CN110083059A - A kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode - Google Patents
A kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode Download PDFInfo
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Abstract
The invention discloses a kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, point stabilization process is divided into the following steps: (1) kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system；(2) nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, using multi tate input sample method by chained form system discretization, and one sensor is installed in nonholonomic mobile robot vehicle body, for constantly transmitting the position coordinates of nonholonomic mobile robot in the planes；(3) constantly collected position data is transferred in sliding mode control algorithm module sensor, so that nonholonomic mobile robot is finally calmed in finite time.A kind of pure geometric operation of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode of the invention, time discretization, control are stablized, lower to hardware device requirement, practical, are easy to be commercialized.
Description
Technical field
The present invention relates to nonholonomic mobile robot movement control technology fields, and in particular to a kind of Discrete-time Sliding Mode it is non-complete
Whole robot stabilized control method.
Background technique
All trades and professions are almost permeated in the application of nonholonomic mobile robot at present.Nonholonomic mobile robot have estimate one's own ability light, carrying is big,
It drives and controls the advantages that relatively convenient, the speed of travel are fast, work efficiency is high, to show one's talent from all kinds of robots.
Solving the problems, such as that finite time is calmed using nonholonomic mobile robot is a challenging task, is led in control
Domain causes more and more concerns.The calm complexity for having its own of finite time, the Stabilization of nonholonomic mobile robot are answered
With very extensive, such as the handover control of vehicle parking task, task.Substantially have for the control algolithm of nonholonomic mobile robot at present
Two kinds: (1) self adaptive control, (2) robust control；But the calculating of these algorithms is complicated, computationally intensive, wants to the real-time of system
Ask high, this will increase algorithm cost of implementation, be unfavorable for practical application.
Therefore, the above problem is not solved, needs to propose that a kind of calculation amount is small, real-time is good, at low cost, utilizes practical application
Nonholonomic mobile robot finite time point stabilization algorithm.
Summary of the invention
The purpose of the present invention is to solve the drawbacks described above in existing nonholonomic mobile robot control technology, provide it is a kind of from
The nonholonomic mobile robot stabilized control method of time sliding formwork is dissipated, the algorithm calculation amount is small, real-time is good, and cost of implementation is low, is convenient for
Practical application.
The invention is characterized in that following technical solution obtains:
A kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, including the following steps:
(1), the kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system；Nonholonomic mobile robot
Kinematics model obtained by formula (1):
In formula (1), [x, y]T∈R2Position coordinates of the nonholonomic mobile robot in plane XOY are represented, θ is before robot
Into directional velocity and X-axis forward direction angle, v indicates its advance space rate, and w indicates the angular speed of its rotation；
(2), nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, utilizes multi-speed
Rate input sample method installs a sensor by chained form system discretization, and in nonholonomic mobile robot vehicle body, for constantly passing
The position coordinates of defeated nonholonomic mobile robot in the planes；
Formula (1) is converted to chained form system, the chained form system after conversion is provided by formula (2):
In formula (2), x1=x, x2=tan θ, x3=y, u1=v1Cos θ, u2=v2sec2θ；
By formula (2) Taylor expansion of chained form system at iteration chained form system, provided by formula (3):
U in formula (3)1(t) and u2(t) it is to keep constant numerical value in τ seconds:
For formula (4) to u2(t) multi-speed sample is used, is provided by formula (5):
Above-mentioned k is constant, and the Double Data Rate sampling model in formula (5), which is substituted into chained form system (3), can be obtained finally
Multi-speed sample equivalent model:
(3), the multi-speed sample equivalent model discrete time sliding formwork control indicated for the formula (6) in step (2)
Device processed；Discrete-time Sliding Mode face is provided by formula (7):
S={ x ∈ R3:x1(k)=x2(k)=x3}, (k)=0 (7)
R represents real number in formula (7), and Discrete-time Sliding Mode controller is provided by formula (8):
K in formula (8)*K τ is represented, Discrete-time Sliding Mode controller ensure that state x1(k), x2(k) and x3(k) having
Zero is converged in limited time.
The present invention has the following advantages that relative to existing control technology and effect:
Nonholonomic mobile robot control algolithm proposed by the present invention is based on rectangular co-ordinate and is obtained using geometry direct derivation, parameter
Simply, physical meaning is clear；Calculating in nonholonomic mobile robot control algolithm is to calculate to complete before point stabilization starts, and is calmed
Process is not necessarily to manual intervention, and calculation amount is small, real-time is good, and cost of implementation is low, is convenient for practical application.
