CN110561433B - Method for improving mechanical arm motion planning control precision - Google Patents

Method for improving mechanical arm motion planning control precision Download PDF

Info

Publication number
CN110561433B
CN110561433B CN201910819330.6A CN201910819330A CN110561433B CN 110561433 B CN110561433 B CN 110561433B CN 201910819330 A CN201910819330 A CN 201910819330A CN 110561433 B CN110561433 B CN 110561433B
Authority
CN
China
Prior art keywords
mechanical arm
control
arm
expressed
motion planning
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910819330.6A
Other languages
Chinese (zh)
Other versions
CN110561433A (en
Inventor
张雨浓
凌一宏
黄焕昌
施妮妮
毛明志
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Sun Yat Sen University
Original Assignee
Sun Yat Sen University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sun Yat Sen University filed Critical Sun Yat Sen University
Priority to CN201910819330.6A priority Critical patent/CN110561433B/en
Publication of CN110561433A publication Critical patent/CN110561433A/en
Application granted granted Critical
Publication of CN110561433B publication Critical patent/CN110561433B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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

Abstract

The invention discloses a method for improving the control precision of mechanical arm motion planning, which comprises the following steps: obtaining a mathematical model of the mechanical arm according to a mechanical mechanism of the mechanical arm; obtaining a control model of the mechanical arm through a kinetic theory analysis according to the mathematical model of the mechanical arm; solving by using an Euler formula and an extrapolation method according to a control model of the mechanical arm; and controlling the motion of the mechanical arm according to the solving result. The invention adopts a dynamic method, and successfully realizes the tracking control of the actual tail end track of the mechanical arm to the ideal track on the speed layer under the ideal condition. Meanwhile, by introducing an extrapolation method, a control model under the condition that a control signal is possibly lost is realized, and the motion planning control precision of the mechanical arm is improved, so that the problem that the tracking performance of the tail end of the mechanical arm is reduced is solved.

