Luận văn design an adaptive controller and a state observer based on neural network for the 4dof parallel robot

LIST OF ABBREVIATIONS Abbreviation Definition 4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom SMC Sliding Mode Control DSC Dynamic Surface Control RBENN Radius B

IIANOI UNIVERSITY OF SCIENCE AND TECIINOLOGY

MASTER THESIS

Design an adaptive controller and a state

observer based on neural network for the

4DOF parallel robot

NGUYEN MANII CUONG

Control Engineering and Automation

Supervisor: Assoc Prof Nguyen Tung Lam

School: School of Electrical and Electronic Engineering

IIA NOI, 2022

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

MASTER THESIS

Design an adaptive controller and a state

observer based on neural network for the

4DOF parallel robot

NGUYEN MANII CUONG

Control Engineering and Automation

Supervisor: Assoc Prof Nguyen Tung Lam _

Supervisor's Signature

School: School of Electrical and Electronic Enginecring

HA NOT, 2022

CONG HOA XA HỘI CHỦ NGHĨA VIỆT NAM

Độc lập — Tự do— Hanh phic

BẢN XÁC NHẬN CHỈNH SỬA LUẬN VĂN THẠC SĨ

Ho va tén tac giả luận văn : Nguyễn Mạnh Cường,

Dé dải luận văn: Thiết kẻ bộ điêu khiển thích nghĩ và bộ quan sắt trạng thái dựa trên mạng nơ ron cho robot song song bên bậc tự do (Design an adaptive

controller and a stats observer based ơn neuai nolwork for thế 4DOE parallel robot)

Chuyên ngành: Kỳ thuật Điều khiển và Tự đông hóa

Mã số SV: 2020201 6M:

Tác giả, Người hưởng dẫn khoa học và Hội đông cham luận văn xác nhận

tác giả dã sửa chữa, bỏ sung luận văn theo biên bản họp Hội đồng ngày 04/05/2022 với các nội dụng sau:

LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

Figure 1.1 Parallel robot applied in the car motion simulator

Figure 1.2 Parallel robot applied in rehabilitation system [4]

From the reference and analysis of the above scientific works, moreover,

intending to reduce the computational complexity and redundant constraints while

still ensuring the necessary motion, the thesis puts focus on the four degrees of freedom parallel robot platform with the movements of rotational and translational

movements along the OZ axis, rotation in the OX axis and the OY axis

1.2 Trajectory tracking controllers and state observers

1.2.1 Trajectory tracking controllers

In robot control, especially in orbital tracking control problems, modern

methods specially put focus on designing control algorithms capable of handling

problems related to uncertainties, perturbations, and unknown structural

components in the system model while still ensuring stability and tracking quality The 4DOFPR parallel robot model is considered to be a model being commonly

affected by nonlinear uncertain elements in practical applications, especially

external forces acting in different directions on the system

The parallel structures are considered a nonlinear model in the control design

field, therefore, a control issue has attracted significant attention in the scientific

community One of these designed methodologies for nonlinear control systems

-TABLE OF CONTENT

CHAPTER 1 OVERVIEW

1.1 The four degrees of freedom parallel robot (ADOFPR) model

1.2 Trajectory trackuig controllers and state ObserVes

1.2.1 Trajectory tracking controllers

32 Controlter design for 4DOFPR - - 10

221 Backstepping aggregated with SMC (BASMC) - 10 2.22 RRFNN-based (RBFNNB) adaptive controller 13 2.2.3 High-gain observer for the adaptive controller - 7

23 Conelusion

CHAPTER 3 SIMULATION RESULT!

3.1 Results of the RBI'NN based adaptive controller (RIINNH)

3.2 Simulation results of the adaptive controller using the high-gain state

LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

Figure 1.1 Parallel robot applied in the car motion simulator

Figure 1.2 Parallel robot applied in rehabilitation system [4]

From the reference and analysis of the above scientific works, moreover,

intending to reduce the computational complexity and redundant constraints while

still ensuring the necessary motion, the thesis puts focus on the four degrees of freedom parallel robot platform with the movements of rotational and translational

movements along the OZ axis, rotation in the OX axis and the OY axis

1.2 Trajectory tracking controllers and state observers

1.2.1 Trajectory tracking controllers

In robot control, especially in orbital tracking control problems, modern

methods specially put focus on designing control algorithms capable of handling

problems related to uncertainties, perturbations, and unknown structural

components in the system model while still ensuring stability and tracking quality The 4DOFPR parallel robot model is considered to be a model being commonly

affected by nonlinear uncertain elements in practical applications, especially

external forces acting in different directions on the system

The parallel structures are considered a nonlinear model in the control design

field, therefore, a control issue has attracted significant attention in the scientific

community One of these designed methodologies for nonlinear control systems

-Figure 1.1 Parallel robot applied in the car motion simulator

Figure 1.2 Parallel robot applied in rehabilitation system [4]

