Into the unknown part of the human limb dynamics identification using a robot : the robot inertial and flexible dynamics' effects and their treatment / Hyunah Kang

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학위논문 Into the unknown part of the human limb dynamics identification using a robot : the robot inertial and flexible dynamics' effects and their treatment

저자명
Hyunah Kang
발행사항
울산 : 울산과학기술원 대학원, 2023.8
청구기호
TD 621.8 -23-1104
형태사항
xiv, 120 p. ; 30 cm
자료실 서울관 서고(열람신청 후 1층 대출대)
제어번호
KDMT12024000008356
주기사항
학위논문(박사) -- 울산과학기술원 대학원, Dept. of Mechanical Engineering, 2023.8. 지도교수: Sang Hoon Kang
연계정보
외부기관 원문

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Title Page

Abstract

Contents

1. Introduction 20

1.1. Motivation 20

1.1.1. Mechanical Impedance 20

1.1.2. Mechanical Impedance Estimation 20

1.1.3. Human Limb Dynamics Identification with a Robot 21

1.2. Objectives 23

1.3. Methods 24

1.3.1. Stochastic Estimation of Human Arm Mechanical Impedance 24

1.3.2. A Commercial Robot Used in This Study 24

1.4. Overviews 26

2. Human Arm Mechanical Impedance Estimation 27

2.1. Detection of Robot dynamics 27

2.1.1. Introduction 27

2.1.2. Detection of Compliance and Vibration 27

2.1.3. Experimental setup 27

2.1.4. End-effector position data analysis 28

2.2. Physical System 29

2.2.1. Introduction 29

2.2.2. Development of 3-D spring array Device 29

2.2.3. Validation with 3-D Spring Array Device: Experimental setup 36

2.2.4. Validation with 3-D Spring Array Device: Estimation Method 40

2.2.5. Validation with 3-D Spring Array Device: Evaluation Method 40

2.3. Human Arm 3-MITFM 41

2.3.1. Introduction 41

2.3.2. Experimental Setup 42

2.3.3. Experiment Procedure 42

2.3.4. Estimation Method 43

2.3.5. Evaluation Method 43

3. Physically Realizable Perturbation for the Stochastic Estimation 44

3.1. Importance of Physically Realizable Perturbation 44

3.1.1. Introduction 44

3.1.2. Physically Unrealizable Perturbation 44

3.1.3. Experimental Results 45

3.1.4. Discussion 48

3.2. Effect of the Arbitrarily Designed Perturbations on 3-D MITFM Estimation 48

3.2.1. Introduction 48

3.2.2. Estimation of A 3-D Spring Array Device MITFM: Experimental Results 48

3.2.3. Discussion 49

3.3. Physically Realizable Perturbation Generation 50

3.3.1. Physically Realizable Perturbation 50

3.3.2. Detection of Robot Dynamics: Compliance and Vibration 50

3.3.3. Estimation of A 3-D Spring Array Device MITFM: Experimental Results 51

3.3.4. Discussion 55

3.4. Modified Physically Realizable Perturbation 55

3.4.1. Introduction 55

3.4.2. Improved Position Perturbations 56

3.4.3. Remained Unmodelled Robot Dynamics 61

3.4.5. Discussion 65

4. Unmodeled High Frequency Dynamics 66

4.1. Flexibility Equation and Spring Array Impedance Calculation 66

4.1.1. Spring Array Impedance with Flexibility: Equation Derivation 67

4.1.2. Estimated Spring Array Impedance 68

4.2. Discussion 70

5. Compensation of Unmodeled Robt Dynamics 71

5.1. Joint Flexibility Compensation 71

5.1.1. Flexible Robot Equation of Motion 71

5.1.2. Operational Space Equation of Motion 72

5.1.3. Linearization 72

5.1.4. Derivation of Parameters 73

5.2. Experimental Data Compensation 74

5.2.1. 3-D MITFM of Spring Array Compensation 74

5.2.2. 3-D MITFM of Human Arm Compensation 79

5.3. Discussion 88

6. Conclusion 89

6.1. Importance of Physically Realizable position perturbation 89

6.2. Unmodeled High Frequency Dynamics Excitation and Configuration 89

6.3. Unmodeled High Frequency Dynamics Compensation 90

Reference 91

Appendices 97

Appendix Ⅰ 97

Appendix Ⅱ 98

Appendix Ⅲ 99

Appendix Ⅳ 115

Appendix Ⅴ 118

Appendix Ⅵ 129

List of Tables

Table 2.1. The lengths and spring constants of the selected springs 34

Table 2.2. The lengths and spring constants of the nonselected springs 35

Table 2.3. Computed stiffness matrix elements (Left: selected springs, Right: nonselected springs) 35

