Guiding Vector Fields for Robot Motion Control (Springer Tracts in Advanced Robotics, 154)

✍ Scribed by Weijia Yao

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 273
• Category: Library

✦ Synopsis

Using a designed vector field to guide robots to follow a given geometric desired path has found a range of practical applications, such as underwater pipeline inspection, warehouse navigation, and highway traffic monitoring. It is thus in great need to build a rigorous theory to guide practical implementations with formal guarantees. It is even so when multiple robots are required to follow predefined desired paths or maneuver on surfaces and coordinate their motions to efficiently accomplish repetitive and laborious tasks.

The book introduces guiding vector fields on Euclidean spaces and Riemannian manifolds for single-robot and multi-robot path-following and motion coordination, provides rigorous theoretical guarantees of vector field guided motion control of robotic systems, and elaborates on the practical implementation of the proposed algorithms on mobile wheeled robots and fixed-wing aircraft. It provides guidelines for the robust, reliable, and safe practical implementations for robotic tasks, including path-following navigation, obstacle-avoidance, and multi-robot motion coordination.

In particular, the book reveals fundamental theoretic underpinnings of guiding vector fields and applies to addressing various robot motion control problems. Notably, it answers many crucial and challenging questions such as:

· How to generate a general guiding vector field on any n-dimensional Riemannian manifold for robot motion control tasks?

· Do singular points always exist in a general guiding vector field?

· How to generate a guiding vector field that is free of singular points?

· How to design control algorithms based on guiding vector fields for different robot motion control tasks including path-following, obstacle-avoidance, and multi-robot distributed motion coordination?

Answering these questions has led to the discovery of fundamental assumptions, a “topological surgery” to create a singularity-free guiding vector field, a robot navigation algorithm with the global convergence property, a provably safe collision-avoidance algorithm and an effective distributed motion control algorithm, etc

