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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 | |