CN114952838A - Mechanical arm joint trajectory planning method based on tail end measurement feedback - Google Patents

Mechanical arm joint trajectory planning method based on tail end measurement feedback Download PDF

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CN114952838A
CN114952838A CN202210582484.XA CN202210582484A CN114952838A CN 114952838 A CN114952838 A CN 114952838A CN 202210582484 A CN202210582484 A CN 202210582484A CN 114952838 A CN114952838 A CN 114952838A
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mechanical arm
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CN114952838B (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
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    • 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
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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 structured environment and the teaching dragging mode needs artificial assistance, and the known discrete points are not needed in the method, 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; according to the method, the joint track of the mechanical arm is planned on line independently, manual dragging demonstration is not needed, the manual workload is reduced, and the efficiency and the autonomy are improved; the method and the device have the advantages that the acceleration of the track is continuous, the smoothness of the track is improved, and the operation burden of an actuator is reduced.

Description

Mechanical arm joint trajectory planning method based on tail end measurement feedback
Technical Field
The invention relates to the technical field of mechanical arm trajectory planning, in particular to a mechanical arm joint trajectory planning method based on tail end measurement feedback.
Background
The requirements of the working environment, the operation object and the operation task of the mechanical arm are increasingly complex, and challenges are provided for the trajectory planning technology of the mechanical arm. The current planning modes based on off-line point interpolation and dragging teaching are obviously insufficient: the offline point interpolation planning method is only applicable to a structured environment, such as: through strict calibration, all the geometric information and the precision information of the operation objects are known in the automobile production line, the food packaging production line and the like; and the mode based on dragging teaching needs manual assistance, which increases the manual workload.
Disclosure of Invention
The purpose of the invention is: aiming at the problems that the existing planning method is only suitable for a structured environment and the teaching dragging mode needs manual assistance, the mechanical arm joint trajectory planning method based on the tail end measurement feedback is provided.
The technical scheme adopted by the invention to solve the technical problems is as follows:
a mechanical arm joint track planning method based on tail end measurement feedback comprises the following steps:
the method comprises the following steps: acquiring position data d and attitude data of a target coordinate system relative to a mechanical arm tail end coordinate system
Figure BDA0003664573630000011
And using 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: obtaining a mechanical arm joint angle vector q l And according to the angle vector q of the mechanical arm joint l Obtaining a pose matrix of the mechanical arm tail end coordinate system relative to the mechanical arm base coordinate system b T e ；
Step three: according to the position and posture matrix of the target coordinate system relative to the tail end coordinate system of the mechanical arm 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 Based on the pose matrix of the target coordinate system relative to the robot arm base coordinate system b T t And obtaining a joint desired position vector q by using inverse kinematics d ；
Step four: based on the joint desired position vector q d Planning to obtain a reference track of the mechanical arm joint;
step five: and 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 attitude data of the target coordinate system relative to the coordinate system of the tail end of the mechanical arm
Figure BDA0003664573630000013
Obtained by a measuring sensor arranged at the tail end of the mechanical arm.
Further, the position and posture matrix of the target coordinate system relative to the 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 terminal coordinate system of the mechanical arm,
Figure BDA0003664573630000021
representing the pose vector of the target coordinate system relative to the robot arm end coordinate system, and wz2mtrx () representing a function that transforms the pose vector into a pose matrix.
Further, the angle vector q of the mechanical arm joint l Measured by a joint position sensor.
Further, the position and posture matrix of the mechanical arm end coordinate system relative to the mechanical arm base coordinate system b T e Expressed as:
b T e ＝forwardkinematics(q l )
wherein q is l Representing the arm joint angle vector, forward kinematics () representing the positive kinematic function of a robot armAnd (4) counting. Further, the joint desired position vector q d Expressed as:
q d ＝inversekinematics( b T t )
b T t ＝ b T e e T t
wherein invertsekinematics () represents the inverse kinematics function of the robot arm, b T t representing a pose matrix of the target coordinate system relative to the robot arm base coordinate system, e T t representing a pose matrix of the target coordinate system relative to the robot arm tip coordinate system,
b T e and representing a pose matrix of the robot arm end coordinate system relative to the robot arm base coordinate system.
