CN112276942B - Consistency compensation method for robot arm - Google Patents

Consistency compensation method for robot arm Download PDF

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CN112276942B
CN112276942B CN202011061256.5A CN202011061256A CN112276942B CN 112276942 B CN112276942 B CN 112276942B CN 202011061256 A CN202011061256 A CN 202011061256A CN 112276942 B CN112276942 B CN 112276942B
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CN112276942A (en
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谷菲
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Chengdu Kanop Robot Technology Co ltd
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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
    • 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
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis

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Abstract

The invention discloses a consistency compensation method for a robot mechanical arm, which is realized based on end detection equipment and position measurement equipment which are matched with each other, wherein the end detection equipment is arranged on the robot mechanical arm and comprises a calibration ball, the method comprises the steps of respectively measuring theoretical coordinate values and actual coordinate values of all sampling points, comparing a theoretical coordinate difference value with an actual coordinate difference value, and judging whether the difference value is within a tolerable range, thereby judging whether further consistency compensation can be carried out. The method of the invention can improve the consistency of the end program of the robot under the condition of not calibrating, so that the error is in a certain measurable range, and belongs to preparation work before automatic calibration of the robot.

Description

Consistency compensation method for robot arm
Technical Field
The invention relates to the technical field of robots, in particular to a consistency compensation method for a robot arm.
Background
The industrial robot has higher repeated positioning accuracy and is suitable for scenes with high requirements on repeatability, such as transportation, spot welding and the like, but for robot offline programming scenes such as curved surface laser cutting, curved surface polishing and the like, the robot is required to have higher repeated positioning accuracy and higher absolute position accuracy. The accuracy of the absolute position of the robot depends on motion parameters including the length of the connecting rod of the robot, zero position, reduction ratio and coupling ratio. Therefore, in order to make the robot have higher absolute position precision, the kinematic parameters are calibrated.
At present, most industrial robot production enterprises use outsourced laser trackers or pull rope code measuring instruments to calibrate industrial robots when leaving factories. The modified parameters are set into the control equipment after the data are acquired by programming and calculated mainly by manpower. This method is not ideal for mass production robots, especially in terms of efficiency and operational inefficiencies, where manual operations are present.
In order to achieve efficient factory calibration with a certain cost, some companies build automatic calibration tools, so that a certain limit error measurement relation can be formed between a robot and calibration equipment when the robot is installed at a fixed position, automatic calibration is completed, and parameters are automatically backed up in an industrial robot controller to achieve a reliable and efficient calibration result.
However, since industrial robots have never been calibrated before they are manufactured, the consistency between the machines is very low, for example, the end of a 1400mm arm may have an error of 48mm at maximum. Therefore, the robot which is just produced is directly calibrated automatically, and the situation that the error exceeds the measuring range, so that the robot crashes and damages the measuring device easily occurs.
Disclosure of Invention
The present invention is directed to overcome the above-mentioned shortcomings in the background art, and provides a consistency compensation method for a robot arm, which can improve the consistency of a terminal program of a robot without calibration, so that the error thereof is within a certain measurable range, and belongs to a preparation work before automatic calibration of the robot.
