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μ¬λ 보ν λΆμ μ°κ΅¬μ κ·Έ κ²°κ³Όλ₯Ό νμ©ν ν΄λ¨Έλ Έμ΄λ λ‘λ΄ λ³΄ν ν¨ν΄ μμ±
νμλ
Όλ¬Έ (λ°μ¬) -- μμΈλνκ΅ λνμ : μ΅ν©κ³ΌνκΈ°μ λνμ μ΅ν©κ³ΌνλΆ(μ§λ₯νμ΅ν©μμ€ν
μ 곡), 2020. 8. λ°μ¬ν₯.λ°μ λ―Έλλ¬μ§μ 보νμ μμ μ±μ λ¨μ΄νΈλ¦¬λ μμΈ μ€ νλμ΄λ€. 보ν μ€ λ°μ λ°μνλ μν μ λ¨λ ₯μ΄ λ°κ³Ό μ§λ©΄ μ¬μ΄μ λ§μ°°λ ₯λ³΄λ€ μ»€μ§λ©΄, λ°μ μ μ΄μ μμ€νκ³ λ―Έλλ¬μ§κ² λλ€. μ¬κΈ°μ, λ°κ³Ό μ§λ©΄ μ¬μ΄μ λ§μ°°λ ₯μ λ°μ μμ©νλ μμ§λ ₯μ μν΄ κ²°μ λκ² λλ€. μ¦, ν΄λ¨Έλ
Έμ΄λ λ‘λ΄ λ³΄ν ν¨ν΄ μμ±μ μΈ‘λ©΄μμ 보μλ©΄, λ‘λ΄ λ°μ λ°μνλ μνλ ₯κ³Ό μμ§λ ₯μ μ΄λ»κ² μ€κ³νλμ§μ λ°λΌ 보ν μ€ λ―Έλλ¬μ§μ κ°λ₯μ±μ΄ λ°λλ€λ κ²μ΄λ€.
μ ν μμ§μ λͺ¨λΈμ ν΄λ¨Έλ
Έμ΄λ λ‘λ΄μ λ¬΄κ² μ€μ¬ κΆ€μ μμ±μ μν΄ μμ£Ό μ¬μ©λμ΄μλ€. μ ν μμ§μ λͺ¨λΈμ λ‘λ΄μ λ¬΄κ² μ€μ¬ λμ΄λ₯Ό μΌμ νκ² μ μ§νλλ‘ μ ννλ€. λ¬΄κ² μ€μ¬μ λμ΄ μ ν λλ¬Έμ λ‘λ΄μ μμ§ λ°©ν₯μ κ°μλλ 보ν μλμ κ΄λ ¨ μμ΄ νμ μ€λ ₯ κ°μλκ° λλ€. κ·Έλ¬λ μν λ°©ν₯μ κ°μλλ 보ν μλκ° μ¦κ°νλ©΄ λΉλ‘νμ¬ μ¦κ°νλ€. λ°λΌμ λΉ λ₯Έ 보ν μλμμλ μμ§λ ₯μ λΉλ‘νλ λ§μ°°λ ₯μ λΉν΄ μν μ λ¨λ ₯μ΄ μ»€μ§λ©΄μ λ°μ λ―Έλλ¬μ§μ΄ λ°μν μ μλ€. μ ν μμ§μ λͺ¨λΈμ μν μΌμ ν μμ§ λμ΄ κ΅¬μ μ‘°κ±΄μ΄ λ‘λ΄ λ°μ λ―Έλλ¬μ§μ μ λ°ν μ μλ€λ κ²μ μμ¬νλ€.
