Comparison of identification and control of 2 axes pam manipulator

Modeling and Control of the 1-Axes PAM Manipulator using MGA-based NARX Fuzzy model 22 3.1 Introduction 22 3.2 Modified genetic algorithm MGA for NARX fuzzy model Identification 23 3.

공학박사 학위논문

2 축 공압 인공근육 매니퓰레이터의

추정 및 제어에 관한 비교 연구

Comparison of Identification and Control of

2-Axes PAM Manipulator

울산대학교 대학원 기계자동차 공학부

Ho Pham Huy Anh

2 축 공압 인공근육 매니퓰레이터의

추정 및 제어에 관한 비교 연구

Comparison of Identification and Control of

2-Axes PAM Manipulator

지도교수 안경관

이 논문을공학박사학위 논문으로 제출함

2008 년 11 월

울산대학교 대학원 기계자동차 공학부

Ho Pham Huy Anh

Ho Pham Huy Anh 의 공학박사 학위 논문을 인준함

울산대학교 대학원 기계자동차 공학부

Thesis for the Degree of Doctor of Philosophy

Comparison of Identification and Control of

2-Axes PAM Manipulator

By

Ho Pham Huy Anh Advisor: Prof KYOUNG KWAN AHN School of Mechanical and Automotive Engineering

Graduate School

University of ULSAN November 2008

Comparison of Identification and Control of

2-Axes PAM Manipulator

By

Ho Pham Huy Anh

Advisor: Prof KYOUNG KWAN AHN

Submitted to the School of Mechanical and Automotive Engineering

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

At Graduate School, University of ULSAN

November 2008

Comparison of Identification and Control of

2-Axes PAM Manipulator

A Dissertation

By

Ho Pham Huy Anh

Approved of styles and contents by:

Chairman BYUNG RYONG LEE

Advisor KYOUNG KWAN AHN Member SOON YOUNG YANG

Member CHEOL GEUN HA Member JUNG HO PARK

November 2008

Acknowledgments

This thesis would not have been completed without the help and unlimited support from professors, colleagues, friends, and my love-family from whom I receive the encouragement, the opportunity, the confidence and by so to whom I want to dedicate my best grateful

Firstly, I want to express my sincere gratitude to my advisor, Prof Kyoung Kwan Ahn, for all of his guidance, advice and support during the course of my research and thesis writing Forever I will remember the opportunities he has provided me, for his constant support and his initiative ideas and suggestions My respect for him will always be in my mind

I am also honored to have Prof Byung Ryong Lee, Prof Soon Young Yang, Prof Cheol Geun Ha and Prof Jung Ho Park in my committee, whose inspiration, support and perseverance made this dissertation become possible I would like to thank them for their interest and encouragement throughout this research

No words for me to express my sincere gratitude towards all my Korean, Bangaldesh and Vietnamese friends (Thanh-Hon-Nam-Hao-Kha-Tu-Truong-Hanh-Hung-JongIl-Amin-Mafuz and others) Not much happy people like me to have their best friend Thanks for helping me

to pass through difficult moments, for yours deep thinking and yours contributions to the realization of my thesis, and especially for the many animated discussions on the subject

This thesis is dedicated to my darling wife Le Tan Loi, my sons Bim-Bum and my girl Bo Special sentiment is also expressed to my sisters, my brother Huy Don and their family for taking care of me during the time I studied abroad

Finally I dedicate this work to my father and my late mother Their endless love for me always supports me in all my life

November 2008

Ho Pham Huy Anh

Contents

Part I: Introduction 1

1 Introduction 2

1.1 Overview 2 1.2 Motivation 4 1.3 Outline of Thesis 6

2 Configuration, experiment setup and characteristic of pneumatic artificial muscle (PAM) manipulator 10

2.1 Introduction 10

2.2 Configuration, experiment setup and characteristic of 2-axes PAM manipulator 11

2.2.1 Configuration of 2-axes PAM manipulator system 11

2.2.2 Experiment setup 12

2.2.3 Configuration of 1-axes PAM manipulator system 14

2.2.4 Basic characteristic of PAM manipulator 16

Part II: Intelligent Models and Model-Based Advanced Control Schemes of 2-Axes PAM Manipulator 20

3 Modeling and Control of the 1-Axes PAM Manipulator using MGA-based NARX Fuzzy model 22

3.1 Introduction 22

3.2 Modified genetic algorithm (MGA) for NARX fuzzy model Identification 23

3.2.1 Conventional genetic algorithm (GA) 23

3.2.2 Modifications to genetic algorithm (MGA) 24

3.2.3 Modified genetic algorithm (MGA) for optimizing fuzzy model’s parameters 27

3.3 MGA-based PAM manipulator NARX fuzzy model identification 31

3.4 Configuration of PAM manipulator system and PRBS training data 33

3.5 Design and Implementation of MGA-based NARX fuzzy model 35

3.6 Results of MGA-based PAM manipulator NARX fuzzy model identification 40

3.6.1 GA-based PAM manipulator TS fuzzy model identification 40

3.6.2 MGA-based PAM manipulator TS fuzzy model identification 44

3.6.3 MGA-based PAM manipulator NARX fuzzy model identification 49

3.7 Conclusion 60

4 Modeling and Model-based Control of 1-Axes PAM Manipulator using Neural NARX model 62

4.1 Introduction 62

4.2 Modeling of 1-Axes PAM manipulator using neural NARX model and INCBP algorithm 63

4.2.1 Recurrent neural NARX model and Back-Propagation (BP) learning algorithm 63

4.2.2 INCBP learning algorithm of Neural NARX model identification 68

4.2.3 Modeling of PAM manipulator Neural NARX model 70

4.3 Experimental results 72

4.4 Advanced Control of PAM manipulator based on neural NARX model 88

4.4.1 PAM manipulator forward and inverse neural NARX model identification 89

4.4.2 Proposed Hybrid Neural NARX Internal Model (NARX-IMC-PID) Control 95

4.4.3 Experimental results 98

4.5 Conclusion 108

5 Modeling and Control of 2-Axes PAM Manipulator using MGA-based Double NARX fuzzy model 109

5.1 Introduction 109

5.2 Modified genetic algorithm (MGA) for NARX fuzzy model Identification 110

5.3 Identification of 2-axes PAM manipulator based on Double NARX fuzzy model 111

5.4 Identification of Inverse and Forward Double NARX fuzzy model 115

5.5 Experimental results 120

5.5.1 Identification of 2-axes PAM manipulator Forward Double NARX fuzzy model 120

5.5.2 Identification of 2-axes PAM manipulator Inverse Double NARX fuzzy model 122

5.6 Advanced Control of PAM manipulator based on Inverse NARX Fuzzy model 124

5.6.1 Implementation of MGA-based inverse NARX fuzzy model 125

5.6.2 Results of MGA-based Inverse NARX Fuzzy model Identification 126

5.6.3 Hybrid Online DNN-PID Feed-forward Inverse NARX Fuzzy Control scheme 130

5.6.4 Experimental results 135

5.7 Conclusion 143

6 Modeling and Control of 2-Axes PAM Manipulator using Neural MIMO NARX model 144

6.1 Introduction 144

6.2 Proposed MIMO Neural NARX model and BP learning algorithm 145

6.3 Identification of Inverse and Forward Neural MIMO NARX model 147

6.4 Proposed Hybrid online neural MIMO NARX Feed-forward PID control system 155

6.4.1 Controller design 155

6.4.2 Experiment setup 158

6.4.3 Experimental results 158

6.5 Conclusion 170

Part IV: Conclusion and discussion 172

7 Conclusion and discussion 173

References 177

Publications 184

List of Figures

Figure 2.1 Structure of the PAM 11

(a) Working of PAM (b) PAM – FESTO Product (c) The structure of PAM Figure 2.2 General configuration of 2-axes PAM manipulator 12

