CN113580128B - Four-degree-of-freedom mechanical arm control method and transformer substation fire-fighting mechanical arm control method - Google Patents

Four-degree-of-freedom mechanical arm control method and transformer substation fire-fighting mechanical arm control method Download PDF

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CN113580128B
CN113580128B CN202110780546.3A CN202110780546A CN113580128B CN 113580128 B CN113580128 B CN 113580128B CN 202110780546 A CN202110780546 A CN 202110780546A CN 113580128 B CN113580128 B CN 113580128B
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mechanical arm
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freedom mechanical
freedom
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CN113580128A (en
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汤锦慧
伍发元
江姗
孙博宇
毛梦婷
代小敏
刘晓磊
刘专
刘平
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Jingdezhen Power Supply Branch Of State Grid Jiangxi Electric Power Co ltd
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jiangxi Electric Power Co Ltd
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Jingdezhen Power Supply Branch Of State Grid Jiangxi Electric Power Co ltd
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jiangxi Electric Power 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1669—Programme controls characterised by programming, planning systems for manipulators characterised by special application, e.g. multi-arm co-operation, assembly, grasping
    • 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]

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Abstract

The invention discloses a control method of a four-degree-of-freedom mechanical arm, which comprises the steps of obtaining working parameters of the four-degree-of-freedom mechanical arm; establishing a coordinate system according to the position of the four-degree-of-freedom mechanical arm; acquiring target position information as position information and corresponding elevation angle information of the tail end of the mechanical arm; calculating control angle information of each joint of the four-degree-of-freedom mechanical arm; and controlling the four-degree-of-freedom mechanical arm to act. The invention also discloses a transformer substation fire-fighting mechanical arm control method comprising the four-degree-of-freedom mechanical arm control method. The invention avoids complex matrix operation, effectively solves the problem of high-precision control of inverse kinematics of the mechanical arm, can ensure that the four-degree-of-freedom mechanical arm can realize precise action and operation, and has high reliability, good precision and accurate positioning.

Description

Four-degree-of-freedom mechanical arm control method and transformer substation fire-fighting mechanical arm control method
Technical Field
The invention belongs to the field of motion control, and particularly relates to a four-degree-of-freedom mechanical arm control method and a transformer substation fire-fighting mechanical arm control method.
Background
With the development and improvement of economic technology, the mechanical arm is widely applied to the production of people, and brings endless convenience to the production of people.
The four-degree-of-freedom mechanical arm is widely applied to occasions such as factories and enterprises. However, in the actual operation process of the four-degree-of-freedom mechanical arm, the problems of low control precision and inaccurate fixed-point positioning of the mechanical arm often exist, so that the popularization and the precise application of the four-degree-of-freedom mechanical arm are influenced.
In addition, the traditional fire-fighting means of the transformer substation mainly adopts fixed spraying, but because the installation position is fixed, the coverage and flexibility are insufficient, and the accurate operation on an over-temperature point or a fire point cannot be carried out, so that the actual requirements of the transformer substation for preventing and reducing the disaster cannot be met. Meanwhile, the four-degree-of-freedom mechanical arm has the characteristics of flexible operation and good working stability, so that the intelligent fire-fighting system with the four-degree-of-freedom mechanical arm as a core execution unit can realize accurate fire-fighting operation. However, if the four-degree-of-freedom mechanical arm is directly used in the intelligent fire-fighting system of the transformer substation, the problems of low control precision and inaccurate fixed-point positioning of the mechanical arm also exist, so that the operation efficiency of the fire-fighting system of the transformer substation is reduced.
Disclosure of Invention
One of the purposes of the invention is to provide a four-degree-of-freedom mechanical arm control method which is high in reliability, good in accuracy and accurate in positioning.
The invention also aims to provide a transformer substation fire-fighting mechanical arm control method comprising the four-degree-of-freedom mechanical arm control method.