Table 2.4. The spring constants of the five configurations 39

Table 3.1. Low-pass filter with different orders and cutoff frequencies at low frequency region. The two filters, filter1-n and filter2-n (n＝1, 2, 3, 4), were combined to generate improve perturbations. 57

Table 5.1. The mean and standard error of VAF and R² of the five spring array configurations with the original estimated 3-D MITFM and compensated 3-D MITFM. The VAF values were significantly... 78

Table 5.2. The 10 heathy subjects' information 82

Table 5.3. The mean and standard error of VAFo and R²o the 10 subjects with the original estimated 3-D MITFM and compensated 3-D MITFM. The accuracy values were significantly for all the terms.[이미지참조] 82

Table 5.4. The mean and standard error of the percentage fit percent as second-order linear system having two zeros. The diagonal term demonstrates an improvement of approximately 40%, while in the... 83

Table 5.5. The mean and standard error of the percentage fit percent as a system having six poles and six zeros of the original impedance data. 83

List of Figures

Fig. 1.1. HapticMater(Moog, the Netherlands) 25

Fig. 1.2. HapticMater mounted on a steel(S45C) base with size of 1200 x 1500 x 15 mm (W x H x D) 25

Fig. 2.1. IMU sensor attached at the end-effector of HapticMaster 28

Fig. 2.2. A 3-D spring array device with spring and mass 29

Fig. 2.3. A 1-D spring array device drawing. The gray rectangle represents mass of the spring array. There are two possible spring that can be connected. k₁a and k₁b are the spring constants.[이미지참조] 30

Fig. 2.4. A 2-D spring array device drawing [2, 3, 5, 17]. The gray rectangle represents mass of the spring array. There are eight possible springs that can be connected. k₁a, k₁b, k₂a, k₂b, k₃a, k₃b, k₄a, and...[이미지참조] 30

Fig. 2.5. Possible spring connections for the 3-D spring array device. (a) k₁a, k₁b, k₂a, k₂b, k₃a, k₃b, k₄a, k₄b (b) k₅a, k₅b, k₆a, k₆b, k₇a, k₇b, k₈a, k₈b (c) k₉a, k₉b, k₁₀a, k₁₀b (d) k₁₁a, k₁₁b, k₁₂a, k₁₂b, k₁₃a, k₁₃b[이미지참조] 31

Fig. 2.6. Apparatus overview. HapticMaster, spring array stand, and chair for the subject experiment are mounted on a base. The 3-D spring array device connected to the stand. 36

Fig. 2.7. Overall structure of 3-D spring array. A total of eight springs could be mounted between the bolts on the inner and outer fixtures to generate different 3-D MITFM. 37

Fig. 2.8. Spring array experiment setup 37

Fig. 2.9. Schematic diagram of the mechanical spring array. A total of eight springs could be mounted between the bolts on the inner and outer fixtures to generate different 3-D MITFM. 39

Fig. 2.10. Experimental setup of 3-D human arm MITFM estimation. HapticMaster and the chair were mounted on a steel base. The subjects' trunk was restrained using seat belts. Hand and forearm were... 41

Fig. 2.11. Shoulder abduction, shoulder flexion, and elbow flexion. For the estimation; shoulder abduction: 20°, shoulder flexion: 60°, and elbow flexion 60° 42

Fig. 3.1. Displacement PSD of desired position perturbations filtered using a second-order Butterworth low pass filter. (a) cutoff frequency: 5 Hz (b) cutoff frequency: 10 Hz 46

