Snake Robots: Modelling, Mechatronics, and Control

Description

Snake Robots is a novel treatment of theoretical and practical topics related to snake robots: robotic mechanisms designed to move like biological snakes and able to operate in challenging environments in which human presence is either undesirable or impossible. Future applications of such robots include search and rescue, inspection and maintenance, and subsea operations. Locomotion in unstructured environments is a focus for this book. The text targets the disparate muddle of approaches to modelling, development and control of snake robots in current literature, giving a unified presentation of recent research results on snake robot locomotion to increase the reader’s basic understanding of these mechanisms and their motion dynamics and clarify the state of the art in the field. The book is a complete treatment of snake robotics, with topics ranging from mathematical modelling techniques, through mechatronic design and implementation, to control design strategies. The development of two snake robots is described and both are used to provide experimental validation of many of the theoretical results. Snake Robots is written in a clear and easily understandable manner which makes the material accessible by specialists in the field and non-experts alike. Numerous illustrative figures and images help readers to visualize the material. The book is particularly useful to new researchers taking on a topic related to snake robots because it  provides an extensive overview of the snake robot literature and also represents a suitable starting point for research in this area. Snake Robots Series Editors' Foreword Preface Contents Chapter 1: Introduction 1.1 Background and Motivation 1.2 Biological Snakes 1.2.1 The Anatomy of Snakes 1.2.2 The Locomotion of Snakes Lateral Undulation Concertina Locomotion Rectilinear Crawling Sidewinding The Control System of Snakes 1.3 Previous Work on Modelling, Mechatronics, and Control of Snake Robots 1.3.1 Previous Work on Modelling and Analysis of Snake Robots Biomechanical Studies of Biological Snakes Modelling of Flat Surface Locomotion with Sideslip Constraints Modelling of Flat Surface Locomotion Without Sideslip Constraints Modelling of Robotic Fish and Eel-Like Mechanisms Modelling of Locomotion in Environments with Obstacles 1.3.2 Previous Work on Implementation of Physical Snake Robots Snake Robots Without Contact Force Sensors Snake Robots with Contact Force Sensors 1.3.3 Previous Work on Control of Snake Robots Control of Flat Surface Locomotion with Sideslip Constraints Control of Flat Surface Locomotion Without Sideslip Constraints Control of Robotic Fish and Eel-Like Mechanisms Control of Locomotion in Environments with Obstacles 1.4 The Scope of This Book 1.4.1 An Analytical Approach 1.4.2 Snake Robots Without a Fixed Base 1.4.3 A Planar Perspective 1.4.4 Locomotion Without Sideslip Constraints 1.4.5 Motion Based on Lateral Undulation 1.5 An Outline of This Book 1.5.1 Outline of Part I-Snake Robot Locomotion on Flat Surfaces Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 1.5.2 Outline of Part II-Snake Robot Locomotion in Cluttered Environments Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 1.6 Publications Underlying This Book Journal Papers Conference Papers Part I: Snake Robot Locomotion on Flat Surfaces Chapter 2: A Complex Model of Snake Robot Locomotion on Planar Surfaces 2.1 The Relation Between This Chapter and Previous Literature 2.2 Basic Notation 2.3 The Parameters of the Snake Robot 2.4 The Kinematics of the Snake Robot 2.5 The Ground Friction Models 2.5.1 The Friction Models and Their Role in This Book 2.5.2 A Coulomb Friction Model 2.5.3 A Viscous Friction Model Isotropic Viscous Friction Anisotropic Viscous Friction 2.6 The Dynamics of the Snake Robot 2.7 Separating Actuated and Unactuated Dynamics 2.8 Partial Feedback Linearisation of the Model 2.9 Chapter Summary Chapter 3: Development of a Mechanical Snake Robot for Motion Across Planar Surfaces 3.1 The Relation Between This Chapter and Previous Literature 3.2 The Joint Actuation Mechanism 3.3 The Passive Wheels 3.4 The Power and Control System 3.5 The Experimental Setup of the Snake Robot 3.6 Chapter Summary Chapter 4: Analysis and Synthesis of Snake Robot Locomotion 4.1 The Relation Between This Chapter and Previous Literature 4.2 Introduction to Nonlinear Controllability Analysis 4.3 Stabilisability Properties of Planar Snake Robots 4.4 Controllability Analysis of Planar Snake Robots 4.4.1 Controllability with Isotropic Viscous Friction 4.4.2 Controllability with Anisotropic Viscous Friction 4.5 Analysis of Propulsive Forces During Snake Locomotion 4.6 Synthesis of Propulsive Motion for the Snake Robot 4.7 The Gait Pattern Lateral