λ¬΄κ² μ€μ¬μ μ μ ν μμ§ μμ§μμ μμ±ν¨μΌλ‘μ¨ ν΄λ¨Έλ
Έμ΄λ λ‘λ΄ λ³΄ν μ€ λ°μ λ―Έλλ¬μ§μ μ€μΌ μ μλ€. μΈκ°κ³΅ν λΆμΌμμλ Available Coefficient of Friction(aCOF)κ³Ό Utilized Coefficient of Friction(uCOF)μ μ΄μ©νμ¬ μ¬λ 보ν μ€ λ°μ λ―Έλλ¬μ§ κ°λ₯μ±μ μμΈ‘νλ μ°κ΅¬λ€μ΄ μνλλ€. μ¬κΈ°μ, aCOFλ λ 물체μ μ¬μ§μ΄λ μνμ μν΄ κ²°μ λλ λ§μ°° κ³μμ΄λ€. λ°λ©΄, uCOFλ 보ν μ€ μ§μ§νλ λ°μ κ°ν΄μ§λ μν μ λ¨λ ₯κ³Ό μμ§λ ₯μ λΉμ΄λ€. μΈκ°κ³΅ν μ°κ΅¬λ€μ λ°λ₯΄λ©΄, uCOFκ° aCOFλ₯Ό μ΄κ³Όν λ λ°μ μ μ΄μ μμ€νκ³ λ―Έλλ¬μ§κ² λλ€. λ‘λ΄ λ°μ λ―Έλλ¬μ§ κ°μλ₯Ό μν΄μλ λ‘λ΄ λ³΄ν μ€ λ°μ λ°μνλ uCOFκ° λ‘λ΄ λ°κ³Ό μ§λ©΄ μ¬μ΄μ aCOF λ³΄λ€ μμμ§λλ‘ μ μ ν μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ μμ±νλ κ²μ΄ νμνλ€. λ€μν ννμ μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μμ±μ΄ κ°λ₯νλ°, κ°λ¨νλ©΄μλ ν¨μ¨μ μΈ λ°©λ²μ λ¬΄κ² μ€μ¬μ μλμ§κ° 보쑴λλλ‘ μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ μμ±νλ κ²μ΄λ€. κΈ°μ‘΄ μ ν μμ§μ λͺ¨λΈμ μ΄μ©ν΄ μν λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ μμ±νκ³ , μ΄λ μλμ§μ μμΉ μλμ§κ° κ΅νλλ©΄μ μ 체 μλμ§κ° 보쑴λλ μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ μΆκ°νλ κ²μ΄λ€. λ¬΄κ² μ€μ¬μ μλμ§ λ³΄μ‘΄ μ리λ₯Ό μ΄μ©νμ¬ λ¬΄κ² μ€μ¬μ μμ μΌ(Mechanical Work) μμ±μ μ΅μνν¨μΌλ‘μ¨ κ΄μ μ μμ μΌ μμ±μ κ°μμν€κ³ , μ΄λ₯Ό ν΅ν΄ 보ν μ€ μλμ§ ν¨μ¨μ λμ΄λ κ²μ΄ κ°λ₯νλ€.
μ΄ λ
Όλ¬Έμ λ°κ³Ό μ§λ©΄ μ¬μ΄μ aCOF λ³΄λ€ μλλ‘ λ³΄ν μ€ uCOFλ₯Ό μ μ§νλ©΄μ λ¬΄κ² μ€μ¬μ μμ μΌμ μ΅μννλ μ μ ν μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ μμ±νλ κ²μ λͺ©νλ‘ νλ€. λ°μ λ―Έλλ¬μ§μ΄ κ°μνλ©΄μ μλμ§ ν¨μ¨μ΄ λμ ν΄λ¨Έλ
Έμ΄λ λ‘λ΄ λ³΄ν ν¨ν΄ μμ±μ μν΄, λ¨Όμ μ¬λ 보ν μ€ uCOFμ κ΄ν μ°κ΅¬μ μ¬λ 보ν μ€ κ΄μ μ μΌμ κ΄ν μ°κ΅¬λ₯Ό μ ννλ€. μ¬λ 보νμ κ΄ν λΆμ μ°κ΅¬μ μ¬λ 보νμ μ리 μ΄ν΄λ₯Ό ν΅ν΄ μ΅μ ν μκ³ λ¦¬μ¦ κΈ°λ° μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μμ± λ°©λ²μ΄ μ μλλ€. μ μλ μκ³ λ¦¬μ¦μ μ΄μ©νμ¬ κ΅¬ν΄μ§ μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ ν΄λ¨Έλ
Έμ΄λ λ‘λ΄ λ³΄ν μ€νμ μ μ©νλ€. κΆκ·Ήμ μΌλ‘ μ΄ λ
Όλ¬Έμ, μμ§ λ°©ν₯μ λ¬΄κ² μ€μ¬ κΆ€μ μ μΆκ°ν¨μΌλ‘μ¨ κΈ°μ‘΄ μ ν μμ§μ λͺ¨λΈμ νκ³λ₯Ό 극볡νμ¬, λ―Έλλ¬μ§μ κ°λ₯μ±μ΄ κ°μνκ³ μλμ§ ν¨μ¨μ΄ λμ ν΄λ¨Έλ
Έμ΄λ λ‘λ΄ λ³΄ν ν¨ν΄μ μμ±νλ€.Foot slippage is one of the factors responsible for the increasing instability during human walking. A slip occurs when the horizontal shear force acting on the foot becomes greater than the frictional force between the foot and the ground, which is proportional to the vertical force. For humanoid robot walking, the possibility of a slip depends upon how the horizontal shear force and vertical force both acting on the foot are designed.