Fig. 3.2. Acceleration PSD of desired position perturbations filtered using a second-order Butterworth low pass filter. (a) cutoff frequency: 5 Hz (b) cutoff frequency: 10 Hz 46

Fig. 3.3. Displacement PSD of the desired trajectory (blue), measured from robot position sensor (measured, red), and measured from the IMU (green). Perturbation generated by using second-order... 47

Fig. 3.4. Acceleration PSD of the desired trajectory (blue), measured from robot position sensor (measured, red), and measured from the IMU (green). Perturbation generated by using second-order... 47

Fig. 3.5. Partial coherence of the estimated 3-D MITFM of sa1. Perturbation generated by using second-order Butterworth low-pass filter. Red line: cutoff frequency 5Hz, Blue line: cutoff frequency 10Hz. 49

Fig. 3.6. Displacement PSD of desired position perturbations filtered using an eighth-order Butterworth low pass filter. (a) cutoff frequency: 5 Hz (b) cutoff frequency: 10 Hz 52

Fig. 3.7. Acceleration PSD of desired position perturbations filtered using an eighth-order Butterworth low pass filter. (a) cutoff frequency: 5 Hz (b) cutoff frequency: 10 Hz 52

Fig. 3.8. Displacement PSD of the desired trajectory (blue), measured from robot position sensor (measured, red), and measured from the IMU (green). Perturbation generated by using eighth-order... 53

Fig. 3.9. Acceleration PSD of the desired trajectory (blue), measured from robot position sensor (measured, red), and measured from the IMU (green). Perturbation generated by using eighth-order... 53

Fig. 3.10. Partial coherence of the estimated 3-D MITFM of sa1. Four kinds of perturbation generated by using second-order and eighth-order Butterworth low-pass filter. 1) Red line: second-order, cutoff... 54

Fig. 3.11. PSD Comparison. (a) Displacement PSD (b) Acceleration PSD. Perturbations generated by using a second-order filter with cutoff frequency 5Hz (blue line) and eighth-order filter with cutoff... 54

Fig. 3.12. Partial coherence of the estimated 3-D MITFM of sa1. Four kinds of improved perturbations generated by filtering a uniformly distributed signal twice. 1) Red line: the first filter combinations,... 57

Fig. 3.13. PSD of perturbations generated by using the first and second filter combinations as listed in Table 3.1. was compared. (a) Displacement PSD (b) Acceleration PSD. Red line: the first filter... 58

Fig. 3.14. PSD of perturbations generated by using the third and fourth filter combinations as listed in Table 3.1. was compared. (a) Displacement PSD (b) Acceleration PSD. Blue line: the third filter... 59

Fig. 3.15. PSD of perturbations generated by using the second and fourth filter combinations as listed in Table 3.1. was compared. a) Displacement PSD b) Acceleration PSD. Green line: the second filter... 60

Fig. 3.16. Displacement PSD of the desired trajectory (blue), measured from robot position sensor (measured, red), and measured from the IMU (green) of the improved perturbation. 62

Fig. 3.17. Acceleration PSD of the desired trajectory (blue), measured from robot position sensor (measured, red), and measured from the IMU (green). Of the improved perturbation. 62

Fig. 3.18. Partial coherence of the estimates 3-D MITFM of sa1 with three kinds of perturbations. (Blue: second-order low-pass filter with cutoff frequency of 10Hz, dashed green: eighth-order low-pass... 63

Fig. 3.19. Estimated impedance of sa1 with the improved perturbation. 64

Fig. 3.20. Estimated (blue) and calculated (dashed red, from Equation 2.2.8) impedance of sa1. 64

Fig. 3.20. Estimated 'From Y to Fy' term of 3-D MITFM of five configurations of the spring array device using the second-order (left), the eighth-order (middle), and the improved (right) position perturbations. 65

Fig. 4.1. Calculated spring array impedance from the flexible joint equation 69

Fig. 4.2. Calculated spring array impedance from the flexible link equation 69

Fig. 4.3. Calculated spring array impedance from the flexible link and joint equation 69

Fig. 4.4. The estimated spring array impedance and the calculated spring array impedance comparison. (Left: experimental data, Right: calculated impedance data) 70