Undulation 4.8 The Control System of the Joints 4.8.1 A Simple Joint Controller 4.8.2 An Exponentially Stable Joint Controller 4.9 Analysis of Turning Motion During Lateral Undulation 4.10 Analysis of Relative Motion Between Consecutive Links During Lateral Undulation 4.11 Chapter Summary Chapter 5: Path Following Control and Analysis of Snake Robots Based on the Poincaré Map 5.1 The Relation Between This Chapter and Previous Literature 5.2 Introduction to Poincaré Maps 5.2.1 General Description of Poincaré Maps 5.2.2 Practical Application of Poincaré Maps Calculating the Poincaré Map Locating Fixed Points of the Poincaré Map Analysing Stability of a Periodic Orbit 5.3 Straight Line Path Following Control of Snake Robots 5.3.1 Control Objective 5.3.2 The Straight Line Path Following Controller 5.4 Stability Analysis of the Path Following Controller Based on the Poincaré Map 5.4.1 Converting the Snake Robot Model to a Time-Periodic Autonomous System 5.4.2 Specification of the Poincaré Section for the Snake Robot 5.4.3 Stability Analysis of the Poincaré Map 5.5 Simulation Study: The Performance of the Path Following Controller 5.6 Chapter Summary Chapter 6: A Simplified Model of Snake Robot Locomotion on Planar Surfaces 6.1 The Relation Between This Chapter and Previous Literature 6.2 Overview of the Modelling Approach 6.3 The Kinematics of the Snake Robot 6.4 The Ground Friction Model 6.5 The Dynamics of the Snake Robot 6.5.1 The Translational Dynamics of the Snake Robot 6.5.2 The Rotational Dynamics of the Snake Robot 6.6 The Complete Simplified Model of the Snake Robot 6.7 Discussion of the Simplified Model 6.7.1 Applications of the Simplified Model 6.7.2 Accuracy Issues of the Simplified Kinematics 6.7.3 Accuracy Issues of the Ground Friction Model 6.7.4 Accuracy Issues of the Rotational Dynamics 6.8 Stabilisability Analysis of the Simplified Model 6.9 Controllability Analysis of the Simplified Model 6.10 Simulation Study: Comparison Between the Complex and the Simplified Model 6.10.1 Simulation Parameters 6.10.2 Relationship Between the Joint Coordinates in the Complex and Simplified Models 6.10.3 Comparison of Straight Motion 6.10.4 Comparison of Turning Motion 6.11 Chapter Summary Chapter 7: Analysis of Snake Robot Locomotion Based on Averaging Theory 7.1 The Relation Between This Chapter and Previous Literature 7.2 Introduction to Averaging Theory 7.3 The Velocity Dynamics During Lateral Undulation 7.4 The Averaged Velocity Dynamics During Lateral Undulation 7.5 The Steady-State Behaviour of the Velocity Dynamics During Lateral Undulation 7.6 Relationships Between the Gait Parameters and the Forward Velocity During Lateral Undulation 7.7 Simulation Study: Comparison Between the Original and the Averaged Velocity Dynamics 7.7.1 Simulation Parameters 7.7.2 Simulation Results 7.8 Simulation Study: Investigation of the Relationships Between Gait Parameters and Forward Velocity 7.8.1 Simulation Parameters 7.8.2 Simulation Results Relationship Between the Forward Velocity and alpha Relationship Between the Forward Velocity and omega Relationship Between the Forward Velocity and delta 7.9 Experimental Study: Investigation of the Relationships Between Gait Parameters and Forward Velocity 7.9.1 Layout of the Experiment Controlling the Joints According to Lateral Undulation Calculating the Forward Velocity of the Robot 7.9.2 Experimental Results Relationship Between the Forward Velocity and alpha Relationship Between the Forward Velocity and omega Relationship Between the Forward Velocity and delta 7.10 Chapter Summary Chapter 8: Path Following Control of Snake Robots Through a Cascaded Approach 8.1 The Relation Between This Chapter and Previous Literature 8.2 Mathematical Preliminaries 8.3 Straight Line Path Following Control of Snake Robots 8.3.1 Control Objective 8.3.2 Assumptions 8.3.3 Model Transformation 8.3.4 The Straight Line Path Following Controller Gait Pattern Controller Heading Controller 8.3.5 The Stability Properties of the Path Following Controller 8.3.6 Proof of Theorem 8.2 8.4 Path Following Control of Snake Robots Along Curved Paths 8.4.1 Comments on the Curved Path Following Controller 8.4.2 The Curved Path Following Controller 8.5 Waypoint Guidance Control of Snake Robots 8.5.1 Description of the Approach 8.5.2 The Waypoint Guidance Strategy 8.6 Simulation Study: The Performance of the Straight Line Path Following Controller 8.6.1 Simulation Parameters 8.6.2 Simulation Results 8.7 Experimental Study: The Performance of the Straight Line Path Following Controller 8.7.1 Implementation Issues 8.7.2 Implementation of the Path Following Controller of the Physical Snake Robot 8.7.3 Experimental Results 8.8 Simulation Study: The Performance of the Waypoint Guidance Strategy 8.8.1 Implementation of the Guidance Strategy