Bio-inspired compliant foot design to enhance walking efficiency and stability in bipedal robot

다국어 초록 (Multilingual Abstract)

This thesis proposes a bio-inspired compliant foot design to improve the walking efficiency and stability of bipedal robots by mimicking the functions of the human metatarsal arch and toes. The proposed foot integrates a spring-like arched mid-forefoot structure and a compliant forefoot (toe) segment implemented with distributed flexures without discrete joints. By tuning the shape to achieve a practical heel-to-toe stiffness ratio (1.6:1), the design induces predictable heel-to-toe rollover, passive energy storage and release, and continuous CoP progression. A comprehensive pipeline from modeling, analysis, prototyping, simulation, to hardware walking was established. At the full-body level, a linear inverted pendulum-based reduced model combined with a two-channel (heel/toe) foot model was used to analyze the effects of compliance on GRF, support time, and disturbance rejection. At the foot level, an equivalent compliance model derived shape-stiffness mappings under closed-form stiffness ratio conditions, which were validated via FEA.

국문 초록 (Abstract)

본 논문은 인간의 중족 아치와 발가락 기능을 모사하여 이족보행 로봇의 보행 효율과 안정성을 향상시키는 순응형 발을 제안한다. 제안 발은 스프링 성질의 아치형 전·중족 구조와 이산 관절 없이 분포형 플렉셔로 구현한 순응형 전족(발가락) 세그먼트를 통합하였고, 실용적 힐-토 강성비(1.6:1)를 달성하도록 형상을 조율하여 예측 가능한 힐→토 롤오버, 수동적 에너지 저장/방출, 연속적 CoP 진행을 유도한다. 모델링-해석-시제품-시뮬레이션-하드웨어 보행에 이르는 파이프라인을 구축하였다. 전신 수준에서는 LNZN계 축약 모델과 힐/전족 2채널 발 모델을 결합해 순응성이 GRF, 지지시간, 외란 내성에 미치는 영향을 해석하였다. 발 수준에서는 등가 순응 모델로 폐형 강성비 조건과 형상-강성 사상을 도출하고 FEA로 검증하였다.

목차 (Table of Contents)

• 1 Introduction 1
• 1.1 Background and Motivation 1
• 1.2 Related work 3
• 1.3 Research Objectives and Scope 5
• 2 Human Gait and Foot Analysis with Conceptual Foot Design 9
• 2.1 Introduction 9
• 2.2 Human Gait Cycle 10
• 2.2.1 Stanceswing composition and support transitions 10
• 2.2.2 Foot-centric view of key events 10
• 2.3 Foot Anatomy and Functional Roles 13
• 2.3.1 Anatomical overview 13
• 2.3.2 The three arches 13
• 2.3.3 Axes of motion and functional summary 14
• 2.4 Design Requirements and Targets for a Bipedal Robot Foot 17
• 2.5 Conceptual Foot Design (First Iteration) 19
• 3 Mathematical Modeling 21
• 3.1 Introduction 21
• 3.2 Bipedal Robot Modeling 23
• 3.2.1 Assumptions and Coordinate Frames 23
• 3.2.2 Equations of Motion and Effects of Foot on GRF 25
• 3.3 Foot Modeling 30
• 3.3.1 Equivalent Compliance and Stiffness-Ratio Condition 35
• 3.3.2 Geometry-Informed Stiffness Estimation 37
• 3.3.3 Finite-Element Validation 40
• 3.3.4 Final Model and Design Implications 41
• 4 Deformable Simulation and Experiment 45
• 4.1 Introduction 45
• 4.2 Prototype Tests with ArUco Markers 46
• 4.2.1 Instrumentation and Calibration 46
• 4.2.2 Results and Consistency with Finite-Element Analysis 49
• 4.2.3 Load Cases and Procedures 52
• 4.3 Isaac Sim Walking Simulation 59
• 4.3.1 Model Integration and Controller 59
• 4.3.2 Scenarios and Parameter Sweeps 60
• 4.3.3 Comparative Results 62
• 4.4 On-Robot Attachment and Comparative Evaluation 66
• 4.4.1 Test Protocols (in-place loads, walking trials) 66
• 4.4.2 Results 72
• 5 Conclusions 80
• Bibliography 83
• 국문요약 87