WO2020007305A1 - 拖动示教系统和方法 - Google Patents

拖动示教系统和方法 Download PDF

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WO2020007305A1
WO2020007305A1 PCT/CN2019/094431 CN2019094431W WO2020007305A1 WO 2020007305 A1 WO2020007305 A1 WO 2020007305A1 CN 2019094431 W CN2019094431 W CN 2019094431W WO 2020007305 A1 WO2020007305 A1 WO 2020007305A1
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robot
link
model
joint
coordinate system
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French (fr)
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朱向阳
李明洋
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Shanghai Jaka Robotics Ltd
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Shanghai Jaka Robotics Ltd
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Priority to EP19830246.5A priority Critical patent/EP3819089A4/en
Priority to US17/257,851 priority patent/US12049006B2/en
Publication of WO2020007305A1 publication Critical patent/WO2020007305A1/zh
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Program-controlled manipulators
    • B25J9/16—Program controls
    • B25J9/1602—Program controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Program-controlled manipulators
    • B25J9/16—Program controls
    • B25J9/1628—Program controls characterised by the control loop
    • B25J9/1653—Program controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Program-control systems
    • G05B19/02—Program-control systems electric
    • G05B19/42—Recording and playback systems, i.e. in which the program is recorded from a cycle of operations, e.g. the cycle of operations being manually controlled, after which this record is played back on the same machine
    • G05B19/423—Teaching successive positions by walk-through, i.e. the tool head or end effector being grasped and guided directly, with or without servo-assistance, to follow a path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/39—Robotics, robotics to robotics hand
    • G05B2219/39181—Compensation of coulomb friction in joint
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/41—Servomotor, servo controller till figures
    • G05B2219/41156—Injection of vibration anti-stick, against static friction, dither, stiction
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/41—Servomotor, servo controller till figures
    • G05B2219/41448—Ffw friction compensation for speed error, derived from position reference
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/43—Speed, acceleration, deceleration control ADC
    • G05B2219/43022—Compensate for friction as function of position
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/50—Machine tool, machine tool null till machine tool work handling
    • G05B2219/50391—Robot
    • Y—GENERAL 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Definitions

  • the present application relates to the field of industrial robot control technology, and in particular, to a drag teaching system and method.
  • Drag teaching also known as direct teaching or manual teaching, is one of the main ways of human-machine cooperation, that is, people directly complete the teaching programming of robots by manual dragging.
  • the traditional teaching method mainly depends on the teaching device, and this teaching method has the characteristics of low work efficiency, tedious and unintuitive process, and high requirements on the knowledge level of the operator.
  • the drag teaching method is relatively intuitive, and the requirements for field operators are greatly reduced.
  • the purpose of this application includes, for example, providing a drag teaching system and method, which can enable a user to easily lift a robot to complete traction teaching.
  • the drag teaching system includes:
  • the model identification module establishes a static model of the robot and identifies the model parameters.
  • the static model includes a gravity model and a Coulomb friction model;
  • Feedforward compensation module according to the identified model parameters, the current loop transmitted to the joint motors of the robot in a feedforward manner
  • the data recording module records the position information of each joint of the robot, and is used for the robot to reproduce the teaching movement.
  • the static model of the robot is expressed as:
  • i represents the i-th link
  • z 0 is the constant vector [0 0 1] T
  • m j is the mass of the j-th link
  • p i-1, j is the i-th link.
  • R j i-1 is a rotation matrix from the j-th link coordinate system to the i-1-th link coordinate system
  • r j Is the centroid coordinate of the link in the j-th link coordinate system
  • g is the vector of gravity acceleration in the world coordinate system
  • f i is the Coulomb friction force of the proximal joint of the link
  • sgn ( ⁇ ) is the sign operator, Is the speed of the i-th joint, n is the number of robot joints;
  • S ( ⁇ ) is a cross product operator
  • Y g is a matrix of (n ⁇ 4n)
  • Y f is a diagonal matrix of (n ⁇ n)
  • z g is a unit vector pointing to the same g;
  • the position information of each joint of the robot includes:
  • the feedback speed of each joint of the robot is filtered by a filter with a preset cut-off frequency to reduce the noise signal in the speed signal; on this basis, a square wave signal with a certain threshold and a certain frequency is superimposed. It is used to overcome the static friction force at the beginning of the drag teaching function.
