CN111687845A - Mechanical arm kinematics parameter calibration method based on inertia measurement unit - Google Patents

Mechanical arm kinematics parameter calibration method based on inertia measurement unit Download PDF

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CN111687845A
CN111687845A CN202010581116.4A CN202010581116A CN111687845A CN 111687845 A CN111687845 A CN 111687845A CN 202010581116 A CN202010581116 A CN 202010581116A CN 111687845 A CN111687845 A CN 111687845A
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mechanical arm
tail end
measurement unit
parameters
kinematic parameters
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CN111687845B (en
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金弘哲
赵杰
周睿
张慧
龙奕琳
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Harbin Institute of Technology
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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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1692—Calibration of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/0095—Means or methods for testing manipulators
    • 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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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
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Abstract

A mechanical arm kinematics parameter calibration method based on an inertia measurement unit comprises the steps of firstly, constructing relational expressions among a linear velocity, a velocity relation and a Jacobian matrix under a Cartesian coordinate at the tail end of a mechanical arm, and obtaining derivatives; secondly, normalizing the derived relational expression; acquiring linear acceleration of the tail end of the mechanical arm in a Cartesian space, and acquiring an angle, an angular velocity and an angular acceleration of the mechanical arm in a joint space; fourthly, identifying the parameters of the mechanical arm by using a recursive least square method to obtain a calculated value of the kinematic parameters of the mechanical arm in each direction; and fifthly, taking the root mean square value of the three obtained values, outputting the final estimated value of the kinematic parameters of the mechanical arm at the moment and drawing a curve. The invention reduces the cost of mechanical arm kinematics calibration. With the continuous improvement of the technology of the inertial measurement unit, the measurement precision of the inertial measurement unit is higher and higher, and the precision of the calibration result is higher and higher.

