CN114952838B - Mechanical arm joint track planning method based on terminal measurement feedback - Google Patents

Mechanical arm joint track planning method based on terminal measurement feedback Download PDF

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CN114952838B
CN114952838B CN202210582484.XA CN202210582484A CN114952838B CN 114952838 B CN114952838 B CN 114952838B CN 202210582484 A CN202210582484 A CN 202210582484A CN 114952838 B CN114952838 B CN 114952838B
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CN114952838A (en
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杨国财
马正航
纪军红
龙沁
李志奇
史士财
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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
    • B25J9/1656—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
    • 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
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    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
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Abstract

A mechanical arm joint track planning method based on terminal measurement feedback relates to the technical field of mechanical arm track planning, and aims at the problems that the existing planning method is only suitable for a structural environment and a dragging teaching mode needs artificial assistance, the method does not need known discrete points, and the joint track of the mechanical arm is directly planned according to an expected position, so that the method is not limited to the known structural environment of geometric information; according to the method, the joint track of the mechanical arm is planned on line autonomously, manual dragging teaching is not needed, the manual workload is reduced, and the efficiency and autonomy are improved; the method and the device realize continuous jerk of the track, improve the smoothness of the track and reduce the running load of the actuator.

Description

Mechanical arm joint track planning method based on terminal measurement feedback
Technical Field
The invention relates to the technical field of mechanical arm track planning, in particular to a mechanical arm joint track planning method based on terminal measurement feedback.
Background
The requirements of the working environment, the operation objects and the operation tasks of the mechanical arm are increasingly complex, and challenges are presented to the track planning technology of the mechanical arm. The current planning modes based on offline point interpolation and dragging teaching have obvious defects: the offline point interpolation planning method is only applicable to the structured environment, such as: through strict calibration, geometric information of all operation objects, and known precision information are used in automobile production lines, food packaging production lines and the like; and the mode based on dragging teaching needs human assistance, so that the manual workload is increased.
Disclosure of Invention
The purpose of the invention is that: aiming at the problems that the existing planning method is only suitable for a structured environment and the dragging teaching mode needs human assistance, the mechanical arm joint track planning method based on terminal measurement feedback is provided.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a mechanical arm joint track planning method based on end measurement feedback comprises the following steps:
step one: acquiring target coordinate system relative to mechanical armPosition data d and attitude data of an end coordinate system
Figure BDA0003664573630000011
And utilize d and->
Figure BDA0003664573630000012
Obtaining a pose matrix of the target coordinate system relative to the tail end coordinate system of the mechanical arm e T t ；
Step two: acquiring a joint angle vector q of a mechanical arm l And according to the angle vector q of the mechanical arm joint l Obtaining a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm b T e ；
Step three: pose matrix relative to tail end coordinate system of mechanical arm according to target coordinate system e T t And a pose matrix of the robot arm end coordinate system relative to the robot arm base coordinate system b T e Obtaining a pose matrix of the target coordinate system relative to the mechanical arm base coordinate system b T t Pose matrix based on target coordinate system relative to mechanical arm base coordinate system b T t And obtaining a joint expected position vector q by adopting inverse kinematics d ；
Step four: based on the expected position vector q of the joint d Planning to obtain a mechanical arm joint reference track;
step five: the mechanical arm joint controller tracks the mechanical arm joint reference track and drives the mechanical arm to move.
Further, the position data d and the posture data of the target coordinate system relative to the tail end coordinate system of the mechanical arm
Figure BDA0003664573630000013
Obtained by a measuring sensor arranged at the tail end of the mechanical arm.
Further, the pose matrix of the target coordinate system relative to the tail end coordinate system of the mechanical arm e T t Expressed as:
Figure BDA00036645736300000210
wherein d represents a position vector of the origin of the target coordinate system under the tail end coordinate system of the mechanical arm,
Figure BDA0003664573630000021
representing the pose vector of the target coordinate system relative to the end of the arm coordinate system, wz2mtrx () represents the function of the pose vector conversion to the pose matrix.
Further, the mechanical arm joint angle vector q l Measured by a joint position sensor.
Further, the pose matrix of the mechanical arm tail end coordinate system relative to the mechanical arm base coordinate system b T e Expressed as:
b T e ＝forwardkinematics(q l )
wherein q l Representing the arm joint angle vector, forwardkinemics () represents the positive kinematic function of the arm. Further, the joint expected position vector q d Expressed as:
q d ＝inversekinematics( b T t )
b T t ＝ b T e e T t
wherein, invertekinematics () represents the inverse kinematics function of the mechanical arm, b T t representing a pose matrix of the target coordinate system relative to a base coordinate system of the mechanical arm, e T t representing a pose matrix of the target coordinate system relative to the end coordinate system of the mechanical arm,
b T e and representing a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm.
