Navigation of Autonomous Marine Robots: Novel Approaches Using Cooperating Teams

Acknowledgements
Danksagung
Contents
List of Figures
List of Tables
Abbreviations
Abstract
Zusammenfassung
1 Introduction
	1.1 Autonomous Systems in Land, Air, and Water
	1.2 Scope and Structure of This Thesis
	1.3 Single‐ and Team‐Oriented Approaches for Autonomous Systems
	1.4 Review of Selected European Research Projects in Cooperative Marine Robotics
		1.4.1 GREX
		1.4.2 CONMAR
		1.4.3 MORPH
	1.5 Contribution of This Thesis to the State of the Art
2 Navigation in Marine Robotics: Methods, Classification and State of the Art
	2.1 The Term ‘Navigation’ in Marine Robotics and Other Domains
	2.2 Structure of Navigation Data in Marine Robotics
		2.2.1 Inertial Reference Frame for Description of Position
		2.2.2 Body‐Fixed Frame for Description of Velocities and Forces/ Moments
		2.2.3 Coordination Transformations
		2.2.4 Physical Meaning of the ⁱz‐ Coordinate
		2.2.5 Difference between Heading and Course Angle
		2.2.6 Topological Navigation
	2.3 Navigation, Guidance and Control in the Autonomous Control for Marine Robots
		2.3.1 Model of the Marine Robot
		2.3.2 Navigation System
		2.3.3 Guidance and Control System
		2.3.4 Example and Literature Study on Guidance and Control
		2.3.5 Requirements of the Navigation System for Guidance and Control
		2.3.6 Summary of the Discussions on Navigation, Guidance, and Control
	2.4 Sensors and Methods for Navigation of Marine Robots
		2.4.1 Sensors With Direct Access to Navigation Data
		2.4.2 Navigation Based On Distance and/or Bearing Measurements to External Objects
		2.4.3 Mapping Based Methods
		2.4.4 A Review of Filtering Techniques
		2.4.5 Cooperative Navigation
		2.4.6 Introduction to the Problem of Optimal Sensor Placement (OSP)
		2.4.7 Summary of Discussions on Navigation Procedures and Methods
	2.5 Navigation Employing Acoustic Measurements
		2.5.1 Long Baseline (LBL)
		2.5.2 Single‐Beacon Navigation
		2.5.3 Short Baseline (SBL)
		2.5.4 Ultra‐Short Baseline (USBL)
		2.5.5 GPS Intelligent Buoys (GIB)
3 Problem Formulation and Definitions for the Discussions to Follow
	3.1 Two Different Concepts: Internal vs. External Navigation
	3.2 Problem Formulation
	3.3 Benchmark Scenarios
		3.3.1 Benchmark Scenario I: Supervision of a Diving Agent
		3.3.2 Benchmark Scenario II: Aided Navigation Within a Small Robot Pack
		3.3.3 Benchmark Scenario III: Range‐Based Navigation Within a Robot Pack With a Minimal Number of Members
4 Mathematical Tools Used From the Areas of Control and Systems Engineering
	4.1 Basic Ideas and Concepts
		4.1.1 The Terms ‘Signal’, ‘System’, and ‘Model’ and Their Most Important Features
			4.1.1.1 Basic Definitions
			4.1.1.2 Classification of Systems and Models
		4.1.2 State Space Representation
			4.1.2.1 Necessity for the Introduction and Comparison With Frequency Domain Approach
			4.1.2.2 Mathematical Introduction of The State Space Representation
			4.1.2.3 Solution of The Vector State Space Differential Equation
			4.1.2.4 Transfer of An ODE into A State Space Representation
			4.1.2.5 Controller Canonical Form
			4.1.2.6 Observer Canonical Form
		4.1.3 Time Discretization
			4.1.3.1 Discretizing Employing Difference Quotients
			4.1.3.2 Precise Time Discretization for A System in State Space Representation
			4.1.3.3 Comparison of The Discussed Approaches Using An Example
	4.2 Evaluation of Observability in State Space
		4.2.1 Observability and Controlability of Linear Systems
			4.2.1.1 Observability and Its Evaluation
			4.2.1.2 Controllability and Duality to Observability
			4.2.1.3 Examples for Evaluation of Observability
		4.2.2 Design of Linear Observers
			4.2.2.1 Structure of Linear Observers
			4.2.2.2 Parameter Computation for Linear Observers
			4.2.2.3 Observer Design for A System in The Observer Canonical Form
		4.2.3 Observability of Nonlinear Systems
			4.2.3.1 The Concept of Indistinguishable States
			4.2.3.2 Different Concepts of Observability for Nonlinear Systems
			4.2.3.3 Evaluation of Observability for Nonlinear Autonomous Systems
			4.2.3.4 Evaluation of Observability for General Nonlinear Systems
		4.2.4 Observability Gramian Matrix
			4.2.4.1 Linear Observability Gramian
			4.2.4.2 Empirical Gramian Matrix for Nonlinear Systems
	4.3 Parameter and Variable Estimation
		4.3.1 Basics of Stochastic Variables and Signals
			4.3.1.1 Probability Experiments, Events, and Probability Measures
			4.3.1.2 Conditional Probability
			4.3.1.3 Stochastic Variables
			4.3.1.4 Normal (or Gaussian) Distribution
			4.3.1.5 Expected Value and Variance
			4.3.1.6 Higher‐Dimensional Stochastic Variables
			4.3.1.7 Stochastic Signals
		4.3.2 Estimation Theory
			4.3.2.1 Bayes Estimation: Basics and Cost Functions
			4.3.2.2 Elementary Bayes Estimators