✦ Table of Contents

Series Editor’s Foreword
Acknowledgments
Contents
Acronyms
List of Figures
1 Introduction
1.1 Background
1.1.1 Path-Following Navigation
1.1.2 An Example of a 2D Guiding Vector Field
1.1.3 Vector-Field Guided Path-Following (VF-PF) Navigation Problem on General Spaces
1.1.4 Review of Guiding Vector Fields in the Literature
1.1.5 Guiding Vector Fields Studied in This Thesis
1.1.6 Comparison with Potential Energy Shaping for Path Planning
1.2 Research Challenges and Contributions
1.3 Thesis Outline
1.4 List of Related Publications
1.5 General Notations
2 Preliminaries
2.1 Nonlinear Systems and Control
2.1.1 Existence and Uniqueness of System Trajectories
2.1.2 Lyapunov Stability
2.1.3 LaSalle's Invariance Principle, Barbalat's Lemma and an Invariance-Like Theorem
2.1.4 Local Input-to-State Stability (ISS)
2.1.5 Nagumo's Theorem
2.1.6 Poicaré-Bendixson Theorem
2.1.7 Index Theorem
2.2 Point-Set Topology
2.3 Topological and Differential Manifolds
Part I Theoretical Foundation
3 Vanishing Level Value and Convergence To Zero-Level Set
3.1 Introduction
3.2 Background and Problem Formulation
3.3 Main Results
3.3.1 Preliminaries
3.3.2 Metrical Convergence and Topological Convergence
3.3.3 Convergence Characterized by Different Level Functions
3.4 Conclusions
4 Path Following Control in 3D Using a Vector Field
4.1 Introduction
4.2 Problem Formulation
4.2.1 The Guiding Vector Field and Assumptions
4.3 Analysis of the Vector Field
4.3.1 Bounded Desired Path
4.3.2 Unbounded Desired Path
4.4 Normalization and Perturbation of the Vector Field
4.5 Control Algorithm for a Fixed-Wing Aircraft
4.6 Simulations
4.7 Conclusions
5 Topological Analysis of Vector-Field Guided Path Following on Manifolds
5.1 Introduction
5.1.1 Contributions
5.1.2 Chapter Structure
5.2 Guiding Vector Field for Path Following
5.2.1 Guiding Vector Fields on Riemannian Manifolds
5.2.2 Standing Assumptions
5.3 Computation of Guiding Vector Fields on Manifolds
5.4 Dichotomy Convergence and Stability Analysis
5.5 Singular Points and Non-path-converging Trajectories
5.5.1 Existence of Singular Points
5.5.2 The Existence of Non-path-converging Trajectories
5.6 Numerical Simulations
5.7 Conclusions
6 The Domain of Attraction of the Desired Path in Vector-Field Guided Path Following
6.1 Introduction
6.2 Problem Formulation
6.2.1 VF-PF on Riemannian manifolds
6.2.2 Assumptions and Problem Statement
6.3 Further Characterization of the DOA
6.3.1 A Property Near a Compact Regular Level Set
6.3.2 DOA of the Desired Path
6.4 Conclusions
7 Refined Dichotomy Convergence in Vector-Field Guided Path-Following on [n]
7.1 Introduction
7.2 Background and Problem Formulation
7.2.1 Guiding Vector Fields on [n]
7.2.2 Assumptions
7.3 Refined Dichotomy Convergence
7.4 Simulations
7.5 Conclusions
Part II Applications with Formal Guarantees
8 Guiding Vector Fields for Following Occluded Paths
8.1 Introduction
8.1.1 Contributions
8.1.2 Chapter Structure
8.2 Problem Formulation
8.2.1 Preliminaries
8.2.2 Desired Paths
8.2.3 Obstacles, Reactive Areas and Repulsive Areas
8.2.4 Problem Formulation
8.3 Composite Vector Field
8.3.1 Path-Following Vector Field and Reactive Vector Field
8.3.2 Behavior with a Single Vector Field
8.3.3 Smooth Zero-In and Zero-Out Functions
8.3.4 Composite Vector Field
8.4 Analysis of the Composite Vector Field
8.5 Switching Vector Field
8.6 Discussions
8.6.1 Moving Obstacles
8.6.2 Higher-Dimensional Spaces
8.6.3 Complicated Robot Models
8.7 Simulations
8.7.1 Smooth Zero-In and Zero-Out Functions
8.7.2 2D Composite Vector Field
8.7.3 Switching Vector Field to Overcome the Deadlock
8.7.4 Moving Obstacles and 2D Dubins Car Model
8.7.5 3D Composite Vector Field and 3D Dubins Car Model
8.8 Conclusions
9 A Singularity-Free Guiding Vector Field for Robot Navigation
9.1 Introduction
9.1.1 Contributions
9.2 Guiding Vector Fields for Path Following
9.2.1 Guiding Vector Fields on [n]
9.2.2 Assumptions
9.3 Issues on the Global Convergence to Desired Paths
9.4 Extended Dynamics and Convergence Results
9.5 High-Dimensional Singularity-Free Guiding Vector Fields
9.5.1 Construction of a Singularity-Free Guiding Vector Field
9.5.2 Features of the Approach
9.6 Experiments with an Autonomous Aircraft
9.6.1 The Autonomous Aircraft and Airfield
9.6.2 Aircraft's Guidance System Design
9.6.3 Accommodating the Guidance to the Aircraft's Dynamics
9.6.4 The 2D Trefoil Curve
9.6.5 The 3D Lissajous Curve
9.7 Discussion: Path Following or Trajectory Tracking?
9.8 An Alternative Proof
9.9 Conclusions
10 Guiding Vector Fields for Multi-robot Coordinated Navigation
10.1 Introduction
10.1.1 Related Work
10.1.2 Contributions
10.2 Preliminaries
10.2.1 Notations
10.2.2 Graph Theory
10.2.3 Guiding Vector Field with a Virtual Coordinate for a Single Robot
10.3 Distributed Motion Coordination on Desired Paths
10.3.1 Mathematical Problem Formulation
10.3.2 Time-Invariant and Time-Varying Coordination Components and Convergence Analysis
10.4 Distributed Coordinated Maneuvering on Surfaces
10.4.1 Coordinated Motion in a Desired Set
10.4.2 Mathematical Problem Formulation
10.4.3 Time-Invariant Coordination Component
10.5 Extending the Vector Field to Incorporate Collision Avoidance
10.6 Saturated Controller for a Dubins-Car-Like Model
10.7 Simulations and Experiments
10.7.1 Simulations
10.7.2 Experiments with Multiple Fixed-Wing Aircraft
10.8 Conclusions
11 Conclusions and Future Research
11.1 Conclusions
11.2 Future Research
Appendix Control Algorithms for a 3D UAV Model and a Dynamics Model
A.1 3D UAV Model
A.2 A Control Algorithm Design Example for a Dynamics Model
References