Description

Mechanical arm kinematics parameter calibration method based on inertia measurement unit
Technical Field
The invention relates to the technical field of robots, in particular to a mechanical arm kinematics parameter calibration method based on an inertia measurement unit.
Background
The factors influencing the positioning accuracy of the tail end of the industrial robot are many, and among the errors, the error generated by geometric parameters is a systematic error and is also a main factor causing the low absolute positioning accuracy of the mechanical arm. In order to not change the hardware configuration of the mechanical arm, the kinematic parameter identification of the mechanical arm is the most economic method.
The end effectors are required in the model-based mechanical arm kinematics calibration method, and the effectors include a laser tracker, a three-coordinate measuring instrument, a ball arm instrument and the like. Newman W S et al have accomplished the kinematics calibration of P8 robot through the laser tracker, Rencheng Wang et al only install the laser range finder at the arm end of the machinery, and fix several predefined planes on the base, can incorporate all kinematic errors into the initial position posture of the local coordinate system, make the error model deriving from plane constraint obtain and show and simplify, Congcong Ye et al have utilized the telescopic cue appearance, seven positions postures of the robot under the static condition have been measured, thus obtain the actual geometric parameter, and finally utilize COMAU NI220 industrial robot to verify the method.
Xiehua, li heroic, zhou xuan, etc., general development of mechanical arm kinematics calibration technology, astronomical measurement technology, 2018, 38(06):29-36, discloses a laser tracker for mechanical arm kinematics calibration, which is subject to environmental interference such as temperature, humidity and air pressure due to calibration using laser, and thus has errors in the obtained measurement point position information. Secondly, the instrument is calibrated in a non-contact mode, so that the requirement on the continuity of laser is high, but in practice, light interruption often occurs in an experiment and re-measurement is needed, so that the measurement efficiency of the method is not high; finally, the existing method has the defects that the number of the measurement products is small, the manufacturing cost is high and millions of products are often produced, so the economic performance of small-scale calibration experiments is poor, in addition, in the aspect of patent literature, CN106799745A is a precision calibration method of an industrial mechanical arm based on synergic kriging, a calibration device consisting of a laser tracker and target balls is disclosed, and the target balls are fixed at the tail end of the mechanical arm. The three-coordinate measuring instrument occupies a large area and has high cost. Even though the ball arm instrument is simple to operate and low in cost, the calibration range is small due to the contact measurement characteristic of the ball arm instrument, and the ball arm instrument is not suitable for calibration of the multi-degree-of-freedom mechanical arm. The publication number CN110561424A discloses an online robot kinematic calibration method based on a multi-sensor hybrid filter, which mainly aims at estimating the position and attitude of the end of a robot by using an inertial measurement unit, and adopts a factorial quaternion algorithm estimation process, wherein the attitude is represented by an euler angle, rather than directly measuring kinematic parameters of a mechanical arm, error compensation is required, and the estimation process is relatively complex.
Disclosure of Invention
The invention provides a mechanical arm kinematics parameter calibration method based on an inertia measurement unit to overcome the defects of the prior art. The method is based on the Jacobian matrix of the mechanical arm, mechanical arm kinematic parameters are extracted, finally, parameter identification is carried out by using a recursive least square method, finally, estimated values of the mechanical arm kinematic parameters are obtained, and calibration is completed.
The technical scheme of the invention is as follows: a mechanical arm kinematic parameter calibration method based on an inertial measurement unit comprises the following steps:
firstly, constructing a relation expression among a linear velocity, a velocity relation in a joint space and a Jacobian matrix under a Cartesian coordinate of the tail end of a mechanical arm, and obtaining a derivative;
step two, normalizing the relation obtained after derivation in the step one to obtain the relation between the linear acceleration and the kinematic parameters of the mechanical arm under the Cartesian coordinate of the tail end of the mechanical arm, and meanwhile, installing an inertia measurement unit on the tail end of the mechanical arm to enable the mechanical arm to move according to a mechanical arm track planned in advance;
acquiring linear acceleration of the tail end of the mechanical arm in a Cartesian space, and acquiring an angle, an angular velocity and an angular acceleration of the mechanical arm in a joint space;
step four, aiming at the relation between the linear acceleration and the mechanical arm kinematic parameters under the Cartesian coordinates of the mechanical arm tail end obtained in the step two, the mechanical arm parameter identification is carried out by using a recursive least square method by using the mechanical arm tail end linear acceleration information and the joint information obtained in the step three, and a calculated value of the mechanical arm kinematic parameters in each direction of an xyz axis is obtained;
and step five, taking the root mean square value of the three values obtained in the step four, outputting the final estimated value of the kinematic parameters of the mechanical arm at the moment and drawing a curve.
Compared with the prior art, the invention has the beneficial effects that:
1. the inertia measurement unit is used for calibrating the kinematics of the mechanical arm, so that the experimental cost of the kinematics calibration of the mechanical arm is greatly reduced, and environmental factors can not seriously interfere with the experimental result. The method is also suitable for small calibration experiments.
2. The method can calibrate the multi-degree-of-freedom mechanical arm, is only attached to the tail end of the mechanical arm, and does not occupy space.
3. The calibration can be carried out only by planning a section of motion track of the mechanical arm, and the operation is simple.
4. The parameter identification is carried out by using a recursive least square method, so that real-time calibration can be carried out.
5. The identification result is the kinematic parameters of the mechanical arm, error compensation is not needed like other calibration methods, the kinematic calibration steps are simplified, and the real kinematic parameters of the mechanical arm can be easily obtained.