Figure 2.3: Working principle of the 2-axes PAM manipulator 12

Figure 2.4a Schematic diagram of the 2-axes PAM manipulator 13

Figure 2.4b Experimental Configuration of the 2-axes PAM manipulator system 14

Figure 2.5 Block diagram for obtaining PRBS input-output data of the 1-link PAM manipulator 15

Figure 2.6 Block diagram of the experimental apparatus of the 1-link PAM manipulator 16

Figure 2.7 Basis Characteristics of the PAM 17

Figure 2.8 Hysteresis of the PAM 18

Figure 2.9 h -F relationships of artificial muscle (extracted from (FESTO, 2005) [29] ) 18

Figure 3.1: The flow chart of conventional GA optimization procedure 25

Figure 3.2: The flow chart of Modified MGA optimization procedure 30

Figure 3.3 Procedure of the PAM manipulator NARX Fuzzy Model Identification 30

Figure 3.4a Block diagram of The MGA-based PAM manipulator’s TS Fuzzy Model Identification 32

Figure 3.4b Block diagram of The MGA-based PAM manipulator’s NARX11 Fuzzy Model Identification 32

Figure 3.4c Block diagram of The MGA-based PAM manipulator’s NARX22 Fuzzy Model Identification 33

Figure 3.5 Experiment data obtained from the PAM manipulator 34

Figure 3.6a Training data obtained from the PAM manipulator 34

Figure 3.6b Validating data obtained from the PAM manipulator 34

Figure 3.7 Validating pseudo-PRBS data obtained from the PAM manipulator 35

Figure 3.8 Triangle input membership function with spacing factor = 2 36

Figure 3.9a The Seed Points and the Grid Points for Rule-Base Construction 37

Figure 3.9b Derived Rule Base 37

Figure 3.10 Fitness Convergence GA-based Fuzzy Model Identification of the PAM manipulator 40

Figure 3.11a Estimation of GA-based Fuzzy Model of the PAM manipulator 41

Figure 3.11b Validation of GA-based Fuzzy Model of the PAM manipulator 41

Figure 3.11c Membership Input-Output & Surf-Viewer of GA-based Fuzzy Model Identification 42

Figure 3.11d Convergence of Principal Parameters of GA-based Fuzzy Model Identification 43

Figure 3.12 Fitness Convergence MGA-based Fuzzy Model Identification of the PAM manipulator 45

Figure 3.13a Membership Input-Output & Surf-Viewer of MGA-based Fuzzy Model Identification 46

Figure 3.13b Estimation of MGA-based TS Fuzzy Model of the PAM manipulator 47

Figure 3.13c Validation of MGA-based TS Fuzzy Model of the PAM manipulator 47

Figure 3.13d Convergence of principal parameters of the MGA-based Fuzzy Model of the PAM manipulator 48

Figure 3.14 Fitness Convergence MGA-based NARX11 Fuzzy Model Identification of the PAM manipulator 50

Figure 3.15a Membership Input-Output & Surf-Viewer of MGA-based NARX11 Fuzzy Model Identification 51

Figure 3.15b Estimation of MGA-based NARX11 Fuzzy Model of the PAM manipulator 52

Figure 3.15c Validation of MGA-based NARX11Fuzzy Model of the PAM manipulator 52

Figure 3.15d Convergence of principal parameters of the MGA-based NARX11 Fuzzy Model 53

Figure 3.16 Fitness Convergence MGA-based NARX22 Fuzzy Model Identification of the PAM manipulator 55

Figure 3.17a Estimation of MGA-based NARX22 Fuzzy Model of the PAM manipulator 55

Figure 3.17b Membership Input-Output & Surf-Viewer of MGA-based NARX22 Fuzzy Model Identification 56

Figure 3.17c Validation of MGA-based NARX22Fuzzy Model of the PAM manipulator 57

Figure 3.17d Convergence of principal parameters of the MGA-based NARX22 Fuzzy Model 58

Figure 3.18 Validation of MGA-based NARX11 Fuzzy model of the PAM manipulator 59

Figure 4.1 Structure of feed-forward MLP Neural Networks 64

Figure 4.2 Structure of Neural NARX22 model 65

Figure 4.3 Block diagram for modeling and identifying the NARX model of the PAM manipulator 72

Figure 4.4 Training data obtained by experiment 73

Figure 4.5 Validating data obtained by experiment 73

Figure 4.6 Structure of neural NARX22 model of the 2nd Link of the PAM manipulator 74

Figure 4.7 Fitness convergence of nonlinear Neural NARX Model 74

Figure 4.8a-b Validation of PAM manipulator Neural NARX22 Model 75

Figure 4.9 Validation of the PAM manipulator 2 nd ARX and 3 rd ARX model, (extracted from [12] ) 75

Figure 4.10 Comparison of PAM manipulator Output and Predicted OE Model Output 76

Figure 4.11 Comparison fitness convergence of Neural NARX22 models with various number of hidden nodes 77

Figure 4.12 Comparison EI of Neural NARX22 models with various number of hidden nodes 77

Figure 4.13 Comparison of fitness convergence of NNARX11 models with various number of hidden nodes 79

Figure 4.14 Comparison EI of Neural NARX11 models with various number of hidden nodes 79

Figure 4.15 Structure of nonlinear Neural NARX44 model with 14 hidden neurons 80

Figure 4.16 Comparison of fitness convergence of Neural NARX44 models with various number of hidden nodes 81

Figure 4.17 Comparison EI of Neural NARX44 models with various number of hidden nodes 81

Figure 4.18 Comparison of fitness convergence of Neural NARX model with various sizes of regression vector N 0 83

Figure 4.19a-b Comparison of PAM manipulator and Neural NARX11 Model response 84

Figure 4.20 Comparison of PAM manipulator and Neural NARX33 Model response 85

Figure 4.21 Comparison of PAM manipulator and Neural NARX22 Model response (BP method & 5 hidden nodes) 86

Figure 4.22 Comparison of PAM manipulator & Neural NARX22 Model Response (BP method & 10 hidden nodes) 87 Figure 4.23 Validation of Neural NARX22 Model [Na=2; Nb=2] of the PAM manipulator 87

Figure 4.24a Forward Neural NARX Model Training data obtained by experiment 89

Figure 4.24b Inverse Neural NARX Model Training data obtained by experiment 90

Figure 4.25a: Structure of Inverse neural NARX11 and Forward neural NARX11 model of PAM manipulator 90

Figure 4.25b: Structure of Inverse neural NARX22 and Forward neural NARX22 model of PAM manipulator 90

Figure 4.26 Block diagram for modeling of the nonlinear Neural NARX model of the PAM manipulator 91

(A)- Forward Neural NARX-11 model; (B)- Inverse Neural NARX-11 model (C)- Forward Neural NARX-22 model; (D)- Inverse Neural NARX-22 model Figure 4.27a: The fitness convergence of nonlinear Forward NARX11 and Forward NARX22 Models 92

Figure 4.27b: Validation of PAM manipulator Forward neural NARX11 and Forward neural NARX22 Models 93

Figure 4.28a: The fitness convergence of Inverse Neural NARX11 and Forward Neural NARX22 Models 93

Figure 4.28b: Validation of PAM manipulator Inverse neural NARX11 and Inverse neural NARX22 Models 93

Figure 4.29 Block diagram of IMC system 95

Fig 4.30 Block diagram of PAM MANIPULATOR Hybrid Neural NARX-IMC-PID position control 97

