Nonlinear Control of Robots and Unmanned Aerial Vehicles : An Integrated Approach book cover
1st Edition

Nonlinear Control of Robots and Unmanned Aerial Vehicles
An Integrated Approach

ISBN 9781498767040
Published August 23, 2016 by CRC Press
562 Pages 28 Color & 122 B/W Illustrations

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Book Description

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.

Table of Contents

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



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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