Description

Method for improving mechanical arm motion planning control precision
Technical Field
The invention relates to the field of mechanical arm control, in particular to a method for improving the motion planning control precision of a mechanical arm.
Background
As a research field with vigorous development, robots have been widely used in industries such as industry and service industry, for example, a guniting robot, a welding robot, a vehicle-mounted mechanical arm, and a customer service robot, a rehabilitation assistance robot, etc. in the industry. Many robot control problems can be classified as mechanical arm motion planning control problems, and the key for solving the problems is to obtain an effective mechanical arm motion planning control model so that the rotation joint angle of the mechanical arm can meet the requirement of tracking the tail end track by an ideal track under certain constraint conditions. Robot arm control systems are generally divided into off-line control systems and on-line control systems. For the mechanical arm off-line control system, a mature technology is researched. However, the mechanical arm online control system has wider application scenes and more important research value. The mechanical arm on-line control system depends on a reliable communication module between a computer and a mechanical arm, but in a complex environment, a phenomenon that a data link is interfered generally exists, and a situation that a control signal is lost occurs occasionally.
Past research has mostly involved on-line planning control of robotic arm movements in ideal environments. In practical application, the control signal of the data link is lost under electromagnetic or other physical interference, and the control signal loss can cause problems of control failure, tracking performance reduction and the like.
Disclosure of Invention
In order to overcome the defects of the prior art and the method, the invention provides a method for improving the motion planning control precision of a mechanical arm. The invention adopts a dynamic method, and successfully realizes the tracking control of the actual tail end track of the mechanical arm on the ideal track on the speed layer under the ideal condition. Meanwhile, by introducing an extrapolation method, a control model under the condition that a control signal is possibly lost is realized, so that the problem that the tracking performance of the tail end of the mechanical arm is reduced is solved.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a method for improving the planning control precision of mechanical arm movement comprises the following steps:
obtaining a mathematical model of the mechanical arm according to a mechanical mechanism of the mechanical arm;
obtaining a control model of the mechanical arm through a kinetic theory analysis according to the mathematical model of the mechanical arm;
solving by using an Euler formula and an extrapolation method according to a control model of the mechanical arm;
and controlling the motion of the mechanical arm according to the solving result.
In the invention, the problems that in practical application, control signals are possibly lost in link transmission between a controller and a mechanical arm, so that the tracking error is increased, the tracking performance of a control model is reduced and the like are solved. Therefore, an extrapolation method is introduced, and high-precision motion planning control of the mechanical arm is realized under the condition that a control signal is possibly lost.
In a preferred embodiment, the mathematical model of the mechanical arm is expressed by the following formula:
Figure BDA0002187102480000021
Figure BDA0002187102480000022
wherein k represents the k-th time, f (-) is a nonlinear mapping function, and θkIs the angle of the joint angle of the robot arm at the k-th moment
Figure BDA0002187102480000023
For the actual end trajectory of the arm at time k, said
Figure BDA0002187102480000024
The ideal tail end track of the mechanical arm at the k-th moment
Figure BDA0002187102480000025
Is the time derivative of the angle of the joint angle of the robot arm at the k-th moment
Figure BDA0002187102480000026
The time derivative of the tip trajectory of the robot arm at the actual time k, J (-) is a jacobian matrix.
In a preferred embodiment, the control model of the robot arm is expressed by the following formula:
Figure BDA0002187102480000027
g (-) is a kinetic mapping function, the
Figure BDA0002187102480000028
The angular velocity of the joint angle of the mechanical arm at the k-1 th moment;
if the signal transmission is successful, then thetakBy usingThe euler formula is expressed by the following formula:
Figure BDA0002187102480000029
h is a control interval; theta iskFor controlling the movement of the joints of the robotic arm;
if the signal transmission fails, then θkExpressed by the following formula using the extrapolation formula:
θk＝2θk-1-θk-2。
in a preferred embodiment, h is 0.03 s.
In a preferred embodiment, the method is based on the analysis of the theory of tensor dynamics
Figure BDA00021871024800000210
Expressed by the following formula:
Figure BDA00021871024800000211
the J is+(θk-1) Is a Jacobian matrix J (theta)k-1) The pseudo inverse matrix of (2), the
Figure BDA00021871024800000212
And the time derivative of the tail end track of the mechanical arm at the ideal k-1 moment is shown as lambda is a tension dynamic design parameter and lambda is more than 0.
In a preferred embodiment, λ 33 is used.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention adopts a dynamic method, and successfully realizes the tracking control of the actual tail end track of the mechanical arm on the ideal track on the speed layer under the ideal condition. Meanwhile, by introducing an extrapolation method, a control model under the condition that a control signal is possibly lost is realized, and the motion planning control precision of the mechanical arm is improved, so that the problem that the tracking performance of the tail end of the mechanical arm is reduced is solved.
Drawings
FIG. 1 is a flowchart of example 2;
FIG. 2 is a schematic diagram of a six-bar robot arm model in an embodiment;
FIG. 3 is a schematic view showing the movement of the robot arm according to embodiment 1;
FIG. 4 is a schematic view of end tracking in example 1;
FIG. 5 is a schematic diagram of error e of example 1;
FIG. 6 is a schematic view showing the movement of the robot arm according to embodiment 2;
FIG. 7 is a schematic view of end tracking in example 2;
fig. 8 is a schematic diagram of an error e in embodiment 2.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1 is an existing open-loop dynamic model of the strategy in the case of possible loss of control signals, and example 2 is an open-loop dynamic model of the extrapolation strategy of this patent in the case of possible loss of control signals.
As shown in fig. 2, embodiments 1 and 2 are based on a six-link robot arm model.
Example 1