Fig 4.31a Real-time SIMULINK diagram of the PAM manipulator Hybrid neural NARX11-IMC-PID control 99

Fig 4.31b Real-time SIMULINK diagram of the PAM manipulator Hybrid neural NARX22-IMC-PID control 99

Fig 4.31c Real-time SIMULINK diagram of the PAM manipulator PID control 100

Fig 4.32 Parameter Configuration of Inverse NARX11 model of proposed neural NARX11-IMC-PID control 100

Fig 4.33 The performance comparison of proposed neural NARX-IMC-PID control and PID control 102

(A)-Load 0.5[kg]; (B)-Load 5[kg] Fig 4.34a.The performance of Triangular Joint Angle output of the PAM manipulator using neural NARX- IMC-PID control with (a)-Load 0.5[kg]; (b)-Load 2[kg]; (c)-Load 5[kg]; (d)-Load 10[kg] 103

Fig 4.34b.Combination of U RNN and U PID of PAM manipulator using neural NARX22-IMC-PID control with (a)-Load 0.5[kg]; (b)-Load 2[kg]; (c)-Load 5[kg]; (d)-Load 10[kg] 104

Fig 4.35a.The performance of Trapezoidal Joint Angle output of the PAM manipulator using neural NARX- IMC-PID control with (a)-Load 0.5[kg]; (b)-Load 2[kg]; (c)-Load 5[kg]; (d)-Load 10[kg] 104

Fig 4.35b.Combination of U RNN and U PID of PAM manipulator using neural NARX22-IMC-PID control with (a)-Load 0.5[kg]; (b)-Load 2[kg]; (c)-Load 5[kg]; (d)-Load 10[kg] 105

Fig 4.36 The performance of Sinusoidal Joint Angle output of PAM manipulator using NARX-IMC-PID control (A)-Load 0.5[kg]; (B)-Load 2[kg] 106

Fig 4.37 Performance of Trapezoidal Joint Angle output of PAM manipulator using neural NARX-IMC-PID control: (a)-Frequency 0.1[Hz]; (b)- Frequency 0.2[Hz]; (c)- Frequency 0.4[Hz] 107

Figure 5.1: Triangle input membership function with spacing factor = 0.5 112

Figure 5.2a: The Seed Points and the Grid Points for Rule-Base Construction 113

Figure 5.2b: Derived Rule Base 113

Figure 5.3 Block diagrams of MGA-based 2-Axes PAM manipulator Inverse Double Fuzzy Model 116

Figure 5.4: Block diagrams of MGA-based 2-Axes PAM manipulator Forward Double Fuzzy Model 117

Figure 5.5 Double NARX Fuzzy Model Identification Procedure 118

Figure 5.6a: Forward Double NARX Fuzzy Model Training data obtained by experiment 119

Figure 5.6b: Inverse Double NARX Fuzzy Model Training data obtained by experiment 119

Figure 5.7 Fitness Convergence of MGA-based Forward Double Fuzzy Model Optimization 121

Figure 5.8 Validation of MGA-based Forward Double Fuzzy Model 122

Figure 5.9 Fitness Convergence of MGA-based Inverse Double Fuzzy Model Optimization 122

Figure 5.10 Validation of MGA-based Inverse Double Fuzzy Model 124

Figure 5.11 Block diagrams of The MGA-based PAM manipulator Inverse Fuzzy Model Identification 126

Figure 5.12 Inverse NARX Fuzzy Model Training data obtained by experiment 127

Figure 5.13 Fitness Convergence MGA-based Inverse Fuzzy Model Identification of the PAM manipulator 127

Figure 5.14a Estimation of MGA-based Inverse Fuzzy Model of the PAM manipulator 129

Figure 5.14b Validation of MGA-based Inverse Fuzzy Model of the PAM manipulator 129

Figure 5.15 Block diagram of proposed Hybrid Online DNN-PID NARX-Fuzzy Feed-forward control 130

Fig 5.16 Structure of MLFNN network system used in proposed online tuning DNN-PID controller 131

Fig 5.17 Experiment SIMULINK model of Hybrid Online DNN-PID NARX11 Fuzzy control 135

Fig 5.18a Performance comparison of Triangular response of PAM manipulator 136

Fig 5.18b Online Tuning Parameters of Neural PID controller (Kp, Ki, Kd) and Gain Scheduler K (Triangular Trajectory) 137

Fig 5.18c Performance of Control Voltages (Ufuzzy, Upid and U) of Neural PID-NARX fuzzy controller

(Triangular Trajectory - Load 0.5[kg] and Load 2[kg]) 137

Fig 5.19a Performance comparison of Trapezoidal response of PAM manipulator 138

Fig 5.19b Online Tuning Parameters of Neural PID controller (Kp, Ki, Kd) and Gain Scheduler K (Trapezoidal Trajectory) 139

Fig 5.19c Performance of Control Voltages (Ufuzzy, Upid and U) of Neural PID-NARX fuzzy controller 139

(Trapezoidal Trajectory - Load 0.5[kg] and Load 2[kg]) Fig 5.20a Performance comparison of Sinusoidal response of PAM manipulator 140

Fig 5.20b Online Tuning Parameters of Neural PID controller (Kp, Ki, Kd) and Gain Scheduler K (Sinusoidal Trajectory) 141

Fig 5.20c Performance of Control Voltages (Ufuzzy, Upid and U) of Neural PID-NARX fuzzy controller (Sinusoidal Trajectory - Load 0.5[kg] and Load 2[kg]) 141

Fig 5.21.Performance comparison of Sinusoidal 0.1[Hz] response of PAM manipulator 142

Fig 6.1 Structure of MIMO Neural NARX11 model 146

Fig 6.2 Forward Neural MIMO NARX Model Training data obtained by experiment 147

Fig 6.3 Inverse Neural MIMO NARX Model Training data obtained by experiment 148

Fig 6.4a Structure of proposed Inverse and Forward MIMO NARX11 models of 2-axes PAM manipulator 149

Fig 6.4b Structure of proposed Inverse and Forward MIMO NARX22 models of 2-axes PAM manipulator 149

Fig 6.5a,b Block diagram for modeling of Inverse Neural MIMO NARX model of 2-axes PAM manipulator 150

(A)- Inverse Neural MIMO NARX11 model; (B)- Inverse Neural MIMO NARX22 model

Fig 6.5c,d Block diagram for modeling of Forward Neural MIMO NARX model of 2-axes PAM manipulator 151

(C)- Forward Neural MIMO NARX11 model; (D)- Forward Neural MIMO NARX22 model Fig 6.6a: Fitness convergence of proposed Forward MIMO NARX11 and Forward MIMO NARX22 Models 152

Fig 6.6b: Fitness convergence of proposed Forward MIMO NARX11 and Forward MIMO NARX22 Models 153

Fig 6.7a Validation of 2-axes PAM manipulator Inverse MIMO NARX11 and Inverse MIMO NARX22 153

Fig 6.7b Validation of 2-axes PAM manipulator Forward MIMO NARX11 and Forward MIMO NARX22 154

Fig 6.8.Block diagram of 2-axes PAM manipulator Hybrid Neural MIMO NARX-FNN-PID position control 156

Fig 6.9a Online SIMULINK diagram of 2-axes PAM manipulator conventional PID control 159

Fig 6.9b Online SIMULINK diagram of 2-axes PAM manipulator Hybrid MIMO NARX11 FNN-PID control 159

Fig 6.9c Online SIMULINK diagram of 2-axes PAM manipulator Hybrid MIMO NARX22 FNN-PID control 160