In the linear inverted pendulum model (LIPM), which is commonly used to generate the center of mass (COM) trajectory of humanoid robots, the vertical height of the COM is kept constant. The constant height of the COM restricts that the vertical force is always equal to the gravitational force at any walking speed. However, upon increasing the walking speed, the horizontal ground reaction force increases in proportion with the forward and lateral accelerations of the COM. This increase in the horizontal ground reaction force, while the vertical ground force is being constant, suggests that the robot-foot slippage can occur because of the restriction of the vertical motion by the LIPM constraint.
By generating the appropriate vertical motion, the robot-foot slippage can be reduced during humanoid robot walking. Researchers in the field of ergonomics have been conducted studies on the relationship between the available coefficient of friction (aCOF) and the utilized coefficient of friction (uCOF) to predict the potential for a slip during human walking. The aCOF is both the static and dynamic coefficient of friction between two objects in contact, and it depends on the properties of the objects. The uCOF is the ratio of the horizontal shear force to the vertical force applied by the supporting foot. Foot slippage occurs when the uCOF exceeds the aCOF. Various types of vertical motion can set the maximum value of the uCOF to be less than the aCOF between the foot and floor for humanoid robot walking. One of the simple and energy-efficient methods is to minimize the mechanical work of the COM by introducing added vertical motion. Therefore, the COM pattern would become more energy efficient by exchanging kinetic energy and potential energy.
This thesis aims to generate the appropriate vertical motion of the COM to maintain the utilized coefficient of friction (uCOF) less than the available coefficient of friction between the foot and the ground, and to minimize the mechanical work during humanoid robot walking. Before generating a slip-safe and energy-efficient COM trajectory for humanoid robot walking, studies on analyzing the COM patterns, mechanical work, and uCOF during human walking are conducted to understand the principle of walking. Vertical motions at various speeds are generated using an optimization method. Subsequently, the generated COM motion patterns are used as reference trajectories of the COM for humanoid robot walking. This thesis suggests a way to generate slip-safe and energy-efficient COM patterns, which, in turn, overcome the limitations of the LIPM by adding vertical COM motion.Chapter 1 Introduction 1
1.1 Research Background 1
1.2 Contributions of Thesis 3
1.3 Overviews of Thesis 4
Chapter 2 Dynamics of Walking 5
2.1 Walking Model 5
2.1.1 Linear Inverted Pendulum Model 5
2.1.2 Spring-Loaded Inverted Pendulum Model 6
2.1.3 Extrapolated Center of Mass Dynamics 9
2.2 Walking Theory 11
2.2.1 Step-to-Step Transition 11
Chapter 3 HumanWalking Analysis 13
3.1 Motion Capture for Walking 13
3.1.1 Motion Capture Technology 13
3.1.2 Joint Kinematics and Kinetics 15
3.2 Joint and COM During Human Walking 17
3.2.1 Introduction 17
3.2.2 Methods 19
3.2.3 Change of Joint Angle and the COM 20
3.2.4 Discussion 26
3.3 Slipping During Human Walking 27
3.3.1 Introduction 27
3.3.2 Methods 31
3.3.3 Change of uCOF and GRF 34
3.3.4 Interaction Effect Between Heel Area and Speed 36
3.3.5 Discussion 39
3.4 Mechanical Work During Human Walking 44
3.4.1 Introduction 44
3.4.2 Methods 46
3.4.3 Calculation for Joint Mechanical Work 48
3.4.4 Change of Joint Mechanical Work 51
3.4.5 Change of Stride Parameters 53
3.4.6 Discussion 54
Chapter 4 Robot Walking Pattern Generation 59
4.1 Introduction 59
4.2 Forward and Lateral COM 61
4.2.1 XcoM Method 61
4.2.2 Preview Control Method 63
4.3 Vertical COM 64
4.3.1 Calculation for uCOF 64
4.3.2 Calculation for ZMP 65
4.3.3 Calculation for COM Mechanical Work 66
4.3.4 Optimization for Vertical COM Generation 68
4.3.5 Results of Optimization for Vertical COM 73
4.4 Slipping During Robot Walking 75
4.4.1 Robot Simulation 75
4.4.2 Robot Experiments 77
4.5 Mechanical Work During Robot Walking 81
4.5.1 Robot Simulation 81
4.5.2 Robot Experiments 82
4.6 Discussion 87
4.6.1 Tracking Errors in Robot Experiments 87
4.6.2 Effect of Vertical Motions on Real Net Power 91
4.6.3 Trade-Off Between Efficiency and Stability 92
4.6.4 Difference Between Human and Robot 93
Chapter 5 Conclusions 95
Bibliography 97
Abstract (Korean) 111Docto