The invention provides a control method of a four-degree-of-freedom mechanical arm, which comprises the following steps:
s1, acquiring working parameters of a four-degree-of-freedom mechanical arm;
s2, establishing a coordinate system according to the position of the four-degree-of-freedom mechanical arm;
s3, acquiring target position information as position information of the tail end of the mechanical arm, and acquiring corresponding elevation angle information;
s4, calculating control angle information of each joint of the four-degree-of-freedom mechanical arm;
and S5, controlling the four-degree-of-freedom mechanical arm to act according to the angle information obtained in the step S4.
Establishing a coordinate system according to the position of the four-degree-of-freedom mechanical arm in the step S2, specifically, establishing a Cartesian rectangular coordinate system OXYZ on a plane where the four-degree-of-freedom mechanical arm is installed, wherein the plane where the four-degree-of-freedom mechanical arm is installed is an OXY plane, and a Z axis is perpendicular to the OXY plane and is collinear with a steering engine rotating shaft of a first joint of the four-degree-of-freedom mechanical arm, which is closest to the OXY plane; and sequentially establishing a Cartesian rectangular coordinate system at four joints of the four-degree-of-freedom mechanical arm.
Step S3, obtaining the target position information as the position information of the end of the mechanical arm and obtaining the corresponding elevation angle information, specifically obtaining the target position information P (x, y, z) as the position information of the end of the mechanical arm and obtaining the corresponding elevation angle information
Figure BDA0003156624580000021
Elevation angle
Figure BDA0003156624580000022
The included angle between the section of the mechanical arm at the farthest end of the four-freedom-degree mechanical arm and the OXY plane in the established coordinate system is defined.
The step S4 of calculating the control angle information of each joint of the four-degree-of-freedom robot arm specifically includes the following steps:
A. by using such asCalculating a first inclination angle theta by a formula 1
Figure BDA0003156624580000023
Where (x, y, z) is the coordinates of the target position P; first inclination angle theta 1 Is the included angle between the first section of mechanical arm and the X axis;
B. the coordinates w of the position P (w, z) of the target position P in the OWZ plane coordinate system are calculated using the following equation:
Figure BDA0003156624580000031
where (x, y, z) is the coordinates of the target position P;
C. calculating a first intermediate variable m, a second intermediate variable n and a third intermediate variable t by the following formula 1 And a fourth intermediate variable t 2 ：
Figure BDA0003156624580000032
Figure BDA0003156624580000033
Figure BDA0003156624580000034
Figure BDA0003156624580000035
In the formula a 4 The length of a section of the mechanical arm at the farthest end of the four-degree-of-freedom mechanical arm; d 1 The length of the section of the mechanical arm at the most proximal end of the four-degree-of-freedom mechanical arm; a is a 3 The length of a section of the mechanical arm at the second last far end of the four-degree-of-freedom mechanical arm; a is 2 At the third last extremity of a four-degree-of-freedom robot armThe length of a section of mechanical arm;
D. c, judging the first to fourth intermediate variables obtained in the step C as follows:
if m 2 +n 2 -(t 1 ) 2 Not less than 0 and m 2 +n 2 -(t 2 ) 2 If the value is more than or equal to 0, performing subsequent step calculation;
otherwise, judging that the four-degree-of-freedom mechanical arm cannot reach the target position P, and ending the algorithm;
E. the fifth intermediate variable Q and the sixth intermediate variable P are used as follows:
Figure BDA0003156624580000036
and Q ∈ [ -1,1]
Figure BDA0003156624580000037
And P ∈ [ -1, 1)]
F. The second inclination angle theta is calculated by adopting the following formula 2 A third inclination angle theta 3 And a fourth inclination angle theta 4 ：
Figure BDA0003156624580000041
Figure BDA0003156624580000042
Figure BDA0003156624580000043
Figure BDA0003156624580000044
In which the second inclination angle theta 2 Is the included angle between the second section of mechanical arm and the X axis; third inclination angle theta 3 The included angle between the third section of mechanical arm and the X axis is formed; fourth angle of inclination theta 4 The included angle between the fourth section of mechanical arm and the X axis is formed;
G. several sets of solutions (theta) obtained for the above steps 1 ,θ 2 ,θ 3 ,θ 4 ) And selecting or rejecting according to the actual condition of the four-degree-of-freedom mechanical arm so as to obtain the final control angle information of each joint of the four-degree-of-freedom mechanical arm.