From the reference and analysis of the above scientific works, moreover,

intending to reduce the computational complexity and redundant constraints while

still ensuring the necessary motion, the thesis puts focus on the four degrees of freedom parallel robot platform with the movements of rotational and translational

movements along the OZ axis, rotation in the OX axis and the OY axis

1.2 Trajectory tracking controllers and state observers

1.2.1 Trajectory tracking controllers

In robot control, especially in orbital tracking control problems, modern

methods specially put focus on designing control algorithms capable of handling

problems related to uncertainties, perturbations, and unknown structural

components in the system model while still ensuring stability and tracking quality The 4DOFPR parallel robot model is considered to be a model being commonly

affected by nonlinear uncertain elements in practical applications, especially

external forces acting in different directions on the system

The parallel structures are considered a nonlinear model in the control design

field, therefore, a control issue has attracted significant attention in the scientific

community One of these designed methodologies for nonlinear control systems

PTER t OVERVIEW

1.1 The four degrees of freedom parallel robot (4D0FPR) model

Nowatlays, robotic systems are being increasingly rapidly developed and applied in several economic and social life fields because they are designed for particularly complex and dangerous tasks or repetitive jobs and require high accuracy Morcover, apart from being almost precise and consistoril, with their flexible operating ability, robots are capable of working in hazardous

environments In addition, the robot can perform tasks with heavy loads and toxic

substances and can adapt to particular environmental conditions Thus, these

advantages have signifieanily contributed to produclivity and qualily

improvement, preventing accidents and saving labor costs

In state-of-the-art technology, parallel robots are increasingly prevalent in the industry, military, medical, and entertainment Various numbers of parallel

structures in |1 |, [2], |3], [4], and [5] have been taken into account, including the

six degrees of freedoms (DOF) robot in [1 J, which is capable of applied in medical surgery, as well as rehabilitation in [1], and some other structures applied into

flight and automobile simulation Most of these models have been implemented

based on the advantages of parallel structure, namely low inertia moment, high

load, and stnooth iansmission vapacity [6] From reality-based car models, lo

assist trainees and drivers have an alternative approach to getting familiar with the automobile’s movements, it is necessary to construct a driving simulation model based on a class of parallel architeclures and motion plai forms developed recently [3] Moreover, car driving simulation models are also constructed with the purpose

of mitigating unexpected forces impacting drivers in practical and virtual reality

cuviomments wi relalion to health care and rehabililation 14], L5]

In order to describe the movement of the robot system, the demand for robot

modeling is imperative Several studies [6], [7] showed the geometrical analysis

of a six DOF constrained parallel robot Regarding the construction of the mathematical model, a forward and inverse kinematics medel of Quanser’s Hexapod robot has been illustrated in [8] In addition, the six DOF parallel robots

have a positive advantage of high accuracy movements However, the complexity

of six actuators’ interaction and coordination gives the rising complexity in

designing trajectory tracking controllers of parallel robots, especially in the presence of massive uncortaintics Therefore, the configuration with fewer joints and DOF is able to mitigate the inevitable hysteresis and redundancy of actuators

shown in [9], [10], and [11], thereby, it would be more convenient in particular

practical applications and controller design considered uncertain elements In addition, in the attempt to reduce computation complexity and redundant constraints, the group of authors has constructed the four DOF platform, comprising the movements of rotating and translating along the vertical axis OZ,

rotating about the OX and OY axis.

LIST OF FIGURES

Figure 1.1 Parallel robot applied in the car motion simtlator 2 Figure 1.2 Parallel robot applied in rehabilitation system [41 2 Figure 2.1 (a) Robot coordinate; (b) Vector diagram of ADOEP

Figure 2.2 Structure of BASMC controller

Figure 2.3 RBENN structure

Higure 2.4 Structure of the adaptive controller .essesessneeneenene -

Figure 3.1 Hxiemal fAT68 uc ceiiroreriiririrariirrrerroreuao T5 Tigure 3.2 Motion trajectory of p 34 Figure 3.3 racking erTor 0 g ào nen — - Figure 3.4 Approximated valies sccssssvestssessenesneenineeietonaeinte 26 Figure 3.5 Motion trajectory of 9 wasssssssuessssernenesneeneeietonaeinte 37 Figure 3.6 Tracking error of a7 Figure 3.7 Uncertain parts in the robot model 29 Figure 3.8 Observed values of q - 30 Tigure 3.9 Observed values of ¢ - - - - 30 Figure 3.10 Observational error of ý oiicenrororoee seo 3] Figure 3.11 Rstimated values from RBFNN 32 Figure 3.12 Robot’s trajectory: ssssssessenesersinessenssneeinete xaeseasao 9) Figure 3.13 Tracking exror „33 Figure 3.14 Observed position with diferent values øŸ sụ, saase34 Tigure 3.15 Observed velocity with diferent values of ø„ ¬—

LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

thai have been inlorested in is the Backstepping technique as in [12], [13], [14],

[15], and [16] in order to ensure the quality of trajectory tracking control, Ilowever, when uncertainties or unmodeled components exist in the system model, the

“oxplosion of lms” phenomena adversely allects the control quality Another prominent control methad is sliding made control (SMC) which las been widely

used because of its robust characteristic as in [17], [1B], and [19] when considering

the existence of unknown elements However, the chattering phenomenon wgonorated by the SMC controller is ikely Lo demolish the aystom [20], as well ax the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance

because it takes advantage of them Then, the robustness characteristic is

enhanced, and the computational cost is reduced as in [20], [21], [22], and [23]

