shaft hole, when a six-dimensional force/torque sensor detects sudden change of the contact force, the pin part is positioned in the shaft hole, then manual traction teaching is carried out to assemble the pin part and the shaft hole, values of torque and angular speed in a cooperative assembly process are recorded, M times of repeated teaching is carried out according to the method, and the torque and the angular speed are collected to form a data set;
step two, model learning, namely coding teaching data by adopting a Gaussian mixture model for a data set generated by repeated teaching for many times, obtaining a relation model of force and angular velocity, and performing Gaussian mixture model training based on an expectation-maximization (EM) algorithm to obtain a function mapping relation of moment and angular velocity;
and step three, assembling the shaft hole, taking the direction and the attitude angle of the shaft hole into consideration, driving the pin to move to the surface position of the shaft hole part by the mechanical arm, searching and positioning the shaft hole on the surface of the shaft hole part, positioning the shaft hole, adjusting the attitude through feedback control of a six-dimensional force/torque sensor, calculating the angular velocity value of the tail end of the mechanical arm according to the function mapping relation of the torque and the angular velocity in model learning, and calculating the joint angle of the six-axis mechanical arm through inverse kinematics by combining the output position coordinate of a position controller, so that the tail end of the mechanical arm is controlled to move, and the shaft hole assembling operation is completed.
In the first step, in the process that the mechanical arm drives the pin part to move on the hole plane and search the shaft hole, the pin searches the position of the shaft hole on the hole plane in an Archimedes spiral motion track, and when the six-dimensional force/torque sensor detects the jump of the force in the z direction, the position of the shaft hole is found, and the hole searching is stopped.
As an improvement, the mechanical arm has a joint torque estimation function, can realize reverse driving, can estimate external environment force according to the joint torque, and is mapped to the motion of the robot, so that the mechanical arm is dragged by the person to finish free motion.
As an improvement, the data set ξ ═ F, X for the teaching]TWherein F ═ { M ═x,My},X={ωxyAnd coding teaching data by adopting a Gaussian mixture model to obtain a force and position relation model, wherein a certain data point xi is in the middle of RD×NThe probability of (c) is:
Figure GDA0002946440810000021
wherein pik∈[0,1]Is a priori probability, and
Figure GDA0002946440810000022
k is the number of Gaussian distributions, R is the real number field, N is the total number of data points, D is the dimensionality of the data, μk∈RD,∑k∈RD×DMean and covariance matrices representing the kth Gaussian distribution, respectively, given an input variable ξXOutput xiFThe conditional probability distribution of (a) is:
Figure GDA0002946440810000031
wherein
Figure GDA0002946440810000032
Mean and variance of the kth gaussian distribution in the posterior probability:
Figure GDA0002946440810000033
Figure GDA0002946440810000034
and is
Figure GDA0002946440810000035
The k-th gaussian distribution means of X and F respectively,
Figure GDA0002946440810000036
is the covariance matrix between X and F:
Figure GDA0002946440810000037
ξFthe probability in the kth Gaussian distribution is
Figure GDA0002946440810000038
Returning the Gaussian mixture to a given xiFLower xiXOf conditional probability distribution
Figure GDA0002946440810000039
Thus, the Gaussian mixture model/Gaussian mixture regression is formed by the parameters
Figure GDA00029464408100000310
Determining the parameter value generally by adopting an expectation maximization algorithm, determining the hyperparameter K as the number of Gaussian distributions by a Bayesian information criterion to obtain the optimal model parameter, and finally obtaining the moment and the angular velocity
Figure GDA00029464408100000311
The adjustment strategy during the assembly task can be completed through the mapping relation between the two components.
In the first step and the third step, when the shaft hole is searched, the admittance controller is used as the position controller to realize the force control tracking, and the contact force in the x and y directions is reduced while the contact force in the direction perpendicular to the plane of the hole is kept unchanged, so that the flexible contact is realized.
