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| Preface | |
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| Table of Contents | |
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| Introduction | |
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| Mathematical Modeling of Robots | |
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| Symbolic Representation of Robots | |
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| The Configuration Space | |
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| The State Space | |
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| The Workspace | |
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| Robots as Mechanical Devices | |
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| Classification of Robotic Manipulators | |
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| Robotic Systems | |
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| Accuracy and Repeatability | |
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| Wrists and End Effectors | |
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| Common Kinematic Arrangements | |
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| Articulated Manipulator (RRR) | |
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| Spherical Manipulator (RRP) | |
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| SCARA Manipulator (RRP) | |
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| Cylindrical Manipulator (RPP) | |
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| Cartesian Manipulator (PPP) | |
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| Parallel Manipulator | |
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| Outline of the Text | |
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| Problems | |
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| Notes and References | |
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| Rigid Motions and Homogeneous Transformations | |
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| Representing Positions | |
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| Representing Rotations | |
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| Rotation in the Plane | |
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| Rotations in Three Dimensions | |
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| Rotational Transformations | |
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| Similarity Transformations | |
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| Composition of Rotations | |
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| Rotation with Respect to the Current Frame | |
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| Rotation with Respect to the Fixed Frame | |
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| Rules for Composition of Rotational Transformations | |
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| Parameterizations of Rotations | |
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| Euler Angles | |
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| Roll, Pitch, Yaw Angles | |
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| Axis/Angle Representation | |
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| Rigid Motions | |
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| Homogeneous Transformations | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Forward and Inverse Kinematics | |
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| Kinematic Chains | |
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| The Denavit-Hartenberg Convention | |
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| Existence and Uniqueness Issues | |
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| Assigning the Coordinate Frames | |
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| Examples | |
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| Inverse Kinematics | |
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| The General Inverse Kinematics Problem | |
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| Kinematic Decoupling | |
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| Inverse Position: A Geometric Approach | |
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| Articulated Configuration | |
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| Spherical Configuration | |
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| Inverse Orientation | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Velocity Kinematics - The Jacobian | |
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| Angular Velocity: The Fixed Axis Case | |
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| Skew Symmetric Matrices | |
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| Properties of Skew Symmetric Matrices | |
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| The Derivative of a Rotation Matrix | |
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| Angular Velocity: The General Case | |
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| Addition of Angular Velocities | |
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| Linear Velocity of a Point Attached to a Moving Frame | |
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| Derivation of the Jacobian | |
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| Angular Velocity | |
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| Linear Velocity | |
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| Combining the Linear and Angular Velocity Jacobians | |
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| The Tool Velocity | |
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| The Analytical Jacobian | |
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| Singularities | |
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| Decoupling of Singularities | |
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| Wrist Singularities | |
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| Arm Singularities | |
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| Static Force/Torque Relationships | |
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| Inverse Velocity and Acceleration | |
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| Manipulability | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Path and Trajectory Planning | |
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| The Configuration Space | |
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| Path Planning Using Potential Fields | |
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| The Attractive Field | |
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| The Repulsive Field | |
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| Mapping Workspace Forces to Joint Torques | |
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| Gradient Descent Planning | |
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| Escaping Local Minima | |
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| Probabilistic Roadmap Methods | |
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| Sampling the Configuration Space | |
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| Connecting Pairs of Configurations | |
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| Enhancement | |
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| Path Smoothing | |
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| Trajectory Planning | |
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| Trajectories for Point to Point Motion | |
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| Trajectories for Paths Specified by Via Points | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Independent Joint Control | |
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| Actuator Dynamics | |
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| Independent Joint Model | |
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| Set-Point Tracking | |
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| PD Compensator | |
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| PID Compensator | |
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| The Effect of Saturation and Flexibility | |
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| Feedforward Control | |
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| Drive Train Dynamics | |
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| State Space Design | |
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| State Feedback Control | |
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| Observers | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Dynamics | |
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| The Euler-Lagrange Equations | |
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| Motivation | |
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| Holonomic Constraints and Virtual Work | |