Nevertheless, the combined controller cannot cope with the chattering and

“explosion of terms” phenomena

On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC} has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step 1Iowever, the errors of the low-pass filter

in the DSC controller are a dilemma, majorly depending ou a filter time constant and being proven by complex malhemalical conditions in (24), which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena

Tu control Iheory, noise components are commonly considered to be an

tnevilable part of the whole system, and analyzing noise is the key Lo finding a way

that assists the (DOFPR system to be more stable and accurate To be more

specific, stochastic disturbances are problematic, impacting the 4DOI'PR system

Tn teras of non-Gaussian noises, the modified extended Masrclicy—Martin filter

constructed in [26] is an efficient approach to handle nonlinear systems when

environmental disturbances influence the whole system Besides, stochastic

parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By laking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight arc moment disturbance as well as

unknown parts However, there have been several kinds of noises in external and

intemal stochastic disturbances because of all range elements [30], from frictions,

vibrations, and changes of sudden forces to the shuft in environmental conditions,

which are considered uncertamies Tn this thesis, we assume Lhal the 4Q0FPR is

the model prone ta the impact of stochastic uncertainty elements

As mentioned above, for many conventional nonlinear controllers such as

SMC or Backstepping, there have been drawbacks in improving control performances whon it is challenging to identify the accurate model because of the

thai have been inlorested in is the Backstepping technique as in [12], [13], [14],

[15], and [16] in order to ensure the quality of trajectory tracking control, Ilowever, when uncertainties or unmodeled components exist in the system model, the

“oxplosion of lms” phenomena adversely allects the control quality Another prominent control methad is sliding made control (SMC) which las been widely

used because of its robust characteristic as in [17], [1B], and [19] when considering

the existence of unknown elements However, the chattering phenomenon wgonorated by the SMC controller is ikely Lo demolish the aystom [20], as well ax the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance

because it takes advantage of them Then, the robustness characteristic is

enhanced, and the computational cost is reduced as in [20], [21], [22], and [23]

Nevertheless, the combined controller cannot cope with the chattering and

“explosion of terms” phenomena

On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC} has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step 1Iowever, the errors of the low-pass filter

in the DSC controller are a dilemma, majorly depending ou a filter time constant and being proven by complex malhemalical conditions in (24), which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena

Tu control Iheory, noise components are commonly considered to be an

tnevilable part of the whole system, and analyzing noise is the key Lo finding a way

that assists the (DOFPR system to be more stable and accurate To be more

specific, stochastic disturbances are problematic, impacting the 4DOI'PR system

Tn teras of non-Gaussian noises, the modified extended Masrclicy—Martin filter

constructed in [26] is an efficient approach to handle nonlinear systems when

environmental disturbances influence the whole system Besides, stochastic

parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By laking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight arc moment disturbance as well as

unknown parts However, there have been several kinds of noises in external and

intemal stochastic disturbances because of all range elements [30], from frictions,

vibrations, and changes of sudden forces to the shuft in environmental conditions,

which are considered uncertamies Tn this thesis, we assume Lhal the 4Q0FPR is

the model prone ta the impact of stochastic uncertainty elements

As mentioned above, for many conventional nonlinear controllers such as

SMC or Backstepping, there have been drawbacks in improving control performances whon it is challenging to identify the accurate model because of the

LIST OF TABLES

Table 3.1 Reference trajectory parameters

‘Table 3.2 Control parameters

‘Table 3.3 Trajectory reference parameters

„38

tờ

LIST OF FIGURES

Figure 1.1 Parallel robot applied in the car motion simtlator 2 Figure 1.2 Parallel robot applied in rehabilitation system [41 2 Figure 2.1 (a) Robot coordinate; (b) Vector diagram of ADOEP

Figure 2.2 Structure of BASMC controller

Figure 2.3 RBENN structure

Higure 2.4 Structure of the adaptive controller .essesessneeneenene -

Figure 3.1 Hxiemal fAT68 uc ceiiroreriiririrariirrrerroreuao T5 Tigure 3.2 Motion trajectory of p 34 Figure 3.3 racking erTor 0 g ào nen — - Figure 3.4 Approximated valies sccssssvestssessenesneenineeietonaeinte 26 Figure 3.5 Motion trajectory of 9 wasssssssuessssernenesneeneeietonaeinte 37 Figure 3.6 Tracking error of a7 Figure 3.7 Uncertain parts in the robot model 29 Figure 3.8 Observed values of q - 30 Tigure 3.9 Observed values of ¢ - - - - 30 Figure 3.10 Observational error of ý oiicenrororoee seo 3] Figure 3.11 Rstimated values from RBFNN 32 Figure 3.12 Robot’s trajectory: ssssssessenesersinessenssneeinete xaeseasao 9) Figure 3.13 Tracking exror „33 Figure 3.14 Observed position with diferent values øŸ sụ, saase34 Tigure 3.15 Observed velocity with diferent values of ø„ ¬—