  • the setting of the threshold value is related to the size of the static friction force.
  • the frequency setting is related to the starting effect. After the robot moves, the square wave signal quickly decays to zero to improve the comfort of dragging teaching.
  • the embodiment of the present application also discloses a drag teaching method, which is characterized in that it includes the following steps:
  • the static model includes a gravity model and a Coulomb friction model
  • the static model of the robot is expressed as:
  • i represents the i-th link
  • z 0 is the constant vector [0 0 1] T
  • m j is the mass of the j-th link
  • p i-1, j is the i-th link.
  • R j i-1 is a rotation matrix from the j-th link coordinate system to the i-1-th link coordinate system
  • r j Is the centroid coordinate of the link in the j-th link coordinate system
  • g is the vector of gravity acceleration in the world coordinate system
  • f i is the Coulomb friction force of the proximal joint of the link
  • sgn ( ⁇ ) is a sign operator, Is the speed of the i-th joint, n is the number of robot joints;
  • S ( ⁇ ) is a cross product operator
  • Y g is a matrix of (n ⁇ 4n)
  • Y f is a diagonal matrix of (n ⁇ n)
  • z g is a unit vector pointing to the same g;
  • the position information of each joint of the robot includes:
  • the feedback speed of each joint of the robot is filtered by a filter with a preset cut-off frequency to reduce the noise signal in the speed signal; on this basis, a square wave signal with a certain threshold and a certain frequency is superimposed. It is used to overcome the static friction force at the beginning of the drag teaching function.
  • the setting of the threshold value is related to the size of the static friction force.
  • the frequency setting is related to the starting effect. After the robot moves, the square wave signal quickly decays to zero to improve the comfort of dragging teaching.
  • a drag teaching system and method according to the present application has the following advantages:
  • the present application does not require a multi-dimensional force sensor, the system is simple, the cost is low, the teaching is flexible, and the teaching efficiency is high, which opens a new way for teaching robots of various types of complex trajectories.
  • FIG. 1 is a block diagram of an overall structure of a drag teaching system according to the present application.
  • 3 is a verification effect verification diagram of a model identification module
  • FIG. 4 is an effect diagram of the sixth joint of the feedforward compensation module
  • FIG. 5 is a trajectory diagram of the sixth joint during a recorded drag teaching process.
  • the drag teaching system includes a model identification module, establishes a static model of the robot, and identifies model parameters, where The static model includes the gravity model and the Coulomb friction model; the feedforward compensation module, according to the identified model parameters, forwards the current loop to the robot joint motors in a feedforward manner; the data recording module records the positions of the robot joints Information for robots to reproduce teaching movements.
  • the static model of the robot is expressed as:
  • i represents the i-th link
  • z 0 is the constant vector [0 0 1] T
  • m j is the mass of the j-th link
  • p i-1, j is the i-th link.
  • R j i-1 is a rotation matrix from the j-th link coordinate system to the i-1-th link coordinate system
  • r j Is the centroid coordinate of the link in the j-th link coordinate system
  • g is the vector of gravity acceleration in the world coordinate system
  • f i is the Coulomb friction of the proximal joint of the link
  • n is the number of robot joints;
  • S ( ⁇ ) is a cross product operator
  • Y g is a matrix of (n ⁇ 4n)
  • Y f is a diagonal matrix of (n ⁇ n)
  • z g is a unit vector pointing to the same g;
  • the position information of each joint of the robot includes: a position of a key point of the robot or a drag track during drag teaching.