The invention also discloses a transformer substation fire-fighting mechanical arm control method comprising the four-degree-of-freedom mechanical arm control method, which specifically comprises the following steps:
(1) a four-degree-of-freedom mechanical arm is adopted as a fire-fighting mechanical arm of the transformer substation;
(2) the four-degree-of-freedom mechanical arm control method is adopted to control the fire-fighting mechanical arm of the transformer substation.
The four-degree-of-freedom mechanical arm control method and the substation fire-fighting mechanical arm control method avoid complex matrix operation, effectively solve the problem of high-precision control of inverse kinematics of the mechanical arm, enable the four-degree-of-freedom mechanical arm to realize precise action and operation, and have high reliability, good precision and accurate positioning.
Drawings
Fig. 1 is a schematic method flow diagram of a four-degree-of-freedom mechanical arm control method according to the present invention.
FIG. 2 is a schematic representation of a linkage model of the present invention labeled with inverse kinematics calculated variables.
Fig. 3 is a schematic diagram of a link model of a four-degree-of-freedom mechanical arm according to an embodiment of the present invention.
FIG. 4 is a schematic view of an initial state of a robotic arm according to an embodiment of the present invention.
FIG. 5 is a schematic diagram of the pose of the mechanical arm in the (0, 66.93, -70.91, 3.98) state of the embodiment of the present invention.
Detailed Description
Fig. 1 is a schematic flow chart of a method of controlling a four-degree-of-freedom robot arm according to the present invention: the invention provides a control method of a four-degree-of-freedom mechanical arm, which comprises the following steps:
s1, acquiring working parameters of a four-degree-of-freedom mechanical arm;
s2, establishing a coordinate system according to the position of the four-degree-of-freedom mechanical arm; specifically, a Cartesian rectangular coordinate system OXYZ is established on a plane where a four-degree-of-freedom mechanical arm is installed, wherein the plane where the four-degree-of-freedom mechanical arm is installed is an OXY plane, and a Z axis is perpendicular to the OXY plane and is collinear with a steering engine rotating shaft of a first joint of the four-degree-of-freedom mechanical arm, which is closest to the OXY plane; then sequentially establishing a Cartesian rectangular coordinate system at four joints of the four-degree-of-freedom mechanical arm;
s3, acquiring target position information as position information of the tail end of the mechanical arm, and acquiring corresponding elevation angle information; specifically, target position information P (x, y, z) is obtained as position information of the tail end of the mechanical arm, and a corresponding elevation angle is obtained at the same time
Figure BDA0003156624580000051
Elevation angle
Figure BDA0003156624580000052
Defining an included angle between a section of the mechanical arm at the farthest end of the four-degree-of-freedom mechanical arm and an OXY plane in the established coordinate system; the model is shown in FIG. 2;
s4, calculating control angle information of each joint of the four-degree-of-freedom mechanical arm; the method specifically comprises the following steps:
A. the first inclination angle theta is calculated by the following formula 1
Figure BDA0003156624580000053
Where (x, y, z) is the coordinates of the target position P; first inclination angle theta 1 Is defined as: the included angle between the first section of mechanical arm and the X axis;
B. the coordinates w of the position P (w, z) of the target position P in the OWZ plane coordinate system are calculated using the following equation:
Figure BDA0003156624580000061
where (x, y, z) is the coordinates of the target position P;
C. calculating a first intermediate variable m, a second intermediate variable n and a third intermediate variable t by the following formula 1 And a fourth intermediate variable t 2 ：
Figure BDA0003156624580000062
Figure BDA0003156624580000063