Fig 6.10a Parameter Configuration of Inverse MIMO NARX11 used in MIMO NARX11-FNN-PIDcontrol 160

Fig 6.10b Parameter Configuration of Inverse MIMO NARX22 used in MIMO NARX22-FNN-PIDcontrol 160

Fig 6.11a Performance comparison with Triangular response of 2-axes PAM manipulator – Load 0.5[kg] 162

Fig 6.11b Performance comparison with Triangular response of 2-axes PAM manipulator – Load 2[kg] 163

Fig 6.12a Performance comparison with Trapezoidal response of 2-axes PAM manipulator – Load 0.5[kg] 164

Fig 6.12b Performance comparison with Trapezoidal response of 2-axes PAM manipulator – Load 2[kg] 165

Fig 6.13 Performance comparison with sinusoidal 0.1[Hz] response of PAM manipulator – Load 0.5[kg] 166

Fig 6.14.Performance comparison with sinusoidal 0.025[Hz] response of PAM manipulator – Load 0.5[kg] 166

Fig 6.15 Performance comparison with sinusoidal 0.2[Hz] response of PAM manipulator – Load 0.5[kg] 167

Fig 6.16 Performance comparison with sinusoidal 0.4[Hz] response of PAM manipulator – Load 0.5[kg] 168

Fig 6.17 Line trajectory tracking of 2-axes PAM manipulator – Load 0.5[kg] 169

Fig 6.18 Circular trajectory tracking of 2-axes PAM manipulator – Load 0.5[kg] 169

List of Tables

Table 2.1 Lists of experimental hardware 14

Table 3.1 GA-based Fuzzy Model Parameters used for encoding 39

Table 3.2 MGA-based Fuzzy Model Parameters used for encoding 44

Table 3.3 MGA-based NARX Fuzzy Model Parameters used for encoding 49

Table 3.4 Rule-base of the MGA-based PAM manipulator Fuzzy Model (Fitness value = 7840) 61

Table 3.5 Rule-base of the MGA-based PAM manipulator NARX22 Fuzzy Model (Fitness value = 18893) 61

Table 3.6 Summary of the MGA-based PAM manipulator Fuzzy Model Configuration Parameters 61

Table 4.1 List of experimental hardware 72

Table 4.2 A Comparison of EI values for different hidden Neurons of NNARX22 Model 78

Table 4.3 A Comparison of EI values with different Neurons of single hidden Layer of NNARX11 Model 81

Table 4.4 A Comparison of EI values for different hidden 82

Table 4.5 A Comparison of EI Values for Different Input Regression Vectors N 0 83

Table 4.6a Resulted weights of Inverse neural NARX11 model – Number of weighting values = 21 94

Table 4.6b Resulted weights of Forward neural NARX11 model – Number of weighting values = 21 94

Table 4.7a Resulted weights of Inverse neural NARX22 model – Number of weighting values = 31 94

Table 4.7b Resulted weights of Forward neural NARX22 model – Number of weighting values = 31 95

Table 5.1 MGA-based Double NARX Fuzzy Model Parameters used for encoding 114

Table 5.2 Summary of the MGA-based PAM manipulator Inverse Fuzzy Model Configuration Parameters 130

Table 6.1a Optimized weights of proposed Inverse MIMO-NARX11–Total Number of weighting values=47 154

Table 6.1b Optimized weights of proposed Forward MIMO-NARX11–Total Number of weighting values=47 155

Table 6.2a Optimized weights of proposed Inverse MIMO-NARX22–Total Number of weighting values=77 155

Table 6.2b Optimized weights of proposed Forward MIMO-NARX22–Total Number of weighting values=77 155

Table 6.3 Parametric values of 2-axes PAM-Based Manipulator PID Controllers 162

E N : Summed error of batch training mode with N input-output samples

F i : Activation function of i th neuron of the output layer

f j : Activation function of j th neuron of the hidden layer

K : Number of steps used to accumulate the error values

m : Number of neurons of output layer

N : Number of input-output training samples

n : Number of neurons of input layer

n a : The order of output y(z -1 )

n b : The order of input u(z -1 )

n k : The time delay (in this paper, n k = T =1)

q : Number of neurons of hidden layer

r : Ratio between predicted error and current error

O j : The j th output from the hidden layer

u l : The l th input to the input layer

W ij : Weight from the j th neuron in the hidden layer to the i th neuron of the output layer

w jl : Weight from the l th neuron in the input layer to the j th neuron of the hidden layer

y i : The i th output from the output layer

i

yˆ : The i th predicted output from the output layer

z l : The l th output from the input layer (in this paper, u l = z l.)

Z N : The training set with N input-output samples

Comparison of Identification and Control of

2-Axes PAM Manipulator

Ho Pham Huy Anh School of Mechanical and Automotive Engineering

Graduate School University of ULSAN

Abstract

Over the past decades, the importance of manipulators in a wide range of applications like industrial manufacturing, and handling of heavy objects or hazardous materials has increased immeasurably They are used for the fast and accurate execution of repeated tasks in an isolated industrial environment This requires a functional design specialized for a specific task with stiff joints and strong actuators Modern manipulators are becoming more and more compact, light and stable, and are often designed to operate in human environments

One of important applications of manipulator focuses on the control performance improvement of pneumatic artificial muscle (PAM) manipulator in order to realize the rehabilitation therapy robot which becomes an urgent work that has led an increasing amount

of research on over the work in the recent years Dealing with that research, the intelligent model-based controllers based on intelligent models which are strongly encouraged in modern control are proposed and applied firstly to 1-axis PAM manipulator and updating to 2 axes PAM manipulator in the way of step by step in this thesis

Since it is difficult to distinguish between the robot working space and the human existing space, the rehabilitation robot must afford a high level of safety and flexibility for humans that are not necessary in general industrial robots Unfortunately, this kind of robot has not been thoroughly studied due to its mechanical structure and motorization Therefore, the orientation

of robotics toward rehabilitation applications requiring greater proximity between the robot and the human operator has recently led researchers to develop novel actuator adapting some analogies with natural skeletal muscle A novel PAM actuator which has becoming increasingly popular to provide lots of advantages such as high strength to weight ratio and high power to weight ratio, low cost, safety, compactness, ease of maintenance, cleanliness, readiness and mobility assistance to humans performing tasks, has been evaluated during the recent decades as an attractive alternative to hydraulic and electric actuators The PAM actuator now undoubtedly plays the most important role for the actuation of future human friendly therapy robots Consequently, PAM actuators are used to operate the PAM manipulator driven for the functional recovery therapy Nevertheless, it still exists lots of drawbacks including the time variance, compliance, hysteresis, nonlinearity, the air compressibility and the lack of damping ability of the PAM actuator cause not only the dynamic delay of the pressure response but also the oscillatory motion as well

In addition, it is desirable in many medical applications to have manipulators which can follow a specific trajectory If a multi-joint manipulator tries to follow a desired trajectory, the appropriate motor commands must be applied to each joint of the arm at all times during the motion Every joint is dependent on its parent joints, and wrong motor commands can lead to undesirable movements; this can result in unpredictable consequences which may cause an adverse impact on the robot’s task and its environment Likewise, the correct motor commands must be adapted over time in order to take into consideration changing physical parameters such as arm load, contact force variation, or joint friction

Furthermore, classic feedback control showed to be inappropriate for compliant

force/position movements since it requires high gains in order to guarantee accuracy However, high gains can result in large correction forces which reduce compliance In order to deal with

this problem, a feed-forward component with an accurate inverse dynamics model of the

manipulator can be used Then, desired motions can be predicted and only small correction forces are required, which increases the compliance Analytical approaches make rigid-body assumptions to calculate the inverse dynamics model Unfortunately, calculating the dynamics analytically is complex, and in many cases, precise dynamics parameters may not be known Rehabilitation robots with large degrees of freedom, lightweight links and flexible joints do not meet rigid body assumptions

