Mobile Robotics. Mathematics, Models, and Methods. HI Cambridge. Alonzo Kelly. Carnegie Mellon University UNIVERSITY PRESS

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1 Mobile Robotics Mathematics, Models, and Methods Alonzo Kelly Carnegie Mellon University HI Cambridge UNIVERSITY PRESS

2 Contents Preface page xiii 1 Introduction Applications of Mobile Robots Types of Mobile Robots Automated Guided Vehicles (AGVs) Service Robots Cleaning and Lawn Care Robots Social Robots Field Robots Inspection, Reconnaissance, Surveillance, and Exploration Robots Mobile Robot 7 Engineering Mobile Robot Subsystems Overview of the Text Fundamentals of Wheeled Mobile Robots References and Further Reading Exercise 11 2 Math Fundamentals Conventions and Definitions Notational Conventions Embedded Coordinate Frames References and Further Reading Matrices Matrix Operations Matrix Functions Matrix Inversion Rank-Nullity Theorem Matrix Algebra Matrix Calculus Leibnitz' Rule References and Further Reading Exercises v

3 vi CONTENTS 2.3 Fundamentals of Rigid Transforms Definitions Why Homogeneous Transforms Semantics and Interpretations References and Further Reading Exercises Kinematics of Mechanisms Forward Kinematics Inverse Kinematics Differential Kinematics References and Further Reading Exercises Orientation and Angular Velocity Orientation in Euler Angle Form Angular Rates and Small Angles Angular Velocity and Orientation Rates in Euler Angle Form Angular Velocity and Orientation Rates in Angle-Axis Form References and Further Reading Exercises Kinematic Models of Sensors Kinematics of Video Cameras Kinematics of Laser Rangefinders References and Further Reading Exercises Transform Graphs and Pose Networks Transforms as Relationships Solving Pose Networks Overconstrained Networks Differential Kinematics Applied to Frames in General Position References and Further Reading Exercises Quaternions Representations and Notation Quaternion Multiplication Other Quaternion Operations Representing 3D Rotations Attitude and Angular Velocity References and Further Reading Exercises Numerical Methods Linearization and Optimization of Functions of Vectors Linearization Optimization of Objective Functions Constrained Optimization References and Further Reading Exercises Systems of Equations Linear Systems Nonlinear Systems 136

4 CONTENTS Vii References and Further Reading Exercises Nonlinear and Constrained Optimization Nonlinear Optimization Constrained Optimization References and Further Reading Exercises Differential Algebraic Systems Constrained Dynamics First- and Second-Order Constrained Kinematic Systems Lagrangian Dynamics Constraints References and Further Reading Exercises Integration ofdifferential Equations Dynamic Models in State Space Integration of State Space Models References and Further Reading Exercises Dynamics Moving Coordinate Systems Context of Measurement Change of Reference Frame Example: Attitude Stability Margin Estimation Recursive Transformations of State ofmotion References and Further Reading Exercises Kinematics of Wheeled Mobile Robots Aspects of Rigid Body Motion WMR Velocity Kinematics for Fixed Contact Point Common Steering Configurations References and Further Reading Exercises Constrained Kinematics and Dynamics Constraints of Disallowed Direction Constraints of Rolling Without Slipping Lagrangian Dynamics Terrain Contact Trajectory Estimation and Prediction References and Further Reading Exercises Aspects of Linear Systems Theory Linear Time-Invariant Systems State Space Representation of Linear Dynamical Systems Nonlinear Dynamical Systems Perturbative Dynamics of Nonlinear Dynamical Systems References and Further Reading Exercises

