Accelerated, High Fidelity Simulation of Deformable Bodies for Physics Abstraction in Robot Learning = 물리 추상화 기반의 로봇 학습을 위한 가속화된 고충실도 변형체 시뮬레이션

국문 초록 (Abstract)

소프트 로보틱스 분야에서 학습 기반 제어의 발전은 연산 속도와 물리적 충실도 사이의 임계적 괴리인 시뮬레이션과 현실 사이의 격차에 의해 근본적으로 제약받고 있다. 본 학위논문은 기존 모델링 패러다임을 엄밀히 분석하여 이 격차를 수학적으로 정의하고, 데이터 기반 추상화의 당위성을 입증한다.

본 연구는 해석적 근사가 외력 하의 필수적인 비선형 거동을 포착하지 못하는 반면, 유한요소법과 같은 수치 해석법은 복잡도가 세제곱으로 증가하여 강화 학습에 요구되는 대규모 데이터 처리가 불가능하다는 점을 밝힌다. 이러한 불일치를 해결하기 위해, 본 논문은 물리적 참값 생성 과정과 런타임 실행을 분리하는 통합 파이프라인을 제안한다.

일련의 연구를 통해 다음 두 가지 핵심 추상화 전략에 대한 이론적 토대를 확립하였다. 첫째, 대체 모델링 (Surrogate modeling)을 통한 모델 차수 축소를 통해 거시적 물체 역학을 고속 강체 호환 형식으로 압축한다. 둘째로 신경망 접촉 모델(neural contact models)을 이용하여 데이터 기반 접촉 모델 근사를 활용하여 접촉 계면의 복잡하고 고차원적인 역학을 포착한다.

이 방법론은 강건한 시뮬레이션 전이학습에 필수적인 연속체 물리학적 특성을 유지하면서도 강체 엔진 수준의 연산 효율성을 달성하여 현실 격차를 해소하는 것을 목표로 한다. 궁극적으로 본 연구는 고차원 유한요소 데이터를 저차원의 필수정보로 추상화하는 일반화된 파이프라인을 제시하며, 이를 로봇 공학 내 변형이 수반되는 주요 시스템에 적용함으로써 확장 가능하고 물리적으로 충실한 학습을 구현한다.

다국어 초록 (Multilingual Abstract)

The advancement of learning-based control in soft robotics is fundamentally constrained by the simulation to real gap, a critical divergence between computational speed and physical fidelity. This thesis provides a rigorous analysis of existing modeling paradigms to define this gap mathematically and justify the necessity for Data-Driven Abstraction. We demonstrate that analytical approximations fail to capture essential non-linear behaviors under external loads, while ground-truth numerical methods, like the finite element method, scale with cubic complexity, rendering them intractable for the massive data throughput required by reinforcement learning. To resolve this discrepancy, this dissertation proposes a unified pipeline that decouples physical ground-truth generation from runtime execution. A series of research studies established the theoretical foundations for two targeted abstraction strategies: (1) Surrogate modeling via model order reduction to compress macroscopic body dynamics into fast, rigid-body-compatible formats, and (2) Neural contact models utilizing data-driven contact model approximations to capture the complex, high-dimensional mechanics of the contact interface. This methodology aims to bridge the reality gap by achieving the computational efficiency of rigid-body engines without sacrificing the continuum physics essential for robust sim-to-real transfer. Ultimately, this work contributes a generalizable pipeline to abstract high-dimensional Finite Element data into low-dimensional but essential features, applying this strategy to the two major domains of deformation-incurring systems in robotics to enable scalable and physically faithful learning.