In order to achieve the technical effects, the invention adopts the following technical scheme:
the consistency compensation method for the robot mechanical arm is realized based on mutually matched terminal detection equipment and position measurement equipment, wherein the terminal detection equipment is arranged on the robot mechanical arm and comprises a calibration ball, and the robot is arranged in a robot coordinate system TrThe position measuring device includes a center detecting unit and a moving unit, the center detecting unit is mounted on the moving unit; the sphere center detection unit comprises four laser displacement sensors, and laser beams of the four laser displacement sensors intersect at the origin O of the coordinate system L of the detection unitL(ii) a The mobile unit comprises a three-axis sliding table, and any two axes of the three-axis sliding table are perpendicular to each other and intersect in a coordinate system T of the measuring equipmentuThe origin of (a); the relative position of the calibration ball and the position measuring equipment is fixed, and the coordinate system L of the detection unit and the coordinate system T of the measuring equipmentuThe relative relationship of (3) is fixed;
the consistency compensation method comprises the following steps:
randomly selecting two sampling points a and b in the movement range of the three-axis sliding table;
measuring the coordinate system T of the sampling point a in the measuring equipment by the position measuring equipmentuThe lower coordinate is Tua; sample point b in measuring equipment coordinate system TuThe lower coordinate is Tub; sphere center C of calibration sphere in measuring equipment coordinate system TuThe lower coordinate is TuoL；
Teaching the robot to obtain a calibration ballThe sphere center C output by the robot when the robot moves to the sampling point a is in the robot coordinate system TrThe lower actual coordinate Tra;
setting the coordinate of the sphere center C of the calibration sphere under the coordinate system L of the detection unit as LC(ii) a According to the coordinate system L of the detection unit and the coordinate system T of the measuring equipmentuThe relative relation of the two points can be used for obtaining the coordinate system T of the sphere center C of the measuring equipment when the calibration sphere moves to the sampling point auThe following theoretical coordinate Tura;
starting the test, moving the robot from a sampling point a to a sampling point b, and collecting the sphere center C output by the robot when the calibration sphere moves to the sampling point b in the robot coordinate system TrThe lower actual coordinate Trb;
according to the coordinate system L of the detection unit and the coordinate system T of the measuring equipmentuThe relative relation of the two points can be used for obtaining the coordinate system T of the sphere center C of the measuring equipment when the calibration sphere moves to the sampling point buThe theoretical coordinate Turb of the following;
computing the coordinate system T of the deviceuThe theoretical difference of coordinates of the sampling points a and b, Turd ═ Tura-Turb, and in the robot coordinate system TrThe actual coordinate difference Trd of the down sampling points a and b is Tra-Trb;
calculating the modulus of the vector under two coordinate systems and calculating the absolute value of the difference to obtain the motion error of the robot
Figure BDA0002712488610000031
Judging whether the motion error of the robot exceeds an error tolerance value, if so, carrying out consistency compensation on the robot and calculating a compensation quantity Trd ═ Turd/kru; wherein kru is Trd/Turd;
and compensating the positions of the sampling points according to the compensation amount and calculating the compensation position of the motion of the robot after compensation.
Further, the four laser displacement sensors are respectively a first laser displacement sensor, a second laser displacement sensor, a third laser displacement sensor and a fourth laser displacement sensor, and the laser beam of the first laser displacement sensor and the laser beam of the third laser displacement sensor are located on an XY plane of the detection unit coordinate system L and are symmetrical with respect to a Y axis of the detection unit coordinate system L.
Furthermore, an included angle between the laser beam of the first laser displacement sensor or the laser beam of the third laser displacement sensor and the Y axis of the detection unit coordinate system L is θ, and the value range of θ is 30 ° to 70 °.
Further, the laser beam of the second laser displacement sensor and the laser beam of the fourth laser displacement sensor are located on the YZ plane of the detection unit coordinate system L and are symmetrical with respect to the Y axis of the detection unit coordinate system L.
Furthermore, an included angle between the laser beam of the second laser displacement sensor or the laser beam of the fourth laser displacement sensor and the Y axis of the detection unit coordinate system L is θ, and the value range of θ is 30 ° to 70 °.
Further, θ takes a value of 40 °.
Furthermore, the origin of the coordinate system L of the detection unit coincides with the initial position of the sphere center of the calibration sphere, and the X axis, the Y axis and the Z axis of the coordinate system L of the detection unit coincide with the coordinate system T of the measuring equipmentuThe X-axis, the Y-axis and the Z-axis have the same direction, and the sphere center C of the calibration sphere is positioned in a coordinate system T of the measuring equipmentuUpper fixed position having coordinates TuoL。
Further, setting
Figure BDA0002712488610000041
And is known
Figure BDA0002712488610000042
Then
Figure BDA0002712488610000043
Further, the coordinate L of the sphere center C under the coordinate system L of the detection unitCThe calculation method of (2) is as follows:
s1, enabling the center C of the sphere to be in contact with the origin O of a coordinate system L of the detection unitLThe values of the four laser displacement sensors at the moment are recorded as
Figure BDA0002712488610000044
Then the emission point C from the four laser sensors at this time1、C2、C3、C4To the origin O of the coordinate system L of the detection unitLThe distance of (a) is:
Figure BDA0002712488610000045
wherein R is the radius of the calibration ball;
s2, enabling the center C of the sphere to be in contact with the origin O of the coordinate system L of the detection unitLNon-coincidence, the values of the four laser displacement sensors are L respectively1、L2、L3、L4Since the position of each laser emitting point under the sphere center and the detecting unit coordinate system L is constant, and each laser emitting point reaches the origin OLIs the same as the initial time, 4 laser beams intersect with the spherical surface1、D2、D3、D4The coordinates in the detection unit coordinate system L are:
Figure BDA0002712488610000051
s3. due to D1、D2、D3、D4All on the sphere, then according to the spherical equation:
Figure BDA0002712488610000052
wherein dx, dy and dz are variables to be solved, and xi、yi、ziI is 1, 2, 3, or 4, and can be obtained according to formula (2);
s4, obtaining the following result by deforming the formula (3):
Figure BDA0002712488610000053
then, the iterative method is used to solve the formula (4), and the values of dx, dy, and dz can be obtained.