Further, the robot joint reference trajectory includes: joint reference jerk vector
Figure BDA0003664573630000022
Joint reference acceleration vector
Figure BDA0003664573630000023
Joint reference velocity vector
Figure BDA0003664573630000024
And a joint reference position vector q r 。
Further, the fourth step specifically comprises:
step four, firstly: setting planning parameters k, xi and omega n The planning parameters k, ξ and ω n Are all positive definite diagonal matrices;
step four and step two: according to the set planning parameters k, xi and omega n Obtaining a position loop feedback gain K p Velocity loop feedback gain K v And acceleration loop gain K a ：
Step four and step three: feedback gain K according to position loop p Velocity loop feedback gain K v Acceleration loop gain K a And a joint desired position vector q d Planning the joint parametersAcceleration vector of test
Figure BDA0003664573630000025
Step four: jerk vector based on joint reference
Figure BDA0003664573630000026
Obtaining a joint reference acceleration vector
Figure BDA0003664573630000027
Joint reference velocity vector
Figure BDA0003664573630000028
And a joint reference position vector q r 。
Further, the position loop feedback gain K p Velocity loop feedback gain K v And 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 a joint reference position vector q r Expressed as:
Figure BDA0003664573630000034
where ^ dt represents an integral.
The beneficial effects of the invention are:
1. the method and the device do not need known discrete points, and plan the joint track of the mechanical arm directly according to the expected position, so that the method and the device are not limited to the known structural environment of geometric information;
2. according to the method, the joint track of the mechanical arm is planned on line independently, manual dragging demonstration is not needed, the manual workload is reduced, and the efficiency and the autonomy are improved;
3. the method and the device have the advantages that the acceleration of the track is continuous, the smoothness of the track is improved, and the operation burden of an actuator is reduced.
Drawings
FIG. 1 is a schematic view of a robot 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 view of a robot arm servo stationary target process 1;
FIG. 5 is a schematic view of a robot arm servo stationary target process 2;
FIG. 6 is a schematic illustration of a robot arm servo stationary target process 3;
FIG. 7 is a reference position vector graph for a joint;
FIG. 8 is a joint reference velocity vector graph;
FIG. 9 is a reference acceleration vector plot for a joint;
FIG. 10 is a graph of joint reference jerk vector;
FIG. 11 is a schematic diagram of the relative positions of the end coordinate system and the target coordinate system of the robot arm;
FIG. 12 is a schematic diagram of the relative poses of the robot arm end coordinate system and the target coordinate system;
FIG. 13 is a schematic view of a robot arm servo moving object process 1;
FIG. 14 is a schematic view of a robot arm servo moving target process 2;
FIG. 15 is a schematic diagram of a robot arm servo moving target process 3;
FIG. 16 is a reference position vector graph for a joint;
FIG. 17 is a joint reference velocity vector graph;
FIG. 18 is a reference acceleration vector plot for a joint;
FIG. 19 is a joint reference jerk vector graph;
FIG. 20 is a schematic diagram of the relative positions of the robot arm tip coordinate system and the target coordinate system;
fig. 21 is a schematic diagram of the relative attitude of the robot arm end coordinate system and the target coordinate system.
Detailed Description
It should be noted that, in the present invention, the embodiments disclosed in the present application may be combined with each other without conflict.