PTER t OVERVIEW

1.1 The four degrees of freedom parallel robot (4D0FPR) model

Nowatlays, robotic systems are being increasingly rapidly developed and applied in several economic and social life fields because they are designed for particularly complex and dangerous tasks or repetitive jobs and require high accuracy Morcover, apart from being almost precise and consistoril, with their flexible operating ability, robots are capable of working in hazardous

environments In addition, the robot can perform tasks with heavy loads and toxic

substances and can adapt to particular environmental conditions Thus, these

advantages have signifieanily contributed to produclivity and qualily

improvement, preventing accidents and saving labor costs

In state-of-the-art technology, parallel robots are increasingly prevalent in the industry, military, medical, and entertainment Various numbers of parallel

structures in |1 |, [2], |3], [4], and [5] have been taken into account, including the

six degrees of freedoms (DOF) robot in [1 J, which is capable of applied in medical surgery, as well as rehabilitation in [1], and some other structures applied into

flight and automobile simulation Most of these models have been implemented

based on the advantages of parallel structure, namely low inertia moment, high

load, and stnooth iansmission vapacity [6] From reality-based car models, lo

assist trainees and drivers have an alternative approach to getting familiar with the automobile’s movements, it is necessary to construct a driving simulation model based on a class of parallel architeclures and motion plai forms developed recently [3] Moreover, car driving simulation models are also constructed with the purpose

of mitigating unexpected forces impacting drivers in practical and virtual reality

cuviomments wi relalion to health care and rehabililation 14], L5]

In order to describe the movement of the robot system, the demand for robot

modeling is imperative Several studies [6], [7] showed the geometrical analysis

of a six DOF constrained parallel robot Regarding the construction of the mathematical model, a forward and inverse kinematics medel of Quanser’s Hexapod robot has been illustrated in [8] In addition, the six DOF parallel robots

have a positive advantage of high accuracy movements However, the complexity

of six actuators’ interaction and coordination gives the rising complexity in

designing trajectory tracking controllers of parallel robots, especially in the presence of massive uncortaintics Therefore, the configuration with fewer joints and DOF is able to mitigate the inevitable hysteresis and redundancy of actuators

shown in [9], [10], and [11], thereby, it would be more convenient in particular

practical applications and controller design considered uncertain elements In addition, in the attempt to reduce computation complexity and redundant constraints, the group of authors has constructed the four DOF platform, comprising the movements of rotating and translating along the vertical axis OZ,

rotating about the OX and OY axis.

thai have been inlorested in is the Backstepping technique as in [12], [13], [14],

[15], and [16] in order to ensure the quality of trajectory tracking control, Ilowever, when uncertainties or unmodeled components exist in the system model, the

“oxplosion of lms” phenomena adversely allects the control quality Another prominent control methad is sliding made control (SMC) which las been widely

used because of its robust characteristic as in [17], [1B], and [19] when considering

the existence of unknown elements However, the chattering phenomenon wgonorated by the SMC controller is ikely Lo demolish the aystom [20], as well ax the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance

because it takes advantage of them Then, the robustness characteristic is

enhanced, and the computational cost is reduced as in [20], [21], [22], and [23]

Nevertheless, the combined controller cannot cope with the chattering and

“explosion of terms” phenomena

On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC} has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step 1Iowever, the errors of the low-pass filter

in the DSC controller are a dilemma, majorly depending ou a filter time constant and being proven by complex malhemalical conditions in (24), which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena

Tu control Iheory, noise components are commonly considered to be an

tnevilable part of the whole system, and analyzing noise is the key Lo finding a way

that assists the (DOFPR system to be more stable and accurate To be more

specific, stochastic disturbances are problematic, impacting the 4DOI'PR system

Tn teras of non-Gaussian noises, the modified extended Masrclicy—Martin filter

constructed in [26] is an efficient approach to handle nonlinear systems when

environmental disturbances influence the whole system Besides, stochastic

parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By laking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight arc moment disturbance as well as

unknown parts However, there have been several kinds of noises in external and

intemal stochastic disturbances because of all range elements [30], from frictions,

vibrations, and changes of sudden forces to the shuft in environmental conditions,

which are considered uncertamies Tn this thesis, we assume Lhal the 4Q0FPR is

the model prone ta the impact of stochastic uncertainty elements

As mentioned above, for many conventional nonlinear controllers such as

SMC or Backstepping, there have been drawbacks in improving control performances whon it is challenging to identify the accurate model because of the

LIST OF FIGURES

Figure 1.1 Parallel robot applied in the car motion simtlator 2 Figure 1.2 Parallel robot applied in rehabilitation system [41 2 Figure 2.1 (a) Robot coordinate; (b) Vector diagram of ADOEP

Figure 2.2 Structure of BASMC controller

Figure 2.3 RBENN structure

Higure 2.4 Structure of the adaptive controller .essesessneeneenene -

Figure 3.1 Hxiemal fAT68 uc ceiiroreriiririrariirrrerroreuao T5 Tigure 3.2 Motion trajectory of p 34 Figure 3.3 racking erTor 0 g ào nen — - Figure 3.4 Approximated valies sccssssvestssessenesneenineeietonaeinte 26 Figure 3.5 Motion trajectory of 9 wasssssssuessssernenesneeneeietonaeinte 37 Figure 3.6 Tracking error of a7 Figure 3.7 Uncertain parts in the robot model 29 Figure 3.8 Observed values of q - 30 Tigure 3.9 Observed values of ¢ - - - - 30 Figure 3.10 Observational error of ý oiicenrororoee seo 3] Figure 3.11 Rstimated values from RBFNN 32 Figure 3.12 Robot’s trajectory: ssssssessenesersinessenssneeinete xaeseasao 9) Figure 3.13 Tracking exror „33 Figure 3.14 Observed position with diferent values øŸ sụ, saase34 Tigure 3.15 Observed velocity with diferent values of ø„ ¬—