Fig. 5.1. The estimated and compensated 3-D MITFM of spring array configuration 2. Blue line: original estimated data, dashed red line: compensated data. 76

Fig. 5.2. The compensated and modeled 3-D MITFM of spring array configuration 2. Green line: modeled data, dashed red line: compensated data. 77

Fig. 5.3. The estimated and compensated 3-D MITFM of subject 9. Blue line: original estimated data, dashed red line: compensated data. 80

Fig. 5.4. The partial and multiple coherence of estimated and compensated 3-D MITFM of subject 9. Blue line: original estimated data, dashed red line: compensated data. 81

Fig. 5.5. The box plots with paired t-test results of 10 subjects' VAFo[이미지참조] 84

Fig. 5.6. The box plots with paired t-test results of 10 subjects' R²o[이미지참조] 85

Fig. 5.7. The line plots with paired t-test results of 10 subjects' VAFo[이미지참조] 86

Fig. 5.8. The box plots with paired t-test results of 10 subjects' R²o[이미지참조] 87

List of Appendix Figures

Fig. C.1. The estimated 3-D MITFM of sa1, with second-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 100

Fig. C.2. The estimated 3-D MITFM of sa1, with eighth-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 101

Fig. C.3. The estimated 3-D MITFM of sa1, with improved position perturbations (filtered twice). Top: MITMF, bottom: coherence functions 102

Fig. C.4. The estimated 3-D MITFM of sa2, with second-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 103

Fig. C.5. The estimated 3-D MITFM of sa2, with eighth-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 104

Fig. C.6. The estimated 3-D MITFM of sa2, with improved position perturbations (filtered twice). Top: MITMF, bottom: coherence functions 105

Fig. C.7. The estimated 3-D MITFM of sa3, with second-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 106

Fig. C.8. The estimated 3-D MITFM of sa3, with eighth-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 107

Fig. C.9. The estimated 3-D MITFM of sa3, with improved position perturbations (filtered twice). Top: MITMF, bottom: coherence functions 108

Fig. C.10. The estimated 3-D MITFM of sa4, with second-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 109

Fig. C.11. The estimated 3-D MITFM of sa4, with eighth-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 110

Fig. C.12. The estimated 3-D MITFM of sa4, with improved position perturbations (filtered twice). Top: MITMF, bottom: coherence functions 111

Fig. C.13. The estimated 3-D MITFM of sa5, with second-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 112

Fig. C.14. The estimated 3-D MITFM of sa5, with eighth-order Butterworth low-pass filtered perturbation with cutoff frequency 10 Hz. Top: MITMF, bottom: coherence functions 113

Fig. C.15. The estimated 3-D MITFM of sa5, with improved position perturbations (filtered twice). Top: MITMF, bottom: coherence functions 114

Fig. D.1 Flexible joint model diagram 115

Fig. D.2. Clamp-free model of flexible link diagram. w＝w(x,t) is flexible deflection. y is total displacement of the point on the beam. qr is the rigid body coordinate rotation angle different from...[이미지참조] 116

Fig. E.1. The estimated and compensated 3-D MITFM of spring array configuration 1. Blue line: original estimated data, dashed red line: compensated data. 119

Fig. E.2. The modeled and compensated 3-D MITFM of spring array configuration 1. Green line: modeled data, dashed red line: compensated data. 120

Fig. E.3. The estimated and compensated 3-D MITFM of spring array configuration 2. Blue line: original estimated data, dashed red line: compensated data. 121

Fig. E.4. The modeled and compensated 3-D MITFM of spring array configuration 2. Green line: modeled data, dashed red line: compensated data. 122

Fig. E.5. The estimated and compensated 3-D MITFM of spring array configuration 3. Blue line: original estimated data, dashed red line: compensated data. 123

Fig. E.6. The modeled and compensated 3-D MITFM of spring array configuration 3. Green line: modeled data, dashed red line: compensated data. 124

Fig. E.7. The estimated and compensated 3-D MITFM of spring array configuration 4. Blue line: original estimated data, dashed red line: compensated data. 125