As an improvement, the robot arm performs fine adjustment of the posture through a torque controller, and the torque controller adopts the above-mentioned mapping relationship between the learned torque and the angular velocity:
Figure GDA00029464408100000312
calculating a target tail end angular velocity value according to the moment acquired in real time, wherein a tail end rotation matrix R (t) is formed by R (t + delta t) ═ delta tS (omega)a)+I3×3) R (t) calculation, ωxyzFor the angular velocity of the end axis of the arm in the x, y, z directions, t represents time, Δ t represents the control period of the control system, I3×3Representing a third order identity matrix, wherein the inverse skew symmetric matrix:
Figure GDA0002946440810000041
after the rotation matrix is calculated according to the control period, the position output coordinate x of the position controller is combined, and the six-axis mechanical arm joint angle is calculated through inverse kinematics, so that the robot is controlled to move, and the anthropomorphic flexible shaft hole operation is realized.
As an improvement, the teaching times M range from 3 to 9.
The invention has the beneficial effects that:
1. teaching learning is applied to assembly, and only manual teaching is needed, so that the shaft hole assembly can be carried out on the workpiece, the complicated calibration work is avoided, and the application threshold is low;
2. the deployment is rapid, high-precision installation and calibration are not needed, and the assembly efficiency is improved;
3. the algorithm is good in universality, based on the ROS system, convenient for algorithm transplantation and suitable for building different robots and sensor systems.
Drawings
FIG. 1 is a schematic view of a robot shaft hole assembly system of the present invention;
FIG. 2 is a block diagram of the robot shaft hole assembly system of the present invention;
FIG. 3 is a diagram of a teaching learning framework;
FIG. 4 is a schematic illustration of the torque versus angular velocity relationship of the present invention;
fig. 5 is a schematic view of an assembly execution control scheme of the robot shaft hole assembly system of the present invention.
The system comprises a mechanical arm 1, a six-dimensional force/torque sensor 2, a passive flexible RCC device 3 and a PC upper computer 4.
Detailed Description
(2) As shown in fig. 2, the control system block diagram contains a mechanical arm 1, a six-dimensional force/torque sensor 2 and a PC upper computer 4, the six-dimensional force/torque sensor 2 is used for measuring the contact force, the mechanical arm 1 is a multi-axis mechanical arm 1 with a motion control function, the six-dimensional force/torque sensor 2 is installed at the tail end of the mechanical arm 1, a passive flexible RCC device 3 is installed on the six-dimensional force/torque sensor 2, the PC upper computer 4 is in communication connection with the mechanical arm 1 and the six-dimensional force/torque sensor 2, in the operation process, the mechanical arm 1 carries a passive flexible RCC device 3 clamping pin part to be assembled in a shaft hole under the control instruction of the PC upper computer 4, and the control system built by the PC upper computer 4 is based on an ROS platform. The control system is based on the ROS platform and comprises a control algorithm node, a feedback node based on a six-dimensional force/torque sensor 2 and a real-time motion control node of the mechanical arm 1. The six-dimensional force/torque sensor 2 and the mechanical arm 1 are both connected to the same local area network through network cables and a PC. Adopt Modbus communication protocol between arm 1 and the PC, adopt unified communication interface among the ROS to realize that arm 1 state reads and motion control. The six-dimensional force/torque sensor 2 adopts an Ethernet protocol to send data to a PC end, receives the states of the sensors in a control algorithm node, and calculates a lower period control instruction.
The mechanical arm 1 is a UR3 mechanical arm, is provided with a ROS-based driving program and a function package, and can realize basic motion control and encoder data reading after being installed, so that the construction of a control system is completed. The six-dimensional force/torque sensor 2 has a ROS-based driving program and feeds back contact force data in real time. In the embodiment, the UR3 robot arm is selected as a robot platform, and the six-dimensional force/torque sensor 2 is a HEX-70-XE-200N six-dimensional force/torque sensor of OPTOFORCE in Hungary.