Detailed description of the invention
Fig. 1 is nonholonomic mobile robot movement schematic diagram.
Specific embodiment
As shown in Figure 1, a kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, including the following steps:
(1), the kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system；Nonholonomic mobile robot
Kinematics model obtained by formula (1):
In formula (1), [x, y]T∈R2Position coordinates of the nonholonomic mobile robot in plane XOY are represented, θ is before robot
Into directional velocity and X-axis forward direction angle, v indicates its advance space rate, and w indicates the angular speed of its rotation；
(2), nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, utilizes multi-speed
Rate input sample method installs a sensor by chained form system discretization, and in nonholonomic mobile robot vehicle body, for constantly passing
The position coordinates of defeated nonholonomic mobile robot in the planes；
Formula (1) is converted to chained form system, the chained form system after conversion is provided by formula (2):
In formula (2), x1=x, x2=tan θ, x3=y, u1=v1Cos θ, u2=v2sec2θ；
By formula (2) Taylor expansion of chained form system at iteration chained form system, provided by formula (3):
U in formula (3)1(t) and u2(t) it is to keep constant numerical value in τ seconds:
For formula (4) to u2(t) multi-speed sample is used, is provided by formula (5):
Above-mentioned k is constant, and the Double Data Rate sampling model in formula (5), which is substituted into chained form system (3), can be obtained finally
Multi-speed sample equivalent model:
(3), the multi-speed sample equivalent model discrete time sliding formwork control indicated for the formula (6) in step (2)
Device processed；Discrete-time Sliding Mode face is provided by formula (7):
S={ x ∈ R3:x1(k)=x2(k)=x3}, (k)=0 (7)
R represents real number in formula (7), and Discrete-time Sliding Mode controller is provided by formula (8):
K in formula (8)*K τ is represented, Discrete-time Sliding Mode controller ensure that state x1(k), x2(k) and x3(k) having
Zero is converged in limited time.Know that nonholonomic mobile robot can calm in finite time and keep in Fig. 1 according to chained form system
Bold line position and attitude.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (1)
1. a kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, it is characterised in that include the following steps:
(1), the kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system；The fortune of nonholonomic mobile robot
Dynamic model of learning is obtained by formula (1):
In formula (1), [x, y]T∈R2Position coordinates of the nonholonomic mobile robot in plane XOY are represented, θ is what robot advanced
The angle of directional velocity and X-axis forward direction, v indicate its advance space rate, and w indicates the angular speed of its rotation；
(2), nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, it is defeated using multi tate
Enter the method for sampling for chained form system discretization, and one sensor is installed in nonholonomic mobile robot vehicle body, it is non-for constantly transmitting
The position coordinates of complete machine people in the planes；
Formula (1) is converted to chained form system, the chained form system after conversion is provided by formula (2):
In formula (2), x1=x, x2=tan θ, x3=y, u1=v1Cos θ, u2=v2sec2θ；
By formula (2) Taylor expansion of chained form system at iteration chained form system, provided by formula (3):
U in formula (3)1(t) and u2(t) it is to keep constant numerical value in τ seconds:
For formula (4) to u2(t) multi-speed sample is used, is provided by formula (5):
Above-mentioned k is constant, the Double Data Rate sampling model in formula (5) is substituted into chained form system (3) can be obtained it is final more
Polydispersity index equivalent model:
(3), the multi-speed sample equivalent model discrete time sliding mode controller indicated for the formula (6) in step (2)；
Discrete-time Sliding Mode face is provided by formula (7):
S={ x ∈ R3:x1(k)=x2(k)=x3}, (k)=0 (7)
R represents real number in formula (7), and Discrete-time Sliding Mode controller is provided by formula (8):
K in formula (8)*K τ is represented, Discrete-time Sliding Mode controller ensure that state x1(k), x2(k) and x3(k) when limited
It is interior to converge to zero.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112769367A (en) * | 2021-01-07 | 2021-05-07 | 山东交通学院 | Permanent magnet linear motor data driving discrete iteration integral sliding mode control method and system |
Citations (18)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090012773A1 (en) * | 2004-11-17 | 2009-01-08 | The Mathworks, Inc. | Analysis of control systems |
| US20090143871A1 (en) * | 2002-04-18 | 2009-06-04 | Cleveland State University | Controllers, observers, and applications thereof |
| US20120078446A1 (en) * | 2010-09-28 | 2012-03-29 | The Boeing Company | Integrated Upsampler and Filtering for Multi-Rate Controller for Electro-Mechanical Flight Actuation System |
| CN102624000A (en) * | 2012-04-12 | 2012-08-01 | 河海大学 | Power system harmonic state estimation method based on automatic differentiation |
| CN103135117A (en) * | 2013-02-05 | 2013-06-05 | 中国人民解放军国防科学技术大学 | Distributed multi-robot synergetic location algorithm |
| CN103291543A (en) * | 2013-06-20 | 2013-09-11 | 上海电力学院 | Design method of fan variable pitch controller method based on sliding mode control theory |
| CN103311930A (en) * | 2013-06-19 | 2013-09-18 | 河海大学常州校区 | Sliding-mode control method for fuzzy PI parameter self-turning feedback linearization of active filter |
| CN103661398A (en) * | 2013-12-24 | 2014-03-26 | 东南大学 | Vehicle non-steering left rear wheel linear speed estimation method based on sliding-mode observer |
| CN104808653A (en) * | 2015-04-24 | 2015-07-29 | 南京理工大学 | Motor servo system additivity fault detection and fault tolerant control method based on slip form |
| CN105607636A (en) * | 2016-01-21 | 2016-05-25 | 浙江工业大学 | Wheel mobile robot master-slave type formation control method based on integration sliding mode algorithm |
| CN205384029U (en) * | 2016-02-04 | 2016-07-13 | 济南大学 | Adopt level and smooth tight integrated navigation system of INSUWB of CRTS between fixed area |
| US20170023438A1 (en) * | 2009-11-16 | 2017-01-26 | Nrg Systems, Inc. | Data Acquisition System for Condition-Based Maintenance |
| CN106444799A (en) * | 2016-07-15 | 2017-02-22 | 浙江工业大学 | Four-rotor unmanned aerial vehicle control method based on fuzzy extended state observer and self-adaptive sliding mode |
| CN106774373A (en) * | 2017-01-12 | 2017-05-31 | 哈尔滨工业大学 | A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods |
| CN108614426A (en) * | 2018-06-06 | 2018-10-02 | 黄山学院 | A kind of Multi Mobile Robots Formation's robust control method based on interference observer |
| CN108875253A (en) * | 2018-07-03 | 2018-11-23 | 曲阜师范大学 | The terminal sliding mode of drive lacking crane system based on interference observer, which disappears, puts control method and system |
| CN109062241A (en) * | 2018-09-29 | 2018-12-21 | 北京航空航天大学 | Autonomous full directive reentry guidance method based on linear pseudo- spectrum model PREDICTIVE CONTROL |
| US20190064791A1 (en) * | 2016-05-09 | 2019-02-28 | Strong Force Iot Portfolio 2016, Llc | Methods and systems for detection in an industrial internet of things data collection environment with intelligent management of data selection in high data volume data streams |
-
2019
- 2019-04-01 CN CN201910255762.9A patent/CN110083059B/en active Active
Patent Citations (18)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090143871A1 (en) * | 2002-04-18 | 2009-06-04 | Cleveland State University | Controllers, observers, and applications thereof |
| US20090012773A1 (en) * | 2004-11-17 | 2009-01-08 | The Mathworks, Inc. | Analysis of control systems |
