Lagrangian Methods & Robot Dynamics Introduction Constraining kinematic chains: Manipulators Manipulator Kinematics: the Denavit & Hartenberg (DH) Parameters Velocity Kinematics: Jacobians Degrees of Freedom: The Gruebler criterion and Kutzbach''s modification Lagangian Formulation of Dynamics The Principle of Virtual Work Principle of Least Action: Hamilton''s Principle Generalised Co-ordinates and Holonomic Dynamic Systems The Euler-Lagrange Equations Application to Manipulators: Parallel and Serial Manipulators Cartesian and spherical manipulators Planar manipulators: Two link Planar Manipulators The SCARA manipulator Two link manipulator on a moving base Two link manipulator with extendable arms The multi-link serial manipulator Rotating Planar Manipulators The PUMA 560 manipulator Spatial Manipulators Manipulator Dynamics in terms of DH Parameters Application to Mobile vehicles Exercises References Unmanned Aerial Vehicles (UAV) Dynamics & Lagrangian Methods Flight Dynamics of UAVs The Newton-Euler Equations of rigid UAVs The Lagrangian & Hamiltonian Formulations Euler-Lagrange Equations of Motion in Quasi-Coordinates The Complete Equations of Motion of UAV Exercises References Feedback Linearisation & Decoupling Lie derivatives, Lie Brackets & Lie Algebras Pure Feedback Form Relative Degree Feedback Linearisation: Pure feedback System Input-Output Feedback Linearisation Partial Feedback Linearisation Input to State Feedback Linearisation Examples Feedback Decoupling Examples Dynamic Feedback Linearisation Example Partial Feedback Linearisation of the ACROBOT Exercises References Linear and Phase Plane Analysis of Stability Introduction The Phase Plane Equilibrium and Stability: Lyapunov''s first method Regular and Singular points The Saddle Sinks: Focus, node, improper node and spiral The Centre Sources The limit cycle Stability analysis of non-linear systems with linear damping Response of non-linear systems: Geometric and Algebraic approaches Non-numerical geometric methods Numerically oriented geometric methods The method of Perturbation Variation of parameters Harmonic balance and describing functions Examples of Non-linear Systems and their analysis Undamped Free Vibrations of a Simple Pendulum The Duffing Oscillator The Van der Pol Oscillator Features of Non-linear System Responses Superharmonic response Jump Phenomenon Subharmonic resonance Combination resonance Self-excited oscillations Exercises References Robot & UAV Control: An Overview Introduction Controlling Robot Manipulators Model Based and Biomimetic Methods of Control Artificial Neural Networks Boolean Logic and its Quantification Fuzzy Sets Operations on Fuzzy Sets Relations between Fuzzy Sets Fuzzy Logic and the implication of a rule Fuzzy Reasoning Fuzzy Logic Control A typical application Exercises References Stability Stability Concepts Input/Output Stability Bounded input bounded output (BIBO) stability L2 stability / Lp stability Internal stability: Input to state Stability Advanced Stability Concepts Passive Systems Linear Systems: The concept of Passivity and positive-real systems Nonlinear Systems: The Concepts of Hyperstability Lure''s Problem Kalman-Yakubovich (KY) and other related lemmas Small-Gain Theorem Total Stability Theorem Exercises References Lyapunov Stability Lyapunov, Asymptotic and Exponential Stability Local & Global stability Lyapunov''s First & Second Methods Lyapunov''s Direct Method: Example Positive Definite & Lyapunov Functions Lyapunov''s Stability Theorem La Salle''s Invariant Set Theorems Linear Time Invariant (LTI) systems Barbalat''s Lemma and Uniform Ultimate Boundedness Exercises References Computed Torque Control Introduction Geometric Path Generation Motion control of a robot manipulator Computer Simulation of Robotic Manipulators in MATLAB/SIMULINK Computed-Torque Control concept PD & PID Auxiliary control laws Simulation of Robot Dynamics and the feedback controller Exercises References Sliding Mode Control Introduction Design