The control algorithm is an active force control algorithm based on force/position hybrid control, the Simulink design is adopted and is converted into a C + + code, the algorithm takes data of a six-dimensional force/torque sensor 2 and a joint encoder of the mechanical arm 1 as input quantities, and based on feedback of the six-dimensional force/torque sensor 2, position and speed control of the mechanical arm 1 is achieved, and assembly operation is completed.
(3) As shown in fig. 3, the teaching learning is to acquire data of a human when executing a task, perform data processing and model training by combining a machine learning method, obtain a skill of the human when completing a certain task, and finally give the skill to the robot, thereby implementing the task execution of robot personification. The teaching learning can be divided into three parts, including manual teaching, model learning and autonomous execution.
The manual teaching process comprises the following steps: a, moving a pin to a hole part, setting the direction and the attitude angle deviation of a hole, and contacting a hole plane and keeping constant contact force; b, in the moving process, the shaft searches the hole position on the hole plane in an Archimedes spiral motion track, when the six-dimensional force/torque sensor 2 detects the jump of the force in the z direction, the hole position is found, and the hole searching is stopped; and C, pressing an I/O button of the end effector to enable the mechanical arm 1 to execute a free driving mode, and realizing the cooperative bolt-in hole of the robot and the mechanical arm 1. And recording the moment M ═ M in the cooperative assembly processx,MyAnd angular velocity ω ═ ωxyThe value of (c) } is repeated a plurality of times, and fig. 4(a) is a phase diagram showing torque and angular velocity of a single teaching. The mechanical arm 1 adopted in the embodiment has a joint torque estimation function, can realize reverse driving, can estimate external environment force according to the joint torque, is mapped to the movement of the robot, and can realize that a person drags the mechanical arm to finish free movement.
Data set xi ═ F, X for teaching]TWherein F ═ { M ═x,My},X={ωxyAnd (6) coding the teaching data by adopting a Gaussian Mixture Model (GMM) and obtaining a relation model of force and position. Wherein a certain data point xi ∈ RD×NThe probability of (c) is:
Figure GDA0002946440810000051
wherein pik∈[0,1]Is a priori probability, and
Figure GDA0002946440810000052
k is the number of Gaussian distributions, R is the real number domain, N is the total number of data points, and D is the dimensionality of the data. Mu.sk∈RD,∑k∈RD×DRespectively representing the mean and covariance matrices of the kth gaussian distribution. Given input variable ξXOutput xiFThe conditional probability distribution of (a) is:
Figure GDA0002946440810000061
wherein
Figure GDA0002946440810000062
Mean and variance of the kth gaussian distribution in the posterior probability:
Figure GDA0002946440810000063
Figure GDA0002946440810000064
and is
Figure GDA0002946440810000065
The k-th gaussian distribution means of X and F respectively,
Figure GDA0002946440810000066
as a covariance matrix:
Figure GDA0002946440810000067
ξFat the k gaussThe probability in the distribution is
Figure GDA0002946440810000068
Gaussian Mixture Regression (GMR) for a given ξFLower xiXOf conditional probability distribution
Figure GDA0002946440810000069
Thus, GMM/GMR is defined by parameters
Figure GDA00029464408100000610
It is decided that the determination of the parameter values generally employs an Expectation Maximization (EM) algorithm. The hyperparameter K is the number of gaussian distributions and is determined by Bayesian Information Criterion (BIC). Obtaining the optimal model parameters, and finally obtaining the moment and the angular velocity
Figure GDA00029464408100000611
The mapping relationship between the two components, i.e., the adjustment strategy for completing the assembly task, is shown in fig. 4(b) as the distribution relationship between the moment and the angular velocity in the x-axis direction.
Figure 5 shows a force feedback based pin-in-hole control scheme. The position and attitude of the shaft needs to be controlled when performing the assembly task. Force controllers are used for shaft position adjustment, while torque controllers are used for shaft attitude adjustment. The whole process of automatically executing the assembly task comprises the following four steps:
moving a pin to a surface position of a hole component;
searching hole positions on the surface of the hole component;
thirdly, based on the control scheme shown in fig. 5, the admittance controller is adopted as the position controller to realize force control tracking and realize flexible contact. The specific controller structure is as follows:
Figure GDA0002946440810000071
wherein M isd,Bd,KdIs a virtual mass, damping, stiffness parameter, x is a three-dimensional coordinate of the target position output by the controller, Fd=[0,0,-20N]TFor a set reference contact force, Fa=[Fax,Fay,Faz]TThe feedback value of the contact force in the actual xyz direction. The admittance controller provided here can achieve tracking of the z-direction 20N contact force while reducing the x-and y-direction contact forces to 0.