As with those problems above of PAM manipulator and the requirements for safety to the human in case of the rehabilitation therapy robot, the intelligent controllers based on intelligent inverse and forward dynamic models are proposed in this thesis as follow:

First, trajectory tracking control of the 1-axis and 2-axes PAM manipulator has been a difficult challenging problem to be solved up to now A lot of research has dealt with it As the most popular approach, computed-torque method or inverse dynamic control method is used most for robot dynamic control However, it is difficult to obtain the desired control performance when the control algorithm is only based on the robot dynamic model based on mathematical equations Rehabilitation robots have to face many uncertainties in their dynamics, in particular structured uncertainty, such as payload parameter or external force variation, and unstructured one, such as friction and disturbance A newly promising concept bases on fuzzy logic, neural network and neuro-fuzzy systems for modeling, identification and control of nonlinear robot dynamics Neural networks make use of nonlinearities, learning ability, parallel processing ability, and function approximation for applications in advanced adaptive control Initiatively, this thesis introduces novel intelligent dynamic models First the newly proposed nonlinear NARX fuzzy model is the first identified and optimized by proposed Modified Genetic Algorithm (MGA) and second the novel nonlinear neural NARX model for 1-axis PAM manipulator is trained and optimized by proposed Incremental Back-Propagation (INCBP) learning algorithm

Second, in order to overcome the drawback of advanced control algorithms often

considering the n-DOF manipulator as n independent decoupling joints which causes consequently all intrinsic coupling features of the n-DOF manipulator have not represented in

its dynamic model respectively To overcome these drawbacks, first a new approach of nonlinear Double NARX fuzzy model is the first identified by proposed MGA and second the nonlinear Neural MIMO NARX model identified by BP learning algorithm, firstly utilized in simultaneous modeling and identification two-joint’s dynamics of the prototype 2-axes PAM manipulator system

Third, novel proposed Inverse NARX Fuzzy model obtaining superb features both in the speed of convergence and in improving the performance This novel proposed technique may leads an increase in the use of proposed NARX Fuzzy Model not only in modeling, simulation and identification the highly nonlinear systems but also in online adaptive and predictive

control the dynamic nonlinear systems in general and the 1-axis and 2-axes PAM manipulator

in particular This thesis introduces the applications of the proposed Hybrid Inverse NARX Fuzzy Feed-forward PID controller and the novel Hybrid Inverse NARX Fuzzy IMC PID controller which were found to assert experimentally not only the excellent performance but also the highly robustness in the presence of intrinsic and external disturbances This facilitates testing under different input conditions and ensures future applications of the PAM manipulator as a rehabilitation device for stroke patients

Fourth, a new intelligent control algorithm is firstly proposed with a gain scheduling adaptive control scheme based on combining inverse NARX fuzzy model, neural dynamic PID and genetic algorithm An inverse NARX fuzzy feed-forward controller is developed This NARX fuzzy model structure is optimally designed by using a modified genetic algorithm (MGA) Furthermore, a neural gain scheduler is designed and online updated by the fast learning Back-Propagation (FLBP) algorithm Simultaneously, FLBP algorithm will tune online the parameters of the neural dynamic PID controller in parallel installation with NARX

fuzzy feed-forward controller Experiment results are shown to demonstrate the efficiency of

the proposed control system applied on highly nonlinear PAM manipulator trajectory tracking control

Finally, based on resulting Inverse MIMO NARX model, a novel MIMO NARX-Dynamic Feed-forward PID control scheme is applied to control the trajectory of the 2-axes PAM manipulator as to improve its trajectory tracking performance The experiment investigation of novel proposed control scheme is carried out on the 2-axes PAM manipulator with 2 different endpoint Payload values and using three different control methods as to demonstrate the performance of proposed control scheme The results of the experiment have demonstrated the feasibility and excellent performance of the novel approach in comparison with the

conventional PID control and neural PID control strategies Consequently, the proposed

MIMO NARX-DFNN-PID Control scheme is quite suitable to be applied for the modeling, identification and control of 2-axes PAM manipulator used as wrist and elbow rehabilitation robot

Research is never finished and researcher is to indicate the focus of future attention In this dissertation, a study on the improvement of modeling identification and control performance

of the 1 axis and 2 axes PAM manipulator is focused in order to realize the 2-axes PAM-based

rehabilitation robot The effectiveness of the proposed intelligent models and intelligent model-based control algorithms are demonstrated through experimental results which are applied successfully on the 1 axis and 2 axes PAM manipulator And the experiment results eventually show that the 2-axes PAM manipulator adapts well for constructing the human friendly 2-axes PAM-based rehabilitation robot based on these new intelligent models and intelligent model-based advanced control schemes

Part I Introduction

Chapter 1 Introduction

1.1 Overview

The pneumatic artificial muscle (PAM) is a flexible actuator having similar characteristics to human muscles The PAM is based on learning the principle of physical movement of human muscle An artificial muscle PAM consists of an internal bladder (rubber tube) surrounded by a braided mesh shell (with flexible yet non-extensible threads) that is attached at either end to fittings or to some tendon-like structure When the internal bladder is pressured, the high-pressure gas pushes against its inner surface and against the external shell, and tends to increase volume Due to the non-extensibility of the threads in the braided mesh shell, the artificial muscle shortens according to its volume increase and/or produces tension if it is coupled to a mechanical load When the air pressure rises in the rubber tube, it inflates along radius direction and subsequently causes tension in the circumference direction With the help of mesh shell, the caused tension is converted to contract force along axis direction Therefore, by modulating the air pressure in the rubber tube, it is able to enable an artificial muscle to change status between contraction and relaxation Then we could utilize two artificial muscles to form an artificial single-freedom joint, similar to a couple of antagonistic muscles of human beings In recent years, artificial muscle is widely used in the fields of medical treatment, nursing, biomedicine and etc [1],

[2], [3] Many nations have begun to do research on it, regarding artificial muscle as a part of new-type robot

PAM actuators have been used in some precision robotic tasks as well as in human exoskeletons for enhancement of strength and mobility PAM possesses all the advantages

of traditional pneumatic actuators (i.e., cheapness, light weight) and in contrast to traditional pneumatic actuator PAM has very high power/weight and power/volume ratios

[4] This is an advantage for robotic and exoskeleton applications, in which heavy actuators can add significantly to the payload

Research into the applications of PAM and their properties has been undertaken at the Human Sensory Feedback (HSF) Laboratory, Wright Patterson Air Force Base, Dayton,

OH [4], [5], [6], [7], the University of SALFORD, U.K [8], the Bio-Robotics Laboratory, University of Washington, Seattle [9], the Intelligent Robotics Laboratory, University of Louisville, Nashville, TN [10], [11], and the Fluid Power Machine Intelligence (FPMI) Laboratory, ULSAN University [12], [13], [14] and so on

PAMs are now widely used in the various fields of medical robots and other industrial applications The orientation of modern robotics toward applications requires greater friendliness between robot actuator and human operator This demand has recently led researchers to develop new actuators sharing some analogies with natural musculature Among them, PAM actuator, which has achieved increasing belief to the ability of providing advantages such as high power/weight ratio, full of hygiene, easiness in preservation and especially the capacity of human compliance which is the most important requirement in medical and human welfare field Therefore PAM has been regarded during the recent decades as an interesting alternative to hydraulic and electric actuators

Consequently, PAM-based applications have been published increasingly Caldwell et al