The first embodiment is as follows: referring to fig. 1, the present embodiment is specifically described, and a method for planning a joint trajectory of a mechanical arm based on end measurement feedback in the present embodiment includes the specific steps of:
the trajectory planning starts, and the following calculation is performed in each period:
step one, calculating a pose matrix of a target coordinate system relative to a mechanical arm tail end coordinate system e T t ；
The method comprises the following steps: a measuring sensor arranged at the tail end of the mechanical arm obtains position data d and attitude data of a target coordinate system relative to a coordinate system at the tail end of the mechanical arm
Figure BDA0003664573630000041
Wherein d is a 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 terminal coordinate system;
the first step is: by d and
Figure BDA0003664573630000043
computing e T t ，
Figure BDA0003664573630000044
Wherein wz2mtrx () is a function of the pose vector transformed into the pose matrix;
step two, according to the angle vector q of the mechanical arm joint l Obtaining a pose matrix of the mechanical arm tail end coordinate system relative to the mechanical arm base coordinate system b T e ；
b T e ＝forwardkinematics(q l )
Wherein q is l Measured by a joint position sensor, forward kinematics () is a positive kinematic function of the mechanical arm;
step three, obtaining the product according to the step one and the step two e T t And b T e and further calculating the attitude matrix of the target coordinate system relative to the robot arm base coordinate system b T t And solving the expected position vector q of the joint by adopting an inverse kinematics function of the mechanical arm d ；
Step three, one, consists of e T t And b T e to obtain b T t ：
b T t ＝ b T e e T t
Step three or two, adopting the inverse kinematics function of the mechanical arm b T t To obtain q d ：
q d ＝inversekinematics( b T t )
Where invertsekinematics () is the inverse kinematics function of the arm.
Step four, obtaining the expected joint position vector q according to the step three d Planning to obtain the reference acceleration vector of the mechanical arm joint
Figure BDA0003664573630000045
Joint reference acceleration vector
Figure BDA0003664573630000046
Joint reference velocity vector
Figure BDA0003664573630000047
And a joint reference position vector q r ；
Step four, firstly: artificially setting planning parameters k, xi and omega n The three parameters are positive definite diagonal matrixes;
step four and step two: obtaining the feedback gain K of the position loop according to the parameters set in the step four p Velocity loop feedback gain K v Sum acceleration loop gain K a ：
K p ＝kω n 2
K v ＝ω n 2 +2kξω n
K a ＝k+2ξω n
Step four and step three: according to K obtained in the fourth step or the second step p 、K v And K a And step three, obtaining a joint expected position vector and a mechanical arm joint angle vector, and planning a joint reference acceleration vector:
Figure BDA0003664573630000051
step four: obtaining corresponding joint reference acceleration vector according to the joint reference acceleration vector obtained in the fourth step and the third step
Figure BDA0003664573630000052
Joint reference velocity vector
Figure BDA0003664573630000053
And a joint reference position vector q r ：
Figure BDA0003664573630000054
Step five: and the mechanical arm joint controller tracks the joint reference track and drives the mechanical arm to move.
This application has been solved among the prior art the mode that drags the teaching and need artificially be supplementary, problem of 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, if: the tail end is provided with a depth camera, an infrared camera, a laser radar and the like, and the relative position and posture between the operation target and the tail end of the mechanical arm can be obtained. The method provides a hardware basis for the autonomous planning of the robot, but how to rapidly plan the motion of the mechanical arm based on the sensing information and ensure the track acceleration and even the acceleration continuity is still a key difficulty. Aiming at the difficulty, 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 structural environment of geometric information; in addition, the acceleration of the track is continuous, the smoothness of the track is improved, and the operation burden of an actuator is reduced.
Example 1:
to verify the validity of the present application, the following uses computer simulation, and the technical solution of the present application is further described with reference to fig. 1 to 12.
A computer simulation platform is built, mechanical arms used in simulation have 6 rotational degrees of freedom, and a target is static. Joint reference position vector q r Has an initial value of [ -7.61,76.2, -133.95, -30.27, -97.35,0.0 [ -7.61,76.2 [ -133.95 [ ]]deg, starting the servo planning when the initial values of the joint reference velocity vector and the joint reference acceleration vector are all 0, and performing the following operations in each planning period as shown in fig. 2:
[ step S1]The relative pose data d of the coordinate system of the tail end of the mechanical arm and the coordinate system of the target are obtained by the measurement of 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 a target coordinate system relative to a machinePose matrix of mechanical arm tail end coordinate system e T t ；
[ step S3]Calculating a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system b T e
[ step S4]According to e T t And b T e calculating out b T t ：
[ step S5]Using inverse kinematics of the arm b T t To obtain q d
[ step S6]Setting planning parameters k, xi and omega n The following are:
k＝2.4I 6×6 ,ξ＝1.2I 6×6 ,ω n ＝0.8U 6×6
wherein, I 6×6 Is a 6 x 6 identity matrix.