And fourthly, fine adjustment of the posture is carried out through a torque controller based on the control scheme shown in the figure 5. The torque controller uses the aforementioned learned mapping relationship between torque and angular velocity:
Figure GDA0002946440810000072
calculating the angular velocity value of the tail end of the target according to the moment acquired in real time, wherein the angular velocity w in the z directionzIs set to 0. The end rotation matrix is formed by R (t + Δ t) — (Δ tS (ω)a)+I3×3) R (t) calculation, wherein the inverse skew symmetric matrix:
Figure GDA0002946440810000073
in this example, the control period Δ t is 0.008 s. After the rotation matrix is calculated, the position output coordinate x of the position controller is combined, and the joint angle of the six-axis mechanical arm 1 is calculated through inverse kinematics, so that the robot is controlled to move, and the assembly operation of the anthropomorphic flexible shaft hole is realized.

Claims (7)

1.一种基于示教学习的机器人轴孔装配方法,该机器人轴孔装配方法采用的设备包括机械臂、六维力/力矩传感器、被动柔性RCC装置以及PC上位机,其特征在于,包括以下步骤:1. a robot shaft hole assembling method based on teaching and learning, the equipment that this robot shaft hole assembling method adopts comprises a mechanical arm, a six-dimensional force/torque sensor, a passive flexible RCC device and a PC host computer, it is characterized in that, comprises the following: step: 步骤一、人工示教,机械臂带动销零件往轴孔部件移动,控制销与孔平面接触并保持恒定的接触力,机械臂带动销零件在孔平面上移动搜索轴孔,当六维力/力矩传感器检测接触力突变,即定位到轴孔,之后人工牵引示教进行销零件和轴孔装配,记录协作装配过程中的力矩和角速度的值,按照上述方法进行M次重复示教,并采集力矩和角速度形成数据集;Step 1. Manual teaching, the mechanical arm drives the pin parts to move toward the shaft hole parts, controls the pin to contact the hole plane and maintains a constant contact force, and the mechanical arm drives the pin parts to move on the hole plane to search for the shaft holes. When the six-dimensional force / The torque sensor detects the sudden change of the contact force, that is, locates the shaft hole, and then manually pulls and teaches to assemble the pin parts and the shaft hole, records the values of the torque and angular velocity during the collaborative assembly process, and repeats the teaching M times according to the above method, and collects Moment and angular velocity form a dataset; 步骤二、模型学习,将多次重复示教产生的数据集通过采用高斯混合模型编码示教数据,并得到力和角速度的关系模型,基于期望最大化算法进行高斯混合模型训练,可得到力矩和角速度的函数映射关系;Step 2, model learning, encode the teaching data by using the Gaussian mixture model to encode the data set generated by repeated teaching, and obtain the relationship model of force and angular velocity, and train the Gaussian mixture model based on the expectation maximization algorithm to obtain the torque and angular velocity. The function mapping relationship of angular velocity; 步骤三、轴孔装配,考虑轴孔的方向以及姿态角度有偏差,机械臂带动销向轴孔部件表面位置进行移动,然后在轴孔部件表面进行轴孔搜索定位,定位轴孔后,通过六维力/力矩传感器反馈控制进行姿态调整,按照模型学习中力矩和角速度的函数映射关系,根据实时采集的力矩计算机械臂末端的角速度值,结合位置控制器的输出位置坐标通过逆运动学计算六轴机械臂关节角度,从而控制机械臂末端运动,完成轴孔装配作业。