with the Simplified Model 8.8.2 Implementation of the Guidance Strategy with the Complex Model 8.8.3 Simulation Results 8.9 Chapter Summary Part II: Snake Robot Locomotion in Cluttered Environments Chapter 9: Introduction to Part II Chapter 10: A Hybrid Model of Snake Robot Locomotion in Cluttered Environments 10.1 The Relation Between This Chapter and Previous Literature 10.2 Hybrid Dynamical Systems and Complementarity Systems 10.2.1 Modelling of Hybrid Dynamical Systems 10.2.2 Complementarity Systems 10.3 The Dynamics of the Snake Robot Without Obstacles 10.3.1 The Ground Friction Model 10.3.2 The Equations of Motion Without Obstacles 10.4 Overview of the Contact Modelling Approach 10.5 Detection of Obstacle Impacts and Detachments 10.6 The Continuous Dynamics of the Snake Robot During Constrained Motion 10.6.1 The Unilateral Constraints from the Obstacles 10.6.2 The Constrained Dynamics of the Snake Robot Without Obstacle Friction 10.6.3 The Constrained Dynamics of the Snake Robot with Obstacle Friction 10.7 The Discontinuous Dynamics of the Snake Robot During Obstacle Impacts and Detachments 10.7.1 The Discontinuous Dynamics of the Snake Robot During Obstacle Impacts 10.7.2 The Discontinuous Dynamics of the Snake Robot During Obstacle Detachments 10.8 The Complete Hybrid Model of the Snake Robot in an Obstacle Environment 10.8.1 The Jump Set 10.8.2 The Jump Map 10.8.3 The Flow Set 10.8.4 The Flow Map 10.8.5 Summary of the Complete Hybrid Plant 10.9 Simulation Study: Comparison of the Hybrid Model with Previous Experimental and Simulation Results 10.10 Chapter Summary Chapter 11: Development of a Mechanical Snake Robot for Obstacle-Aided Locomotion 11.1 The Relation Between This Chapter and Previous Literature 11.2 Overview of the Snake Robot Design 11.3 The Exterior Gliding Surface 11.4 The Contact Force Measurement System 11.4.1 Assumptions Underlying the Sensor System 11.4.2 The Sensor System Setup 11.4.3 Calculation of Contact Forces 11.5 The Power and Control System 11.5.1 The Power System 11.5.2 The Control System 11.6 The Performance of the Snake Robot 11.6.1 Experimental Validation of the Contact Force Measurement System 11.6.2 Demonstration of Motion Patterns 11.7 The Experimental Setup of the Snake Robot 11.8 An Alternative Approach for Measuring External Contact Forces 11.9 Chapter Summary Chapter 12: Hybrid Control of Obstacle-Aided Locomotion 12.1 The Relation Between This Chapter and Previous Literature 12.2 Preliminary Note on Hybrid Controllers 12.3 Control Objective 12.4 Notation and Basic Assumptions 12.5 The Hybrid Controller for Obstacle-Aided Locomotion 12.5.1 The Leader-Follower Scheme 12.5.2 The Jam Detection Scheme 12.5.3 The Jam Resolution Scheme 12.5.4 The Joint Angle Controller 12.5.5 The Complete Hybrid Controller The Jump Set The Jump Map The Flow Set The Flow Map Calculation of the Control Input for the Plant 12.6 Summary of the Closed-Loop System 12.7 Simulation Study: The Performance of the Hybrid Controller 12.7.1 Simulation Parameters 12.7.2 Attempting Lateral Undulation in Open-Loop in a Structured Obstacle Environment 12.7.3 Hybrid Controller in an Obstacle Environment 12.8 Experimental Study: The Performance of the Hybrid Controller 12.8.1 Experimental Setup 12.8.2 Experimental Results 12.9 Chapter Summary Chapter 13: Path Following Control of Snake Robots in Cluttered Environments 13.1 The Relation Between This Chapter and Previous Literature 13.2 A Controller Framework for Snake Robot Locomotion 13.3 Straight Line Path Following Control in Cluttered Environments 13.3.1 Control Objective 13.3.2 Notation and Basic Assumptions 13.3.3 The Body Wave Component 13.3.4 The Environment Adaptation Component 13.3.5 The Heading Control Component 13.3.6 The Joint Angle Controller 13.3.7 Summary of the Path Following Controller 13.4 Waypoint Guidance Control in Cluttered Environments 13.5 Simulation Study: The Performance of the Path Following Controller 13.5.1 Simulation Parameters 13.5.2 Simulation Results 13.6 Experimental Study: The Performance of the Environment Adaptation Strategy 13.6.1 Experimental Setup 13.6.2 Experimental Results 13.7 Chapter Summary Chapter 14: Future Research Challenges of Snake Robot Locomotion 14.1 Control Design Challenges Analysable Mathematical Models Feedback Control Laws Based on Environment Sensing SLAM Motion Planning Strategies 14.2 Hardware Design Challenges Environment Sensing Vision Solutions for Untethered Operations Ground Friction Force Limitation Robust and Strong Actuation Mechanisms Dustproofing and Waterproofing Appendix A: Proof of Lemma 8.2 Appendix B: Proof of Lemma 8.3 Appendix C: Low-Pass Filtering Reference Models C.1 A 2nd-Order Low-Pass Filtering Reference Model C.2 A 3rd-Order Low-Pass Filtering Reference Model Glossary References Index