CN110666794A - Tail end load force compensation method for dragging of multi-degree-of-freedom cooperative robot - Google Patents

Tail end load force compensation method for dragging of multi-degree-of-freedom cooperative robot Download PDF

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CN110666794A
CN110666794A CN201910913566.6A CN201910913566A CN110666794A CN 110666794 A CN110666794 A CN 110666794A CN 201910913566 A CN201910913566 A CN 201910913566A CN 110666794 A CN110666794 A CN 110666794A
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coordinate system
robot
moment
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CN110666794B (en
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肖聚亮
曾帆
王铭礼
王云鹏
赵炜
匡加伦
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Tianjin University
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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—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses

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Abstract

The invention discloses a method for compensating tail end load force dragged by a multi-degree-of-freedom cooperative robot, which comprises the following steps: (1) establishing a mathematical model of the stress and the moment of a flange at the tail end of the robot; (2) establishing a joint coordinate system, a base coordinate system and a terminal flange coordinate system of the robot and calculating a conversion matrix for conversion among the joint coordinate system, the base coordinate system and the terminal flange coordinate system; (3) measuring a centroid parameter of the load; (4) establishing a new coordinate system and calculating static force and static moment generated by the tool load at the origin of the new coordinate system; (5) calculating the power and the moment of power generated by the tool load at the origin of the new coordinate system; (6) calculating a Jacobian matrix of the robot terminal coordinate system relative to the base coordinate system; (7) the forces and moments caused by the tool load are compensated to each joint of the robot. The loaded robot is more portable to drag by compensating the force and moment generated by the load, and the method does not need to add an additional force or moment sensor.