PTER t OVERVIEW

1.1 The four degrees of freedom parallel robot (4D0FPR) model

Nowatlays, robotic systems are being increasingly rapidly developed and applied in several economic and social life fields because they are designed for particularly complex and dangerous tasks or repetitive jobs and require high accuracy Morcover, apart from being almost precise and consistoril, with their flexible operating ability, robots are capable of working in hazardous

environments In addition, the robot can perform tasks with heavy loads and toxic

substances and can adapt to particular environmental conditions Thus, these

advantages have signifieanily contributed to produclivity and qualily

improvement, preventing accidents and saving labor costs

In state-of-the-art technology, parallel robots are increasingly prevalent in the industry, military, medical, and entertainment Various numbers of parallel

structures in |1 |, [2], |3], [4], and [5] have been taken into account, including the

six degrees of freedoms (DOF) robot in [1 J, which is capable of applied in medical surgery, as well as rehabilitation in [1], and some other structures applied into

flight and automobile simulation Most of these models have been implemented

based on the advantages of parallel structure, namely low inertia moment, high

load, and stnooth iansmission vapacity [6] From reality-based car models, lo

assist trainees and drivers have an alternative approach to getting familiar with the automobile’s movements, it is necessary to construct a driving simulation model based on a class of parallel architeclures and motion plai forms developed recently [3] Moreover, car driving simulation models are also constructed with the purpose

of mitigating unexpected forces impacting drivers in practical and virtual reality

cuviomments wi relalion to health care and rehabililation 14], L5]

In order to describe the movement of the robot system, the demand for robot

modeling is imperative Several studies [6], [7] showed the geometrical analysis

of a six DOF constrained parallel robot Regarding the construction of the mathematical model, a forward and inverse kinematics medel of Quanser’s Hexapod robot has been illustrated in [8] In addition, the six DOF parallel robots

have a positive advantage of high accuracy movements However, the complexity

of six actuators’ interaction and coordination gives the rising complexity in

designing trajectory tracking controllers of parallel robots, especially in the presence of massive uncortaintics Therefore, the configuration with fewer joints and DOF is able to mitigate the inevitable hysteresis and redundancy of actuators

shown in [9], [10], and [11], thereby, it would be more convenient in particular

practical applications and controller design considered uncertain elements In addition, in the attempt to reduce computation complexity and redundant constraints, the group of authors has constructed the four DOF platform, comprising the movements of rotating and translating along the vertical axis OZ,

rotating about the OX and OY axis.

TABLE OF CONTENT

CHAPTER 1 OVERVIEW

1.1 The four degrees of freedom parallel robot (ADOFPR) model

1.2 Trajectory trackuig controllers and state ObserVes

1.2.1 Trajectory tracking controllers

32 Controlter design for 4DOFPR - - 10

221 Backstepping aggregated with SMC (BASMC) - 10 2.22 RRFNN-based (RBFNNB) adaptive controller 13 2.2.3 High-gain observer for the adaptive controller - 7

23 Conelusion

CHAPTER 3 SIMULATION RESULT!

3.1 Results of the RBI'NN based adaptive controller (RIINNH)

3.2 Simulation results of the adaptive controller using the high-gain state

PTER t OVERVIEW

1.1 The four degrees of freedom parallel robot (4D0FPR) model

Nowatlays, robotic systems are being increasingly rapidly developed and applied in several economic and social life fields because they are designed for particularly complex and dangerous tasks or repetitive jobs and require high accuracy Morcover, apart from being almost precise and consistoril, with their flexible operating ability, robots are capable of working in hazardous

environments In addition, the robot can perform tasks with heavy loads and toxic

substances and can adapt to particular environmental conditions Thus, these

advantages have signifieanily contributed to produclivity and qualily

improvement, preventing accidents and saving labor costs

In state-of-the-art technology, parallel robots are increasingly prevalent in the industry, military, medical, and entertainment Various numbers of parallel

structures in |1 |, [2], |3], [4], and [5] have been taken into account, including the

six degrees of freedoms (DOF) robot in [1 J, which is capable of applied in medical surgery, as well as rehabilitation in [1], and some other structures applied into

flight and automobile simulation Most of these models have been implemented

based on the advantages of parallel structure, namely low inertia moment, high

load, and stnooth iansmission vapacity [6] From reality-based car models, lo

assist trainees and drivers have an alternative approach to getting familiar with the automobile’s movements, it is necessary to construct a driving simulation model based on a class of parallel architeclures and motion plai forms developed recently [3] Moreover, car driving simulation models are also constructed with the purpose

of mitigating unexpected forces impacting drivers in practical and virtual reality

cuviomments wi relalion to health care and rehabililation 14], L5]

