Linux Pocket Guide: Essential Commands

If you use Linux in your day-to-day work, then Linux Pocket Guide is the perfect on-the-job reference. This thoroughly updated 20th anniversary edition explains more than 200 Linux commands, including new commands for file handling, package management, version control, file format conversions, and more. In this concise guide, author Daniel Barrett provides the most useful Linux commands grouped by functionality. Whether you're a novice or an experienced user, this practical book is an ideal reference for the most important Linux commands. You'll learn: Essential concepts—commands, shells, users, and the filesystem File commands-creating, organizing, manipulating, and processing files of all kinds Sysadmin basics-superusers, processes, user management, and software installation Filesystem maintenance-disks, RAID, logical volumes, backups, and more Networking commands-working with hosts, network connections, email, and the web Getting stuff done-everything from math to version control to graphics and audio Preface Acknowledgements How to Use This Book Chapter Organization Part I Fundamentals of Geometric Algebra Part II Interpolation, Kinematics, and Dynamics Part III Robot Control Part IV Applications I: Robot Vision, Quadrotor Part V Applications II: Medical Robotics Part VI Appendix Interdependence of the Book Chapters Audience Exercises Use of Computer Geometric Algebra Programs Use as a Textbook Contents 1 Geometric Algebra for Modeling in Robotic Physics 1.1 The Roots of Geometry and Algebra 1.2 Geometric Algebra a Unified Mathematical Language 1.3 What Does Geometric Algebra Offer for Geometric Computing? 1.3.1 Coordinate-Free Mathematical System 1.3.2 Models for Euclidean and Pseudo-Euclidean Geometry 1.3.3 Subspaces as Computing Elements 1.3.4 Representation of Orthogonal Transformations 1.3.5 Objects and Operators 1.3.6 Extension of Linear Transformations 1.3.7 Signals and Wavelets in the Geometric Algebra Framework 1.3.8 Kinematics and Dynamics 1.4 Solving Problems in Perception and Action Systems References Part I Fundamentals of Geometric Algebra 2 Introduction to Geometric Algebra 2.1 History of Geometric Algebra 2.2 What Is Geometric Algebra? 2.2.1 Basic Definitions 2.2.2 Nonorthonormal Frames and Reciprocal Frames 2.2.3 Reciprocal Frames with Curvilinear Coordinates 2.2.4 Some Useful Formulas 2.3 Multivector Products 2.3.1 Further Properties of the Geometric Product 2.3.2 Projections and Rejections 2.3.3 Projective Split 2.3.4 Generalized Inner Product 2.3.5 Geometric Product of Multivectors 2.3.6 Contractions and the Derivation 2.3.7 Hodge Dual 2.3.8 Dual Blades and Duality in the Geometric Product 2.4 Multivector Operations 2.4.1 Involution, Reversion, and Conjugation Operations 2.4.2 Join and Meet Operations 2.4.3 Multivector-Valued Functions and the Inner Product 2.4.4 The Multivector Integral 2.4.5 Convolution and Correlation of Scalar Fields 2.4.6 Clifford Convolution and Correlation 2.5 Linear Algebra 2.5.1 Linear Algebra Derivations 2.6 Simplexes 2.7 Exercises References 3 Lie Algebras, Lie Groups, and Algebra of Incidence 3.1 Introduction 3.2 Lie Algebras and Bivector Algebras 3.3 Lie Groups and Lie Algebras of Rotors 3.3.1 Lie Group of Rotors 3.3.2 Bivector Algebra 3.4 Complex Structures and Unitary Groups 3.4.1 The Doubling Bivector 3.4.2 Unitary Groups