Figure BDA0003156624580000064
Figure BDA0003156624580000065
In the formula a 4 The length of a section of the mechanical arm at the farthest end of the four-degree-of-freedom mechanical arm; d 1 The length of the section of the mechanical arm at the most proximal end of the four-degree-of-freedom mechanical arm; a is 3 The length of a section of the mechanical arm at the second last far end of the four-degree-of-freedom mechanical arm; a is 2 The length of a section of the mechanical arm at the third last far end of the four-degree-of-freedom mechanical arm;
D. c, judging the first to fourth intermediate variables obtained in the step C as follows:
if m 2 +n 2 -(t 1 ) 2 Not less than 0 and m 2 +n 2 -(t 2 ) 2 If the value is more than or equal to 0, performing subsequent step calculation;
otherwise, judging that the four-degree-of-freedom mechanical arm cannot reach the target position P, and ending the algorithm;
E. the fifth intermediate variable Q and the sixth intermediate variable P are used as follows:
Figure BDA0003156624580000066
and Q ∈ [ -1,1]
Figure BDA0003156624580000067
And P ∈ [ -1, 1)]
F. The second inclination angle theta is calculated by adopting the following formula 2 A third inclination angle theta 3 And a fourth inclination angle theta 4 ：
Figure BDA0003156624580000068
Figure BDA0003156624580000071
Figure BDA0003156624580000072
Figure BDA0003156624580000073
In which the second inclination angle theta 2 Is the included angle between the second section of mechanical arm and the X axis; third inclination angle theta 3 The included angle between the third section of mechanical arm and the X axis is formed; fourth angle of inclination theta 4 The included angle between the fourth section of mechanical arm and the X axis is formed;
G. several sets of solutions (theta) obtained for the above steps 1 ,θ 2 ,θ 3 ,θ 4 ) Selecting or rejecting according to the actual condition of the four-degree-of-freedom mechanical arm so as to obtain the final control angle information of each joint of the four-degree-of-freedom mechanical arm;
in specific implementation, the solution is rejected according to the actual reachable angle range of each joint of the mechanical arm, and the final result may have no solution, one group of solutions or a plurality of groups of solutions;
and S5, controlling the four-degree-of-freedom mechanical arm to act according to the angle information obtained in the step S4.
The process of the invention is further illustrated below with reference to one example:
aiming at a four-degree-of-freedom mechanical arm, a Cartesian rectangular coordinate system OXYZ is established on the horizontal ground where the mechanical arm is located, the horizontal ground is an OXY plane, and a Z axis is perpendicular to the OXY plane and is collinear with a steering engine rotating shaft at a joint 1. And then sequentially establishing a coordinate system at the four joints according to requirements. The arm link model is shown in fig. 3, and the D-H parameter list is shown in table 1.
TABLE 1 four-DOF mechanical arm D-H parameter schematic table
Number of coordinate system a i-1 (mm) α i-1 (°) θ i (°) d i (mm)
1 0 0 θ 1 96
2 0 90 θ 2 0
3 104 0 θ 3 0
4 88 0 θ 4 0
5 108 0
The transformation matrix of each adjacent coordinate system can be obtained according to the D-H parameter list as follows:
Figure BDA0003156624580000081
Figure BDA0003156624580000082
Figure BDA0003156624580000083
Figure BDA0003156624580000084
Figure BDA0003156624580000085
then, multiplying the four matrixes in sequence to obtain the positive motion equation of the mechanical arm as follows:
Figure BDA0003156624580000091
because the four-degree-of-freedom mechanical arm inverse kinematics solution matrix is very complicated, and the algorithm cannot be succinctly written into codes to be embedded into a mechanical arm upper computer control program, the complicated matrix algorithm is abandoned, and the algorithm for directly solving the inverse kinematics problem by the geometric constraint relation of the mechanical arm connecting rod model is provided starting from the definition of inverse kinematics control. The model labeled with the arm parameters is shown in fig. 2.