In order to describe the movement of the robot system, the demand for robot

modeling is imperative Several studies [6], [7] showed the geometrical analysis

of a six DOF constrained parallel robot Regarding the construction of the mathematical model, a forward and inverse kinematics medel of Quanser’s Hexapod robot has been illustrated in [8] In addition, the six DOF parallel robots

have a positive advantage of high accuracy movements However, the complexity

of six actuators’ interaction and coordination gives the rising complexity in

designing trajectory tracking controllers of parallel robots, especially in the presence of massive uncortaintics Therefore, the configuration with fewer joints and DOF is able to mitigate the inevitable hysteresis and redundancy of actuators

shown in [9], [10], and [11], thereby, it would be more convenient in particular

practical applications and controller design considered uncertain elements In addition, in the attempt to reduce computation complexity and redundant constraints, the group of authors has constructed the four DOF platform, comprising the movements of rotating and translating along the vertical axis OZ,

rotating about the OX and OY axis.

thai have been inlorested in is the Backstepping technique as in [12], [13], [14],

[15], and [16] in order to ensure the quality of trajectory tracking control, Ilowever, when uncertainties or unmodeled components exist in the system model, the

“oxplosion of lms” phenomena adversely allects the control quality Another prominent control methad is sliding made control (SMC) which las been widely

used because of its robust characteristic as in [17], [1B], and [19] when considering

the existence of unknown elements However, the chattering phenomenon wgonorated by the SMC controller is ikely Lo demolish the aystom [20], as well ax the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance

because it takes advantage of them Then, the robustness characteristic is

enhanced, and the computational cost is reduced as in [20], [21], [22], and [23]

Nevertheless, the combined controller cannot cope with the chattering and

“explosion of terms” phenomena

On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC} has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step 1Iowever, the errors of the low-pass filter

in the DSC controller are a dilemma, majorly depending ou a filter time constant and being proven by complex malhemalical conditions in (24), which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena

Tu control Iheory, noise components are commonly considered to be an

tnevilable part of the whole system, and analyzing noise is the key Lo finding a way

that assists the (DOFPR system to be more stable and accurate To be more

specific, stochastic disturbances are problematic, impacting the 4DOI'PR system

Tn teras of non-Gaussian noises, the modified extended Masrclicy—Martin filter

constructed in [26] is an efficient approach to handle nonlinear systems when

environmental disturbances influence the whole system Besides, stochastic

parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By laking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight arc moment disturbance as well as

unknown parts However, there have been several kinds of noises in external and

intemal stochastic disturbances because of all range elements [30], from frictions,

vibrations, and changes of sudden forces to the shuft in environmental conditions,

which are considered uncertamies Tn this thesis, we assume Lhal the 4Q0FPR is

the model prone ta the impact of stochastic uncertainty elements

As mentioned above, for many conventional nonlinear controllers such as

SMC or Backstepping, there have been drawbacks in improving control performances whon it is challenging to identify the accurate model because of the

LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

thai have been inlorested in is the Backstepping technique as in [12], [13], [14],

[15], and [16] in order to ensure the quality of trajectory tracking control, Ilowever, when uncertainties or unmodeled components exist in the system model, the

“oxplosion of lms” phenomena adversely allects the control quality Another prominent control methad is sliding made control (SMC) which las been widely

used because of its robust characteristic as in [17], [1B], and [19] when considering

the existence of unknown elements However, the chattering phenomenon wgonorated by the SMC controller is ikely Lo demolish the aystom [20], as well ax the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance

because it takes advantage of them Then, the robustness characteristic is

enhanced, and the computational cost is reduced as in [20], [21], [22], and [23]

Nevertheless, the combined controller cannot cope with the chattering and

“explosion of terms” phenomena

On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC} has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step 1Iowever, the errors of the low-pass filter

in the DSC controller are a dilemma, majorly depending ou a filter time constant and being proven by complex malhemalical conditions in (24), which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena

Tu control Iheory, noise components are commonly considered to be an

tnevilable part of the whole system, and analyzing noise is the key Lo finding a way

that assists the (DOFPR system to be more stable and accurate To be more

specific, stochastic disturbances are problematic, impacting the 4DOI'PR system

Tn teras of non-Gaussian noises, the modified extended Masrclicy—Martin filter

constructed in [26] is an efficient approach to handle nonlinear systems when

environmental disturbances influence the whole system Besides, stochastic

parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By laking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight arc moment disturbance as well as

unknown parts However, there have been several kinds of noises in external and

intemal stochastic disturbances because of all range elements [30], from frictions,

vibrations, and changes of sudden forces to the shuft in environmental conditions,

which are considered uncertamies Tn this thesis, we assume Lhal the 4Q0FPR is

the model prone ta the impact of stochastic uncertainty elements

As mentioned above, for many conventional nonlinear controllers such as

SMC or Backstepping, there have been drawbacks in improving control performances whon it is challenging to identify the accurate model because of the

TABLE OF CONTENT

CHAPTER 1 OVERVIEW

1.1 The four degrees of freedom parallel robot (ADOFPR) model

1.2 Trajectory trackuig controllers and state ObserVes

1.2.1 Trajectory tracking controllers

32 Controlter design for 4DOFPR - - 10

221 Backstepping aggregated with SMC (BASMC) - 10 2.22 RRFNN-based (RBFNNB) adaptive controller 13 2.2.3 High-gain observer for the adaptive controller - 7

23 Conelusion

CHAPTER 3 SIMULATION RESULT!