A method for planning and controlling the motion of a mechanical arm comprises the following steps:
obtaining a mathematical model of the mechanical arm according to a mechanical mechanism of the mechanical arm, wherein the mathematical model is expressed by the following formula:
Figure BDA0002187102480000031
Figure BDA0002187102480000032
k denotes the kth time, f (-) is a nonlinear mapping function, θkIs the angle of the joint angle of the robot arm at the k-th time,
Figure BDA0002187102480000041
the actual end trajectory of the robot arm at time k,
Figure BDA0002187102480000042
the ideal end trajectory of the robot arm at time k,
Figure BDA0002187102480000043
is the time derivative of the angle of the joint angle of the robot arm at the k-th moment,
Figure BDA0002187102480000044
j (-) is a jacobian matrix, which is the time derivative of the end trajectory of the manipulator at the actual kth time;
according to the mathematical model of arm, through the theoretical analysis of dynamics, obtain the control model of arm, the control model expresses through the following formula:
Figure BDA0002187102480000045
g (-) is a kinetic mapping function,
Figure BDA0002187102480000046
is the angular velocity of the joint angle of the robot arm at the k-1 th time, and if the signal transmission is successful, theta iskExpressed by the following formula using the euler formula:
Figure BDA0002187102480000047
h is a control interval; theta.theta.kFor controlling the movement of the joints of the robotic arm;
if the signal transmission fails, then θkExpressed by the following formula using the extrapolation formula:
θk＝θk-1；
based on the analysis of the theory of the tensor dynamics,
Figure BDA0002187102480000048
expressed by the following formula:
Figure BDA0002187102480000049
the J is+(θk-1) Is a Jacobian matrix J (theta)k-1) The pseudo inverse matrix of, the
Figure BDA00021871024800000410
And the time derivative of the tail end track of the mechanical arm at the ideal k-1 moment is shown as lambda is a tension dynamic design parameter and lambda is more than 0.
And controlling the motion of the mechanical arm according to the solving result.
Example 2
As shown in fig. 1, a method for improving the control accuracy of the mechanical arm motion planning includes the following steps:
obtaining a mathematical model of the mechanical arm according to a mechanical mechanism of the mechanical arm, wherein the mathematical model is expressed by the following formula:
Figure BDA00021871024800000411
Figure BDA00021871024800000412
k denotes the k-th time, f (-) is a non-linear mapping function, θkIs the angle of the joint angle of the robot arm at the k-th time,
Figure BDA00021871024800000413
the actual end trajectory of the robot arm at time k,
Figure BDA00021871024800000414
the ideal end trajectory of the robot arm at time k,
Figure BDA00021871024800000415
is the time derivative of the angle of the joint angle of the robot arm at the k-th moment,
Figure BDA00021871024800000416
j (-) is a jacobian matrix, which is the time derivative of the end trajectory of the manipulator at the actual kth time;
according to the mathematical model of arm, through the theoretical analysis of dynamics, obtain the control model of arm, the control model expresses through the following formula:
Figure BDA00021871024800000417
g (-) is a kinetic mapping function,
Figure BDA0002187102480000051
the angular velocity of the joint angle of the mechanical arm at the k-1 st moment;
solving by using an Euler formula and an extrapolation method according to a control model of the mechanical arm;
if the signal transmission is successful, then thetakExpressed by the following formula using the euler formula:
Figure BDA0002187102480000052
h is a control interval; theta.theta.kFor controlling the movement of the joints of the robotic arm;
if the signal transmission fails, then θkExpressed by the following formula using the extrapolation formula:
θk＝2θk-1-θk-2；
based on the analysis of the theory of the tensor dynamics,
Figure BDA0002187102480000053
expressed by the following formula:
Figure BDA0002187102480000054
the J is+(θk-1) Is a Jacobian matrix J (theta)k-1) The pseudo inverse matrix of (2), the
Figure BDA0002187102480000055
And the time derivative of the tail end track of the mechanical arm at the ideal k-1 moment is shown as lambda is a tension dynamic design parameter and lambda is more than 0.
And controlling the motion of the mechanical arm according to the solving result.
When computer simulations are performed on examples 1 and 2, the relevant parameters are as follows: the control interval h is 0.03s, the single arm length of the mechanical arm is 1m, the tensile dynamic design parameter lambda is 33, and the initial angle theta is0Pi/6, -pi/4, pi/6, pi/3, pi/6 rad, the ideal trajectory at the end is a circle with radius r of 0.5m, the control signal loss probability is set to p of 0.1, and the execution time is set to 8 seconds.
The experimental data and analysis are as follows:
example 1
Fig. 3, fig. 4, and fig. 5 correspond to a schematic diagram of the motion of the mechanical arm, a schematic diagram of the tip tracking, and a schematic diagram of the tracking error e | in the trajectory tracking control process according to embodiment 1, respectively. From these simulation diagrams, the actual tip trajectory r of the robot armaIn a manner of large error (about 10)-2～10-1) Tracking an ideal tip trajectory rdThe trace tracking control effect of the conventional strategy-free tensor dynamics model is poor under the condition that the control signal is possibly lost.
Example 2
FIG. 6, FIG. 7 and FIG. 8 are respectively shown as corresponding to the embodimentsThe schematic diagram of the mechanical arm movement, the schematic diagram of the end tracking, and the schematic diagram of the tracking error e | in the trajectory tracking control process in embodiment 2. From these simulation diagrams, the actual tip trajectory r of the robot armaThe ideal tip trajectory r can be tracked with less errordComparing fig. 5 and 8, it can be seen that the error e of embodiment 2 is reduced to 10-3～10-2(i.e., an order of magnitude improvement in accuracy), the actual tip trajectory is more accurate for tracking the ideal tip trajectory. It is demonstrated that in the case of possible loss of control signals, embodiment 2 indeed effectively improves the accuracy of the robot arm motion planning tracking control.
The terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For example, the embodiments h-0.03 s, l-1 m, λ -33, p-0.1 and r-0.5 m are merely examples, and other parameter values still fall within the protection scope of the present patent, and are not limited to the examples in the embodiments. In the following, the embodiments are illustrated by a six-bar robot arm for comparison, and the present invention is also applicable to other robot arm types, and not only the connection manner of the embodiments is taken as a limitation of the present invention.
Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And thus are not exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (5)