Description

Tail end load force compensation method for dragging of multi-degree-of-freedom cooperative robot
Technical Field
The invention relates to a collaborative robot, in particular to a collaborative robot dragging teaching method with a tool and a load.
Background
With the application of industrial robots in the fields of grinding, polishing, spraying, gluing, welding and the like, the robot cooperation control technology develops towards the directions of flexibility, smoothness, safety and high efficiency. In order to realize the man-machine co-fusion cooperative work, new requirements are provided for the robot teaching technology. Compared with the traditional teaching technology of a demonstrator, the direct-dragging teaching technology has the advantages of flexibility, flexibility and the like, and has low requirements on an operator, so that the direct-dragging teaching technology becomes a key direction for teaching technology development. The current guiding teaching is mainly three, firstly, the guiding teaching based on the installation of a multi-dimensional force/torque sensor at the tail end of a robot is higher in cost, and only the tail end of the robot can be dragged; secondly, the joint can be dragged based on the guide teaching of a joint sensor (a torque sensor or a double encoder), but the joint sensor has a complex structure and high cost; and thirdly, the sensorless guide teaching based on the joint moment compensation zero force control has the lowest cost, and the mode can be dragged by points and tracks, has strong adaptability and can be applied to various occasions.
The dragging teaching function is already the standard matching of the cooperative robot, however, most of the cooperative robots in the market are harder to drag and only point position dragging can be realized. Although direct dragging teaching can be realized by dynamic torque compensation aiming at a cooperative robot without an external torque sensor, the zero-force control effect is poor due to incompleteness and inaccuracy of a dynamic model, the dragging flexibility is influenced, point-to-point dragging can be realized only, and track dragging is difficult to realize. Therefore, it is necessary to research a robot zero-force control technology based on accurate dynamic model identification and without external torque sensing, so as to improve the flexibility and flexibility of the direct dragging teaching of the cooperative robot. In order to ensure that the joint output torque of the robot can still balance the weight of the robot body, the tool and the load after the tool is mounted on the end of the robot and the tool grips the load, a force compensation method is needed to balance the forces/torques generated by the tool and the load.
After the tool load is mounted at the end of the cooperative robot, to estimate the external force, the weight and center of mass of the load need to be known to calculate the gravitational and gravitational moments generated by the load in different poses. However, both gravity and gravity moments are static forces and moments. In order to obtain a better dragging effect, it is necessary to take into account the power generated by the load of the implement.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a tail end load force compensation method dragged by a multi-degree-of-freedom cooperative robot.
The technical scheme of the invention is as follows:
a method of robot end-of-tool load force/torque compensation comprising the steps of:
step S1, establishing a mathematical model of the stress and the moment of the robot end flange, wherein the model is as follows:
Figure BDA0002215410840000021
in the formula, FendAnd TendExternal forces to which the robot end flange is subjected, including static forces F generated by tool loadssAnd static moment TsPower FdSum moment of force Td；
Step S2, the n-freedom degree robot is equivalent to an n-freedom degree rigid connecting rod, and a base coordinate system { o ] of the robot is established0-x0y0z0Robot end flange coordinate system { o }end-xendyendzendCalculating a robot end flange coordinate system { o }end-xendyendzendTo the base coordinate system of the robot { o }0-x0y0z0The conversion matrix of0Tend；
Step S3, creating a new coordinate systeme′o-e′xe′ye′z, then calculating a base coordinate system of the robot { o }0-x0y0z0To a new coordinate systeme′o-e′xe′ye′z } transformation matrixe′T0(ii) a The direction of the new coordinate system is consistent with that of the base coordinate system, and the origin of the new coordinate system is superposed with that of the flange coordinate system at the tail end of the robot;
the conversion matrixe′T0The calculation method of (2) is as follows:
Figure BDA0002215410840000031
wherein, Px、PyAnd PzThe position coordinates of the robot end flange coordinate system obtained by positive kinematics calculation in a base coordinate system;
step S4, measuring the coordinates of the center of mass of the tool load mounted on the robot end flange in the robot end flange coordinate system, noted asendP(xend,yend,zend) Then the centroid of the tool load is located at the new coordinate systeme′o-e′xe′ye′z } coordinates ine′P(e′x,e′y,e′z) is:
step S5, calculating tool load as a last page of new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the origin of the static and static moments:
Figure BDA0002215410840000033
wherein the content of the first and second substances,e′Fscontaining a tool load in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the static force generated by the origin of z-,e′Tscontaining a tool load in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the origin of the moment;
Figure BDA0002215410840000041
opening for gravitational acceleration in new coordinate systeme′o-e′xe′ye′z } components in the directions of three coordinate axes;
step S6, the tool load being held in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } origin of the powere′FdMoment of sume′Td：
Figure BDA0002215410840000042
Wherein the content of the first and second substances,e′Fdcontaining a tool load in a new coordinate systeme′o-e′xe′ye′z } of the kinetic energy in the kinetic energy,e′Tdcontaining a tool load in a new coordinate systeme′o-e′xe′ye′Moment of kinetic force in z, mtoolIs the mass of the load, sendFor loads of a first mass moment relative to the coordinate system of the end flange, IendIs the inertia of the load relative to the terminal coordinate system;
Figure BDA0002215410840000043
and ωe′Respectively the tool load in a new coordinate systeme′o-e′xe′ye′z } and angular velocity,containing a tool load in a new coordinate systeme′o-e′xe′ye′z } linear acceleration;
step S7, substituting the static and static moments obtained in step S5 and the dynamic and dynamic moments obtained in step S6 into the formula of step S1 to obtain a final image in the new coordinate systeme′o-e′xe′ye′z tool load couple new coordinate systeme′o-e′xe′ye′z } the origin of the force and moment, the formula is as follows:
Figure BDA0002215410840000045
step S8, solving a Jacobian matrix of the robot terminal coordinate system relative to the base coordinate system;
step S9, compensating the force and moment caused by the tool load to each joint of the robot, and obtaining the compensation moment of each joint of the robot as follows:
Figure BDA0002215410840000046
and n is the degree of freedom of the robot.
The invention has the advantages that: the loaded dragging of the cooperative robot is more portable by adopting the method, and the cooperative robot with the load can still keep balance in a moment mode when no external force is applied. The operator drags the cooperative robot with the load more conveniently, and the portability of the quick and slow dragging is greatly improved compared with unpowered compensation. The method is suitable for the multi-degree-of-freedom robot, additional force/torque sensors are not required to be added, and the method is not limited by the installation mode of the robot.