Further, the error tolerance value is 5mm, and the specific value can be adjusted according to the actual situation.
Compared with the prior art, the invention has the following beneficial effects:
the consistency compensation method for the robot mechanical arm can perform early consistency compensation on the robot which is not calibrated, so that the error range of the robot is in an identifiable range, and subsequent automatic calibration is performed conveniently.
Drawings
Fig. 1 is a schematic diagram of a robotic arm and end-point detection device and position measurement device of the present invention.
FIG. 2 is a schematic view of the position measurement device of the present invention.
FIG. 3 is a schematic diagram of a calibration sphere and a laser displacement sensor of the present invention.
Fig. 4 is a schematic position diagram of the first laser displacement sensor and the third laser displacement sensor and the calibration ball according to the present invention.
Fig. 5 is a schematic position diagram of a second laser displacement sensor and a fourth laser displacement sensor and a calibration ball according to the present invention.
Reference numerals: 1-a robot mechanical arm, 12-a calibration rod, 13-a calibration ball, 21-a sphere center detection unit, 22-a moving unit, 211-a first laser displacement sensor, 212-a second laser displacement sensor, 213-a third laser displacement sensor and 214-a fourth laser displacement sensor.
Detailed Description
The invention will be further elucidated and described with reference to the embodiments of the invention described hereinafter.
Example (b):
the first embodiment is as follows:
as shown in fig. 1, a consistency compensation method for a robot arm 1 is implemented based on a terminal detection device and a position measurement device that are matched with each other, in this embodiment, the terminal detection device is installed on the robot arm 1 and includes a calibration rod 12 and a calibration ball 13, and the calibration ball 13 is installed at the terminal of the robot arm 1 through the calibration rod 12. Wherein the robot is mounted in a robot coordinate system TrOf the origin.
Specifically, as shown in fig. 2, the position measuring apparatus includes a center detecting unit 21 and a moving unit 22, the center detecting unit 21 being mounted on the moving unit 22; the sphere center detection unit 21 comprises four laser displacement sensors, and the laser beams of the four laser displacement sensors intersect at the origin O of the detection unit coordinate system LL。
Specifically, as shown in fig. 3, the four laser displacement sensors are a first laser displacement sensor 211, a second laser displacement sensor 212, a third laser displacement sensor 213 and a fourth laser displacement sensor 214, respectively, and the laser beam of the first laser displacement sensor 211 and the laser beam of the third laser displacement sensor 213 are located on the XY plane of the detection unit coordinate system L and are symmetrical about the Y axis of the detection unit coordinate system L.
As shown in fig. 4 and 5, an included angle between the laser beam of the first laser displacement sensor 211 or the laser beam of the third laser displacement sensor 213 and the Y axis of the detection unit coordinate system L is θ, and the value range of θ is 30 ° to 70 °. The laser beam of the second laser displacement sensor 212 and the laser beam of the fourth laser displacement sensor 214 are located on the YZ plane of the sensing unit coordinate system L and are symmetrical with respect to the Y axis of the sensing unit coordinate system L. The included angle between the laser beam of the second laser displacement sensor 212 or the laser beam of the fourth laser displacement sensor 214 and the Y axis of the detection unit coordinate system L is theta, and the value range of the theta is 30-70 degrees. Preferably, θ is 40 ° in this embodiment.