Step 3: Assembly of the shaft hole. Considering the deviation of the direction of the shaft hole and the attitude angle, the mechanical arm drives the pin to move to the surface position of the shaft hole part, and then searches and locates the shaft hole on the surface of the shaft hole part. Dimensional force/torque sensor feedback control performs attitude adjustment, according to the function mapping relationship between torque and angular velocity in model learning, calculates the angular velocity value of the end of the manipulator according to the torque collected in real time, and combines the output position coordinates of the position controller to calculate through inverse kinematics VI. The joint angle of the axis manipulator can control the movement of the end of the manipulator and complete the assembly of the shaft hole. 2.如权利要求1所述的机器人轴孔装配方法,其特征在于:步骤一中,机械臂带动销零件在孔平面上移动搜索轴孔过程中,销在孔平面以阿基米德螺旋线运动轨迹进行轴孔位置的搜索,当六维力/力矩传感器检测到z方向的力的跳变时,表明轴孔位置已经找到,停止搜孔。2. The robot shaft hole assembling method as claimed in claim 1, wherein in step 1, the mechanical arm drives the pin parts on the hole plane to move and search the shaft hole process, and the pin is in the hole plane with an Archimedes spiral. The motion trajectory is used to search the position of the shaft hole. When the six-dimensional force/torque sensor detects the force jump in the z direction, it indicates that the position of the shaft hole has been found, and the hole search is stopped. 3.如权利要求1所述的机器人轴孔装配方法,其特征在于:所述机械臂具有关节力矩估计功能,可以实现反向驱动,根据关节力矩可以估计外界环境力,并映射到机器人运动中,可实现人拖动机械臂完成自由运动。3. The robot shaft hole assembling method according to claim 1, wherein the mechanical arm has a joint torque estimation function, which can realize reverse driving, and can estimate the external environment force according to the joint torque, and map it into the robot motion , which can realize the free movement of the manipulator by dragging the manipulator. 4.如权利要求1所述的机器人轴孔装配方法,其特征在于:针对示教的数据集ξ=[F,X]T,其中F={Mx,My},X={ωxy},采用高斯混合模型编码示教数据,并得到力和位置的关系模型,其中某个数据点ξ∈RD×N的概率为:4. The robot shaft hole assembling method according to claim 1, wherein: for the taught data set ξ=[F,X] T , wherein F={M x ,M y },X={ω xy }, use Gaussian mixture model to encode the teaching data, and get the relationship model of force and position, where the probability of a data point ξ∈R D×N is:
Figure FDA0002946440800000011
Figure FDA0002946440800000011
其中πk∈[0,1]为先验概率,且
Figure FDA0002946440800000012
K为高斯分布的个数,R为实数域,N为数据点的总数,D为数据的维度,μk∈RD,∑k∈RD×D分别表示第k个高斯分布的均值和协方差矩阵,给定输入变量ξX,输出ξF的条件概率分布为:
where π k ∈ [0,1] is the prior probability, and
Figure FDA0002946440800000012
K is the number of Gaussian distributions, R is the real number domain, N is the total number of data points, D is the dimension of the data, μ k ∈ R D , ∑ k ∈ R D×D represent the mean and covariance of the kth Gaussian distribution, respectively The variance matrix, given the input variable ξ X , the conditional probability distribution of the output ξ F is:
Figure FDA0002946440800000021
Figure FDA0002946440800000021
其中
Figure FDA0002946440800000022
表示后验概率中第k个高斯分布的均值和方差:
in
Figure FDA0002946440800000022
Represent the mean and variance of the k-th Gaussian distribution in the posterior probability:
Figure FDA0002946440800000023
Figure FDA0002946440800000023
Figure FDA0002946440800000024
Figure FDA0002946440800000024
Figure FDA0002946440800000025
分别为X和F的第k个高斯分布均值,
Figure FDA0002946440800000026
为X和F之间的协方差矩阵:
and
Figure FDA0002946440800000025
are the k-th Gaussian distribution mean of X and F, respectively,
Figure FDA0002946440800000026
is the covariance matrix between X and F:
Figure FDA0002946440800000027