[ step S7]Calculating position loop feedback gain K p Velocity loop feedback gain K v Sum 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 a joint reference jerk vector: the flow chart of the mechanical arm joint jerk planning method is shown in fig. 3.
Figure BDA0003664573630000061
Step S9 obtains a joint reference acceleration vector, a joint reference velocity vector, and a joint reference position vector:
Figure BDA0003664573630000062
step S10 the robot joint controller tracks the joint reference position vector and drives the robot arm to move.
[ step S ]11]According to the relative pose data d and d of the tail end coordinate system and the target coordinate system of the mechanical arm
Figure BDA0003664573630000063
Judging whether the mechanical arm is in place for servo, if so, completing the servo, and exiting; if not, the process returns to step S1]. The process of the robot arm servo-resting the target is shown in figure 4. The joint reference trajectory of the robot arm servo the stationary target is shown in fig. 5. The process diagram of the robot arm servo moving the target is shown in fig. 12. The joint reference trajectories of the robot arm servo moving object are shown in fig. 13-16.
The joint reference position vector graph, the joint reference velocity vector graph, the joint reference acceleration vector graph, and the joint reference jerk vector graph are shown in fig. 6-9.
FIGS. 10 and 11 are relative poses of the end coordinate system and the target coordinate system when the robot arm is servoed on a stationary target;
the relative positions of the end coordinate system and the object coordinate system when the robot arm servos the moving object are shown in fig. 20 and 21.
Example 2:
in case 2, the object moves. Joint reference position vector q r Has an initial value of [ -7.61,76.2, -133.95, -30.27, -97.35,0.0 [ -7.61,76.2 [ -133.95 [ ]]deg, joint reference velocity vector, and joint reference acceleration vector are all 0. Starting servo planning, and performing the following operations in each planning period:
[ step S1]Position data d and attitude data of the target coordinate system relative to the coordinate system of the tail end of the mechanical arm are obtained by measuring with an external sensor arranged at the tail end of the mechanical arm
Figure BDA0003664573630000064
[ step S2]Calculating a pose matrix of the target coordinate system relative to the tail end coordinate system of the mechanical arm e T t ；
[ step S3]Calculating a pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system b T e
[ step S4]According to e T t And b T e computing b T t ：
[ step S5]Using inverse kinematics of the arm b T t To obtain q d
[ step S6]Setting planning parameters k, xi and omega n The following are:
k＝18I 6×6 ,ξ＝1.2I 6×6 ,ω n ＝6U 6×6
wherein, I 6×6 Is a 6 x 6 identity matrix.
[ step S7]Calculating position loop feedback gain K p Velocity loop feedback gain K v Sum 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 a joint reference jerk vector:
Figure BDA0003664573630000071
step S9 obtains a joint reference acceleration vector, a joint reference velocity vector, and a joint reference position vector:
Figure BDA0003664573630000072
step S10 the robot joint controller tracks the joint reference position vector and drives the robot arm to move.
[ step S11]According to the relative pose data d and d of the tail end coordinate system and the target coordinate system of the mechanical arm
Figure BDA0003664573630000073
Judging whether the mechanical arm is in place for servo, if so, completing the servo, and exiting; if not, the process returns to step S1]。
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.

Claims (10)

1. A mechanical arm joint track planning method based on tail end measurement feedback is characterized by comprising the following steps:
the method comprises the following steps: acquiring position data d and attitude data of a target coordinate system relative to a mechanical arm tail end coordinate system
Figure FDA0003664573620000014
And using d and
Figure FDA0003664573620000015
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: obtaining a mechanical arm joint angle vector q l And according to the angle vector q of the mechanical arm joint l Obtaining a pose matrix of the mechanical arm tail end coordinate system relative to the mechanical arm base coordinate system b T e ；
Step three: according to the position and posture matrix of the target coordinate system relative to the tail end coordinate system of the mechanical arm 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 Based on the pose matrix of the target coordinate system relative to the robot arm base coordinate system b T t And obtaining a joint desired position vector q by using inverse kinematics d ；
Step four: based on the joint desired position vector q d Planning to obtain a reference track of the mechanical arm joint;
step five: and the mechanical arm joint controller tracks the mechanical arm joint reference track and drives the mechanical arm to move.