(2003) in [1] have developed and controlled of a PAM-based Soft-Actuated Exoskeleton for

use in physiotherapy and training Kobayashi et al (2003) in [2] have applied PAM as to

develop a Muscle suit for Upper Body Noritsugu et al (2005) in [3] have used PAM for developing an Active Support Splint among them

A major difficulty inherent in PAM technology, as with PAM actuators in general, is the problem of controlling them precisely This is because they are highly nonlinear and time varying Since the rubber tube and plastic sheath are continually in contact with each other and the PAM shape is continually changing, the PAM temperature varies with use, changing the properties of the actuator over time Up to now, approaches to PAM control have included PID control, adaptive control [11], nonlinear optimal predictive control [15], variable structure control [6][16], gain scheduling in Repperger et al.(1999)[17], and various soft computing approaches including neural network Kohonen training algorithm control [18]

and neuro-fuzzy/genetic control in Carbonell, et al (2001)[19], in Lilly and Chang (2003)[20] This thesis addresses the intelligent modeling of a PAM manipulator actuated by one and two groups of antagonistic PAM pair Due to their highly nonlinear and time-varying

parameter nature, PAM manipulator modeling and identification presents a challenging nonlinear model problem that has been approached via many methodologies Related literature has appeared lots of ways aiming for modeling the PAM actuator such as Lilly in

[11], Medrano-Cerda in [21], Repperger et al in [17], Chan, Lilly et al., (2003) in [22] and so on Recently, Ahn and Anh (2006) in [12] applied modified genetic algorithm (MGA) for optimizing parameters of linear ARX model of the PAM manipulator which can be modified online with adaptive self-tuning control algorithm Consequently, the performance of ARX model-based adaptive control algorithm obtains the precision within (-0.5-+0.5) [deg][13] Nevertheless modern manipulators are aiming at obtaining the error index more and more precise

Although many intelligent control algorithms based on neural network have been proposed, such as an intelligent control using a neuro-fuzzy network was proposed by Iskarous and Kawamura [23]; a hybrid network that combines fuzzy and neural network was used to model and control complex dynamic systems like the PAM system[11]; an adaptive controller based on the neural network was applied to the artificial hand which is composed

of the PAM [24] Here, the neural network was used as a controller, which had the form of compensator or the inverse of the model It was not easy to apply these control algorithms

to the PAM manipulator with high hysteresis which is still not yet modeled successfully in the nonlinear inverse dynamics, to the quickly-changing external load condition systems and to reconcile both damping and response speed in high gain control

Such these difficulties prove that up to now, it always exists a challenging problem of a

simple and quite efficient intelligent model for the 1-link and 2-link PAM manipulator

which will be utilized effectively not only in modeling, identification and simulation but also able to be applied in adaptive online control of the highly nonlinear systems like PAM manipulator In order to be used in advanced robotics, in particularly used for human friendly PAM-based rehabilitation robot, these problems above need to be handled and it is the goal as to be solved in my thesis

1.2 Motivation

A new intelligent approach of Modeling Identification and Control of PAM manipulator was studied in order to realize the rehabilitation robot in the near future is mentioned with the motivations and solutions as follow:

6 To utilize in therapy robot in the near future such as rehabilitation robot for recovery function of upper and lower limbs, it is necessary to improve the performance of transient response, even if the external load conditions change severely This leads to urgent requirement of novel dynamic model of PAM manipulator as to be applied efficiently in modeling, simulation and advanced control as well An intelligent NARX Fuzzy model optimized by Modified Genetic Algorithm is newly proposed MGA algorithm processes the experiment input-output training data from the real PAM system and optimizes the NARX fuzzy model parameters This is referred to perform fuzzy identification by which generates automatically the appropriate fuzzy

if-then rules to characterize the dynamic nonlinear features of the real plant The

object of the study is to formulate a highly efficient dynamic NARX Fuzzy model in both of 1st order NARX11 and 2nd order NARX22 as well so that it would be quite suitable for precise parameter identification as well as for advanced model-based control of the highly nonlinear PAM manipulator

6 To realize the precise position control and to improve the robust control performance without regard the various external load conditions, the effect of nonlinear factors contained in the PAM manipulator will be handled by using an advanced model-based controller based on novel proposed neural NARX model optimized by newly proposed Incremental Back-Propagation (INCBP) learning algorithm Results of training and testing on the complex dynamic systems such as PAM manipulator show that the proposed neural NARX model presented in this study can be used in adaptive online model-based control with better dynamic property, strong robustness and thus resulting Neural NARX model is suitable to be applied for the modeling of various plants, including dynamic and nonlinear process

6 To efficiently execute rehabilitation process, the 2-axes PAM manipulator used as an elbow and wrist rehabilitation robot needs to overcome the disturbance of coupled effects inherent in its operation Thus, a novel concept of intelligent neural MIMO NARX model is newly introduced The experimental results shown that the proposed Neural MIMO NARX model had a good modeled and identified performance for the highly nonlinear MIMO system, such as the 2-axes PAM manipulator The proposed

Inverse and Forward Neural MIMO NARX model had an excellently adaptive capability both in simulation and in real-time advanced control as well

6 To satisfy highly precise requirement in position control, a newly proposed intelligent controller which includes both dynamic inverse neural NARX model used in Feed-forward controller and the error feedback compensator of conventional PID controller Due to the excellent capacity of online tuning of neural NARX model’s weighting values based on novel fast-learning BP algorithm (FLBP) which is used to control of complex dynamics systems such as PAM manipulator without regard the changes of external environments Consequently a superb hybrid of feedback PID regulator and the neural NARX model’s powerful capability of learning, adaptive and tackle nonlinearity bring us a good-tracking trajectory control for such PAM manipulators The performance of the proposed hybrid online neural NARX feed-forward PID control scheme is proved excellently in experiment thank to the mixture between the robust feed-forward + feedback structure with the good approximation and prediction

of proposed inverse neural NARX model

6 The precise trajectory tracking control performance of PAM manipulator can be obtained without regard the various frequencies and the load variations by applying a new concept of online tuning Dynamic Neural PID and the Feed-forward NARX Fuzzy model control scheme The Inverse NARX fuzzy model is optimally designed

by Modified genetic algorithm (MGA) Furthermore, a neural gain scheduler is designed and online updated by the fast learning Back-Propagation (FLBP) algorithm Simultaneously, FLBP algorithm will tune online the optimal parameters of the neural dynamic PID controller in parallel installation with NARX fuzzy model-based feed-

forward controller Experimental results are shown to demonstrate the efficiency of

the proposed control system applied on highly nonlinear PAM manipulator trajectory control

1.3 Outline of thesis

The research outline of this dissertation is arranged as follows:

A general hardware configuration of the 2-axes PAM manipulator is given in Chapter 2 Totally experiment setup for developing the new concept of intelligent model and

intelligent model-based advanced control algorithms and the characteristics of PAM manipulator are also given in detail Furthermore, an introduction to the operation of PAM manipulator system is included in order to explain clearly its extremely complexity and high nonlinearity as well

The improvement of the novel intelligent models of nonlinear PAM manipulator and its real-time intelligent model-based control applications is given in Part II with 4 Chapters which are MGA-based nonlinear NARX fuzzy model identification; modeling and identification of PAM manipulator based on proposed neural NARX model optimized with proposed INCBP learning algorithm; advanced MGA-based Double NARX fuzzy model identification of the 2-axes PAM manipulator and novel proposed identification of 2-axes PAM manipulator using nonlinear neural MIMO NARX model Through 4 Chapters of Part