The four-degree-of-freedom mechanical arm inverse kinematics calculation is converted into the following geometrical problems: knowing the P point position at the end of the mechanical arm as P (x, y, z) and the elevation angle as P (x, y, z)
Figure BDA0003156624580000092
(link 4 Angle with the OXY plane) to solve for θ 1 ～θ 4 。
Firstly, using a formula
Figure BDA0003156624580000093
Calculated to obtain theta 1 ；
Then, due to link 2 、link 3 And link 4 The motion process is always in the same plane, and the rotation angle value of the joint is irrelevant to the selection of a coordinate system, so that the mechanical arm connecting rod model can be projected to a two-dimensional plane for solving. Establishing a W-axis and an X-axis in an XY plane as theta 1 The plane OWZ is link 2 、link 3 And link 4 The plane of motion is located at position P (w, z) in OWZ plane coordinate system at the end point P of the mechanical arm, link 4 Included angle with W axis is equal to
Figure BDA0003156624580000094
Wherein
Figure BDA0003156624580000095
Problem(s)Further simplification is as follows: the position P of the tail end P of the mechanical arm is known to be P (w, z) in the plane, and the elevation angle is known to be P
Figure BDA0003156624580000096
Solving for theta 2 ～θ 4 ；
From the geometric constraint relationship, the following system of equations can be derived:
Figure BDA0003156624580000097
the solution to this system of equations is expressed as:
Figure BDA0003156624580000101
wherein
Figure BDA0003156624580000102
θ 2 ～θ 4 And the actual angle constraint condition is met.
Thus, in summary, a method flowchart of the method of the invention is obtained as shown in fig. 1.
The process of the invention is described below with reference to one example:
the connecting rod of the four-degree-of-freedom mechanical arm is shown in fig. 3, and the D-H parameter of the mechanical arm is shown in table 1;
according to the D-H parameters in the table 1, a mechanical arm connecting rod model is established, the initial state is shown in figure 4, and theta 1 Limited to [ -90 DEG, 90 DEG ]]By change of between, theta 2 ～θ 4 Is limited to-170 deg. and 170 deg. respectively]To change between.
And verifying the inverse kinematics calculation result by using a simulation experiment. Assuming the expected pose of the end of the arm is: the end coordinates are (236,0,186) and the end effector elevation is 0. The result of the inverse kinematics using the embedded robot arm control program is (theta) 1 ,θ 2 ,θ 3 ,θ 4 )＝(0°,66.93 °, -70.91 °,3.98 °). Substituting the data into a model built by MATLAB to perform forward kinematics calculation, wherein the pose of the mechanical arm is shown in figure 5 at this time, and the forward kinematics equation of the mechanical arm can be solved as follows:
Figure BDA0003156624580000111
the end coordinates are therefore (236.5,0,185.6). This proves that the inverse kinematics solution method provided by the invention is accurate and effective.