3.1 Results of the RBI'NN based adaptive controller (RIINNH)

3.2 Simulation results of the adaptive controller using the high-gain state

thai have been inlorested in is the Backstepping technique as in [12], [13], [14],

[15], and [16] in order to ensure the quality of trajectory tracking control, Ilowever, when uncertainties or unmodeled components exist in the system model, the

“oxplosion of lms” phenomena adversely allects the control quality Another prominent control methad is sliding made control (SMC) which las been widely

used because of its robust characteristic as in [17], [1B], and [19] when considering

the existence of unknown elements However, the chattering phenomenon wgonorated by the SMC controller is ikely Lo demolish the aystom [20], as well ax the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance

because it takes advantage of them Then, the robustness characteristic is

enhanced, and the computational cost is reduced as in [20], [21], [22], and [23]

Nevertheless, the combined controller cannot cope with the chattering and

“explosion of terms” phenomena

On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC} has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step 1Iowever, the errors of the low-pass filter

in the DSC controller are a dilemma, majorly depending ou a filter time constant and being proven by complex malhemalical conditions in (24), which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena

Tu control Iheory, noise components are commonly considered to be an

tnevilable part of the whole system, and analyzing noise is the key Lo finding a way

that assists the (DOFPR system to be more stable and accurate To be more

specific, stochastic disturbances are problematic, impacting the 4DOI'PR system

Tn teras of non-Gaussian noises, the modified extended Masrclicy—Martin filter

constructed in [26] is an efficient approach to handle nonlinear systems when

environmental disturbances influence the whole system Besides, stochastic

parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By laking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight arc moment disturbance as well as

unknown parts However, there have been several kinds of noises in external and

intemal stochastic disturbances because of all range elements [30], from frictions,

vibrations, and changes of sudden forces to the shuft in environmental conditions,

which are considered uncertamies Tn this thesis, we assume Lhal the 4Q0FPR is

the model prone ta the impact of stochastic uncertainty elements

As mentioned above, for many conventional nonlinear controllers such as

SMC or Backstepping, there have been drawbacks in improving control performances whon it is challenging to identify the accurate model because of the

Figure 1.1 Parallel robot applied in the car motion simulator

Figure 1.2 Parallel robot applied in rehabilitation system [4]

From the reference and analysis of the above scientific works, moreover,

intending to reduce the computational complexity and redundant constraints while

still ensuring the necessary motion, the thesis puts focus on the four degrees of freedom parallel robot platform with the movements of rotational and translational

movements along the OZ axis, rotation in the OX axis and the OY axis

1.2 Trajectory tracking controllers and state observers

1.2.1 Trajectory tracking controllers

In robot control, especially in orbital tracking control problems, modern

methods specially put focus on designing control algorithms capable of handling

problems related to uncertainties, perturbations, and unknown structural

components in the system model while still ensuring stability and tracking quality The 4DOFPR parallel robot model is considered to be a model being commonly

affected by nonlinear uncertain elements in practical applications, especially

external forces acting in different directions on the system

The parallel structures are considered a nonlinear model in the control design

field, therefore, a control issue has attracted significant attention in the scientific

community One of these designed methodologies for nonlinear control systems

-LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

LIST OF ABBREVIATIONS

Abbreviation Definition

4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom

SMC Sliding Mode Control

DSC Dynamic Surface Control

RBENN Radius Basis !’unction Neural Network

BASMC Backstepping aggregated with Sliding Mode

Conirol RBFXNR Radius Basis Function Neural Network-

based

TABLE OF CONTENT

CHAPTER 1 OVERVIEW

1.1 The four degrees of freedom parallel robot (ADOFPR) model

1.2 Trajectory trackuig controllers and state ObserVes

1.2.1 Trajectory tracking controllers

32 Controlter design for 4DOFPR - - 10

221 Backstepping aggregated with SMC (BASMC) - 10 2.22 RRFNN-based (RBFNNB) adaptive controller 13 2.2.3 High-gain observer for the adaptive controller - 7

23 Conelusion

CHAPTER 3 SIMULATION RESULT!

3.1 Results of the RBI'NN based adaptive controller (RIINNH)

3.2 Simulation results of the adaptive controller using the high-gain state

LIST OF FIGURES

Figure 1.1 Parallel robot applied in the car motion simtlator 2 Figure 1.2 Parallel robot applied in rehabilitation system [41 2 Figure 2.1 (a) Robot coordinate; (b) Vector diagram of ADOEP

Figure 2.2 Structure of BASMC controller

Figure 2.3 RBENN structure

Higure 2.4 Structure of the adaptive controller .essesessneeneenene -

Figure 3.1 Hxiemal fAT68 uc ceiiroreriiririrariirrrerroreuao T5 Tigure 3.2 Motion trajectory of p 34 Figure 3.3 racking erTor 0 g ào nen — - Figure 3.4 Approximated valies sccssssvestssessenesneenineeietonaeinte 26 Figure 3.5 Motion trajectory of 9 wasssssssuessssernenesneeneeietonaeinte 37 Figure 3.6 Tracking error of a7 Figure 3.7 Uncertain parts in the robot model 29 Figure 3.8 Observed values of q - 30 Tigure 3.9 Observed values of ¢ - - - - 30 Figure 3.10 Observational error of ý oiicenrororoee seo 3] Figure 3.11 Rstimated values from RBFNN 32 Figure 3.12 Robot’s trajectory: ssssssessenesersinessenssneeinete xaeseasao 9) Figure 3.13 Tracking exror „33 Figure 3.14 Observed position with diferent values øŸ sụ, saase34 Tigure 3.15 Observed velocity with diferent values of ø„ ¬—