Further, the mechanical arm joint reference track includes: joint reference jerk vector
Figure BDA0003664573630000022
Joint reference acceleration vector->
Figure BDA0003664573630000023
Joint reference velocity vector +.>
Figure BDA0003664573630000024
And joint reference position vector q r 。
Further, the specific steps of the fourth step are as follows:
step four, first: setting programming parameters k, ζ and ω n The planning parameters k, ζ and ω n Are positive diagonal matrixes;
step four, two: according to the set planning parameters k, ζ and ω n Obtaining the feedback gain K of the position loop p Feedback gain K of speed loop v Acceleration loop gain K a ：
And step four, three: feedback gain K according to position loop p Feedback gain K of speed loop v Acceleration loop gain K a Joint expected position vector q d Planning joint reference jerk vectors
Figure BDA0003664573630000025
And step four: based on joint reference jerk vectors
Figure BDA0003664573630000026
Obtaining a joint reference acceleration vector->
Figure BDA0003664573630000027
Joint reference velocity vector +.>
Figure BDA0003664573630000028
Joint reference position vector q r 。
Further, the position loop feeds back the gain K p Feedback gain K of speed loop v Acceleration loop gain K a Expressed as:
K p ＝kω n 2
K v ＝ω n 2 +2kξω n
K a ＝k+2ξω n 。
further, the joint reference jerk vector
Figure BDA0003664573630000029
Expressed as:
Figure BDA0003664573630000031
the joint reference acceleration vector
Figure BDA0003664573630000032
Joint reference velocity vector +.>
Figure BDA0003664573630000033
And joint reference position vector q r Expressed as:
Figure BDA0003664573630000034
where ≡represents the integral.
The beneficial effects of the invention are as follows:
1. the method does not need known discrete points, and the joint track of the mechanical arm is directly planned according to the expected position, so that the method is not limited to the known structured environment of geometric information;
2. according to the method, the joint track of the mechanical arm is planned on line autonomously, manual dragging teaching is not needed, the manual workload is reduced, and the efficiency and autonomy are improved;
3. the method and the device realize continuous jerk of the track, improve the smoothness of the track and reduce the running load of the actuator.
Drawings
FIG. 1 is a schematic diagram of a robotic arm joint coordinate system;
FIG. 2 is a schematic diagram of the present application;
FIG. 3 is a flow chart of the present application;
FIG. 4 is a schematic diagram 1 of a process of a robot arm servo stationary target;
FIG. 5 is a schematic diagram of a process of a robot arm servo stationary target 2;
FIG. 6 is a schematic diagram 3 of a process of a robotic arm servoing a stationary target;
FIG. 7 is a graph of joint reference position vectors;
FIG. 8 is a graph of joint reference velocity vectors;
FIG. 9 is a graph of joint reference acceleration vectors;
FIG. 10 is a graph of joint reference jerk vector;
FIG. 11 is a schematic diagram of the relative positions of the robot arm end coordinate system and the target coordinate system;
FIG. 12 is a schematic diagram of relative poses of a robot arm end coordinate system and a target coordinate system;
FIG. 13 is a schematic diagram 1 of a process of a robot arm servo moving target;
FIG. 14 is a schematic diagram of a process of a robotic arm servo motion target 2;
FIG. 15 is a schematic diagram of a process of a robotic arm servo motion target 3;
FIG. 16 is a graph of joint reference position vectors;
FIG. 17 is a graph of joint reference velocity vectors;
FIG. 18 is a graph of joint reference acceleration vectors;
FIG. 19 is a graph of joint reference jerk vector;
FIG. 20 is a schematic diagram of the relative positions of the robot arm end coordinate system and the target coordinate system;
FIG. 21 is a schematic diagram of relative poses of a robot arm end coordinate system and a target coordinate system.
Detailed Description
It should be noted in particular that, without conflict, the various embodiments disclosed herein may be combined with each other.