Specifically, in this embodiment, the origin of the coordinate system L of the detection unit coincides with the initial position of the center of the calibration sphere 13, and the X-axis, the Y-axis, and the Z-axis of the coordinate system L of the detection unit coincides with the coordinate system T of the measuring deviceuHas the same X-axis, Y-axis and Z-axis directions, and the center C of the calibration ball 13 is located in the coordinate system T of the measuring deviceuUpper fixed position having coordinates TuoL。
The mobile unit 22 comprises three axes of sliding, any two axes of which are perpendicular to each other and intersect in the coordinate system T of the measuring deviceuThe origin of (a); the relative position of the calibration ball 13 and the position measuring device is fixed, and the coordinate system L of the detection unit and the coordinate system T of the measuring device are determineduThe relative relationship of (a) and (b) is fixed.
Specifically, the consistency compensation method comprises the following steps:
firstly, two sampling points a and b are arbitrarily selected in the movement range of the three-axis sliding table (specifically in the range defined by A, B, C, D as the bottom surface boundary in the embodiment);
then, measuring the coordinate system T of the sampling point a in the measuring equipment by the position measuring equipmentuThe lower coordinate is Tua; sample point b in measuring equipment coordinate system TuThe lower coordinate is Tub; the sphere center C of the calibration sphere 13 is located in the coordinate system T of the measuring equipmentuThe lower coordinate is TuoL。
Specifically, in the present embodiment, the specific measurement is
Figure BDA0002712488610000081
Then, the robot is taught to obtain the sphere center C output by the robot when the calibration sphere 13 moves to the sampling point a in the robot coordinate system TrThe lower actual coordinate Tra; in the present embodiment, the first and second electrodes are,
Figure BDA0002712488610000082
the coordinate of the center C of the calibration ball 13 in the coordinate system L of the detection unit is set as LC(ii) a In the present embodiment, the first and second electrodes are,
Figure BDA0002712488610000083
according to the coordinate system L of the detection unit and the coordinate system T of the measuring deviceuThe relative relationship can be used to determine the coordinate system T of the measuring device for the center C of the calibration ball 13 when the calibration ball moves to the sampling point auThe following theoretical coordinate Tura; in the present embodiment, the first and second electrodes are,
Figure BDA0002712488610000084
wherein, only
Figure BDA0002712488610000085
The specific calculation method for the value to be calculated is specifically described in the following.
Then, the test is started, and the robot moves from the sampling point a to the sampling point b, and then the test is carried outThe center C of the sphere output by the robot when the calibration sphere 13 moves to the sampling point b is collected in the robot coordinate system TrThe lower actual coordinate Trb; in the present embodiment, the first and second electrodes are,
Figure BDA0002712488610000086
then, according to the coordinate system L of the detection unit and the coordinate system T of the measuring deviceuThe relative relationship of the two points can be used to determine the coordinate system T of the measuring device when the center C of the calibration ball 13 moves to the sampling point buThe theoretical coordinate Turb of the following; in the present embodiment, the first and second electrodes are,
Figure BDA0002712488610000091
and then further calculate the coordinate system T of the deviceuThe theoretical difference of coordinates of the sampling points a and b, Turd ═ Tura-Turb, and in the robot coordinate system TrThe actual difference Trd between the coordinates of the down-sampling points a and b is Tra-Trb.
Then, calculating the modulus of the vector under the two coordinate systems and calculating the absolute value of the difference to obtain the robot motion error
Figure BDA0002712488610000092
And then further judging whether the robot motion error exceeds an error tolerance value, specifically, in the embodiment, setting the specific error tolerance value to be 5 mm. If so, carrying out consistency compensation on the robot and calculating a compensation quantity Trd ═ Turd/kru; wherein kru is Trd/Turd; if dur is more than 5mm, the robot needs to be subjected to consistency compensation in the next step.
And compensating the positions of the sampling points according to the compensation amount and calculating the compensation position of the motion of the robot after compensation, wherein for the sampling point b, the compensation position to which the robot needs to move after compensation is Trb '═ Tra-Trd' in the embodiment.
The automatic test and the automatic compensation can be carried out on all other sampling points later.