U(n) and Unitary Lie Algebras u(n) 3.5 Geometric Algebra of Reciprocal Null Cones 3.5.1 Reciprocal Null Cones 3.5.2 The Universal Geometric Algebra Gn,n 3.5.3 Representations and Operations Using Bivector Matrices 3.5.4 Bivector Representation of Linear Operators 3.5.5 The Standard Bases of Gn,n 3.5.6 Endomorphisms of Gn,n 3.5.7 The Bivectors of Gn,n 3.5.8 Mappings Acting on the Null Space 3.5.9 The Bivector or Lie Algebra of Gn,n 3.6 The General Linear Group as Spin Group 3.6.1 The Special Linear Group SL(n,mathbbR) 3.6.2 The Pin(n) and Spin(n) Groups 3.7 The Pinsp(3,3) 3.7.1 Line Geometry Using Null Geometric Algebra Over mathbbR3,3 3.7.2 Projective Transformations Using Null Geometric Algebra Over mathbbR3,3 3.7.3 Lie Groups in mathbbR3,3 3.8 2D Projective Geometry in mathbbR3,3 3.9 Horosphere and n-Dimensional Affine Plane 3.9.1 The Horosphere 3.9.2 The n-Dimensional Affine Plane 3.10 The General Linear Algebra gl(calN) of the General Linear Lie Group GL(calN) 3.10.1 The General Linear Lie Group GL(calN) 3.10.2 The General Linear Algebra gl(calN) 3.10.3 The Orthogonal Groups 3.10.4 Computing Rigid Motion in the Affine Plane 3.10.5 The Lie Algebra of the Affine Plane 3.11 The Algebra of Incidence 3.11.1 Incidence Relations in the Affine n-Plane 3.11.2 Directed Distances 3.11.3 Incidence Relations in the Affine 3-Plane 3.11.4 Geometric Constraints as Flags 3.12 Conclusion 3.13 Exercises References 4 2D, 3D, and 4D Geometric Algebras 4.1 Complex, Double, and Dual Numbers 4.2 2D Geometric Algebras of the Plane 4.3 3D Geometric Algebra for the Euclidean 3D Space 4.3.1 The Algebra of Rotors 4.3.2 Orthogonal Rotors 4.3.3 Recovering a Rotor 4.4 Quaternion Algebra 4.5 4D Geometric Algebra for 3D Kinematics 4.5.1 Motor Algebra 4.5.2 Motors, Rotors, and Translators in G+3,0,1 4.5.3 Properties of Motors 4.5.4 The Klein Manifold 4.5.5 Reciprocal Screws 4.5.6 The Study Manifold 4.6 4D Geometric Algebra for Projective 3D Space 4.7 Conclusion 4.8 Exercises References 5 Kinematics of the 2D and 3D Spaces 5.1 Introduction 5.2 Representation of Points, Lines, and Planes Using 3D Geometric Algebra 5.3 Representation of Points, Lines, and Planes Using Motor Algebra 5.4 Representation of Points, Lines, and Planes Using 4D Geometric Algebra 5.5 Motion of Points, Lines, and Planes in 3D Geometric Algebra 5.6 Motion of Points, Lines, and Planes Using Motor Algebra 5.7 Motion of Points, Lines, and Planes Using 4D Geometric Algebra 5.8 Spatial Velocity of Points, Lines, and Planes 5.8.1 Rigid Body Spatial Velocity Using Matrices 5.8.2 Angular Velocity Using Rotors 5.8.3 Rigid Body Spatial Velocity Using Motor Algebra 5.8.4 Point, Line, and Plane Spatial Velocities Using Motor Algebra 5.9 Differential Kinematics 5.10 Incidence Relations Between Points, Lines, and Planes 5.10.1 Flags of Points, Lines, and Planes 5.11 Conclusion 5.12 Exercises References 6 Conformal Geometric Algebra 6.1 Introduction 6.1.1 Conformal Split 6.1.2 Conformal Splits for Points and Simplexes 6.1.3 Euclidean and Conformal Spaces 6.1.4 Stereographic Projection 6.1.5 Inner and Outer Product Null Spaces 6.1.6 Spheres and Planes 6.1.7 Geometric Identities, Dual, Meet, and Join Operations 6.1.8 Simplexes and Spheres 6.2 The 3D Affine Plane 6.2.1 Lines and Planes 6.2.2 Directed Distance 6.3 The Lie Algebra 6.4 Conformal Transformations 6.4.1 Inversion 6.4.2 Reflection 