LIST OF TABLES

Table 3.1 Reference trajectory parameters

‘Table 3.2 Control parameters

‘Table 3.3 Trajectory reference parameters

„38

tờ

TABLE OF CONTENT

CHAPTER 1 OVERVIEW

1.1 The four degrees of freedom parallel robot (ADOFPR) model

1.2 Trajectory trackuig controllers and state ObserVes

1.2.1 Trajectory tracking controllers

32 Controlter design for 4DOFPR - - 10

221 Backstepping aggregated with SMC (BASMC) - 10 2.22 RRFNN-based (RBFNNB) adaptive controller 13 2.2.3 High-gain observer for the adaptive controller - 7

23 Conelusion

CHAPTER 3 SIMULATION RESULT!

3.1 Results of the RBI'NN based adaptive controller (RIINNH)

3.2 Simulation results of the adaptive controller using the high-gain state

LIST OF FIGURES

Figure 1.1 Parallel robot applied in the car motion simtlator 2 Figure 1.2 Parallel robot applied in rehabilitation system [41 2 Figure 2.1 (a) Robot coordinate; (b) Vector diagram of ADOEP

Figure 2.2 Structure of BASMC controller

Figure 2.3 RBENN structure

Higure 2.4 Structure of the adaptive controller .essesessneeneenene -

Figure 3.1 Hxiemal fAT68 uc ceiiroreriiririrariirrrerroreuao T5 Tigure 3.2 Motion trajectory of p 34 Figure 3.3 racking erTor 0 g ào nen — - Figure 3.4 Approximated valies sccssssvestssessenesneenineeietonaeinte 26 Figure 3.5 Motion trajectory of 9 wasssssssuessssernenesneeneeietonaeinte 37 Figure 3.6 Tracking error of a7 Figure 3.7 Uncertain parts in the robot model 29 Figure 3.8 Observed values of q - 30 Tigure 3.9 Observed values of ¢ - - - - 30 Figure 3.10 Observational error of ý oiicenrororoee seo 3] Figure 3.11 Rstimated values from RBFNN 32 Figure 3.12 Robot’s trajectory: ssssssessenesersinessenssneeinete xaeseasao 9) Figure 3.13 Tracking exror „33 Figure 3.14 Observed position with diferent values øŸ sụ, saase34 Tigure 3.15 Observed velocity with diferent values of ø„ ¬—

PTER t OVERVIEW

1.1 The four degrees of freedom parallel robot (4D0FPR) model

Nowatlays, robotic systems are being increasingly rapidly developed and applied in several economic and social life fields because they are designed for particularly complex and dangerous tasks or repetitive jobs and require high accuracy Morcover, apart from being almost precise and consistoril, with their flexible operating ability, robots are capable of working in hazardous

environments In addition, the robot can perform tasks with heavy loads and toxic

substances and can adapt to particular environmental conditions Thus, these

advantages have signifieanily contributed to produclivity and qualily

improvement, preventing accidents and saving labor costs

In state-of-the-art technology, parallel robots are increasingly prevalent in the industry, military, medical, and entertainment Various numbers of parallel

structures in |1 |, [2], |3], [4], and [5] have been taken into account, including the

six degrees of freedoms (DOF) robot in [1 J, which is capable of applied in medical surgery, as well as rehabilitation in [1], and some other structures applied into

flight and automobile simulation Most of these models have been implemented

based on the advantages of parallel structure, namely low inertia moment, high

load, and stnooth iansmission vapacity [6] From reality-based car models, lo

assist trainees and drivers have an alternative approach to getting familiar with the automobile’s movements, it is necessary to construct a driving simulation model based on a class of parallel architeclures and motion plai forms developed recently [3] Moreover, car driving simulation models are also constructed with the purpose

of mitigating unexpected forces impacting drivers in practical and virtual reality

cuviomments wi relalion to health care and rehabililation 14], L5]

In order to describe the movement of the robot system, the demand for robot

modeling is imperative Several studies [6], [7] showed the geometrical analysis

of a six DOF constrained parallel robot Regarding the construction of the mathematical model, a forward and inverse kinematics medel of Quanser’s Hexapod robot has been illustrated in [8] In addition, the six DOF parallel robots

have a positive advantage of high accuracy movements However, the complexity

of six actuators’ interaction and coordination gives the rising complexity in

designing trajectory tracking controllers of parallel robots, especially in the presence of massive uncortaintics Therefore, the configuration with fewer joints and DOF is able to mitigate the inevitable hysteresis and redundancy of actuators

shown in [9], [10], and [11], thereby, it would be more convenient in particular

practical applications and controller design considered uncertain elements In addition, in the attempt to reduce computation complexity and redundant constraints, the group of authors has constructed the four DOF platform, comprising the movements of rotating and translating along the vertical axis OZ,

rotating about the OX and OY axis.