  • the present application also discloses a drag teaching method applied to the above-mentioned drag teaching system, as shown in FIG. 2, including the following steps:
  • the static model includes a gravity model and a Coulomb friction model.
  • the current loops transmitted to the joint motors of the robot in a feedforward manner According to the identified model parameters, the current loops transmitted to the joint motors of the robot in a feedforward manner.
  • a square wave signal with a certain threshold and a certain frequency is superimposed to overcome the static friction force at the beginning of the drag teaching function.
  • the setting of the threshold value is related to the magnitude of the static friction force, and the frequency setting is related to the starting effect. After the robot moves, the square wave signal quickly decays to zero to improve the comfort of dragging teaching.
  • model parameters of the robot are identified.
  • a Foxconn robot with a model number A-05-2 is taken as an example, and its DH parameters are shown in Table 1.
  • the robot's regression matrix Y (6 ⁇ 30) can be calculated.
  • the first, 2, 3, 4, 7, 8, 10 in Y can be obtained.
  • 12, 14, 16, 18, 20, 23, 24 columns can be removed to get Y * (6 ⁇ 16).
  • the robot is controlled by dSPACE's MicroLabBox.
  • each joint of the robot is tracked by a sinusoidal signal with a period of 400s, and its amplitude is ⁇ , 0.4 from the first axis to the sixth axis. ⁇ , 0.3 ⁇ , ⁇ , ⁇ , ⁇ ;
  • the feedback position and current / torque command of each joint are recorded and converted to the link side.
  • 500 data points are randomly selected from the two pieces of data in the positive and negative directions, respectively, and Y * is calculated, and then ⁇ , Y * corresponding to each point are arranged in the following form:
  • Y is a matrix of (6000 ⁇ 16)
  • T is a column vector of (6000 ⁇ 1).
  • the identified model parameters are applied to formula (2), and can be added to the current loop with a feedforward method after appropriate improvement.
  • the sixth joint as an example to introduce the improvement in detail.
  • the noise in the signal is filtered by a first-order filter with a cut-off frequency of 10 Hz.
  • Second, because of the Discontinuity Replace here The unit is radians per second and K is 500.
  • a square wave with a frequency of 20 Hz and a frequency of twice the identified friction force when the sixth joint is stationary is superimposed on the six joint current loop, and its amplitude varies with The speed of the sixth joint increases and it decays exponentially.
  • the final compensation effect is shown in Figure 4.
  • the sixth joint stays still for the first five seconds and the square wave can be clearly seen.
  • the sixth joint is dragged by the hand for the next five seconds With reciprocating motion, it can be seen that the square wave decays to almost zero, while Coulomb friction compensation dominates.
  • the drag track of the sixth joint recorded by the data recording module is recorded at an isochronous interval, and the track can be easily scaled in time, so that when the teaching path is reproduced, it can be different. Speed execution.
  • the drag teaching system and method provided by this application can enable users to easily lift the robot and complete the traction teaching without multidimensional force sensors, and the system is simple, low cost, flexible teaching, high teaching efficiency, and various types. Robot teaching with complex motion trajectories opens up new ways.