6. Along with the gradual maturity of the technical level of the inertia measurement unit, the precision of the inertia measurement unit is higher and higher, so that the calibration result of the mechanical arm kinematics calibration method based on the inertia measurement unit is more and more accurate, and the method has a wide development prospect.
The technical scheme of the invention is further explained by combining the drawings and the embodiment:
drawings
FIG. 1 is a flow chart of the operation of the present invention.
Fig. 2 is a schematic diagram of measuring UR10 industrial robot arm kinematic parameters;
FIG. 3 is a graph showing the variation of linear acceleration of the end of the robot arm with time at different sampling points in the embodiment;
FIG. 4 is a graph showing the angle of each joint with time according to the embodiment;
fig. 5 is a diagram illustrating the result of estimating the kinematic parameters of the robot arm in the embodiment.
Detailed Description
As described with reference to fig. 1, the present embodiment is based on a jacobian matrix of the robot arm, and the jacobian matrix is an expression that links the linear velocity in cartesian space at the end of the robot arm to the velocity in joint space, as follows:
Figure BDA0002553222400000031
in the formula: v and omega represent linear velocity and terminal angular velocity of the mechanical arm; j is a Jacobian matrix, q represents the joint angle,
Figure BDA0002553222400000032
indicating the joint angular velocity. Since the kinematic parameters of the robot arm to be estimated are independent of the tip angular velocity of the robot arm, this equation does not introduce the tip angular velocity.
In order to establish a relational expression of the linear acceleration of the tail end of the mechanical arm in the cartesian space and the kinematic parameters of the mechanical arm, the obtained expression of the relation between the linear velocity of the tail end in the cartesian space and the velocity of the joint space needs to be derived as follows:
Figure BDA0002553222400000033
in the formula
Figure BDA0002553222400000034
Respectively the linear acceleration of the mechanical arm along the respective coordinate axis direction,
Figure BDA0002553222400000035
represents the joint angular acceleration;
after obtaining the expression shown as the formula (2), carrying out normalization processing on the expression, extracting the kinematic parameters of the mechanical arm, and obtaining a normalization matrix phi, so that the relational expression of the linear acceleration and the kinematic parameters of the mechanical arm tail end in a Cartesian space can be obtained, and the form of the relational expression is as follows:
Figure BDA0002553222400000036
n represents the number of the mechanical arm parameters; l1...lnRepresenting the identified kinematic parameters of the mechanical arm;
and phi is ═ phi1,φ2,φ3]T(4)
After the inertia measurement unit is placed at the tail end of the mechanical arm, according to the planned mechanical arm track, in the motion process of the mechanical arm, the linear acceleration of the tail end of the mechanical arm in a Cartesian space and the angle, the angular velocity and the angular acceleration of the mechanical arm in a joint space are continuously acquired. And finally, performing parameter identification on the mechanical arm by using a recursive least square method, wherein the recursive least square method has a real-time calculation function, so that the kinematic parameters of the mechanical arm can be measured in real time.
Respectively carrying out parameter identification on linear accelerations in three directions, and carrying out the same treatment on the y and z axes, namely:
Figure BDA0002553222400000041
therefore, each mechanical arm kinematics parameter needing to be identified can obtain three calculated values, and finally, the three calculated values are subjected to square root averaging, namely, the three calculated values are estimated values of the mechanical arm kinematics parameters.
Figure BDA0002553222400000042
l1x，l1y，l1zRepresenting the kinematic parameters of the arm as a function of orientation.
And outputting the final estimated value of the kinematic parameters of the mechanical arm at the moment and drawing a curve.
The following is further illustrated by an example:
taking the measurement of UR10 industrial robot kinematic parameters as an example, the UR robot is shown in fig. 2: the DH parameters are substituted to obtain the transformation matrix of all adjacent coordinate systems as follows:
Figure BDA0002553222400000043
Figure BDA0002553222400000044
Figure BDA0002553222400000045
Figure BDA0002553222400000046
Figure BDA0002553222400000051
Figure BDA0002553222400000052
deriving the jacobian matrix for the UR robot from the above formula yields the following jacobian matrix for each column:
Figure BDA0002553222400000053
Figure BDA0002553222400000054
Figure BDA0002553222400000055
Figure BDA0002553222400000056
Figure BDA0002553222400000057
Figure BDA0002553222400000058
after the normalization process, the expressions of Φ are as follows:
Figure BDA0002553222400000061
Figure BDA0002553222400000062
Figure BDA0002553222400000063
Figure BDA0002553222400000064
Figure BDA0002553222400000065
then planning the track of the mechanical arm, and substituting the linear acceleration of each sampling point at the tail end of the mechanical arm in a Cartesian space, and the angle, the angular velocity and the angular acceleration in a joint space into the following formula
Figure RE-GDA0002610106420000066
In the method, the parameters of the mechanical arm in the directions of an x axis, a y axis and a z axis are respectively identified by using a recursive least square method,
the linear acceleration of the tail end of the mechanical arm in the cartesian space is shown in fig. 3, the joint angle of the mechanical arm is shown in fig. 4, the mechanical arm calibration method provided by the embodiment calibrates the kinematic parameters of the mechanical arm, and the final calibration result is shown in fig. 5.
Fig. 3 shows the time-dependent acceleration in cartesian space along three coordinate axes at the end of the robot arm, wherein the solid line represents the acceleration along the x-axis, the dotted line represents the acceleration along the y-axis, and the dotted curve represents the acceleration along the z-axis.
Fig. 4 shows a graph of the rotation angle of each joint of the robot arm as a function of time, in which a solid line indicates the angle of the joint 1, a dotted line indicates the angle of the joint 2, a dotted line indicates the angle of the joint 3, a "+" line indicates the angle of the joint 4, a "+" line indicates the angle of the joint 5, and a dotted curve indicates the angle of the joint 6.
FIG. 5 shows the results of parameter calibration using the kinematic calibration method proposed herein, and the solid line indicates l1Calibration results of (1), dotted line type denotes2The dotted line indicates3The "+" line indicates that4The line indicates the result of the calibration of (1) ("+") line5And (4) calibrating results.
Since no noise signal is added, the final calibration result is identical to the actual parameter.
The present invention is not limited to the above embodiments, and those skilled in the art can make various changes and modifications without departing from the scope of the invention.