Example Phase Plane Trajectory Shaping Sliding Line and Sliding Mode The Lyapunov Approach: Choosing the Control Law The Closed Loop System: The general case Principles of Variable Structure Control Design of Sliding Mode Control Laws Application Example Higher Order Sliding Mode Control Application Example Exercises References Parameter Identification Introduction & Concept Transfer Function Identification Model Parameter Identification Regression & Least Squares Solution Recursive Parameter Updating Matrix Inversion Lemma The Recursive Algorithm Application Examples: Example 1 Least Squares Estimation The Generalised Least Squares Problem The Solution to the Generalised Least Squares Problem in Recursive Form The Nonlinear Least Squares Problem Application Examples: Example 2 Exercises References Adaptive & Model Predictive Control Adaptive Control Concept Basics of Adaptive Control Self-Tuning Control Methods of Parameter Identification Model Reference Adaptive Control Indirect & Direct Adaptive Control Inverted Pendulum on a Cart Model Adaptive Control of a Two-Link manipulator Robust Adaptive Control of a Linear Plant Robust Adaptive Control of a Robot Manipulator Neural Network Based Adaptive Control Model Predictive Control (MPC) MPC with Linear Prediction Model MPC with a Nonlinear Prediction Model MPC with a Nonlinear Filter/Controller MPC with a Nonlinear H ∞controller Exercises References Lyapunov Design: The Back-stepping Approach Lyapunov Stability: Review Positive Definite Function: Review Second Method of Lyapunov: Review Motivating Examples The Back-Stepping Principle The Back-Stepping Lemma: Relationship to H∞ control Model Matching, Decoupling and Inversion Application of the Back-Stepping Lemma: Examples Design of a Back-Stepping Control Law for the ACROBOT Exercises References Hybrid Position & Force Control Introduction Hybrid Position & Force Control (Direct Force Control) Hybrid Position & Force Control: The general theory Indirect Adaptive Control of Position and Force Direct Adaptive Control of Impedance Sliding Mode Control of Impedance and Position The Operational Space Concept Active Interaction Control Coordinated spatial control of multiple serial manipulators in contact with an object Coordinated spatial control of multiple serial manipulators in contact with a constrained object Exercises References UAV Control Introduction Aircraft/UAV Parameter Estimation Application of Parameter Estimation to Stability and Control Motion Control of Rigid Bodies Nonlinear Dynamic Inversion Scalar and Vector Backstepping Dynamics of a Quadrotor UAV Back-stepping Control of the Quadrotor Back-stepping Control of a Fixed Wing Aircraft Adaptive Control of UAVs Flight Control of UAVs with Dynamic Inversion Control Stability of the Closed Loop without adaptation Adaptive Dynamic Inversion Stability of the Closed Loop with adaptation Adaptive Flight Path Tracking of Fixed Wing UAVS Adaptive Attitude Control of Fixed Wing UAVS Attitude Control of Fixed Wing UAVS with Adaptive Dynamic Inversion Guidance of UAVs Basic Flight Planning Line of sight (LOS) based pursuit guidance Straight-line guidance Exercises References moving base Two link manipulator with extendable arms The multi-link serial manipulator Rotating Planar Manipulators The PUMA 560 manipulator Spatial Manipulators Manipulator Dynamics in terms of DH Parameters Application to Mobile vehicles Exercises References Unmanned Aerial Vehicles (UAV) Dynamics & Lagrangian Methods Flight Dynamics of UAVs The Newton-Euler Equations of rigid UAVs The Lagrangian & Hamiltonian Formulations Euler-Lagrange Equations of Motion in Quasi-Coordinates The Complete Equations of Motion of UAV Exercises References Feedback Linearisation & Decoupling Lie derivatives, Lie Brackets & Lie Algebras Pure Feedback Form Relative Degree Feedback Linearisation: Pure feedback System Input-Output Feedback Linearisation Partial Feedback Linearisation Input to State Feedback Linearisation Examples Feedbac.