1. A method for improving the planning control precision of mechanical arm motion is characterized by comprising the following steps:
obtaining a mathematical model of the mechanical arm according to a mechanical mechanism of the mechanical arm;
obtaining a control model of the mechanical arm through a kinetic theory analysis according to the mathematical model of the mechanical arm;
the control model of the mechanical arm is expressed by the following formula:
Figure FDA0003570213500000011
g (-) is a kinetic mapping function, the
Figure FDA0003570213500000012
The angular velocity of the joint angle of the mechanical arm at the k-1 th moment;
if the signal transmission is successful, then thetakExpressed by the following formula using the euler formula:
Figure FDA0003570213500000013
h is a control interval; theta is a value ofkFor controlling the movement of the joints of the robotic arm;
if the signal transmission fails, then θkExpressed by the following formula using the extrapolation formula:
θk＝2θk-1-θk-2；
solving by using an Euler formula and an extrapolation method according to a control model of the mechanical arm;
and controlling the motion of the mechanical arm according to the solving result.
2. The method for improving the control accuracy of mechanical arm motion planning as claimed in claim 1, wherein the mathematical model of the mechanical arm is expressed by the following formula:
Figure FDA0003570213500000014
Figure FDA0003570213500000015
wherein k represents the k-th time, f (-) is a nonlinear mapping function, and thetakIs the angle of the joint angle of the robot arm at the k-th moment
Figure FDA0003570213500000016
The actual k-th time of the tail end track of the mechanical arm
Figure FDA0003570213500000017
The ideal tail end track of the mechanical arm at the k-th moment
Figure FDA0003570213500000018
Is the time derivative of the angle of the joint angle of the robot arm at the k-th moment,
Figure FDA0003570213500000019
j (-) is a jacobian matrix, which is the time derivative of the tip trajectory of the robotic arm at the actual k-th time instant.
3. The method for improving the control accuracy of the motion planning of the mechanical arm according to claim 2, wherein h is 0.03 s.
4. The method for improving the control accuracy of the mechanical arm motion planning as claimed in claim 2 or 3, wherein the method is based on the analysis of the theory of tensor dynamics
Figure FDA00035702135000000110
Expressed by the following formula:
Figure FDA0003570213500000021
the J is+(θk-1) Is a Jacobian matrix J (theta)k-1) The pseudo inverse matrix of, the
Figure FDA0003570213500000022
The time derivative of the tail end track of the mechanical arm at the ideal k-1 time is shown, wherein lambda is a tensile dynamic design parameter and is larger than 0.
5. The method for improving control accuracy of robotic arm motion planning as claimed in claim 4, wherein λ -33.
CN201910819330.6A 2019-08-31 2019-08-31 Method for improving mechanical arm motion planning control precision Active CN110561433B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910819330.6A CN110561433B (en) 2019-08-31 2019-08-31 Method for improving mechanical arm motion planning control precision