II, Intelligent models have been developed as to be applied not only to 1-axes PAM manipulator (Chapter 3 and 4) but also to 2-axes PAM manipulator (Chapter 5 and 6) which is eventually used as a 2-axes PAM-based rehabilitation robot

Chapter 3 provides a MGA-based NARX fuzzy model of the 1-axes PAM manipulator which perfectly combines the extraordinary approximating capacity of fuzzy model with powerful predictive and adaptive potentiality of the nonlinear ARX structure embedded in proposed NARX Fuzzy model The object of this study is to exploit novel proposed MGA for building an effective NARX Fuzzy model obtaining good features both in speed convergence and in improving performance This novel proposed technique may leads an increase in the use of proposed NARX Fuzzy Model not only in modeling, simulation and identification of highly nonlinear systems but also in advanced model-based control of dynamic nonlinear systems in general and the prototype PAM manipulator in particular As

to apply in real-time control, a novel Hybrid Inverse NARX Fuzzy Feed-forward PID control scheme applied for PAM manipulator position control is described The experimental results show that the proposed control scheme had a good control performance for the highly nonlinear PAM manipulator system The controller designed by this method only need an offline training procedure in advance, with its requirement only the input and output training data from the plant for the adaptation of proposed Inverse NARX Fuzzy model Consequently, it was verified that the proposed NARX fuzzy model

and its control application presented in this chapter was precise and flexible with simple structure and obtain perfect dynamic property and strong robustness

Forwardly, in Chapter 4 a novel nonlinear neural NARX model is initiated to match more efficiently the serious nonlinearity and high hysteresis, as well as the compliance, time variance, which have made PAM manipulator quite difficult to model and to control with high performance and accuracy as well A novel neural NARX model based on advanced Back Propagation (INCBP) training algorithm is given in detail in this chapter Consequently, the full research of nonlinear Neural NARX model of 1-axes PAM manipulator with various input nodes as well as various hidden layer nodes is successfully discussed Compared with classic BP algorithm, novel INCBP algorithm has better convergence, stability, and more potential for later use Based on powerful neural NARX model, model-based advanced control research would flourish naturally in fields of online neural NARX controller, adaptive self-tuning control using neural NARX model and so on Thus, a novel proposed Hybrid neural NARX-Internal Model Control (IMC)-PID control method based on forward and inverse neural NARX model is introduced This controller designed based on Neural NARX model only need an offline training procedure in advance, and then run online efficiently by combining the robust IMC structure with the excellent approximation, parallel processing and predictive capacity of neural NARX model and the refined regulating capacity of feedback PID-based regulator From the experiments of the position control of the 1-axes PAM manipulator, it was verified that the proposed control algorithm is really an effective control method to develop a practically available PAM-based rehabilitation robot

In order to improve the performance of novel concept of NARX fuzzy model, based Double NARX fuzzy model identification of the 2-axes PAM-based rehabilitation robot is newly proposed in Chapter 5 This new approach of Double NARX Fuzzy model firstly utilized in modeling and identification of the prototype 2-axes PAM-based rehabilitation robot system which has overcome successfully the nonlinear coupled effects

MGA-of the 2-axes PAM system and resulting Double NARX Fuzzy model surely enhance the control performance of the 2-axes PAM system, due to the extraordinary capability in learning nonlinear characteristics and coupled effects as well of this novel intelligent model Results from training and testing on the 2-axes PAM system shows that the newly proposed

Double NARX Fuzzy model can be used in online control with better dynamic property and strong robustness Consequently, this resulting Double NARX Fuzzy model is quite suitable to be applied for the modeling, identification and control of various plants, including linear and nonlinear MIMO process without regard greatly changing external environments As to demonstrate the power of novel Double NARX Fuzzy model, an intelligent model-based control scheme which combines all advantages of NARX fuzzy model, dynamic online neural PID and genetic algorithm optimization is depicted in this chapter This hybrid NARX fuzzy feed-forward + neural online PID controller was developed and obtained excellent performance and robustness in the 2-axes PAM-based rehabilitation robot trajectory tracking control

Finally, Chapter 6 describes an intelligent MIMO neural NARX model, which combines harmoniously the nonlinear approximation, parallel processing and superb prediction of recurrent neural networks and nonlinear ARX structure, to model and adapt all of complex dynamics features and coupled effects of the 2-axes PAM-based rehabilitation robot Proposed MIMO NARX model firstly utilized in modeling and identification of the highly nonlinear 2-axes PAM system which has overcome successfully the coupled effects and nonlinear characteristic of the 2-axes PAM-based rehabilitation robot In addition, results of training and testing on the complex dynamic systems such as the 2-axes PAM manipulator show that the newly proposed MIMO NARX model presented in this study can be used in online control with better dynamic property and strong robustness The rest of this chapter describes the novel hybrid MIMO neural NARX Dynamic Feed-forward PID controller for the 2-axes PAM-based rehabilitation robot position control It has shown that the proposed method had a good control performance for the highly nonlinear system, such as the 2-axes PAM manipulator The controller had an adaptive control capability and the neural MIMO NARX model parameters were optimized via the fast learning back propagation (FLBP) learning algorithm Consequently, the proposed MIMO NARX-DFNN-PID Control scheme based on novel neural MIMO NARX model is quite suitable to be applied for the position control of 2-axes PAM manipulator used as wrist and elbow rehabilitation robot

The final Part III is with the conclusions and discussion given in Chapter 7 Summarizing the outcomes of this thesis is mainly described in this Chapter

Chapter 2

Configuration, Experiment Setup and Characteristics of 2-Axes PAM Manipulator

2.1 Introduction

The pneumatic artificial muscle (PAM) was developed in artificial limb research in the 1950s and 1960s [25-26] They have recently been commercialized by the Bridgestone Rubber Company of Japan for robotic applications [27], and re-engineered by Prof Jack Winters for construction of bio-mechanically realistic skeletal models Pneumatic artificial muscles consist

of an internal bladder surrounded by a braided mesh shell (with flexible yet non-extensible threads) that is attached at either end to fittings or to some tendon-like structure The structure

of the pneumatic artificial muscle is shown in Fig 2.1 When the internal bladder is pressurized, the high pressure gas pushes against its inner surface and against the external shell, and tends to increase its volume Due to the non-extensibility (or very high longitudinal stiffness) of the threads in the braided mesh shell, the actuator shortens according to its volume increase and/or produces tension if it is coupled to a mechanical load This physical configuration causes pneumatic artificial muscles to have variable-stiffness spring-like characteristics, non-linear passive elasticity, physical flexibility, and very light weight compare to other kinds of artificial actuators [28]

Thus, the development of one component of a rehabilitation therapy robot, pneumatic artificial muscle manipulator, is reported, which its configuration is explained in next section [32]

.