Claims (2)

1. A control method of a four-degree-of-freedom mechanical arm comprises the following steps:
s1, acquiring working parameters of a four-degree-of-freedom mechanical arm;
s2, establishing a coordinate system according to the position of the four-degree-of-freedom mechanical arm; specifically, a Cartesian rectangular coordinate system OXYZ is established on a plane where a four-degree-of-freedom mechanical arm is installed, wherein the plane where the four-degree-of-freedom mechanical arm is installed is an OXY plane, and a Z axis is perpendicular to the OXY plane and is collinear with a steering engine rotating shaft of a first joint of the four-degree-of-freedom mechanical arm, which is closest to the OXY plane; then sequentially establishing a Cartesian rectangular coordinate system at four joints of the four-degree-of-freedom mechanical arm;
s3, acquiring target position information as position information of the tail end of the mechanical arm, and acquiring corresponding elevation angle information; specifically, target position information P (x, y, z) is obtained as position information of the tail end of the mechanical arm, and a corresponding elevation angle is obtained at the same time
Figure FDA0003682196420000011
Elevation angle
Figure FDA0003682196420000012
Defining an included angle between a section of the mechanical arm at the farthest end of the four-degree-of-freedom mechanical arm and an OXY plane in the established coordinate system;
s4, calculating control angle information of each joint of the four-degree-of-freedom mechanical arm; the method specifically comprises the following steps:
A. using the following calculationFormula (I) calculates a first inclination angle theta 1
Figure FDA0003682196420000013
Where (x, y, z) is the coordinates of the target position P; first inclination angle theta 1 Is the included angle between the first section of mechanical arm and the X axis;
B. the coordinates w of the position P (w, z) of the target position P in the OWZ plane coordinate system are calculated using the following equation:
Figure FDA0003682196420000014
where (x, y, z) is the coordinates of the target position P;
C. calculating a first intermediate variable m, a second intermediate variable n and a third intermediate variable t by the following formula 1 And a fourth intermediate variable t 2 ：
Figure FDA0003682196420000021
Figure FDA0003682196420000022
Figure FDA0003682196420000023
Figure FDA0003682196420000024
In the formula a 4 The length of a section of the mechanical arm at the farthest end of the four-degree-of-freedom mechanical arm; d 1 The length of the section of the mechanical arm at the most proximal end of the four-degree-of-freedom mechanical arm; a is 3 Is one of the penultimate far ends of the four-degree-of-freedom mechanical armThe length of the segment mechanical arm; a is a 2 The length of a section of the mechanical arm at the third last far end of the four-degree-of-freedom mechanical arm;
D. c, judging the first to fourth intermediate variables obtained in the step C as follows:
if m 2 +n 2 -(t 1 ) 2 Not less than 0 and m 2 +n 2 -(t 2 ) 2 If the value is more than or equal to 0, performing subsequent step calculation;
otherwise, judging that the four-degree-of-freedom mechanical arm cannot reach the target position P, and ending the algorithm;
E. the fifth intermediate variable Q and the sixth intermediate variable P are used as follows:
Figure FDA0003682196420000025
and Q ∈ [ -1,1]
Figure FDA0003682196420000026
And P ∈ [ -1, 1)]
F. The second inclination angle theta is calculated by adopting the following formula 2 A third inclination angle theta 3 And a fourth inclination angle theta 4 ：
Figure FDA0003682196420000027
Figure FDA0003682196420000028
Figure FDA0003682196420000029
Figure FDA00036821964200000210
In which the second inclination angle theta 2 Is the included angle between the second section of mechanical arm and the X axis; third inclination angle theta 3 The included angle between the third section of mechanical arm and the X axis is formed; fourth angle of inclination theta 4 The included angle between the fourth section of mechanical arm and the X axis is formed;
G. several sets of solutions (theta) obtained for the above steps 1 ,θ 2 ,θ 3 ,θ 4 ) Selecting or rejecting according to the actual condition of the four-degree-of-freedom mechanical arm so as to obtain the final control angle information of each joint of the four-degree-of-freedom mechanical arm;
and S5, controlling the four-degree-of-freedom mechanical arm to act according to the angle information obtained in the step S4.
2. A substation fire-fighting mechanical arm control method comprising the four-degree-of-freedom mechanical arm control method according to claim 1 is characterized by comprising the following steps:
(1) a four-degree-of-freedom mechanical arm is adopted as a fire-fighting mechanical arm of the transformer substation;
(2) the four-degree-of-freedom mechanical arm control method of claim 1 is adopted to control the substation fire-fighting mechanical arm.
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CN108000477A (en) * 2017-12-05 2018-05-08 哈尔滨工业大学 A kind of complete main passive compliance robot of pose and screw valve method using the robot
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CN111993414A (en) * 2020-07-28 2020-11-27 北京轩宇智能科技有限公司 Mechanical arm multi-joint linkage control method

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