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910819330.6A CN110561433B (en) 2019-08-31 2019-08-31 Method for improving mechanical arm motion planning control precision

Publications (2)

Publication Number Publication Date
CN110561433A CN110561433A (en) 2019-12-13
CN110561433B true CN110561433B (en) 2022-07-19

Family

ID=68777217

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910819330.6A Active CN110561433B (en) 2019-08-31 2019-08-31 Method for improving mechanical arm motion planning control precision

Country Status (1)

Country Link
CN (1) CN110561433B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114738338B (en) * 2022-04-27 2023-02-10 浙江大学 Sliding mode control method for underwater multi-degree-of-freedom hydraulic mechanical arm

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19810341A1 (en) * 1998-03-10 1999-09-16 Deutsch Zentr Luft & Raumfahrt Method of automatic collision prevention for manipulator in working area bounded by obstructions
CN103331756A (en) * 2013-06-04 2013-10-02 浙江工业大学 Mechanical arm motion control method
CN106054599A (en) * 2016-05-25 2016-10-26 哈尔滨工程大学 Master-slave underwater robotic arm delay control method
CN106945020A (en) * 2017-05-18 2017-07-14 哈尔滨工业大学 A kind of space double mechanical arms system motion control method for coordinating
CN107102617A (en) * 2017-06-26 2017-08-29 北京艾利特科技有限公司 A kind of high-precision spatial elliptic curve Real-time Interpolation
CN107145640A (en) * 2017-04-12 2017-09-08 西北工业大学 The Dynamic Scaling planing method of pedestal and mechanical arm is floated in Neutral buoyancy test
CN108297093A (en) * 2017-12-29 2018-07-20 中国海洋大学 A kind of step identification method of Manipulator Dynamics parameter
CN109927032A (en) * 2019-03-28 2019-06-25 东南大学 A kind of mechanical arm Trajectory Tracking Control method based on High-Order Sliding Mode observer

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19810341A1 (en) * 1998-03-10 1999-09-16 Deutsch Zentr Luft & Raumfahrt Method of automatic collision prevention for manipulator in working area bounded by obstructions
CN103331756A (en) * 2013-06-04 2013-10-02 浙江工业大学 Mechanical arm motion control method
CN106054599A (en) * 2016-05-25 2016-10-26 哈尔滨工程大学 Master-slave underwater robotic arm delay control method
CN107145640A (en) * 2017-04-12 2017-09-08 西北工业大学 The Dynamic Scaling planing method of pedestal and mechanical arm is floated in Neutral buoyancy test
CN106945020A (en) * 2017-05-18 2017-07-14 哈尔滨工业大学 A kind of space double mechanical arms system motion control method for coordinating
CN107102617A (en) * 2017-06-26 2017-08-29 北京艾利特科技有限公司 A kind of high-precision spatial elliptic curve Real-time Interpolation
CN108297093A (en) * 2017-12-29 2018-07-20 中国海洋大学 A kind of step identification method of Manipulator Dynamics parameter
CN109927032A (en) * 2019-03-28 2019-06-25 东南大学 A kind of mechanical arm Trajectory Tracking Control method based on High-Order Sliding Mode observer

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于作业任务的UVMS协调控制方法的研究;罗姗姗;《中国优秀博硕士学位论文全文数据库(硕士)》;20190115(第1期);全文 *

Also Published As

Publication number Publication date
CN110561433A (en) 2019-12-13

Similar Documents

Publication Publication Date Title
CN109159151B (en) Mechanical arm space trajectory tracking dynamic compensation method and system
CN110103225B (en) Data-driven method and device for controlling repeated motion of mechanical arm
WO2021135405A1 (en) Mechanical arm-oriented non-kinematic model trajectory tracking method and mechanical arm system
CN107966907B (en) Obstacle avoidance solution applied to redundant manipulator
CN107351088B (en) Robot external motion path control method
CN113146600B (en) Flexible robot trajectory planning method and device based on kinematics iterative learning control
Zou et al. Learning-based optimization algorithms combining force control strategies for peg-in-hole assembly
CN110561433B (en) Method for improving mechanical arm motion planning control precision
CN114942593A (en) Mechanical arm self-adaptive sliding mode control method based on disturbance observer compensation
CN116494250B (en) Mechanical arm control method, controller, medium and system based on speed compensation
CN113263496A (en) Method for optimizing path of six-degree-of-freedom mechanical arm and computer equipment
CN110026986B (en) Multi-arm cooperative operation compliance control method
CN110434854B (en) Redundant manipulator visual servo control method and device based on data driving
Zhu et al. Automatic Control System Design for Industrial Robots Based on Simulated Annealing and PID Algorithms
CN114378830B (en) Robot wrist joint singular avoidance method and system
CN115157262A (en) Obstacle avoidance and optimization control method and system for joint-limited redundant mechanical arm and robot
CN114851184B (en) Reinforced learning rewarding value calculating method for industrial robot
Li et al. Fault-tolerant motion planning of redundant manipulator with initial position error
CN109531573B (en) Robot posture smooth path generation method based on sample lines
Jiang et al. Autonomous behavior intelligence control of self-evolution mobile robot for high-voltage transmission line in complex smart grid
Yan et al. Integrated Drill Boom Hole-Seeking Control via Reinforcement Learning
CN117075525B (en) Mobile robot control method based on constraint model predictive control
Zhou et al. An Enhanced Positional Error Compensation Method for Rock Drilling Robots Based on LightGBM and RBFN
CN114375431A (en) Trajectory simplification method and device for industrial robot, computer storage medium and industrial robot operating platform
CN117055361B (en) Mobile robot control method based on sliding mode model predictive control

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant