Robotics Components and Structure of Robots Common Kinematic Anangements Outline of the Text RlGID MOTIONS AND HOMOGENEOUS TRANSFORMATIONS Composition of Rotations Further Properties of Rotations Homogeneous Tiansfoimations Skew Symmetńc Matrices Angulai Yelocity and Acceleration Addition of Angular Velocities Refeiences and Suggested Reading Problems JOINT CONTROL FORWARD KlNEMATICS: THE DENAVIT- HARTENBERG REPRESENTATION Kinematic Chains Denavit-Hartenberg Representation INVERSE KlNEMATICS Kinematic Decoupling Inverse Position: A Geometrie Approach Inverse Orientation References and Suggested Reading Problems VELOCITY KlNEMATICS— THE MANIPULATOR JACOBIAN Derivation of the Jacobian Singularities Inverse Velocity and Acceleration References and Suggested Reading Problems F LINEARIZATION DYNAMICS Euler-L agra nge E q u a ti on s Expressions for Kinetic and Potential Energy Equations of Motion Some Common Configurations Newton-Euler Formulation Planar Elbow Manipulator Revisited References and Suggested Reading Problems INDEPENDENT JOINT CONTROLActuator Dynamics Set-Point Tracking Dńve Train Dynamics Trajectory Interpolation Feedforward Control and Computed Torąue CHAPTER EIGHT: MULTIVARIABLE CONTROLPD Control Revisited Inveise Dynamics Implementation and Robustness Issues Robust Outer Loop DesignFORCE CONTROL Natural and Aitificial Constiaints Stiffness and Compliance Inveise Dynamics in Task Space Impedance Control Hybrid Position/Force ControlFEEDBACK LINEAR1ZATION Background: The Frobenius Theorem Single-Input Systems Feedback Linearization for N-Link Robots Intioduction to Outer Loop Design Outer Loop Design by Lyapunov’s Second Method The metod of sliding modes Adaptive control