Snake Robots: Modelling, Mechatronics, and Control

✍ Scribed by Pål Liljebäck, Kristin Ytterstad Pettersen, Øyvind Stavdahl, Jan Tommy Gravdahl

• Publisher: Springer
• Year: 2012
• Tongue: English
• Leaves: 316
• Series: Advances in Industrial Control
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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