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| D'Alembert's Principle | |
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| Kinetic and Potential Energy | |
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| The Inertia Tensor | |
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| Kinetic Energy for an n-Link Robot | |
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| Potential Energy for an n-Link Robot | |
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| Equations of Motion | |
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| Some Common Configurations | |
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| Properties of Robot Dynamic Equations | |
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| Skew Symmetry and Passivity | |
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| Bounds on the Inertia Matrix | |
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| Linearity in the Parameters | |
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| Newton-Euler Formulation | |
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| Planar Elbow Manipulator Revisited | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Multivariable Control | |
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| PD Control Revisited | |
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| The Effect of Joint Flexibility | |
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| Inverse Dynamics | |
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| Joint Space Inverse Dynamics | |
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| Task Space Inverse Dynamics | |
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| Robust and Adaptive Motion Control | |
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| Robust Inverse Dynamics | |
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| Adaptive Inverse Dynamics | |
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| Passivity-Based Motion Control | |
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| Passivity-Based Robust Control | |
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| Passivity-Based Adaptive Control | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Force Control | |
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| Coordinate Frames and Constraints | |
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| Reciprocal Bases | |
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| Natural and Artificial Constraints | |
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| Network Models and Impedance | |
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| Impedance Operators | |
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| Classification of Impedance Operators | |
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| Thevenin and Norton Equivalents | |
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| Task Space Dynamics and Control | |
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| Task Space Dynamics | |
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| Impedance Control | |
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| Hybrid Impedance Control | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Geometric Nonlinear Control | |
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| Background | |
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| Manifolds, Vector Fields, and Distributions | |
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| The Frobenius Theorem | |
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| Feedback Linearization | |
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| Single-Input Systems | |
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| Feedback Linearization for N-Link Robots | |
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| Nonholonomic Systems | |
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| Involutivity and Holonomy | |
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| Driftless Control Systems | |
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| Examples of Nonholonomic Systems | |
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| Chow's Theorem | |
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| Control of Driftless Systems | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Computer Vision | |
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| The Geometry of Image Formation | |
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| The Camera Coordinate Frame | |
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| Perspective Projection | |
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| The Image Plane and the Sensor Array | |
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| Camera Calibration | |
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| Extrinsic Camera Parameters | |
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| Intrinsic Camera Parameters | |
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| Determining the Camera Parameters | |
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| Segmentation by Thresholding | |
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| A Brief Statistics Review | |
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| Automatic Threshold Selection | |
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| Connected Components | |
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| Position and Orientation | |
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| Moments | |
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| The Centroid of an Object and Central Moments | |
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| The Orientation of an Object | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Vision-Based Control | |
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| Design Considerations | |
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| Camera Configuration | |
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| Image-Based vs. Position-Based Approaches | |
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| Camera Motion and the Interaction Matrix | |
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| The Interaction Matrix for Point Features | |
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| Velocity of a Fixed Point Relative to a Moving Camera | |
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| Constructing the Interaction Matrix | |
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| Properties of the Interaction Matrix for Points | |
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| The Interaction Matrix for Multiple Points | |
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| Image-Based Control Laws | |
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| Computing Camera Motion | |
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| Proportional Control Schemes | |
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| Performance of IBVS systems | |
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| End Effector and Camera Motions | |
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| Partitioned Approaches | |
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| Motion Perceptibility | |
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| Summary | |
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| Problems | |
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| Notes and References | |
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| Trigonometry | |
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| The Two-Argument Arctangent Function | |
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| Useful Trigonometric Formulas | |
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| Linear Algebra | |
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| Vectors | |
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| Differentiation of Vectors | |
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| Linear Independence | |
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| Matrices | |
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| Change of Coordinates | |
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| Eigenvalues and Eigenvectors | |
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| Singular Value Decomposition (SVD) | |
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| Dynamical Systems | |
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| Lyapunov Stability | |
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| Quadratic Forms and Lyapunov Functions | |
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| Lyapunov Stability | |
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| Global and Exponential Stability | |
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| Lyapunov Stability for Linear Systems | |
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| Lasalle's Theorem | |
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| Index | |