목차 (Table of Contents)

• Chapter1 Introduction 1
• 1.1 Deformable Systems in Robotic Interactions 1
• 1.2 Challenges in Deformable Robot Simulation 2
• 1.2.1 The Data Scarcity Crisis in Deformable Interaction 2
• 1.2.2 Computational Bottleneck of Continuum Mechanics 3
• 1.2.3 The Fidelity-Efficiency Tradeoff in Physics-Based Simulation 4
• 1.3 Motivation of the Dissertation 6
• 1.4 Methodological Framework 7
• 1.5 Contributions and Organization 9
• Chapter 2. Related Works 11
• 2.1 Modeling Deformable Continuum Physics 11
• 2.2 The Fidelity-Efficiency Conflict and the Sim-to-Real Gap 12
• 2.3 Division of Action and Perception in Deformation System 14
• 2.4 Surrogate Kinematics Model 15 2.5 Simulation for Soft Contact 16
• 2.6 Rationale for Method Selection 17
• 2.6.1 Comparison with Rigid Body and Position-Based Dynamics 17
• 2.6.2 Comparison with Differentiable Physics Engines 18
• 2.6.3 The Unique Position of Data-Driven Abstraction 18
• Chapter 3. Hardware Platforms and Ground-Truth Data 20
• 3.1 Prototypes for Soft Continuum Manipulation 21
• 3.1.1 Modularized Origami Manipulator 21
• 3.1.2 Bellows-Driven Continuum Manipulator 23
• 3.2 Vision-Based Tactile Sensing for Physical Perception 25
• 3.3 Rationale for Hardware Selection 26
• 3.4 Overview of Methodological Implementation 27
• 3.4.1 Surrogate Modeling for Soft Continuum Dynamics 28
• 3.4.2 Contact Refinement Networks for Tactile Perception 29
• Chapter 4. Kinematic Abstraction and Modeling of Soft Manipulator 31
• 4.1 Analytic Modeling of the Origami Cylinder Module 31
• 4.1.1 Design Parameters of the Yoshimura Cylinder Origami 32
• 4.1.2 Theoretical Assumptions for the Pattern Analysis 34
• 4.1.3 Kinematics Modeling of the Yoshimura Cylinder 36
• 4.1.4 Inverse Kinematic Mapping 42
• 4.1.5 Extended Model for the Origami Manipulator 43
• 4.1.6 Characterization 48
• 4.1.7 System Integration and Experimental Validation 49
• 4.1.8 Applications 51
• 4.2 Results 52
• 4.2.1 Validation of the OCM Kinematics Model 52
• 4.2.2 Evaluation of Experimental Task Implementation 54
• 4.2.3 Practical Applications and Task Validation 58
• 4.3 Conclusion and Discussion 59
• Chapter 5. Data-Driven Surrogate Modeling of Whole Body Soft Robot Dynamics 62
• 5.1 Motivation for a Data-driven Approach 62
• 5.2 Soft Robot Simulation 62
• 5.2.1 Soft Robotics and Modeling Challenges 62
• 5.2.2 Towards a Unified Framework 63
• 5.3 Framework Overview 65
• 5.4 Model Calibration 66
• 5.4.1 FEM Simulation Model 66
• 5.4.2 FEM Simulation Scene 67
• 5.4.3 Material Characterization and Property Estimation 68
• 5.4.4 Domain Mapping Functions 69
• 5.4.5 Model Order Reduction by Proper Orthogonal Decomposition 70
• 5.5 Surrogate Dynamics Model 72
• 5.5.1 Transformer-based Physics-Informed Dynamics Modeling 72
• 5.5.2 Inverse Dynamics Modeling 75
• 5.6 Surrogate Architecture for Physics-Based Simulation 76
• 5.6.1 Geometric Design Based on FEM Node Analysis 76
• 5.6.2 URDF Implementation and Design Specifications 79
• 5.7 Aligning Between Two Actuation Spaces 80
• 5.8 Customized Gymnasium Environment 83
• 5.8.1 Reinforcement Learning Environment Configuration 83