The first embodiment is as follows: referring to fig. 1, a specific description is given of a method for planning a joint track of a mechanical arm based on end measurement feedback according to the present embodiment, which specifically includes the following steps:
track planning begins, and the following calculation is performed in each period:
step one, calculating a pose matrix of a target coordinate system relative to a tail end coordinate system of the mechanical arm e T t ；
The method comprises the following steps: the measuring sensor installed at the tail end of the mechanical arm obtains position data d and attitude data of a target coordinate system relative to the tail end coordinate system of the mechanical arm
Figure BDA0003664573630000041
Wherein d is the position vector of the origin of the target coordinate system in the terminal coordinate system, +.>
Figure BDA0003664573630000042
Is the pose vector of the target coordinate system relative to the end coordinate system;
step two: from d and
Figure BDA0003664573630000043
calculation of e T t ，
Figure BDA0003664573630000044
Wherein wz2mtrx () is a function of the pose vector converted to a pose matrix;
step two, according to the joint angle vector q of the mechanical arm l Obtaining a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm b T e ；
b T e ＝forwardkinematics(q l )
Wherein q l Measured by joint position sensors, forwardkinemics () is a positive kinematic function of the robotic arm;
step three, according to the step one and the step two e T t And b T e further calculate the gesture matrix of the target coordinate system relative to the base coordinate system of the mechanical arm b T t Solving the expected position vector q of the joint by adopting the inverse kinematics function of the mechanical arm d ；
Step III, by e T t And b T e obtaining b T t ：
b T t ＝ b T e e T t
Step three, adopting a mechanical arm inverse kinematics function to obtain the final product b T t Obtaining q d ：
q d ＝inversekinematics( b T t )
Where invertekinethematics () is the inverse kinematics function of the robotic arm.
Step four, according to the joint expected position vector q obtained in the step three d Planning to obtain a reference jerk vector of the mechanical arm joint
Figure BDA0003664573630000045
Joint reference acceleration vector->
Figure BDA0003664573630000046
Joint reference velocity vector +.>
Figure BDA0003664573630000047
And joint reference position vector q r ；
Step four, first: setting programming parameters k, ζ and ω by human n The three parameters are positive diagonal matrixes;
step four, two: obtaining a position loop feedback gain K according to the parameters set in the fourth step p Speed loop feedback gain K v And acceleration loop gain K a ：
K p ＝kω n 2
K v ＝ω n 2 +2kξω n
K a ＝k+2ξω n
And step four, three: according to K obtained in step IV p 、K v And K a Step three, obtaining a joint expected position vector and a mechanical arm joint angle vector, and planning a joint reference jerk vector:
Figure BDA0003664573630000051
and step four: obtaining a corresponding joint reference acceleration vector from the joint reference jerk vector obtained in the fourth step
Figure BDA0003664573630000052
Joint reference velocity vector +.>
Figure BDA0003664573630000053
And joint reference position vector q r ：
Figure BDA0003664573630000054
Step five: the mechanical arm joint controller tracks the joint reference track and drives the mechanical arm to move.
The mode of dragging teaching among the prior art has been solved to this application needs the manual work to assist, problem that inefficiency, in addition, along with the development of sensing measurement technique, the arm is equipped with abundant sensor, has improved the ability of perception external environment information by a wide margin, like: the tail end is provided with a depth camera, an infrared camera, a laser radar and the like, so that the relative position and the gesture between the operation target and the tail end of the mechanical arm can be obtained. This provides a hardware basis for autonomous planning of robots, but how to rapidly plan the motion of the robotic arm based on these sensory information and ensure track acceleration, even jerk continuity, remains a key difficulty. The method aims at the difficulty, and the joint track of the mechanical arm is planned directly according to the expected position, so that the method is not limited to the known structural environment of the geometric information; and the method realizes continuous jerk of the track, improves the smoothness of the track and reduces the running load of the actuator.
Example 1:
to verify the effectiveness of the present application, the following uses computer simulation to further describe the technical solution of the present application with reference to fig. 1 to 12.
And (3) building a computer simulation platform, wherein a mechanical arm used in the simulation has 6 rotational degrees of freedom, and the target is stationary. Joint reference position vector q r The initial value is [ -7.61,76.2, -133.95, -30.27, -97.35,0.0]The initial values of the reference velocity vector and the reference acceleration vector of the joint are 0, the servo programming is started, the specific implementation steps are shown in fig. 2, and the following operation is performed in each programming period:
step S1]The relative pose data d and the relative pose data of the coordinate system of the tail end of the mechanical arm and the target coordinate system are measured by an external sensor arranged at the tail end of the mechanical arm
Figure BDA0003664573630000055
The main coordinate system related to the mechanical arm joint jerk planning method is shown in fig. 1.