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Automation & Control Theory (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Numerical Control (AREA)

Abstract

一种拖动示教系统和方法，其中，拖动示教系统包含：模型辨识模块，建立机器人的静力学模型，并辨识出模型参数，其中，静力学模型包含重力学模型和库仑摩擦力模型；前馈补偿模块，根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环；数据记录模块，记录机器人各关节的位置信息，用于机器人复现示教的动作。该系统和方法可以使用户很轻松地推起机器人，完成牵引示教。

Description

拖动示教系统和方法
相关申请的交叉引用
本申请要求于2018年07月03日提交中国专利局的申请号为201810711257.6、名称为“拖动示教系统和方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请涉及工业机器人控制技术领域，具体涉及一种拖动示教系统和方法。
背景技术
拖动示教又称直接示教或者手动示教，是人机协作的主要方式之一，即人直接通过手动拖动的方式完成对机器人的示教编程工作。传统的示教方式主要依赖于示教器，而这样的示教方式具有工作效率较低，过程繁琐不直观，对操作人员知识水平要求高的特点。采用拖动示教的方式比较直观，且对现场操作人员的要求大大降低。
发明内容
本申请的目的包括例如提供一种拖动示教系统和方法，可以使用户很轻松地推起机器人，完成牵引示教。
本申请通过实施例实现了一种拖动示教系统，其特点是，适用于机器人，该拖动示教系统包含：
模型辨识模块，建立机器人的静力学模型，并辨识出模型参数，其中，静力学模型包含重力学模型和库仑摩擦力模型；
前馈补偿模块，根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环；
数据记录模块，记录机器人各关节的位置信息，用于机器人复现示教的动作。
可选地，在本申请实施例中，所述机器人的静力学模型表示为：
Figure PCTCN2019094431-appb-000001
式(1)中i表示第i个连杆，z 0为常向量[0 0 1]T，m j为第j个连杆的质量，p i-1,j为在第i-1个连杆坐标系下由该坐标系原点指向第j个连杆坐标系原点的向量，R j i-1为第j个连杆坐标系到第i-1个连杆坐标系的旋转矩阵，r j为第j个连杆坐标系下的连杆质心坐标，g 为世界坐标系下的重力加速度向量，f i为该连杆近端关节的库仑摩擦力，sgn(·)为取符号运算符，
Figure PCTCN2019094431-appb-000002
为第i关节速度，n为机器人关节数；
令τ＝[τ 1 ... τ i ... τ n] T，
Figure PCTCN2019094431-appb-000003
其中，
Figure PCTCN2019094431-appb-000004
g为加速度常数，π f＝[f 1 ... f i ... f n] T，则式(1)可表述为；
τ＝Y·π   (2)
式中，Y＝[Y g Y f]，即回归矩阵，
Figure PCTCN2019094431-appb-000005
Figure PCTCN2019094431-appb-000006
式中，S(·)为叉积算子，Y g为(n×4n)的矩阵，Y f为(n×n)的对角矩阵，z g为指向和g相同的单位向量；
依据式(2)并应用最小二乘法辨识出机器人的静力学模型，即：
π *＝(Y T.Y) -1.Y T.T   (3)
式中，
Figure PCTCN2019094431-appb-000007
π *＝(Y T·Y) -1·Y T·T。
可选地，在本申请实施例中，所述机器人各关节的位置信息包含：
机器人关键点的位置或拖动示教时的拖动轨迹。
可选地，在本申请实施例中，将机器人各关节反馈速度经过一预设截至频率的滤波器滤波，以降低速度信号中的噪声信号；在此基础上叠加一定阈值一定频率的方波信号用以克服拖动示教功能起始时的静摩擦力，阈值的设置和静摩擦力的大小有关，频率的设置与启动效果有关。在机器人运动起来后，该方波信号迅速衰减至零以提升拖动示教的舒适性。