| US20170023438A1 (en) * | 2009-11-16 | 2017-01-26 | Nrg Systems, Inc. | Data Acquisition System for Condition-Based Maintenance |
| US20120078446A1 (en) * | 2010-09-28 | 2012-03-29 | The Boeing Company | Integrated Upsampler and Filtering for Multi-Rate Controller for Electro-Mechanical Flight Actuation System |
| CN102624000A (en) * | 2012-04-12 | 2012-08-01 | 河海大学 | Power system harmonic state estimation method based on automatic differentiation |
| CN103135117A (en) * | 2013-02-05 | 2013-06-05 | 中国人民解放军国防科学技术大学 | Distributed multi-robot synergetic location algorithm |
| CN103311930A (en) * | 2013-06-19 | 2013-09-18 | 河海大学常州校区 | Sliding-mode control method for fuzzy PI parameter self-turning feedback linearization of active filter |
| CN103291543A (en) * | 2013-06-20 | 2013-09-11 | 上海电力学院 | Design method of fan variable pitch controller method based on sliding mode control theory |
| CN103661398A (en) * | 2013-12-24 | 2014-03-26 | 东南大学 | Vehicle non-steering left rear wheel linear speed estimation method based on sliding-mode observer |
| CN104808653A (en) * | 2015-04-24 | 2015-07-29 | 南京理工大学 | Motor servo system additivity fault detection and fault tolerant control method based on slip form |
| CN105607636A (en) * | 2016-01-21 | 2016-05-25 | 浙江工业大学 | Wheel mobile robot master-slave type formation control method based on integration sliding mode algorithm |
| CN205384029U (en) * | 2016-02-04 | 2016-07-13 | 济南大学 | Adopt level and smooth tight integrated navigation system of INSUWB of CRTS between fixed area |
| US20190064791A1 (en) * | 2016-05-09 | 2019-02-28 | Strong Force Iot Portfolio 2016, Llc | Methods and systems for detection in an industrial internet of things data collection environment with intelligent management of data selection in high data volume data streams |
| CN106444799A (en) * | 2016-07-15 | 2017-02-22 | 浙江工业大学 | Four-rotor unmanned aerial vehicle control method based on fuzzy extended state observer and self-adaptive sliding mode |
| CN106774373A (en) * | 2017-01-12 | 2017-05-31 | 哈尔滨工业大学 | A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods |
| CN108614426A (en) * | 2018-06-06 | 2018-10-02 | 黄山学院 | A kind of Multi Mobile Robots Formation's robust control method based on interference observer |
| CN108875253A (en) * | 2018-07-03 | 2018-11-23 | 曲阜师范大学 | The terminal sliding mode of drive lacking crane system based on interference observer, which disappears, puts control method and system |
| CN109062241A (en) * | 2018-09-29 | 2018-12-21 | 北京航空航天大学 | Autonomous full directive reentry guidance method based on linear pseudo- spectrum model PREDICTIVE CONTROL |
Non-Patent Citations (13)
| Title |
|---|
| BEI GU: "Co-Simulation of Algebraically Coupled Dynamic Subsystems", 《IEEE TRANSACTIONS ON CYBERNETICS》 * |
| S. SINAN: "Study_of_Nonsingular_Fast_Terminal_Sliding-Mode_Fault-Tolerant_Control", 《2018 INTERNATIONAL CONFERENCE ON RENEWABLE ENERGY AND POWER ENGINEERING (REPE) 》 * |
| SENDREN SHENG-DONG XU: "Distributed_Generator_in_Grid-Connected_Mode_Using_Improved_Exponential_Sliding_Mode_Control", 《 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS ( VOLUME: 62, ISSUE: 6, JUNE 2015)》 * |
| 孙彪: "基于幂次函数的预测滑模控制算法", 《信息与控制》 * |
| 常江: "非完整轮试移动机器人的轨迹跟踪滑模控制", 《控制工程》 * |
| 张勇: "拖挂式移动机器人反馈镇定控制问题研究", 《控制工程》 * |
| 徐光智: "无抖振离散滑模输出反馈控制方法及仿真研究", 《计算机测量与控制》 * |
| 徐英: "采用动态多维阶数控制的暂态稳定计算方法", 《中国电机工程学报》 * |
| 李金林: "水下机器人-机械手结构设计及自适应神经网络控制研究", 《中国优秀博硕士学位论文全文数据库(硕士)信息科技辑》 * |
| 杨朋松: "一种不确定离散***输出反馈滑模控制", 《31ST CHINESE CONTROL CONFERENCE》 * |
| 杨轲: "BLDC 位置伺服***的离散滑模输出反馈控制", 《江南大学学报( 自然科学版)》 * |
| 董琦: "基于光滑二阶滑模的可重复使用运载器有限时间再入姿态控制", 《控制理论与应用》 * |
| 陈曦: "终端滑模的(1,2)型非完整机器人有限时间镇定", 《控制工程》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112769367A (en) * | 2021-01-07 | 2021-05-07 | 山东交通学院 | Permanent magnet linear motor data driving discrete iteration integral sliding mode control method and system |
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