Specifically, the coordinate L of the sphere center C under the coordinate system L of the detection unitCThe calculation method of (2) is as follows:
s1, enabling the center C of the sphere to be detectedOrigin O of unit coordinate system LLThe values of the four laser displacement sensors at the moment are recorded as
Figure BDA0002712488610000093
Then the emission point C from the four laser sensors at this time1、C2、C3、C4To the origin O of the coordinate system L of the detection unitLThe distance of (a) is:
Figure BDA0002712488610000094
wherein R is the radius of the calibration ball 13.
S2, enabling the center C of the sphere to be in contact with the origin O of the coordinate system L of the detection unitLNon-coincidence, the values of the four laser displacement sensors are L respectively1、L2、L3、L4Since the position of each laser emitting point under the sphere center and the detecting unit coordinate system L is constant, and each laser emitting point reaches the origin OLIs the same as the initial time, 4 laser beams intersect with the spherical surface1、D2、D3、D4The coordinates in the detection unit coordinate system L are:
Figure BDA0002712488610000101
s3. due to D1、D2、D3、D4All on the sphere, then according to the spherical equation:
Figure BDA0002712488610000102
wherein dx, dy and dz are variables to be solved, and xi、yi、ziWhere i is 1, 2, 3, or 4, and can be obtained from the formula (2)
S4, obtaining the following result by deforming the formula (3):
Figure BDA0002712488610000103
then, the iterative method is used to solve the formula (4), and the values of dx, dy, and dz can be obtained.
It will be understood that the above embodiments are merely exemplary embodiments taken to illustrate the principles of the present invention, which is not limited thereto. It will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the spirit and substance of the invention, and these modifications and improvements are also considered to be within the scope of the invention.

Claims (9)

1. The consistency compensation method for the robot mechanical arm is characterized by being realized based on mutually matched terminal detection equipment and position measurement equipment, wherein the terminal detection equipment is arranged on the robot mechanical arm and comprises a calibration ball, and the robot is arranged on a robot coordinate system TrThe position measuring device includes a center detecting unit and a moving unit, the center detecting unit is mounted on the moving unit; the sphere center detection unit comprises four laser displacement sensors, and laser beams of the four laser displacement sensors intersect at the origin O of the coordinate system L of the detection unitL(ii) a The mobile unit comprises a three-axis sliding table, and any two axes of the three-axis sliding table are perpendicular to each other and intersect in a coordinate system T of the measuring equipmentuThe origin of (a); the relative position of the calibration ball and the position measuring equipment is fixed, and the coordinate system L of the detection unit and the coordinate system T of the measuring equipmentuThe relative relationship of (3) is fixed;
the consistency compensation method comprises the following steps:
randomly selecting two sampling points a and b in the movement range of the three-axis sliding table;
measuring the coordinate system T of the sampling point a in the measuring equipment by the position measuring equipmentuThe lower coordinate is Tua; sample point b in measuring equipment coordinate system TuThe lower coordinate is Tub; sphere center C of calibration sphere in measuring equipment coordinate system TuThe lower coordinate is TuoL；
Teaching a robot to obtain calibrationThe sphere center C output by the robot when the ball moves to the sampling point a is in the robot coordinate system TrThe lower actual coordinate Tra;
setting the coordinate of the sphere center C of the calibration sphere under the coordinate system L of the detection unit asLC; according to the coordinate system L of the detection unit and the coordinate system T of the measuring equipmentuThe relative relation of the two points can be used for obtaining the coordinate system T of the sphere center C of the measuring equipment when the calibration sphere moves to the sampling point auThe following theoretical coordinate Tura;
starting the test, moving the robot from a sampling point a to a sampling point b, and collecting the sphere center C output by the robot when the calibration sphere moves to the sampling point b in the robot coordinate system TrThe lower actual coordinate Trb;
according to the coordinate system L of the detection unit and the coordinate system T of the measuring equipmentuThe relative relation of the two points can be used for obtaining the coordinate system T of the sphere center C of the measuring equipment when the calibration sphere moves to the sampling point buThe theoretical coordinate Turb of the following;
computing the coordinate system T of the deviceuThe theoretical difference of coordinates of the sampling points a and b, Turd ═ Tura-Turb, and in the robot coordinate system TrThe actual coordinate difference Trd of the down sampling points a and b is Tra-Trb;
calculating the modulus of the vector under two coordinate systems and calculating the absolute value of the difference to obtain the motion error of the robot
Figure FDA0003239868070000021
Judging whether the motion error of the robot exceeds an error tolerance value, if so, carrying out consistency compensation on the robot and calculating a compensation quantity Trd ═ Turd/kru; wherein kru is Trd/Turd;
and compensating the positions of the sampling points according to the compensation amount and calculating the compensation position of the motion of the robot after compensation.