可选地，在本申请实施例中，按照公式τ＝Y *gπ *将一个完整周期的实验数据带入Y *中，算出一组由所述静力学模型预测的转矩值，并将所述转矩值与记录的电流指令做比较，以验证辨识的静力学模型参数正确与否。
本申请实施例还公开了一种拖动示教方法，其特点是，包含以下步骤：
S1、建立机器人的静力学模型，并辨识出模型参数，其中，静力学模型包含重力学模型和库仑摩擦力模型；
S2、根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环；
S3、记录机器人各关节的位置信息，用于机器人复现示教的动作。
可选地，在本申请实施例中，所述机器人的静力学模型表示为：
Figure PCTCN2019094431-appb-000008
式(1)中i表示第i个连杆，z 0为常向量[0 0 1]T，m j为第j个连杆的质量，p i-1,j为在第i-1个连杆坐标系下由该坐标系原点指向第j个连杆坐标系原点的向量，R j i-1为第j个连杆坐标系到第i-1个连杆坐标系的旋转矩阵，r j为第j个连杆坐标系下的连杆质心坐标，g为世界坐标系下的重力加速度向量，f i为该连杆近端关节的库仑摩擦力，sgn(·)为取符号运算符，
Figure PCTCN2019094431-appb-000009
为第i关节速度，n为机器人关节数；
令τ＝[τ 1 ... τ i ... τ n] T，
Figure PCTCN2019094431-appb-000010
其中，
Figure PCTCN2019094431-appb-000011
g为加速度常数，π f＝[f 1 ... f i ... f n] T，则式(1)可表述为；
τ＝Y·π   (2)
式中，Y＝[Y g Y f]，即回归矩阵，
Figure PCTCN2019094431-appb-000012
Figure PCTCN2019094431-appb-000013
式中，S(·)为叉积算子，Y g为(n×4n)的矩阵，Y f为(n×n)的对角矩阵，z g为指向和g相同的单位向量；
依据式(2)并应用最小二乘法辨识出机器人的静力学模型，即：
π *＝(Y T.Y) -1.Y T.T   (3)
式中，
Figure PCTCN2019094431-appb-000014
π *＝(Y T·Y) -1·Y T·T。
可选地，在本申请实施例中，所述机器人各关节的位置信息包含：
机器人关键点的位置或拖动示教时的拖动轨迹。
可选地，在本申请实施例中，将机器人各关节反馈速度经过一预设截至频率的滤波器滤波，以降低速度信号中的噪声信号；在此基础上叠加一定阈值一定频率的方波信号用以克服拖动示教功能起始时的静摩擦力，阈值的设置和静摩擦力的大小有关，频率的设置与启动效果有关。在机器人运动起来后，该方波信号迅速衰减至零以提升拖动示教的舒适性。
可选地，在本申请实施例中，按照公式τ＝Y *gπ *将一个完整周期的实验数据带入Y *中，算出一组由所述静力学模型预测的转矩值，并将所述转矩值与记录的电流指令做比较，以验证辨识的静力学模型参数正确与否。
根据本申请的一种拖动示教系统和方法与现有技术相比具有以下优点：
本申请无需多维力传感器，系统简洁、成本低、示教灵活，示教效率高，为各类运动轨迹复杂的机器人示教开辟了新途径。
附图说明
图1为根据本申请的一种拖动示教系统的整体结构框图；
图2为根据本申请的一种拖动示教方法的流程图；
图3为模型辨识模块的辨识效果验证图；
图4为前馈补偿模块的第六关节效果图；
图5为记录的拖动示教过程中的第六关节轨迹图。
具体实施方式
体现本申请特征与优点的实施例将在后段的说明中详细叙述。应理解的是本申请能够在不同的示例上具有各种的变化，其皆不脱离本申请的范围，且其中的说明及图示在本质上当作说明之用，而非用以限制本申请。
本申请实施例公开了一种拖动示教系统，适用于机器人，如图1所示，该拖动示教系统包含：模型辨识模块，建立机器人的静力学模型，并辨识出模型参数，其中，静力学模型包含重力学模型和库仑摩擦力模型；前馈补偿模块，根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环；数据记录模块，记录机器人各关节的位置信息，用于机器人复现示教的动作。