			4.3.2.3 Nonrandom Estimation: Basics and Criteria for Comparison of Estimators
			4.3.2.4 Maximum Likelihood Estimation and Cramér‐Rao‐Bound
		4.3.3 State Estimation
			4.3.3.1 Kalman Filter: System Description and Basics
			4.3.3.2 A Priori Estimation
			4.3.3.3 A Posteriori Estimation
			4.3.3.4 Summary: Kalman Filter for Linear Discrete‐Time Systems
			4.3.3.5 Kalman Filter for Continuous‐Time Systems
			4.3.3.6 Extended Kalman Filter for Nonlinear Systems
			4.3.3.7 Unscented Kalman Filter (UKF)
	4.4 Comparison Between Observation and Estimation
5 Methods for Cooperative Navigation
	5.1 Static Navigation Problem
		5.1.1 Problem Formulation
		5.1.2 On Parameter Estimation
			5.1.2.1 Direct Solution
			5.1.2.2 Iterative Solution
		5.1.3 Position Estimation Based on Squared Range Measurements
			5.1.3.1 Properties of Squared Range Measurements
			5.1.3.2 Unconstrained Least Squares Algorithm
			5.1.3.3 Centered Least Squares Algorithm
		5.1.4 Position Estimation by Minimizing the Maximum Likelihood Function
			5.1.4.1 Maximum Likelihood With Ranges (ML‐R)
			5.1.4.2 Maximum Likelihood With Squared Ranges (ML‐SR)
			5.1.4.3 Maximum Likelihood With Centered Squared Ranges (ML‐CSR)
		5.1.5 Comparison and Evaluation
	5.2 External Navigation: Supervision of a Diver by Three Surface Robots
		5.2.1 General Setup
		5.2.2 Solution Copied from The GIB Concept
			5.2.2.1 Target Model
			5.2.2.2 Measurement Model
			5.2.2.3 Back‐And‐Forward Approach
			5.2.2.4 EKF Design for GIB Approach
		5.2.3 Necessary Advances Beyond the GIB Concept
			5.2.3.1 New Simplistic Measurement Model
			5.2.3.2 New Advanced Measurement Model
		5.2.4 Simulative Validation
			5.2.4.1 Simulative Environment
			5.2.4.2 Simulations Without Communication Losses
			5.2.4.3 Simulations With Communication Losses
		5.2.5 Validation in Sea Trials
			5.2.5.1 Experimental Setup
			5.2.5.2 Results
		5.2.6 Conclusions and Further Paths
	5.3 Internal Navigation: Relative Position Estimation Within a Marine Robot Team
		5.3.1 Basic Mission Scenario Under Discussion
		5.3.2 Modeling of the Acoustic Communication
		5.3.3 Modeling of the USBL Measurements
		5.3.4 Description of the Several Navigation Filters
		5.3.5 Linear Kalman Filter for Velocity Estimation
		5.3.6 Modeling and Estimation for a Linearized Approach
			5.3.6.1 Target Model and A Priori Estimation
			5.3.6.2 Measurement Model and A Posteriori Estimation
			5.3.6.3 Simulative Validation
		5.3.7 Modeling and Estimation for a Nonlinear Approach Using an Unscented Kalman Filter
			5.3.7.1 Nonlinear Target Model
			5.3.7.2 Nonlinear Measurement Model
			5.3.7.3 Simulative Validation
		5.3.8 Conclusions of Cooperative Navigation
6 Optimal Sensor Placement in Marine Robotics
	6.1 The Concept of Optimal Sensor Placement
	6.2 Optimal Angular Configuration for Distance Measuring Sensors
		6.2.1 Scenario Under Discussion
		6.2.2 Computation of the Determinant of the Fisher Information Matrix (FIM)
			6.2.2.1 The Fisher Information Matrix
			6.2.2.2 The Determinant for the 2D Case
			6.2.2.3 The Determinant for the 3D Case
		6.2.3 Optimal Angular Configuration of the ROs
			6.2.3.1 Scenario Under Discussion
			6.2.3.2 Mathematical Derivation of the Result
			6.2.3.3 Conclusion and Goals for the Following Investigations
	6.3 Finding the Optimal Range for Distance Sensors With the Likelihood‐ Function
		6.3.1 Overall Set‐Up
		6.3.2 Computation of the Optimal Range
			6.3.2.1 2D Case
			6.3.2.2 3D Case
		6.3.3 Numerical Validation
			6.3.3.1 Set‐Up of the Simulation
			6.3.3.2 Results of Simulations
	6.4 Investigation On Observable States and Optimal Trajectory Based On Gramians
		6.4.1 Checking the Observability of Different Systems States in a Setup With Several ROs
			6.4.1.1 Mission Scenario and Modelling
			6.4.1.2 Observability Analysis by Empirical Gramians
			6.4.1.3 Simulations and Results
		6.4.2 Determining of an Optimal Trajectory for a Single Reference Object Based on Gramians
			6.4.2.1 Mission Scenarios Under Investigation
			6.4.2.2 Trajectory Planning for a Single RO
			6.4.2.3 Simulation and Results for a Stationary Target
			6.4.2.4 Simulation and Results for a Moving Target
			6.4.2.5 Investigation On Optimal Speed of the RO
	6.5 Conclusion on the Research in Optimal Sensor Placement
7 Combination of Cooperative Navigation and Optimal Sensor Placement
	7.1 Basic Idea
	7.2 Simple Approach – Optimal Positioning of ROs to Maximize the Fisher Information
		7.2.1 Scenario Under Discussion
		7.2.2 Guidance Controller
		7.2.3 Simulative Validation
	7.3 STAP – Simultaneous Trajectory Planning and Position Estimation
		7.3.1 Scenario Under Discussion
		7.3.2 Estimation Method and Guidance Controller
		7.3.3 Simulative Validation
8 Conclusion and Outlook
Bibliography