2. The consistency compensation method for a robotic arm of claim 1, wherein the four laser displacement sensors are a first laser displacement sensor, a second laser displacement sensor, a third laser displacement sensor and a fourth laser displacement sensor, respectively, and the laser beam of the first laser displacement sensor and the laser beam of the third laser displacement sensor are located in an XY plane of the detection unit coordinate system L and are symmetric with respect to a Y axis of the detection unit coordinate system L.
3. The consistency compensation method for a robotic arm of claim 2, wherein an angle θ is an angle between a laser beam of the first laser displacement sensor and a laser beam of the third laser displacement sensor and a Y-axis of a coordinate system L of the detection unit1，θ1The value range of (A) is 30-70 degrees.
4. The consistency compensation method for a robotic arm of claim 3, wherein the laser beam of the second laser displacement sensor and the laser beam of the fourth laser displacement sensor are located in a YZ plane of the detection unit coordinate system L and are symmetric with respect to a Y axis of the detection unit coordinate system L.
5. The consistency compensation method for a robotic arm of claim 4, wherein an angle θ is an angle between a laser beam of the second laser displacement sensor and a laser beam of the fourth laser displacement sensor and a Y-axis of a coordinate system L of the detection unit2，θ2The value range of (A) is 30-70 degrees.
6. The uniformity compensation method for a robotic arm of claim 5, wherein an origin of said detection unit coordinate system L coincides with an initial position of a calibration sphere center, and an X-axis, a Y-axis and a Z-axis of said detection unit coordinate system L and a measurement device coordinate system TuThe X-axis, the Y-axis and the Z-axis have the same direction, and the sphere center C of the calibration sphere is positioned in a coordinate system T of the measuring equipmentuUpper fixed position having coordinates TuoL。
7. A uniformity compensation method for a robotic arm according to claim 6, characterized in that setting
Figure FDA0003239868070000031
And is known
Figure FDA0003239868070000032
Then
Figure FDA0003239868070000033
8. The consistency compensation method for a robotic arm according to claim 7, wherein coordinates of the center of sphere C under a detection unit coordinate system LLThe calculation method of C is as follows:
s1, enabling the center C of the sphere to be in contact with the origin O of a coordinate system L of the detection unitLThe values of the four laser displacement sensors at the moment are recorded as
Figure FDA0003239868070000034
Then the emission point C from the four laser sensors at this time1、C2、C3、C4To the origin O of the coordinate system L of the detection unitLThe distance of (a) is:
Figure FDA0003239868070000035
wherein R is the radius of the calibration ball;
s2, enabling the center C of the sphere to be in contact with the origin O of the coordinate system L of the detection unitLNon-coincidence, the values of the four laser displacement sensors are L respectively1、L2、L3、L4Since the position of each laser emitting point under the sphere center and the detecting unit coordinate system L is constant, and each laser emitting point reaches the origin OLIs the same as the initial time, 4 laser beams intersect with the spherical surface1、D2、D3、D4The coordinates in the detection unit coordinate system L are:
Figure FDA0003239868070000041
Figure FDA0003239868070000042
Figure FDA0003239868070000043
Figure FDA0003239868070000044
s3. due to D1、D2、D3、D4All on the sphere, then according to the spherical equation:
Figure FDA0003239868070000045
wherein dx, dy and dz are variables to be solved, and xi、yi、ziI is 1, 2, 3, or 4, and can be obtained according to formula (2);
s4, obtaining the following result by deforming the formula (3):
Figure FDA0003239868070000051
then, the iterative method is used to solve the formula (4), and the values of dx, dy, and dz can be obtained.
9. A method of consistency compensation for a robotic arm according to any of claims 1 to 8, wherein the error tolerance value is 5 mm.
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