6.4.3 Translation 6.4.4 Transversion 6.4.5 Rotation 6.4.6 Rigid Motion Using Flags 6.4.7 Dilation 6.4.8 Involution 6.4.9 Conformal Transformation 6.5 Ruled Surfaces 6.5.1 Cone and Conics 6.5.2 Cycloidal Curves 6.5.3 Helicoid 6.5.4 Sphere and Cone 6.5.5 Hyperboloid, Ellipsoids, and Conoid 6.6 Exercises References 7 The Geometric Algebras G6,0,2+, G6,3, G9,3+, G6,0,6+ 7.1 Introduction 7.2 The Double Motor Algebra G6,0,2+ 7.2.1 The Shuffle Product 7.2.2 Equations of Motion 7.3 The Geometric Algebra G6,3 7.3.1 Additive Split of G6,3 7.3.2 Geometric Entities of G6,3 7.3.3 Intersection of Surfaces 7.3.4 Transformations of G6,3 7.4 The Geometric Subalgebras G9,3+ and G6,0,6+ 7.5 Exercises References 8 Programming Issues 8.1 Main Issues for an Efficient Implementation 8.1.1 Specific Aspects for the Implementation 8.2 Implementation Practicalities 8.2.1 Specification of the Geometric Algebra Gp,q 8.2.2 The General Multivector Class 8.2.3 Optimization of Multivector Functions 8.2.4 Factorization 8.2.5 Speeding up Geometric Algebra Expressions 8.2.6 Multivector Software Packets 8.2.7 Specialized Hardware to Speed up Geometric Algebra Algorithms References Part II Interpolation, Kinematics, and Dynamics 9 Rigid Motion Interpolation 9.1 The Motor Spherical Linear Interpolation Function 9.2 Study Quadric Interpolation Algorithm 9.2.1 Interpolation Algorithm 9.2.2 Motor Interpolation 9.3 GPU Acceleration 9.3.1 Methodology 9.3.2 Standard GPU Implementation 9.3.3 Multi-streaming Implementation 9.4 Experimental Results 9.4.1 Serial and Parallel Speed-Up Comparison 9.4.2 Multi-streaming Implementation 9.5 Conclusions References 10 Robot Kinematics 10.1 Introduction 10.2 Screw Theory 10.2.1 Reciprocal Screws 10.3 Elementary Transformations of Robot Manipulators 10.3.1 The Denavit–Hartenberg Parameterization 10.3.2 Representations of Prismatic and Revolute Transformations 10.3.3 Grasping by Using Constraint Equations 10.4 Direct Kinematics of Robot Manipulators 10.4.1 Maple Program for Motor Algebra Computations 10.5 Inverse Kinematics of Robot Manipulators Using Motor Algebra 10.5.1 The Rendezvous Method 10.5.2 Computing θ1, θ2, and d3 Using a Point 10.5.3 Computing θ4 and θ5 Using a Line 10.5.4 Computing θ6 Using a Plane Representation 10.6 Inverse Kinematic Using the 3D Affine Plane 10.7 Inverse Kinematic Using Conformal Geometric Algebra 10.8 Conclusion References 11 Robot Dynamics 11.1 Introduction 11.2 D'Alembert's Principle 11.3 Newtonian Mechanics 11.3.1 Screw and Twist 11.3.2 Momentum and Wrench 11.3.3 Compliance 11.3.4 Moments of Inertia 11.3.5 Rigid Transformation of the Inertia 11.3.6 Time Derivatives of the Inertia 11.4 Newton–Euler Recursive Algorithm for Serial Robot Manipulators 11.4.1 Single Robot Link 11.4.2 Two Robot Links 11.4.3 N Robot Links 11.4.4 Recursive Algorithm 11.5 Euler–Lagrange Dynamics 11.5.1 Kinetic Energy 11.5.2 Potential Energy 11.5.3 Lagrange's Equations 11.5.4 Computing mathcalM 11.5.5 Computing G 11.6 Constrained Variational Problems 11.6.1 Optimization 11.7 Euler–Lagrange Multivector Equations 11.8 Hamiltonian Mechanics on Phase Space 11.8.1 Symplectic Structure on Vector Manifolds 11.8.2 The Hamiltonian and the Poisson Bracket 11.9 Integral Invariants 11.9.1 Lagrangian and Hamiltonian for Electromechanical or Robot Systems 11.10 Iterative Computing of the Local Hamiltonian and the Derivative of