Step S2]Calculating pose matrix of target coordinate system relative to tail end coordinate system of mechanical arm e T t ；
Step S3]Calculating pose matrix of mechanical arm tail end coordinate system relative to base coordinate system b T e
Step S4]According to e T t And b T e calculation of b T t ：
Step S5]By using mechanical arm inverse kinematics function b T t Obtaining q d
Step S6]Setting programming parameters k, ζ and ω n The following are provided:
k＝2.4I 6×6 ,ξ＝1.2I 6×6 ,ω n ＝0.8U 6×6
wherein I is 6×6 Is a 6 x 6 identity matrix.
Step S7]Calculating the position loop feedback gain K p Speed loop feedback gain K v And acceleration loop gain K a ：
K p ＝kω n 2 ＝1.536I 6×6 ,K v ＝ω n 2 +2kξω n ＝5.248I 6×6 ,
K a ＝k+2ξω n ＝4.32I 6×6
Step S8, planning joint reference jerk vector: the flow chart of the mechanical arm joint jerk planning method is shown in fig. 3.
Figure BDA0003664573630000061
Step S9, obtaining a joint reference acceleration vector, a joint reference velocity vector and a joint reference position vector:
Figure BDA0003664573630000062
step S10, the joint controller of the mechanical arm tracks the joint reference position vector and drives the mechanical arm to move.
Step S11]According to the relative pose data d and the relative pose data of the tail end coordinate system of the mechanical arm and the target coordinate system
Figure BDA0003664573630000063
Judging whether the mechanical arm is in place, if so, finishing the servo and exiting; if not, return to step S1]. The process of the robotic arm servoing the stationary object is shown in fig. 4. The joint reference trajectory of the robot arm servo stationary target is shown in fig. 5. A process diagram of the robotic arm servoing the moving object is shown in fig. 12. The joint reference track of the servo moving object of the mechanical arm is shown in fig. 13-16.
The joint reference position vector graph, joint reference velocity vector graph, joint reference acceleration vector graph, and joint reference jerk vector graph are shown in fig. 6-9.
FIGS. 10 and 11 are relative positions of the end coordinate system and the target coordinate system when the robot arm is servoing the stationary target;
the relative pose of the end coordinate system and the target coordinate system when the robot arm servos the moving target is shown in fig. 20 and 21.
Example 2:
in case 2, the target moves. Joint reference position vector q r The initial value is [ -7.61,76.2, -133.95, -30.27, -97.35,0.0]deg, joint reference velocity vector, initial value of joint reference acceleration vector is 0. Starting servo programming, and performing the following operation in each programming period:
step S1]The position data d and the attitude data of the target coordinate system relative to the tail end coordinate system of the mechanical arm are measured by an external sensor arranged at the tail end of the mechanical arm
Figure BDA0003664573630000064
Step S2]Calculating pose matrix of target coordinate system relative to tail end coordinate system of mechanical arm e T t ；
Step S3]Calculating pose matrix of mechanical arm tail end coordinate system relative to base coordinate system b T e
Step S4]According to e T t And b T e calculation of b T t ：
Step S5]By using mechanical arm inverse kinematics function b T t Obtaining q d
Step S6]Setting programming parameters k, ζ and ω n The following are provided:
k＝18I 6×6 ,ξ＝1.2I 6×6 ,ω n ＝6U 6×6
wherein I is 6×6 Is a 6 x 6 identity matrix.
Step S7]Calculating the position loop feedback gain K p Speed loop feedback gain K v And acceleration loop gain K a ：
K p ＝kω n 2 ＝648I 6×6 ,K v ＝ω n 2 +2kξω n ＝295.2I 6×6 ,
K a ＝k+2ξω n ＝32.4I 6×6
Step S8, planning joint reference jerk vector:
Figure BDA0003664573630000071
step S9, obtaining a joint reference acceleration vector, a joint reference velocity vector and a joint reference position vector:
Figure BDA0003664573630000072
step S10, the joint controller of the mechanical arm tracks the joint reference position vector and drives the mechanical arm to move.
Step S11]According to the relative pose data d and the relative pose data of the tail end coordinate system of the mechanical arm and the target coordinate system
Figure BDA0003664573630000073
Judging whether the mechanical arm is in place, if so, finishing the servo and exiting; if not, return to step S1]。
It should be noted that the detailed description is merely for explaining and describing the technical solution of the present invention, and the scope of protection of the claims should not be limited thereto. All changes which come within the meaning and range of equivalency of the claims and the specification are to be embraced within their scope.

