1st Edition

Nonlinear Control of Robots and Unmanned Aerial Vehicles An Integrated Approach

By Ranjan Vepa Copyright 2017
    562 Pages 28 Color & 122 B/W Illustrations
    by CRC Press

    562 Pages 28 Color & 122 B/W Illustrations
    by CRC Press

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    Nonlinear Control of Robots and Unmanned Aerial Vehicles: An Integrated Approach presents control and regulation methods that rely upon feedback linearization techniques. Both robot manipulators and UAVs employ operating regimes with large magnitudes of state and control variables, making such an approach vital for their control systems design. Numerous application examples are included to facilitate the art of nonlinear control system design, for both robotic systems and UAVs, in a single unified framework. MATLAB® and Simulink® are integrated to demonstrate the importance of computational methods and systems simulation in this process.

    Lagrangian Methods & Robot Dynamics


    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



    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



    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


    Feedback Decoupling


    Dynamic Feedback Linearisation


    Partial Feedback Linearisation of the ACROBOT



    Linear and Phase Plane Analysis of Stability


    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


    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



    Robot & UAV Control: An Overview


    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




    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



    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



    Computed Torque Control


    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



    Sliding Mode Control


    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



    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



    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



    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:


    Design of a Back-Stepping Control Law for the ACROBOT



    Hybrid Position & Force Control


    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




    UAV Control


    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




    Dr. Ranjan Vepa earned his PhD in applied mechanics from Stanford University, California. He currently serves as a lecturer in the School of Engineering and Material Science, Queen Mary University of London, where he has also been the programme director of the Avionics Programme since 2001.. Dr. Vepa is a member of the Royal Aeronautical Society, London; the Institution of Electrical and Electronic Engineers (IEEE), New York; a fellow of the Higher Education Academy; a member of the Royal Institute of Navigation, London; and a chartered engineer.

    "In one volume Vepa has done a very good job of concisely presenting methodologies and theories for realising the control of unmanned aerial vehicles and robots. It is written in such a way that is easy to understand and hence apply. It is like a toolkit of methodologies and equations to understand various Robot platform problems and challenges as well as control theories and approaches one could bring to bear to solve them in various scenarios. It is also a good book for those who are interested in model based design of control systems.
    The way the book is written enables a reader to read each chapter independently thereby making it suited for a quick read to learn a concept or brush up on one’s knowledge. I believe this book will appeal to a wide readership of industrial engineers as well as academics interested in extending the frontiers of control theory on UAVs and Robots."
    The Aeronautical Journal, May 2018 Issue