Fig. E.8. The modeled and compensated 3-D MITFM of spring array configuration 4. Green line: modeled data, dashed red line: compensated data. 126

Fig. E.9. The estimated and compensated 3-D MITFM of spring array configuration 5. Blue line: original estimated data, dashed red line: compensated data. 127

Fig. E.10. The modeled and compensated 3-D MITFM of spring array configuration 5. Green line: modeled data, dashed red line: compensated data. 128

Fig. F.1. The estimated and compensated 3-D MITFM of human upper limb, subject 1. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 130

Fig. F.2. The estimated and compensated 3-D MITFM of human upper limb, subject 2. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 131

Fig. F.3. The estimated and compensated 3-D MITFM of human upper limb, subject 3. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 132

Fig. F.4. The estimated and compensated 3-D MITFM of human upper limb, subject 4. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 133

Fig. F.5. The estimated and compensated 3-D MITFM of human upper limb, subject 5. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 134

Fig. F.6. The estimated and compensated 3-D MITFM of human upper limb, subject 6. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 135

Fig. F.7. The estimated and compensated 3-D MITFM of human upper limb, subject 7. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 136

Fig. F.8. The estimated and compensated 3-D MITFM of human upper limb, subject 8. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 137

Fig. F.9. The estimated and compensated 3-D MITFM of human upper limb, subject 10. Blue line: original estimated data, dashed red line: compensated data. Top: MITMF, bottom: coherence functions 138

초록보기

This thesis presents the importance of the physical realizability of position perturbations and the consideration of robot dynamics for the reliable and accurate estimation of the 3-dimensional (3-D) mechanical impedance transfer function matrix (MITFM) with a nonparametric stochastic estimation method.

The mechanical impedance of the human arm is a physical measure that relates to the clinical evaluation of muscle tone, representing the resistance of a muscle to passive elongation or stretch. The mechanical impedance has been estimated for 1) understanding the fundamental physiological characteristics of muscles, 2) testing various hypotheses about maintaining posture or controlling motion depending on the presence or absence of an environment or object, 3) figuring out a human-robot interaction system, and 4) to quantitatively measure spasticity/stiffness in stroke patients. To estimate the 3-D human upper limb MITFM of post-stroke, the stochastic estimation method is promising. Compared with previous studies, stochastic estimation has the following advantages: obviating the need for suppressing voluntary reaction, providing frequency-rich information, no need for a specific impedance model, and having a short measurement time.

By employing the stochastic estimation method, the mechanical impedance is estimated from the 3-D random position perturbations to the limb by a robot and the force exerted by the endpoint of the subject's arm. For the estimation, it was assumed that the position perturbations are accurately realized by the robot and given to the endpoint of a subject's arm regardless of arm dynamics, and the realized perturbations are measured accurately. Because of the assumption, the perturbations were designed without considering the robot dynamics and the mechanical impedance was estimated using the measured position and measured force by the robot sensors. However, the assumption was never verified.

The impact of the physically impractical position perturbations which a physical system cannot follow and the unmodeled robot dynamics which was neglected for the purpose of control-system analysis and design on the estimation performance of mechanical impedance was investigated with a commercial robot, HapticMaster, in this thesis. To verify the effect, the mechanical impedance of a physical system, a 3-D spring array device which was developed in this thesis, was estimated with different position perturbations generated by low-pass filtering random perturbations. The results indicated that the physically impractical position perturbations and unmodeled high frequency non ideal dynamics of the robot substantially degraded the impedance estimation performance.

From the experimental results, the physically realizable position perturbation that a physical system can follow and less excite the robot's unmodeled high frequency dynamics was identified. Also, it was observed that the unmodeled high frequency dynamics of the robot came from the joint flexibility which many commercial robots have in the frequency range of 5-25Hz. Thus, in present study, a physically realizable perturbation and a method to compensate the flexibility are proposed for the reliable and accurate estimation of the mechanical impedance.

Based on these findings, it is probable that the physical realizability of position perturbations and the unmodeled robot dynamics will be considered when estimating human limb 3-D MITFM. Furthermore, the compensation method for more reliable and accurate estimation of the mechanical impedance will be useful in measuring 3-D human limb MITFM.

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