在本申请实施例中，作为一种实施方式，所述机器人的静力学模型表示为：
Figure PCTCN2019094431-appb-000015
式(1)中i表示第i个连杆，z 0为常向量[0 0 1]T，m j为第j个连杆的质量，p i-1,j为在第i-1个连杆坐标系下由该坐标系原点指向第j个连杆坐标系原点的向量，R j i-1为第j个连杆坐标系到第i-1个连杆坐标系的旋转矩阵，r j为第j个连杆坐标系下的连杆质心坐标，g 为世界坐标系下的重力加速度向量，f i为该连杆近端关节的库仑摩擦力，
Figure PCTCN2019094431-appb-000016
为取符号运算符，
Figure PCTCN2019094431-appb-000017
为第i关节速度，n为机器人关节数；
令τ＝[τ 1 ... τ i ... τ n] T，
Figure PCTCN2019094431-appb-000018
其中，
Figure PCTCN2019094431-appb-000019
g为加速度常数，π f＝[f 1 ... f i ... f n] T，则式(1)可表述为；
τ＝Y·π   (2)
式中，Y＝[Y g Y f]，即回归矩阵，
Figure PCTCN2019094431-appb-000020
Figure PCTCN2019094431-appb-000021
式中，S(·)为叉积算子，Y g为(n×4n)的矩阵，Y f为(n×n)的对角矩阵，z g为指向和g相同的单位向量；
依据式(2)并应用最小二乘法辨识出机器人的静力学模型，即：
π *＝(Y T.Y) -1.Y T.T   (3)
式中，
Figure PCTCN2019094431-appb-000022
π *＝(Y T·Y) -1·Y T·T。
在本申请实施例中，作为一种实施方式，所述机器人各关节的位置信息包含：机器人关键点的位置或拖动示教时的拖动轨迹。
结合上述的拖动示教系统，本申请还公开了一种应用于上述拖动示教系统的拖动示教方法，如图2所示，包含以下步骤：
S1、建立机器人的静力学模型，并辨识出模型参数，其中，静力学模型包含重力学模型和库仑摩擦力模型。
S2、根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环。
具体地，将机器人各关节反馈速度经过一预设截至频率的滤波器滤波，以降低速度信号中的噪声信号；
在此基础上叠加一定阈值一定频率的方波信号用以克服拖动示教功能起始时的静摩擦力，阈值的设置和静摩擦力的大小有关，频率的设置与启动效果有关。在机器人运动起来后，该方波信号迅速衰减至零以提升拖动示教的舒适性。
在本申请实施例中，作为一种具体示例，辨识出机器人的模型参数，这里以型号为A-05-2的富士康机器人为例，其DH参数参见表1。
表1 该串联旋转关节机器人DH参数表
Figure PCTCN2019094431-appb-000023
按照公式(2)，可以算出该机器人的回归矩阵Y(6×30)，按照去除Y中线性相关列向量的规则，可以得出Y中第1、2、3、4、7、8、10、12、14、16、18、20、23、24列可以去除，从而得到Y *(6×16)。
在本申请实施例中，用dSPACE的MicroLabBox控制该机器人；在实验过程中，让机器人每个关节跟踪一个周期为400s的正弦信号，其幅值从第一轴到第六轴依次为π、0.4π、0.3π、π、π、π；同时每个关节的反馈位置和电流/转矩指令被记录下来并转换到连杆侧。在本实施例中，分别从正负向两段数据中随机抽取500个数据点，分别计算Y *，继而将各点对应的τ，Y *按以下形式排列：
Figure PCTCN2019094431-appb-000024
式中Y为(6000×16)的矩阵，T为(6000×1)的列向量。
最后按照公式(3)计算出静力学模型参数π *(见表2)，其中前10个模型参数为重力参数，后6个模型参数为摩擦力参数；为验证辨识的静力学模型参数正确与否，按照公式τ＝Y *gπ *将一个完整周期的实验数据带入Y *中，算出一组由静力学模型预测的转矩值，并将其与记录的电流指令(连杆侧)做比较，结果如图3所示，预测指令和实验数据一致性很好，说明辨识的模型参数是正确的。
表2 辨识的静力学模型参数值