the Momenta 11.11 Conclusion References Part III Robot Control 12 Control of Robot Manipulators 12.1 Robot Controllers Using Screw Theory 12.2 Experimental Analysis of Controllers Using Screw Theory 12.3 Robot Controllers Using Hamiltonians 12.3.1 Localized Hamiltonian Bang–Bang Control 12.4 PD and Sliding Mode Controllers for Localized Hamiltonian Control 12.5 Experimental Analysis of Controllers Using the Robot Hamiltonians 12.5.1 Bang–Bang Control 12.5.2 PD and Sliding Mode Control 12.6 Conclusion References 13 Robot Neurocontrol 13.1 Introduction 13.2 Quaternion Spiking Neural Networks 13.2.1 Neuronal Model 13.2.2 Neuronal Architecture 13.3 Training Algorithm 13.3.1 Rotation with Quaternions 13.3.2 Quaternion Spike Neural Network 13.4 Control of a Simulated Nonlinear System 13.5 Control of a Real Nonlinear System 13.5.1 Forward Kinematics 13.5.2 The Jacobian 13.5.3 Inverse Kinematics 13.5.4 Control 13.6 Neural Network Signal Processing 13.6.1 Myo Bracelet 13.6.2 Physiology of Robotic Prosthesis 13.6.3 Preprocessing and Training 13.6.4 Evaluation and Control 13.7 Control of a Hand Prosthesis 13.8 Conclusions References 14 Robot Control and Tracking 14.1 Introduction 14.2 Optimization Using Geometric Constraints 14.2.1 Desired Motion 14.2.2 Collision Avoidance 14.2.3 Quadratic Programming 14.2.4 Control 14.3 Integral Sliding Mode Control 14.4 Experimental Analysis 14.4.1 Parameters of the Dynamic Model 14.4.2 Integral Sliding Mode Controller 14.5 Conclusion References Part IV Applications I: Robot Vision, Quadrotor 15 Rigid Motion Estimation Using Line Observations 15.1 Introduction 15.2 Batch Estimation Using SVD Techniques 15.2.1 Solving AX = XB Using Motor Algebra 15.2.2 Estimation of the Hand–Eye Motor Using SVD 15.3 Experimental Results 15.4 Discussion 15.5 Recursive Estimation Using Kalman Filter Techniques 15.5.1 The Kalman Filter 15.5.2 The Extended Kalman Filter 15.5.3 The Rotor Extended Kalman Filter 15.6 The Motor Extended Kalman Filter 15.6.1 Representation of the Line Motion Model in Linear Algebra 15.6.2 Linearization of the Measurement Model 15.6.3 Enforcing a Geometric Constraint 15.6.4 Operation of the MEKF Algorithm 15.6.5 Estimation of the Relative Positioning of a Robot End-Effector 15.7 Conclusion References 16 Tracker Endoscope Calibration and Body-Sensor Calibration 16.1 Device-Camera Calibration 16.1.1 Rigid Body Motion in CGA 16.1.2 Hand–Eye Calibration in CGA 16.1.3 Tracker Endoscope Calibration 16.2 Body-Sensor Calibration 16.2.1 Body–Eye Calibration 16.2.2 Algorithm Simplification 16.3 Conclusions-1 References 17 Tracking, Grasping, and Object Manipulation 17.1 Tracking 17.1.1 Exact Linearization via Feedback 17.1.2 Visual Jacobian 17.1.3 Exact Linearization via Feedback 17.1.4 Experimental Results 17.2 Barrett Hand Direct Kinematics 17.3 Pose Estimation 17.3.1 Segmentation 17.3.2 Object Projection 17.4 Grasping Objects 17.4.1 First Style of Grasping 17.4.2 Second Style of Grasping 17.4.3 Third Style of Grasping 17.5 Target Pose 17.5.1 Object Pose 17.6 Visually Guided Grasping 17.6.1 Results 17.7 Fuzzy Logic and Conformal Geometric Algebra for Grasping 17.7.1 Mandami Fuzzy System 17.7.2 Direct Kinematics of the Barrett Hand 17.7.3 Fussy Grasping of Objects 17.8 Conclusion References 18 3D Maps, Navigation, and Relocalization 18.1 Map Building 18.1.1 Matching Laser Readings 18.1.2 Map