Claims (5)

1. The mechanical arm kinematics parameter calibration method based on the inertia measurement unit is characterized by comprising the following steps: it comprises
Firstly, constructing relational expression among a linear velocity, a velocity relation in joint space and a Jacobian matrix at the tail end of a mechanical arm under a Cartesian coordinate, and obtaining a derivative;
step two, normalizing the relation obtained after derivation in the step one to obtain the relation between the linear acceleration and the kinematic parameters of the mechanical arm under the Cartesian coordinate of the tail end of the mechanical arm, and meanwhile, installing an inertia measurement unit on the tail end of the mechanical arm to enable the mechanical arm to move according to a mechanical arm track planned in advance;
acquiring linear acceleration of the tail end of the mechanical arm in a Cartesian space, and acquiring an angle, an angular velocity and an angular acceleration of the mechanical arm in a joint space;
step four, aiming at the relation between the linear acceleration and the mechanical arm kinematic parameters under the Cartesian coordinates of the mechanical arm tail end obtained in the step two, the mechanical arm parameter identification is carried out by using a recursive least square method to obtain the calculated value of the mechanical arm kinematic parameters in each direction of the xyz axis;
and step five, taking the root mean square value of the three values obtained in the step four, outputting the final estimated value of the kinematic parameters of the mechanical arm at the moment and drawing a curve.
2. The mechanical arm kinematics parameter calibration method based on the inertial measurement unit according to claim 1, wherein: the Jacobian matrix expression constructed in the first step is as follows:
Figure FDA0002553222390000011
in the formula: v and omega respectively represent the linear velocity and the angular velocity of the tail end of the mechanical arm;
Figure FDA0002553222390000012
representing the angular velocity vector of the joint, and because the kinematic parameters of the mechanical arm to be estimated are irrelevant to the angular velocity of the tail end of the mechanical arm, omega can not be introduced into the formula;
thus, the relationship derived from equation (1) is:
Figure FDA0002553222390000013
in the formula
Figure FDA0002553222390000014
Respectively, the linear acceleration of the tail end of the mechanical arm along the directions of respective coordinate axes.
3. The mechanical arm kinematics parameter calibration method based on the inertial measurement unit according to claim 2, wherein: the relationship between the linear acceleration of the tail end of the mechanical arm under the Cartesian coordinate and the kinematic parameters of the mechanical arm after normalization processing in the second step is as follows:
Figure FDA0002553222390000021
the normalized matrix Φ can be represented as: phi is ═ phi1,φ2,φ3]T(4)
N represents the number of the mechanical arm parameters; l1...lnRepresenting the identified robot arm kinematics parameters.
4. The mechanical arm kinematics parameter calibration method based on the inertial measurement unit according to claim 3, wherein: the parameters of the mechanical arm in the directions of the x axis, the y axis and the z axis are identified by using a recursive least square method,
Figure FDA0002553222390000022
and respectively obtaining calculated values of the kinematic parameters of the mechanical arm in the directions of the x axis, the y axis and the z axis, and calculating the root mean square value of the three values.
5. The mechanical arm kinematics parameter calibration method based on the inertial measurement unit according to claim 3, wherein: when UR10 industrial machinery kinematic parameters are calibrated, DH parameters are substituted to obtain conversion matrixes of all adjacent coordinate systems, and the conversion matrixes are as follows:
Figure FDA0002553222390000023
Figure FDA0002553222390000024
Figure FDA0002553222390000025
Figure FDA0002553222390000031
Figure FDA0002553222390000032
Figure FDA0002553222390000033
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CN112643670A (en) * 2020-12-07 2021-04-13 洛阳尚奇机器人科技有限公司 Flexible joint control method based on sliding-mode observer
CN113094642A (en) * 2021-04-14 2021-07-09 电子科技大学 Newly-added sampling method for estimating positioning error of mechanical arm in region
CN113834500A (en) * 2021-09-16 2021-12-24 东莞安普川自动化技术有限公司 Method and system for calibrating track sensor by using multi-degree-of-freedom equipment

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112643670A (en) * 2020-12-07 2021-04-13 洛阳尚奇机器人科技有限公司 Flexible joint control method based on sliding-mode observer
CN112643670B (en) * 2020-12-07 2022-07-29 洛阳尚奇机器人科技有限公司 Flexible joint control method based on sliding-mode observer
CN113094642A (en) * 2021-04-14 2021-07-09 电子科技大学 Newly-added sampling method for estimating positioning error of mechanical arm in region
CN113834500A (en) * 2021-09-16 2021-12-24 东莞安普川自动化技术有限公司 Method and system for calibrating track sensor by using multi-degree-of-freedom equipment
CN113834500B (en) * 2021-09-16 2024-04-09 东莞安普川自动化技术有限公司 Method and system for calibrating track sensor by using multi-degree-of-freedom equipment

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