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FIG. 1 is a schematic diagram of the transformation relationship of coordinate systems of an n-DOF robot;
FIG. 2 is a schematic illustration of static/static moment generated by tool loading at a robot end flange;
fig. 3 is a flowchart of compensating for the end load force dragged by the n-degree-of-freedom cooperative robot.
Detailed Description
In the following, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method for compensating load force/moment of a robot tail end tool, which comprises the following steps:
step S1, corresponding to the flowchart of fig. 3, a mathematical model of the robot end flange stress and moment is established, which model is as follows:
Figure BDA0002215410840000051
in the formula, FendAnd TendExternal forces to which the robot end flange is subjected, including static forces F generated by tool loadssAnd static moment TsPower FdSum moment of force Td。
Step S2, as shown in FIG. 1, the n-degree-of-freedom robot is equivalent to an n-degree-of-freedom rigid connecting rod, and a base coordinate system { o ] of the robot is established0-x0y0z0Robot end flange coordinate system { o }end-xendyendzendCalculating a robot end flange coordinate system { o }end-xendyendzendTo the base coordinate system of the robot { o }0-x0y0z0The conversion matrix of0Tend。
The conversion matrix0TendThe calculation method of (2) is as follows:
0Tend＝0T1 1T2…i-1Ti…n-2Tn-1 n-1Tend
i-1Tifor universal change between two equivalent connecting rodsMatrix (see Song Pengyu, a non-orthogonal 6-degree-of-freedom collaborative robot kinematics and dynamics analysis [ D ]]Tianjin university, 2017.), and n is the degree of freedom of the robot.
The establishment of the base coordinate system and the end flange coordinate system in the step can be established according to the requirements of users, and although the coordinate systems established by different users may be different and the transformation matrix is also different, the effect of final end load force compensation is not influenced.
Step S3, as shown in FIG. 1, establishing a new coordinate systeme′o-e′xe′ye′z, then calculating a base coordinate system of the robot { o }0-x0y0z0To a new coordinate systeme′o-e′xe′ye′z } transformation matrixe′T0(ii) a The direction of the new coordinate system is consistent with that of the base coordinate system, and the origin of the new coordinate system is superposed with that of the flange coordinate system at the tail end of the robot.
The conversion matrixe′T0The calculation method of (2) is as follows:
Figure BDA0002215410840000061
wherein, Px、PyAnd PzIs the position coordinate of the robot end flange coordinate system in the base coordinate system obtained by positive kinematic calculation.
Step S4, measuring (by using the existing measuring method, such as the hanging method) the coordinates of the center of mass of the tool load installed on the end flange of the robot in the robot end flange coordinate system, and recording the coordinates as the center of massendP(xend,yend,zend) Then the centroid of the tool load is located at the new coordinate systeme′o-e′xe′ye′z } coordinates ine′P(e′x,e′y,e′z) is:
Figure BDA0002215410840000071
step S5, as shown in FIG. 2, calculating tool loade′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the origin of the static and static moments:
Figure BDA0002215410840000072
wherein the content of the first and second substances,e′Fscontaining a tool load in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the static force generated by the origin of z-,e′Tscontaining a tool load in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the origin of the moment.
Figure BDA0002215410840000073
Opening for gravitational acceleration in new coordinate systeme′o-e′xe′ye′z, the component in the direction of three coordinate axes, and the item is related to the installation mode of the robot.
Step S6, corresponding to the flowchart in fig. 3, the tool load being held at the new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } origin of the powere′FdMoment of sume′Td：
Figure BDA0002215410840000074
Wherein the content of the first and second substances,e′Fdcontaining a tool load in a new coordinate systeme′o-e′xe′ye′z } of the kinetic energy in the kinetic energy,e′Tdcontaining a tool load in a new coordinate systeme′o-e′xe′ye′Moment of kinetic force in z, mtoolIs the mass of the load, sendFor loads of a first mass moment relative to the coordinate system of the end flange, IendIs the inertia of the load relative to the terminal coordinate system;
Figure BDA0002215410840000081
and ωe′Respectively the tool load in a new coordinate systeme′o-e′xe′ye′z } and angular velocity,
Figure BDA0002215410840000082
containing a tool load in a new coordinate systeme′o-e′xe′ye′z } linear acceleration;
Figure BDA0002215410840000083
the method can be obtained through calculation of a Jacobian matrix or direct measurement; sendAnd IendThe method is obtained by identifying the parameters of the robot, and the specific calculation method comprises the following steps: zhang Qiong, cooperative robot moment compensation and detection control research based on parameter identification [ D]Tianjin university, 2019; omegae′、
Figure BDA0002215410840000084
And
Figure BDA0002215410840000085
can be obtained by reading the parameters of a driver connected with a robot joint motor and calculating a Jacobian matrix of the robot.
Step S7, substituting the static and static moments obtained in step S5 and the dynamic and dynamic moments obtained in step S6 into the formula of step S1 to obtain a final image in the new coordinate systeme′o-e′xe′ye′z tool load couple new coordinate systeme′o-e′xe′ye′z } the origin of the force and moment, the formula is as follows:
step S8, solving a Jacobian matrix of the robot terminal coordinate system relative to the base coordinate system, which comprises the following steps: corresponding to flow chart 3, the Jacobian matrix J (q) relates joint velocities to Cartesian velocities of the end flanges, with JT(q) the joint moment can be associated with the Cartesian force and moment of the end flange, and the Jacobian matrix of the robot end coordinate system relative to the base coordinate system is provided (the specific calculation method is shown in Van Kajie, modularization six-freedom-degree mechanical arm kinematics and track planning research [ D ]]University of Anhui Engineers, 2018.):
Figure BDA0002215410840000087
wherein Z isiIs a unit vector of a Z axis in an i-th joint coordinate system (a joint coordinate system established according to a DH method),iPn 0is based on the position of the origin of the coordinate system of the end flange relative to the coordinate system of the joint { i } in the base coordinate system { o }0-x0y0z0Denotes in (b) }.
And n is the degree of freedom of the robot.
Step S9, corresponding to the flowchart of fig. 3, compensates the force and moment caused by the tool load to each joint of the robot, and obtains the compensation moment of each joint of the robot as:
and n is the degree of freedom of the robot.
The method for compensating the tail end load force dragged by the multi-degree-of-freedom cooperative robot, provided by the embodiment of the invention, has the following characteristics:
1. the method is suitable for various robots and is not limited to the degree of freedom of the robots and the structures of the robots.
2. No additional sensors need to be added.
3. The mounting manner of the robot is various.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention. The scope of the invention is defined by the appended claims and their full range of equivalents.