Figure PCTCN2019094431-appb-000025
Figure PCTCN2019094431-appb-000026
在这基础上，将辨识的模型参数应用到公式(2)中，经适当改进就可以用前馈的方式加入电流环中，这里以第六关节为例具体介绍改进之处，首先为去除速度信号中的噪声，用截至频率为10Hz的一阶滤波器对其滤波；其次，由于公式(2)中的
Figure PCTCN2019094431-appb-000027
具有不连续性，用连续函数
Figure PCTCN2019094431-appb-000028
替换，这里
Figure PCTCN2019094431-appb-000029
的单位为弧度每秒，K取500；最后，在六关节电流环中叠加一个频率为20Hz幅值在第六关节静止时为辨识出的摩擦力大小两倍的方波，并且其幅值随第六关节速度增大而成指数形式衰减，最后的补偿效果如图4所示，前五秒第六关节保持静止，可以明显看到方波，后五秒第六关节在手的拖动下往复运动，可以看到方波几乎衰减到零，而库伦摩擦补偿占据主导地位。
S3、记录机器人各关节的位置信息，用于机器人复现示教的动作。
具体地，如图5所示，为数据记录模块记录的第六关节的拖动轨迹，由于等时间隔记录，该轨迹可以很方便对时间进行缩放，从而在复现示教路径时能够以不同速度执行。
尽管本申请的内容已经通过上述优选实施例作了详细介绍，但应当认识到上述的描述不应被认为是对本申请的限制。在本领域技术人员阅读了上述内容后，对于本申请的多种修改和替代都将是显而易见的。因此，本申请的保护范围应由所附的权利要求来限定。
工业实用性
本申请提供的拖动示教系统和方法可以使用户很轻松地推起机器人，完成牵引示教，无需多维力传感器，且系统简洁、成本低、示教灵活，示教效率高，为各类运动轨迹复杂的机器人示教开辟了新途径。

Claims (10)

  1. 一种拖动示教系统，其特征在于，适用于机器人，该拖动示教系统包含：
    模型辨识模块，建立机器人的静力学模型，并辨识出模型参数，其中，所述静力学模型包含重力学模型和库仑摩擦力模型；
    前馈补偿模块，根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环；
    数据记录模块，记录机器人各关节的位置信息，用于机器人复现示教的动作。
  2. 如权利要求1所述的拖动示教系统，其特征在于，所述机器人的静力学模型表示为：
    Figure PCTCN2019094431-appb-100001
    式(1)中i表示第i个连杆，z 0为常向量[0 0 1]T，m j为第j个连杆的质量，p i-1,j为在第i-1个连杆坐标系下由该坐标系原点指向第j个连杆坐标系原点的向量，R j i-1为第j个连杆坐标系到第i-1个连杆坐标系的旋转矩阵，r j为第j个连杆坐标系下的连杆质心坐标，g为世界坐标系下的重力加速度向量，f i为该连杆近端关节的库仑摩擦力，sgn(·)为取符号运算符，
    Figure PCTCN2019094431-appb-100002
    为第i关节速度，n为机器人关节数；
    令τ＝[τ 1 … τ i … τ n] T,
    Figure PCTCN2019094431-appb-100003
    其中，
    Figure PCTCN2019094431-appb-100004
    g为加速度常数，π f＝[f 1 … f i … f n] T，则式(1)可表述为；
    τ＝Y·π  (2)
    式中，Y＝[Y g Y f]，即回归矩阵，
    Figure PCTCN2019094431-appb-100005
    Figure PCTCN2019094431-appb-100006
    式中，S(·)为叉积算子，Y g为(n×4n)的矩阵，Y f为(n×n)的对角矩阵，z g为指向和g相同的单位向量；
    依据式(2)并应用最小二乘法辨识出所述机器人的静力学模型，即：
    Figure PCTCN2019094431-appb-100007
    式中，
    Figure PCTCN2019094431-appb-100008
    π *＝(Y T·Y) -1·Y T·T。
  3. 如权利要求1或2所述的拖动示教系统，其特征在于，所述机器人各关节的位置信息包含：