Figure 2.1 Structure of the PAM actuator [32]

2.2 Configuration, experiment setup and characteristic of the 2-axes pneumatic

artificial muscle (PAM) manipulator

2.2.1 Configuration of the 2-axis PAM manipulator system

A general configuration and working principle of 2-axis PAM manipulator is shown in Fig 2.2 and Fig 2.3 This configuration is totally built for the purpose of researches such as the novel intelligent nonlinear Double NARX Fuzzy model and novel intelligent neural MIMO NARX model modeling and identification, proposed Hybrid Inverse MIMO NARX Feed-forward PID using neural MIMO NARX model Thus, with respect to the purpose of research

in next 4 chapters of Part 2 and in next 4 chapters of Part 3, some components in the 2-axes

(a) Working of PAM

(b) PAM – FESTO Product

(c) The structure of PAM

PAM manipulator system may be redundant, but they do not make effect to total system More detail of the 2-axes PAM manipulator system will be come in next section

Figure 2.2 General configuration of 2- axes PAM manipulator

Figure 2.3: Working principle of the 2-axes PAM manipulator

2.2.2 Experiment setup

Totally the schematic diagram of the pneumatic artificial muscle manipulator is shown in Fig 2.4a and Fig 2.4b The hardware includes an IBM compatible PC (Pentium 1.7 GHz)

which sends the voltage signals u 1 (t) and u 2 (t) to control the two proportional valves (FESTO,

MPYE-5-1/8HF-710B), through a D/A board (ADVANTECH, PCI 1720 card) which changes

digital signals from PC to analog voltage u 1 (t) and u 2 (t) respectively

The rotating torque is generated by the pneumatic pressure difference supplied from compressor between the antagonistic artificial muscles Consequently, the both of joints of the

air-2-axes PAM manipulator will be rotated to follow the desired joint angle references (Y REF1 (k)

and Y REF2 (k)) respectively The joint angles, θ1[deg] and θ2[deg], are detected by two rotary encoders (METRONIX, H40-8-3600ZO) and fed back to the computer through a 32-bit counter board (COMPUTING MEASUREMENT, PCI QUAD-4 card) which changes digital

pulse signals to joint angle values y 1 (t) and y 2 (t) The pneumatic line is conducted under the

pressure of 4[bar] and the software control algorithm of the closed-loop system is coded in mex program code run in Real-Time Windows Target of MATLAB-SIMULINK environment Table 2.1 presents the configuration of the hardware set-up installed from Fig.2.4a and Fig.2.4b A photograph of the experimental apparatus is shown in Fig 2.2

C-Figure 2.4a Schematic diagram of the 2-axes PAM manipulator

Fig.2.4b: Experimental Configuration of the 2-axes PAM manipulator system

Table 2.1 Lists of the experimental hardware set-up

2.2.3 Configuration of 1-axis PAM manipulator system

The 1-axis PAM manipulator derived from the prototype 2-axes PAM manipulator with the

1st Joint of the 2-axes PAM manipulator is fixed and proposed control algorithm is applied to control the joint angle position of the 2nd Joint of the prototype 2-axes PAM manipulator The block diagram of the 1-axis PAM manipulator’s experiment apparatus are shown in Fig 2.5 and Fig 2.6

Air

Compressor

Proportional Valve 1

PC

Computer

D/A Board

Counter Board

PAM 1

PAM 2

Pneumatic line Control line

Rotary Encoder1

Proportional Valve 2

MEASUREMENT

The air pressure servo valve manufactured by FESTO Corporation is used The resolution

of the counter and the D/A converter is both set at 32 bits The angle encoder sensor is used to measure the output angle of the joint The entire system is a closed loop system through

computer It first sends the initial voltage value u 0 (t)= 5[V] to proportional valve as to inflate

the artificial muscles with air pressure at P0 = 5[bar] to render the joint initial status By

changing the control voltage value u(t), we could set the air pressures of the two artificial muscles at (P 0 + ∆P) and (P 0 - ∆P), respectively As a result, the joint is forced to rotate for a certain angle Then we can measure the joint angle rotation through the rotary encoder and the counter board

The hardware includes an IBM compatible PC (Pentium 1.7 GHz) which sends the testing

voltage signal u(t) to control the proportional valve (FESTO, MPYE-5-1/8HF-710B), through

a D/A board (ADVANTECH, PCI 1720 card) which change digital signal from PC to analog

voltage u(t) The rotating torque is generated by the pneumatic pressure difference supplied

from air-compressor between the antagonistic artificial muscles Consequently, the prototype PAM manipulator will be rotated The joint angle, θ [deg], is detected by a rotary encoder

(METRONIX, H40-8-3600ZO) and fed back to the computer through a 32-bit counter board (COMPUTING MEASUREMENT, PCI QUAD-4 card) which changes digital pulse signals to

joint angle value y(t) Payload at endpoint of the PAM manipulator is taken 1[kg] The

pneumatic line is conducted under the pressure of 5[bar] and the software is coded in C-mex file A schematic diagram of the experimental apparatus is shown in Fig 2.6

Fig.2.5 Block diagram for obtaining PRBS input-output data of the 1-link PAM manipulator

PAM 1

PAM 2

Pneumatic line Control line

θ

P1

P2 Joint-Angle y(t)

u(t)

Joint of PAM manipulator

Rotary Encoder

Figure 2.6 Block diagram of the experimental apparatus of the 1-link PAM manipulator

2.2.4 Basis Characteristic of pneumatic artificial muscle manipulator

The PAM is a tube clothed with a sleeve made of twisted fiber-code, and fixed at both ends

by fixtures The muscle is expanded to the radial direction and constricted to the vertical direction by raising an inner pressure of the muscle through a power-conversion mechanism of the fiber-codes The PAM has a property like a spring, and can change its own compliance by the inner pressure A few slide parts and a little friction are favorable to a delicate power control But the PAM has characteristics of hysteresis, non-linearity and low damping Particularly, the system dynamics of the PAM changes drastically by the compressibility of air

in cases of changing external loads

When using the PAM for the control of manipulator, it is necessary to understand its characteristics such as the high hysteresis, and serious nonlinearity and so on Therefore the following experiments are performed to investigate the characteristics of the PAM Figure 2.7 and 2.8 demonstrate the hysteresis characteristics for the joint This hysteresis can be shown

by rotating a joint along a pressure trajectory from P1=Pmax, P2=0 to P1=0, P2=Pmax and back again by incrementing and decrementing the pressures by controlling the proportional valve The hysteresis of the PAM is shown in Fig 2.7 The width of the gap between the two curves depends on how fast the pressures are changed; the slower the change in the pressures, the narrower the gap The trajectory, control input to the proportional valve, velocity, and pressure

of each chamber of the PAM are depicted in Fig 2.8 The velocity is numerically computed from the position Near the extreme values, the joint velocity decreases since the increase in exerted force for a constant change in pressure is less

-30 -20 -10 0

θ o []

0 5 10

θ o [/s]

0.0 0.2

Figure 2.8 Hysteresis of the PAM [32]

2.2.5 CHARACTERISTICS OF PNEUMATIC ARTIFICIAL MUSCLE

The basic mechanics characteristic of artificial muscle can be depicted with the equation below:

])1

∆ P [MPa]

The highly nonlinear feature of PAM is shown in Fig 2.9, which is extracted from (FESTO, 2005) [29], representing the relationship between the percentage of contraction rate h [%] and the exerting force F [N] of a pneumatic artificial muscle (PAM)

Equation (2.1) indicates that F, P and h are three critical variables to determine the characteristics of artificial muscle PAM When pressure P [bar] is constant, exerting force F [N] is nonlinear with h [%] Fig 2.9 illustrates the h-F relationships of artificial muscle

Meanwhile, Tondu and Lopez in [30] proved that due to the friction and wire resistance between rubber tubes and mesh shell during PAM works, the relation between pressure, contraction and force always contains a hysteresis Thus it means that the time-varying property of air muscle is existed through its intrinsic hysteresis feature [30][31] In order to overcome the disadvantages of nonlinear characteristics and hysteresis of artificial muscle, this thesis tries to apply novel proposed intelligent models (NARX Fuzzy model and neural NARX model) for modeling and identifying all dynamic and nonlinear features of the PAM manipulator system Forwardly based on proposed intelligent models, proposed advanced model-based control schemes will be applied as to efficiently, robustly and accurately position control the 2-axes PAM-based manipulator used as an elbow and wrist rehabilitation robot

Part II Intelligent Models and Advanced Model-Based Control Schemes of 2-Axes PAM Manipulator