5 viii CONTENTS 4.5 Predictive Modeling and System Identification Optimal Braking Turning Vehicle Rollover Wheel Slip and Yaw Stability Parameterization and Linearization of Dynamic Models System Identification References and Further Reading Exercises 269 Estimation Random Variables, Processes, and Transformation Characterizing Uncertainty Random Variables Transformation of Uncertainty Random Processes References and Further Reading Exercises Covariance Propagation and Optimal Estimation Variance of Continuous Integration and Averaging Processes Stochastic Integration Optimal Estimation References and Further Reading Exercises State Space Kalman Filters Introduction Linear Discrete Time Kalman Filter Kalman Filters for Nonlinear Systems Simple Example: 2D Mobile Robot Pragmatic Information for Kalman Filters Other Forms of the Kalman Filter References and Further Reading Exercises Bayesian Estimation Definitions Bayes' Rule Bayes' Filters Bayesian Mapping Bayesian Localization References and Further Reading Exercises State Estimation Mathematics of Pose Estimation Pose Fixing versus Dead Reckoning Pose Fixing Error Propagation in Triangulation Real Pose Fixing Systems Dead Reckoning Real Dead Reckoning Systems References and Further Reading Exercises 397

6 CONTENTS ix 6.2 Sensors for State Estimation Articulation Sensors Ambient Field Sensors Inertial Frames ofreference Inertial Sensors References and Further Reading Exercises Inertial Navigation Systems Introduction Mathematics of Inertial Navigation Errors and Aiding in Inertial Navigation Example: Simple Odometry-Aided Attitude and Heading Reference System References and Further Reading Exercises Satellite Navigation Systems Introduction Implementation State Measurement Performance Modes of Operation References and Further Reading Exercises Control Classical Control Introduction Virtual Spring-Damper Feedback Control Model Referenced and Feedforward Control References and Further Reading Exercises State Space Control Introduction State Space Feedback Control Example: Robot Trajectory Following Perception Based Control Steering Trajectory Generation References and Further Reading Exercises Optimal and Model Predictive Control Calculus ofvariations Optimal Control Model Predictive Control Techniques for Solving Optimal Control Problems Parametric Optimal Control References and Further Reading Exercises 492

7 X CONTENTS 7.4 Intelligent Control Introduction Evaluation Representation Search References and Further Reading Exercises Perception Image Processing Operators and Algorithms Taxonomy of Computer Vision Algorithms High-Pass Filtering Operators Low-Pass Operators Matching Signals and Images Feature Detection Region Processing References and Further Reading Exercises Physics and Principles of Radiative Sensors Radiative Sensors Techniques for Range Sensing Radiation Lenses, Filters, and Mirrors References and Further Reading Exercises Sensors for Perception Laser Rangefinders Ultrasonic Rangefinders Visible Wavelength Cameras Mid to Far Infrared Wavelength Cameras Radars References and Further Reading Exercises Aspects of Geometric and Semantic Computer Vision Pixel Classification Computational Stereo Vision Obstacle Detection References and Further Reading Exercises Localization and Mapping Representation and Issues Introduction Representation Timing and Motion Issues Related Localization Issues Structural Aspects Example: Unmanned Ground Vehicle (UGV) Terrain Mapping References and Further Reading Exercises 593

8 CONTENTS xi 9.2 Visual Localization and Motion Estimation Introduction Aligning Signals for Localization and Motion Estimation Matching Features for Localization and Motion Estimation Searching for the Optimal Pose References and Further Reading Exercises Simultaneous Localization and Mapping Introduction Global Consistency in Cyclic Maps Revisiting EKF SLAM for Discrete Landmarks Example: Autosurveying of Laser Reflectors References and Further Reading Exercises Motion Planning Introduction Introducing Path Planning Formulation of Path Planning Obstacle-Free Motion Planning References and Further Reading Exercises Representation and Search for Global Path Planning Sequential Motion Planning Big Ideas in Optimization and Search Uniform Cost Sequential Planning Algorithms Weighted Sequential Planning Representation for Sequential Motion Planning References and Further Reading Exercises Real-Time Global Motion Planning: Moving in Unknown and Dynamic Environments Introduction Depth-Limited Approaches Anytime Approaches Plan Repair Approach: D* Algorithm Hierarchical Planning References and Further Reading Exercise 690 Index 691

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