    机器人关键点的位置或拖动示教时的拖动轨迹。
  4. 如权利要求1-3中任一项所述的拖动示教系统，其特征在于，将机器人各关节反馈速度经过一预设截至频率的滤波器滤波，以降低速度信号中的噪声信号；在此基础上叠加一定阈值一定频率的方波信号用以克服拖动示教功能起始时的静摩擦力，所述阈值的设置和所述静摩擦力的大小有关，所述频率的设置与启动效果有关；在所述机器人运动起来后，所述方波信号迅速衰减至零。
  5. 如权利要求2-4中任一项所述的拖动示教系统，其特征在于，按照公式τ＝Y *gπ *将一个完整周期的实验数据带入Y *中，算出一组由所述静力学模型预测的转矩值，并将所述转矩值与记录的电流指令做比较，以验证辨识的静力学模型参数正确与否。
  6. 一种拖动示教方法，其特征在于，包含以下步骤：
    S1、建立机器人的静力学模型，并辨识出模型参数，其中，静力学模型包含重力学模型和库仑摩擦力模型；
    S2、根据辨识出的模型参数，以前馈的方式传送给机器人各关节电机的电流环；
    S3、记录机器人各关节的位置信息，用于机器人复现示教的动作。
  7. 如权利要求6所述的拖动示教方法，其特征在于，所述机器人的静力学模型表示为：
    Figure PCTCN2019094431-appb-100009
    式(1)中i表示第i个连杆，z 0为常向量[0 0 1]T，m j为第j个连杆的质量，p i-1,j为在第i-1个连杆坐标系下由该坐标系原点指向第j个连杆坐标系原点的向量，R j i-1为第j个连杆坐标系到第i-1个连杆坐标系的旋转矩阵，r j为第j个连杆坐标系下的连杆质心坐标，g为世界坐标系下的重力加速度向量，f i为该连杆近端关节的库仑摩擦力，sgn(·)为取符号运算符，
    Figure PCTCN2019094431-appb-100010
    为第i关节速度，n为机器人关节数；
    令τ＝[τ 1 … τ i … τ n] T,
    Figure PCTCN2019094431-appb-100011
    其中，
    Figure PCTCN2019094431-appb-100012
    g为加速度常数，π f＝[f 1 … f i … f n] T，则式(1)可表述为；
    τ＝Y·π  (2)
    式中，Y＝[Y g Y f]，即回归矩阵，
    Figure PCTCN2019094431-appb-100013
    Figure PCTCN2019094431-appb-100014
    式中，S(·)为叉积算子，Y g为(n×4n)的矩阵，Y f为(n×n)的对角矩阵，z g为指向和g相同的单位向量；
    依据式(2)并应用最小二乘法辨识出所述机器人的静力学模型，即：
    π *＝(Y T·Y) -1·Y T·T  (3)
    式中，
    Figure PCTCN2019094431-appb-100015
    π *＝(Y T·Y) -1·Y T·T。
  8. 如权利要求6或7所述的拖动示教方法，其特征在于，所述机器人各关节的位置信息包含：
    机器人关键点的位置或拖动示教时的拖动轨迹。
  9. 如权利要求6-8中任一项所述的拖动示教系统，其特征在于，将机器人各关节反馈速度经过一预设截至频率的滤波器滤波，以降低速度信号中的噪声信号；在此基础上叠加一定阈值一定频率的方波信号用以克服拖动示教功能起始时的静摩擦力，所述阈值的设置和所述静摩擦力的大小有关，所述频率的设置与启动效果有关；在所述机器人运动起来后，所述方波信号迅速衰减至零。
  10. 如权利要求7-9中任一项所述的拖动示教系统，其特征在于，按照公式τ＝Y *gπ *将一个完整周期的实验数据带入Y *中，算出一组由所述静力学模型预测的转矩值，并将所述转矩值与记录的电流指令做比较，以验证辨识的静力学模型参数正确与否。
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CN108839023B (zh) 2021-12-07
EP3819089A1 (en) 2021-05-12

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