Building 18.1.3 Line Map 18.1.4 3D Map Building 18.2 Navigation 18.2.1 Localization 18.2.2 Adding Objects to the 3D Map 18.2.3 Path Following 18.3 3D Map Building Using Laser and Stereo Vision 18.3.1 Laser Rangefinder 18.3.2 Stereo Camera System with Pan–Tilt Unit 18.4 Relocation Using Lines and the Hough Transform 18.5 Experiments 18.6 Conclusions References 19 Quadrotor 19.1 Introduction 19.2 Rigid Body Spatial Velocity Using Motor Algebra 19.3 Mathematical Model Based on Motor Algebra to Multi-copter 19.4 Control Design 19.5 Simulation Results 19.6 Conclusion References Part V Applications II: Medical Robotics 20 Modeling and Registration of Medical Data 20.1 Background 20.1.1 Union of Spheres 20.1.2 The Marching Cubes Algorithm 20.2 Segmentation 20.3 Marching Spheres 20.3.1 Experimental Results for Modeling 20.4 Registration of Two Models 20.4.1 Sphere Matching 20.4.2 Experimental Results for Registration 20.5 Conclusions References 21 Geometric Computing for Minimal Invasive Surgery 21.1 Tracker Endoscope Calibration 21.2 Planning Surgical Paths in Virtual World 21.3 Execution of Surgical Maneuvers 21.4 Registration of the Organ 21.5 Representing the Elasticity on the Organ Surface 21.6 Procedure for Surgery Cuts 21.6.1 Handling the US Probe 21.6.2 Suture 21.7 Conclusions References Appendix A Notation Appendix B Useful Formulas for Geometric Algebra Index This Book Presents A Unified Mathematical Treatment Of Diverse Problems In The General Domain Of Robotics And Associated Fields Using Clifford Or Geometric Alge- Bra. By Addressing A Wide Spectrum Of Problems In A Common Language, It Offers Both Fresh Insights And New Solutions That Are Useful To Scientists And Engineers Working In Areas Related With Robotics. It Introduces Non-specialists To Clifford And Geometric Algebra, And Provides Ex- Amples To Help Readers Learn How To Compute Using Geometric Entities And Geomet- Ric Formulations. It Also Includes An In-depth Study Of Applications Of Lie Group Theory, Lie Algebra, Spinors And Versors And The Algebra Of Incidence Using The Universal Geometric Algebra Generated By Reciprocal Null Cones. Featuring A Detailed Study Of Kinematics, Differential Kinematics And Dynamics Using Geometric Algebra, The Book Also Develops Euler Lagrange And Hamiltoni- Ans Equations For Dynamics Using Conformal Geometric Algebra, And The Recursive Newton-euler Using Screw Theory In The Motor Algebra Framework. Further, It Comprehensively Explores Robot Modeling And Nonlinear Controllers, And Discusses Several Applications In Computer Vision, Graphics, Neurocomputing, Quantum Com- Puting, Robotics And Control Engineering Using The Geometric Algebra Framework. The Book Also Includes Over 200 Exercises And Tips For The Development Of Future Computer Software Packages For Extensive Calculations In Geometric Algebra, And A Entire Section Focusing On How To Write The Subroutines In C++, Matlab And Maple To Carry Out Efficient Geometric Computations In The Geometric Algebra Framework. Lastly, It Shows How Program Code Can Be Optimized For Real-time Computations. An Essential Resource For Applied Physicists, Computer Scientists, Ai Researchers, Roboticists And Mechanical And Electrical Engineers, The Book Clarifies And Demon- Strates The Importance Of Geometric Computing For Building Autonomous Systems To Advance Cognitive Systems Research.