2. The method for planning the joint trajectory of the mechanical arm based on the end measurement feedback as claimed in claim 1, wherein the position data d and the attitude data of the target coordinate system relative to the end coordinate system of the mechanical arm
Figure FDA0003664573620000011
Obtained by a measuring sensor arranged at the tail end of the mechanical arm.
3. The method for planning the joint trajectory of the mechanical arm based on the end measurement feedback as claimed in claim 1, wherein the pose matrix of the target coordinate system relative to the end coordinate system of the mechanical arm e T t Expressed as:
Figure FDA0003664573620000012
wherein d represents a position vector of the origin of the target coordinate system under the terminal coordinate system of the mechanical arm,
Figure FDA0003664573620000013
representing the pose vector of the target coordinate system relative to the robot arm end coordinate system, and wz2mtrx () representing a function that transforms the pose vector into a pose matrix.
4. The mechanical arm joint trajectory planning method based on end measurement feedback as claimed in claim 1, wherein the mechanical arm joint angle vector q is l Measured by a joint position sensor.
5. The method for planning the joint trajectory of the mechanical arm based on the tail end measurement feedback as claimed in claim 1, wherein the pose matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm is defined as b T e Expressed as:
b T e ＝forwardkinematics(q l )
wherein q is l Representing the arm joint angle vector, forward kinematics () represents the positive kinematics function of the arm.
6. The mechanical arm joint trajectory planning method based on end measurement feedback as claimed in claim 1, wherein the joint desired position vector q is d Expressed as:
q d ＝inversekinematics( b T t )
b T t ＝ b T e e T t
wherein invertsekinematics () represents the inverse kinematics function of the robot arm, b T t representing a pose matrix of the target coordinate system relative to the robot arm base coordinate system, e T t representing a pose matrix of the target coordinate system relative to the robot arm tip coordinate system, b T e and the position matrix of the tail end coordinate system of the mechanical arm relative to the base coordinate system of the mechanical arm is shown.
7. The method for planning the robot joint trajectory based on the end measurement feedback according to claim 1, wherein the robot joint reference trajectory comprises: joint reference jerk vector
Figure FDA0003664573620000021
Joint reference acceleration vector
Figure FDA0003664573620000022
Joint reference velocity vector
Figure FDA0003664573620000023
And a joint reference position vector q r 。
8. The mechanical arm joint trajectory planning method based on the end measurement feedback as claimed in claim 7, wherein the specific steps of the fourth step are as follows:
step four, firstly: setting planning parameters k, xi and omega n The planning parameters k, ξ and ω n Are all positive definite diagonal matrices;
step four and step two: according to the set planning parameters k, xi and omega n Obtaining a position loop feedback gain K p Velocity loop feedback gain K v And acceleration loop gain K a ：
Step four and step three: feedback gain K according to position loop p Velocity loop feedback gain K v Acceleration loop gain K a And a joint desired position vector q d Planning joint reference jerk vector
Figure FDA0003664573620000024
Step four: jerk vector based on joint reference
Figure FDA0003664573620000025
Obtaining a joint reference acceleration vector
Figure FDA0003664573620000026
Joint reference velocity vector
Figure FDA0003664573620000027
And a joint reference position vector q r 。
9. The method for planning the joint trajectory of the mechanical arm based on the tail end measurement feedback as claimed in claim 8, wherein the position loop feedback gain K p Velocity loop feedback gain K v And acceleration loop gain K a Expressed as:
K p ＝kω n 2
K v ＝ω n 2 +2kξω n
K a ＝k+2ξω n 。
10. the mechanical arm joint trajectory planning method based on end measurement feedback as claimed in claim 9, wherein the joint is referenced to a jerk vector
Figure FDA0003664573620000028
Expressed as:
Figure FDA0003664573620000029
the joint reference acceleration vector
Figure FDA00036645736200000210
Joint reference velocity vector
Figure FDA00036645736200000211
And a joint reference position vector q r Expressed as:
Figure FDA00036645736200000212
where ^ dt represents an integral.
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