Adaptive Robust Control for Planar Snake Robots

Description

This book shows how a conventional multi-layered approach can be used to control a snake robot on a desired path while moving on a flat surface. To achieve robustness to unknown variations in surface conditions, it explores various adaptive robust control methods. The authors propose a sliding-mode control approach designed to achieve robust maneuvering for bounded uncertainty with a known upper bound. The control is modified by addition of an adaptation law to alleviate the overestimation problem of the switching gain as well as to circumvent the requirement for knowledge regarding the bounds of uncertainty. The book works toward non-conservativeness, achieving efficient tracking in the presence of slowly varying uncertainties with a specially designed framework for time-delayed control. It shows readers how to extract superior performance from their snake robots with an approach that allows robustness toward bounded time-delayed estimation errors. The book also demonstrates how the multi-layered control framework can be simplified by employing differential flatness for such a system. Finally, the mathematical model of a snake robot moving inside a uniform channel using only side-wall contact is discussed. The model has further been employed to demonstrate adaptive robust control design for such a motion. Using numerous illustrations and tables, Adaptive Robust Control for Planar Snake Robots will interest researchers, practicing engineers and postgraduate students working in the field of robotics and control systems. Preface Contents Abbreviations and Notation 1 Introduction 1.1 Why Snake Robots? 1.2 Mechanics of Planar Snake Robots 1.2.1 System Kinematics 1.2.2 Friction Force Model 1.2.3 System Dynamics 1.3 Control Problem of Snake Robots 1.4 Virtual Holonomic Constraint 1.4.1 Virtual Holonomic Constraint for Euler–Lagrange System 1.4.2 Virtual Holonomic Constraint for Double Pendulum 1.5 Body-Shape Control 1.5.1 Serpenoid Gait Function 1.5.2 Virtual Holonomic Constraint-Based Control for Planar Snake Robots 1.6 Output-Based Control 1.6.1 Constraint System 1.6.2 Head-Angle Control 1.6.3 Velocity Control 1.7 Toward a Practical Control Framework 1.7.1 Robustness for Planar Snake Robots 1.7.2 Multi-layered Control Methodology 1.7.3 Modeling Other Modes of Propagation 1.8 The Theme 1.9 Organization of the Book References 2 Adaptive Sliding-Mode Control for Velocity and Head-Angle Tracking 2.1 Problem Formulation 2.2 Brief Outline of Sliding-Mode and Adaptive Sliding-Mode Control 2.2.1 Sliding-Mode Control 2.2.2 Adaptive Sliding-Mode Control 2.3 Sliding-Mode Control for Planar Snake Robot 2.3.1 Sliding-Mode Control Law 2.3.2 Stability Analysis 2.4 Adaptive Sliding-Mode Control for Planar Snake Robots 2.4.1 Adaptive Sliding-Mode Control Law 2.4.2 Stability Analysis 2.5 Simulation Results 2.5.1 Simulation Scenario 2.5.2 Results for Sliding-Mode Control 2.5.3 Results for Adaptive Sliding-Mode Control 2.5.4 Discussion 2.6 Summary References 3 Time-Delayed Control for Planar Snake Robots 3.1 Control Description 3.1.1 Outer Layer Time-Delayed Control 3.1.2 Inner Layer Time-Delayed Control 3.2 Stability Analysis 3.3 Simulation Environment and Results 3.4 Summary References 4 Adaptive Robust Time-Delayed Control for Planar Snake Robots 4.1 Control Description 4.1.1 Outer Layer Adaptive Robust Time-Delayed Control 4.1.2 Inner Layer Adaptive Robust Time-Delayed Control 4.2 Stability Analysis 4.2.1 Stability Analysis of Dual-Adaptive Robust Time-Delayed Control 4.2.2 Selection of Parameters 4.3 Simulation Results 4.3.1 Discussion 4.4 Summary References 5 Differential Flatness and Its Application to Snake Robots 5.1 Brief on Differential Flatness 5.2 Flatness for Wheeled Mobile Robots 5.2.1 Robot Kinematics 5.2.2 Error Model of Robot Kinematics 5.2.3 Error Model as Flat System 5.2.4 Flatness-Based Control Law 5.2.5 Stability Analysis 5.2.6 Simulation Results 5.3 Flatness of Snake Robot Utilizing Serpenoid Gait 5.3.1 Establishing Flatness 5.3.2 Flat System 5.4 Feedback Control Law 5.4.1 Stability Analysis 5.4.2 Simulation Results 5.4.3 Discussion 5.5 Adaptive Robust Control Design for Flat Systems 5.5.1 Robust Control Law for Flat Systems with Uncertainties 5.5.2 Adaptation Law 5.5.3 Stability Analysis 5.5.4 Simulation Results 5.5.5 Discussion 5.6 Summary References 6 Modeling of In-Pipe Snake Robot Motion 6.1 Dynamic Modeling 6.1.1 Contact Force Model 6.1.2 Friction Force Model 6.1.3 Moment Due to Contact and Friction Forces 6.1.4 Dynamic Equations 6.1.5 Serpenoid Gait Function 6.2 Conventional Control Methodology 6.2.1 Body-Shape Control 6.2.2 Head-Angle Control 6.2.3 Velocity Control 6.2.4 Simulation Results 6.2.5 Discussion 6.3 Flatness-Based Adaptive Robust Control 6.3.1 Flat System 6.3.2 Adaptive Robust Control Law 6.3.3 Adaptation Law 6.3.4 Simulation Results 6.3.5 Discussions 6.4 Summary References 7 Conclusions Appendix A Boundedness of the Time-Delayed Estimation Error for Outer Layer Time-Delayed Control Appendix B Boundedness of the Time-Delayed Estimation Error for Inner Layer Time-Delayed Control Appendix C Boundedness of Switching Gains for Adaptive Robust Time-Delayed Control C.1 Boundedness of Outer Layer Switching Gain ηg C.2 Boundedness of Inner Layer Switching Gain ησ References Index