2.1.2 Three Dimensional Motion 2.1.3 Walking Phases
2.1.4 Static Walk 2.1.5 Dynamic Walk
2.2
Approach of Walking Trajectory
2.2.1 Cubic Polynomial Trajectory 2.3 Zero Moment Point and Stable Walking
2.3.1 Zero Moment Point
2.3.2 Relationship ZMP and Support Polygon 2.4 NAO Speed Walking
9 10
12 13
15 16
19 19
20
24
3 METHODOLOGY
3.1 Trajectory Planning 3.2 Real versus Simulated Robots
3.3
NAO Inverse Kinematics
3.4 Project Setup 3.4.1 Experiment 1
3.4.2 Experiment 2
25
25 26
27 31
31 32
4 RESULT AND DISCUSSION
4.1 Introduction 4.2 Result Experiment 1
4.3 Result Experiment 2
34
34 34
46
5 CONCLUSION AND RECOMMENDATIONS
5.1 Conclusion
5.2 Recommendation 49
49
50
REFERENCES 51
APPENDICES 53
LIST OF TABLES
TABLE TITLE
PAGE
2.1 Joint types and range for NAO robot Lower Limb
9 3.1
NAO Humanoid Robot Parameter 27
3.2 Walking pattern with different values of step length
33 4.1
Joint angle value for Left Foot in 1 second 35
4.2 Joint angle value for Right Foot in 1 second
35 4.3
Initial Angle for Left and Right Foot for 1 seconds 35
LIST OF FIGURES
FIGURE TITLE
PAGE
2.1 Aldebaran-Robotics NAO
[6]
7 2.2
Detailed kinematics of NAO
[3]
8 2.3
Humanoid in anatomical position, base-frame-origin and world planes
[4]
10
2.4 Typical shapes of the Support Polygon SP, in grey
[4]
11 2.5
Gait Phase
[4]
12 2.6
NAO gaits parameter 14
2.7 Several possible path shapes for single joint
[5]
17 2.8
ZMP Concept
[7]
19 2.9
The robot stays within the support polygon 21
2.10 Zero-Moment-Point
22 2.11
The support polygon in three typical cases 23
3.1 Overview of trajectory generation
26 3.2
Inverse Kinematic Parameters from Hip to Ankle 27
3.3 Joint Angle Parameters
29 4.1
Joint Angle Trajectories for Right Ankle Roll and Left Ankle Roll 36
4.2 Velocity Profiles for Right Ankle Roll and Left Ankle Roll
37 4.3
Acceleration Profiles for Right Ankle Roll and Left Ankle Roll 37
4.4 Joint Angle Trajectories for Right Ankle Pitch and Left Ankle Pitch
38 4.5
Velocity Profiles for Right Ankle Pitch and Left Ankle Pitch 39
4.6 Acceleration Profiles for Right Ankle Pitch and Left Ankle Pitch
39 4.7
Joint Angle Trajectories for Right Knee Pitch and Left Knee Pitch 40
4.8 Velocity Profiles for Right Knee Pitch and Left Knee Pitch
40 4.9
Acceleration Profiles for Right Knee Pitch and Left Knee Pitch 40
4.10 Joint Angle Trajectories for Right Hip Pitch and Left Hip Pitch
41 4.11
Velocity Profiles for Right Hip Pitch and Left Hip Pitch 41
4.12 Acceleration Profiles for Right Hip Pitch and Left Hip Pitch
42 4.13
Joint Angle Trajectories for Right Hip Roll and Left Hip Roll 42
4.14 Velocity Profiles for Right Hip Roll and Left Hip Roll
43 4.15
Acceleration Profiles for Right Hip Roll and Left Hip Roll 43
4.16 Lifting Height for NAO using Inverse Kinematic H=0.015m
44 4.17
Lifting Height for NAO using Cubic Polynomial Method H=0.015m
44
4.18 NAO Behavior during walking
45 4.19
Stability Pattern 1 Step Length= 0.07m 46
4.20 Stability Pattern 2 Step Length= 0.10m
47 4.21
Stability Pattern 3 Step Length= 0.13m 48
LIST OF SYMBOLS
F -
Force g
- Gravity = 9.81 ms
I -
Moment of inertia 1
- Length m
P -
Pressure V
- Velocity
a -
Acceleration
LISTS OF ABBREVIATIONS
DOF -
Degrees of freedom CoM
- Center of mass
CoP -
Center of pressure FSR
- Force sensitive resistor
ZMP -
Zero Moment Point DS
- Double Support
SS -
Single Support PH
- Point Hip
PR -
Point Right PL
- Point Left
LIP -
Linear Inverted Pendulum 3D LIP
- 3 Dimensional Linear Inverted Pendulum
LISTS OF APPENDICES
APPENDIX TITLE PAGE
A Inverse Kinematic Parameter 52 B ZMP Computation
55 C Python Programming
60 D Matlab Calculation
67
E Cubic Polynomial Parameter 72
CHAPTER 1
INTRODUCTION
1.1 Project Background