• 5.8.2 Observation and Action Space Definitions 84
• 5.8.3 Force Calibration of the Surrogate Model 85
• 5.8.4 Task Design and Implementation 85
• 5.8.5 Reward Function Design 87
• 5.8.6 Policy Learning and Evaluation 88
• 5.8.7 Sim-to-Real Policy Transfer 89
• 5.9 Experiment 90
• 5.9.1 Sim-to-Real Learning Framework and Hardware Configuration 90
• 5.9.2 Data Acquisition and Learning Methodology 92
• 5.9.3 Validation Tasks and Control Performance 93
• 5.10 Result 94
• 5.10.1 Calibration and Validation 94
• 5.10.2 Evaluation of Forward and Inverse Dynamics Models 95
• 5.10.3 Comparative Policy Evaluation and Domain Transfer 97
• 5.10.4 Additional Validation of Performance and Robustness 100
• 5.11 Discussion 102
• 5.12 Summary of Modeling Soft Manipulator 104
• 5.12.1 Comparative Analysis of Modeling Approaches 105
• 5.12.2 Impact of Model Fidelity on Sim-to-Real Transfer 106
• Chapter 6. Modeling the Deformable Contact Interface 109
• 6.1 Vision-Based Tactile Sensor 109
• 6.2 Motivation of Tactile Simulation 111
• 6.3 Data Generation Pipeline 112
• 6.4 High-Fidelity Tactile Simulation 114
• 6.4.1 Material Calibration and Mesh Preparation 114
• 6.4.2 Real-Time Simulation via Model Order Reduction 115
• 6.4.3 Integrated Simulation Scene in SOFA 116
• 6.5 Calibration Metrics 116
• 6.5.1 Nodal Position Error 118
• 6.5.2 Contact Patch Geometry 118
• 6.5.3 Force-Depth Correspondence 118
• 6.6 Bidirectional Tactile Perception and Rendering Networks 119
• 6.6.1 Perception Network From Visual to Physical State 119
• 6.6.2 Rendering Network From Physical to Visual State 121
• 6.6.3 Hyperparameter Summary 124
• 6.7 Experimental Methodology 124
• 6.7.1 Material Calibration Procedure 124
• 6.7.2 Paired Dataset Acquisition 125
• 6.8 Result 127
• 6.8.1 Calibration Precision 127
• 6.8.2 Perception Network Validation 128
• 6.8.3 Rendering Network Validation 129
• 6.8.4 Generalization to Unseen Data 130
• 6.9 Discussion 132
• 6.9.1 Comparison to Prior Work 133
• 6.9.2 Physically Grounded Learning 134
• 6.9.3 Quantitative Performance 134
• 6.9.4 Reproducibility and Future Directions 135
• Chapter 7. Geometry-Aware Contact Refinement for Real-Time High-Fidelity Tactile Simulation 136
• 7.1 Motivation 136
• 7.2 Introduction 136
• 7.3 Related Works 138
• 7.4 Tactile-Informed Task Learning Framework 140
• 7.4.1 Physics-Grounded Truth Data Generation 140
• 7.4.2 Finite Element Modeling of the Tactile Interface 143
• 7.4.3 Geometry-Aware Contact Refinement Network 145
• 7.4.4 Shared Latent Space 149
• 7.5 Experiment and Simulation Setup 149
• 7.6 Result 152
• 7.6.1 Generative Surrogate Model for FEM Data Synthesis 152
• 7.6.2 Evaluation of Contact Refinement Network 154
• 7.6.3 Behavioral Cloning and Sim to Real Validation 155
• 7.6.4 Sim to real transfer performance 156
• 7.6.5 Comparison with related works 157
• 7.6.6 Cross Platform Compatibility and Framework Universality 158
• 7.7 Discussion 158
• Chapter 8. Conclusion of Dissertation 161
• 8.1 Integrated Methodological Framework 161
• 8.2 Summary of Contributions 162
• 8.3 Limitations 163
• 8.4 Future Works 164
• Bibliography 166
• 국문 초록 187