Claims (1)

1. A method of robot end-of-tool load force/torque compensation comprising the steps of:
step S1, establishing a mathematical model of the stress and the moment of the robot end flange, wherein the model is as follows:
Figure FDA0002215410830000011
in the formula, FendAnd TendExternal forces to which the robot end flange is subjected, including static forces F generated by tool loadssAnd static moment TsPower FdSum moment of force Td；
Step S2, the n-freedom degree robot is equivalent to an n-freedom degree rigid connecting rod, and a base coordinate system { o ] of the robot is established0-x0y0z0Robot end flange coordinate system { o }end-xendyendzendCalculating a robot end flange coordinate system { o }end-xendyendzendTo the base coordinate system of the robot { o }0-x0y0z0The conversion matrix of0Tend；
Step S3, creating a new coordinate systeme′o-e′xe′ye′z, then calculating a base coordinate system of the robot { o }0-x0y0z0To a new coordinate systeme′o-e′xe′ye′z } transformation matrixe′T0(ii) a Said new coordinate systemThe direction of the new coordinate system is consistent with the direction of the base coordinate system, and the origin of the new coordinate system is superposed with the origin of the flange coordinate system at the tail end of the robot;
the conversion matrixe′T0The calculation method of (2) is as follows:
Figure FDA0002215410830000012
wherein, Px、PyAnd PzThe position coordinates of the robot end flange coordinate system obtained by positive kinematics calculation in a base coordinate system;
step S4, measuring the coordinates of the center of mass of the tool load mounted on the robot end flange in the robot end flange coordinate system, noted asendP(xend,yend,zend) Then the centroid of the tool load is located at the new coordinate systeme′o-e′xe′ye′z } coordinates ine′P(e′x,e′y,e′z) is:
Figure FDA0002215410830000021
step S5, calculating tool load as a last page of new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the origin of the static and static moments:
wherein the content of the first and second substances,e′Fscontaining a tool load in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the static force generated by the origin of z-,e′Tscontaining a tool load in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } the origin of the moment;
Figure FDA0002215410830000023
opening for gravitational acceleration in new coordinate systeme′o-e′xe′ye′z } components in the directions of three coordinate axes;
step S6, the tool load being held in a new coordinate systeme′o-e′xe′ye′z middle to new coordinate systeme′o-e′xe′ye′z } origin of the powere′FdMoment of sume′Td：
Figure FDA0002215410830000024
Wherein the content of the first and second substances,e′Fdcontaining a tool load in a new coordinate systeme′o-e′xe′ye′z } of the kinetic energy in the kinetic energy,e′Tdcontaining a tool load in a new coordinate systeme′o-e′xe′ye′Moment of kinetic force in z, mtoolIs the mass of the load, sendFor loads of a first mass moment relative to the coordinate system of the end flange, IendIs the inertia of the load relative to the terminal coordinate system;
Figure FDA0002215410830000025
and ωe′Respectively the tool load in a new coordinate systeme′o-e′xe′ye′z } and angular velocity,
Figure FDA0002215410830000026
containing a tool load in a new coordinate systeme′o-e′xe′ye′z } linear acceleration;
step S7, the static force and static moment obtained in step S5 and the dynamic force and dynamic moment obtained in step S6Substituting into the formula of step S1 to obtain a final image in the new coordinate systeme′o-e′xe′ye′z tool load couple new coordinate systeme′o-e′xe′ye′z } the origin of the force and moment, the formula is as follows:
Figure FDA0002215410830000031
step S8, solving a Jacobian matrix of the robot terminal coordinate system relative to the base coordinate system;
step S9, compensating the force and moment caused by the tool load to each joint of the robot, and obtaining the compensation moment of each joint of the robot as follows:
Figure FDA0002215410830000032
and n is the degree of freedom of the robot.
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CN113664813A (en) * 2021-08-25 2021-11-19 深圳市优必选科技股份有限公司 Method and device for controlling double-arm robot, double-arm robot and readable storage medium
CN113664813B (en) * 2021-08-25 2022-07-29 深圳市优必选科技股份有限公司 Method and device for controlling double-arm robot, double-arm robot and readable storage medium
CN113829350A (en) * 2021-10-12 2021-12-24 北京卫星环境工程研究所 Method for compensating inertial force of spacecraft assembling robot
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