Claims (7)

1. The mechanical arm joint track planning method based on the end measurement feedback is characterized by comprising the following steps of:
step one: acquiring position data d and attitude data of a target coordinate system relative to a tail end coordinate system of a mechanical arm
Figure FDA0004159608760000011
And utilize d and->
Figure FDA0004159608760000012
Obtaining a pose matrix of the target coordinate system relative to the tail end coordinate system of the mechanical arm e T t ；
Step two: acquiring a joint angle vector q of a mechanical arm l And according to the angle vector q of the mechanical arm joint l Obtaining a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm b T e ；
Step three: pose matrix relative to tail end coordinate system of mechanical arm according to target coordinate system e T t And a pose matrix of the robot arm end coordinate system relative to the robot arm base coordinate system b T e Obtaining a pose matrix of the target coordinate system relative to the mechanical arm base coordinate system b T t Pose matrix based on target coordinate system relative to mechanical arm base coordinate system b T t And obtaining a joint expected position vector q by adopting inverse kinematics d ；
Step four: based on the expected position vector q of the joint d Planning to obtain a mechanical arm joint reference track;
step five: the mechanical arm joint controller tracks the mechanical arm joint reference track and drives the mechanical arm to move;
the mechanical arm joint reference track comprises: joint reference jerk vector
Figure FDA0004159608760000013
Joint reference acceleration vector->
Figure FDA0004159608760000014
Joint reference velocity vector +.>
Figure FDA0004159608760000015
And joint reference position vector q r ；
The specific steps of the fourth step are as follows:
step four, first: setting programming parameters k, ζ and ω n The planning parameters k, ζ and ω n Are positive diagonal matrixes;
step four, two: according to the set planning parameters k, ζ and ω n Obtaining the feedback gain K of the position loop p Feedback gain K of speed loop v Acceleration loop gain K a ：
And step four, three: feedback gain K according to position loop p Feedback gain K of speed loop v Acceleration loop gain K a Joint expected position vector q d Planning joint reference jerk vectors
Figure FDA0004159608760000016
And step four: based on joint reference jerk vectors
Figure FDA0004159608760000017
Obtaining a joint reference acceleration vector->
Figure FDA0004159608760000018
Joint reference velocity vector +.>
Figure FDA0004159608760000019
Joint reference position vector q r ；
The joint reference jerk vector
Figure FDA00041596087600000110
Expressed as:
Figure FDA00041596087600000111
the joint reference acceleration vector
Figure FDA00041596087600000112
Joint reference velocity vector +.>
Figure FDA00041596087600000113
And joint reference position vector q r Expressed as:
Figure FDA00041596087600000114
where ≡represents the integral.
2. The method for planning a joint trajectory of a manipulator based on end measurement feedback of claim 1, wherein the target coordinate system is position data d and attitude data with respect to the manipulator end coordinate system
Figure FDA0004159608760000021
Obtained by a measuring sensor arranged at the tail end of the mechanical arm.
3. The method for planning a joint trajectory of a manipulator based on end measurement feedback of claim 1, wherein the target coordinate system is a pose matrix relative to the manipulator end coordinate system e T t Expressed as:
Figure FDA0004159608760000022
wherein d represents a position vector of the origin of the target coordinate system under the tail end coordinate system of the mechanical arm,
Figure FDA0004159608760000023
representing the pose vector of the target coordinate system relative to the end of the arm coordinate system, wz2mtrx () represents the function of the pose vector conversion to the pose matrix.
4. The method for planning a trajectory of a joint of a manipulator based on end measurement feedback according to claim 1, wherein the manipulator joint angle vector q l Measured by a joint position sensor.
5. The mechanical arm joint track gauge based on tail end measurement feedback of claim 1The scribing method is characterized in that the pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm b T e Expressed as:
b T e ＝forwardkinematics(q l ）
wherein q l Representing the arm joint angle vector, forwardkinemics () represents the positive kinematic function of the arm.
6. The method for planning a trajectory of a joint of a manipulator based on feedback of end measurement according to claim 1, wherein the desired position vector q of the joint is d Expressed as:
q d ＝inversekinematics( b T t )
b T t ＝ b T e e T t
wherein, invertekinematics () represents the inverse kinematics function of the mechanical arm, b T t representing a pose matrix of the target coordinate system relative to a base coordinate system of the mechanical arm, e T t representing a pose matrix of the target coordinate system relative to the end coordinate system of the mechanical arm, b T e and representing a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm.
7. The method for planning a joint trajectory of a manipulator based on end measurement feedback of claim 1, wherein the position loop feedback gain K p Feedback gain K of speed loop v Acceleration loop gain K a Expressed as:
K p ＝kω n 2
K v ＝ω n 2 +2kξω n
K a ＝k+2ξω n 。
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