Figure FDA0002946440800000027
ξF在第k个高斯分布中的概率为The probability of ξ F in the kth Gaussian distribution is
Figure FDA0002946440800000028
Figure FDA0002946440800000028
高斯混合回归为给定ξF下ξX的条件概率分布的期望Gaussian mixture regression is the expectation of the conditional probability distribution of ξ X given ξ F
Figure FDA0002946440800000029
Figure FDA0002946440800000029
因此,高斯混合模型/高斯混合回归由参数
Figure FDA00029464408000000210
所决定,参数值的确定采用期望最大化算法,超参数K为高斯分布的个数,由贝叶斯信息准则决定,得到最佳的模型参数,最终得到力矩和角速度
Figure FDA00029464408000000211
之间的映射关系,即可完成装配任务时的调整策略。
Therefore, the Gaussian mixture model/Gaussian mixture regression is determined by the parameter
Figure FDA00029464408000000210
It is determined that the parameter value is determined by the expectation maximization algorithm, and the hyperparameter K is the number of Gaussian distributions, which is determined by the Bayesian information criterion to obtain the best model parameters, and finally obtain the torque and angular velocity.
Figure FDA00029464408000000211
The mapping relationship between them can be used to complete the adjustment strategy when the assembly task is completed.
5.如权利要求1所述的机器人轴孔装配方法,其特征在于:所述步骤一和步骤三中,进行轴孔搜索时,采用导纳控制器作为位置控制器实现力控跟踪,在保持与孔平面垂直方向接触力不变的同时,减小x和y方向的接触力,实现柔性接触。5. The robot shaft hole assembling method according to claim 1, characterized in that: in the steps 1 and 3, when the shaft hole is searched, an admittance controller is used as a position controller to realize force-controlled tracking. While the contact force in the vertical direction to the hole plane remains unchanged, the contact force in the x and y directions is reduced to achieve flexible contact. 6.如权利要求1所述的机器人轴孔装配方法,其特征在于:所述机械臂通过力矩控制器来进行姿态的微调,力矩控制器采用上述的学习到的力矩与角速度之间的映射关系:
Figure FDA00029464408000000212
根据实时采集到的力矩,计算目标末端角速度值,末端旋转矩阵R(t)由R(t+Δt)=(ΔtS(ωa)+I3×3)R(t)计算,ωxyz为机械臂末端轴在x,y,z方向的角速度,t表示时间,Δt表示控制系统的控制周期,I3×3表示三阶单位矩阵,其中反斜对称矩阵:
6. The robot shaft hole assembling method as claimed in claim 1, wherein the mechanical arm performs fine-tuning of the attitude through a torque controller, and the torque controller adopts the mapping relationship between the above-mentioned learned torque and angular velocity :
Figure FDA00029464408000000212
Calculate the angular velocity value of the target end according to the moment collected in real time. The end rotation matrix R(t) is calculated by R(t+Δt)=(ΔtS(ω a )+I 3×3 )R(t), ω xy , ω z are the angular velocities of the end axis of the manipulator in the x, y, z directions, t is the time, Δt is the control period of the control system, I 3×3 is the third-order unit matrix, and the inverse symmetric matrix is:
Figure FDA0002946440800000031
Figure FDA0002946440800000031
根据控制周期计算出旋转矩阵后,结合位置控制器的位置输出坐标x,通过逆运动学计算六轴机械臂关节角度,从而控制机器人运动,实现拟人化柔性轴孔作业。After the rotation matrix is calculated according to the control period, combined with the position output coordinate x of the position controller, the joint angle of the six-axis manipulator is calculated through inverse kinematics, so as to control the robot movement and realize the anthropomorphic flexible shaft hole operation.
7.如权利要求1所述的机器人轴孔装配方法,其特征在于:所述示教的次数M的范围为3-9次。7 . The method for assembling a shaft hole of a robot according to claim 1 , wherein the number of times M of teaching is in the range of 3-9 times. 8 .
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