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Book Dynamics and Robust Control of Robot environment Interaction

Download or read book Dynamics and Robust Control of Robot environment Interaction written by Miomir Vukobratovi? and published by World Scientific. This book was released on 2009 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the most attractive problem in robot control, dealing with the direct interaction between a robot and a dynamic environment, including the human-robot physical interaction. It provides comprehensive theoretical and experimental coverage of interaction control problems, starting from the mathematical modeling of robots interacting with complex dynamic environments, and proceeding to various concepts for interaction control design and implementation algorithms at different control layers. Focusing on the learning principle, it also shows the application of new and advanced learning algorithms for robotic contact tasks.The ultimate aim is to strike a good balance between the necessary theoretical framework and theoretical aspects of interactive robots.

Book Dynamics and Robust Control of Robot Environment Interaction

Download or read book Dynamics and Robust Control of Robot Environment Interaction written by Miomir Vukobratovic and published by World Scientific. This book was released on 2009 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the most attractive problem in robot control, dealing with the direct interaction between a robot and a dynamic environment, including the human-robot physical interaction. It provides comprehensive theoretical and experimental coverage of interaction control problems, starting from the mathematical modeling of robots interacting with complex dynamic environments, and proceeding to various concepts for interaction control design and implementation algorithms at different control layers. Focusing on the learning principle, it also shows the application of new and advanced learning algorithms for robotic contact tasks.

Book Robust Control of Robots

Download or read book Robust Control of Robots written by Adriano A. G. Siqueira and published by Springer Science & Business Media. This book was released on 2011-08-14 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust Control of Robots bridges the gap between robust control theory and applications, with a special focus on robotic manipulators. It is divided into three parts: robust control of regular, fully-actuated robotic manipulators; robust post-failure control of robotic manipulators; and robust control of cooperative robotic manipulators. In each chapter the mathematical concepts are illustrated with experimental results obtained with a two-manipulator system. They are presented in enough detail to allow readers to implement the concepts in their own systems, or in Control Environment for Robots, a MATLAB®-based simulation program freely available from the authors. The target audience for Robust Control of Robots includes researchers, practicing engineers, and graduate students interested in implementing robust and fault tolerant control methodologies to robotic manipulators.

Book Human Robot Interaction Control Using Reinforcement Learning

Download or read book Human Robot Interaction Control Using Reinforcement Learning written by Wen Yu and published by John Wiley & Sons. This book was released on 2021-10-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive exploration of the control schemes of human-robot interactions In Human-Robot Interaction Control Using Reinforcement Learning, an expert team of authors delivers a concise overview of human-robot interaction control schemes and insightful presentations of novel, model-free and reinforcement learning controllers. The book begins with a brief introduction to state-of-the-art human-robot interaction control and reinforcement learning before moving on to describe the typical environment model. The authors also describe some of the most famous identification techniques for parameter estimation. Human-Robot Interaction Control Using Reinforcement Learning offers rigorous mathematical treatments and demonstrations that facilitate the understanding of control schemes and algorithms. It also describes stability and convergence analysis of human-robot interaction control and reinforcement learning based control. The authors also discuss advanced and cutting-edge topics, like inverse and velocity kinematics solutions, H2 neural control, and likely upcoming developments in the field of robotics. Readers will also enjoy: A thorough introduction to model-based human-robot interaction control Comprehensive explorations of model-free human-robot interaction control and human-in-the-loop control using Euler angles Practical discussions of reinforcement learning for robot position and force control, as well as continuous time reinforcement learning for robot force control In-depth examinations of robot control in worst-case uncertainty using reinforcement learning and the control of redundant robots using multi-agent reinforcement learning Perfect for senior undergraduate and graduate students, academic researchers, and industrial practitioners studying and working in the fields of robotics, learning control systems, neural networks, and computational intelligence, Human-Robot Interaction Control Using Reinforcement Learning is also an indispensable resource for students and professionals studying reinforcement learning.

Book Learning for Adaptive and Reactive Robot Control

Download or read book Learning for Adaptive and Reactive Robot Control written by Aude Billard and published by MIT Press. This book was released on 2022-02-08 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods by which robots can learn control laws that enable real-time reactivity using dynamical systems; with applications and exercises. This book presents a wealth of machine learning techniques to make the control of robots more flexible and safe when interacting with humans. It introduces a set of control laws that enable reactivity using dynamical systems, a widely used method for solving motion-planning problems in robotics. These control approaches can replan in milliseconds to adapt to new environmental constraints and offer safe and compliant control of forces in contact. The techniques offer theoretical advantages, including convergence to a goal, non-penetration of obstacles, and passivity. The coverage of learning begins with low-level control parameters and progresses to higher-level competencies composed of combinations of skills. Learning for Adaptive and Reactive Robot Control is designed for graduate-level courses in robotics, with chapters that proceed from fundamentals to more advanced content. Techniques covered include learning from demonstration, optimization, and reinforcement learning, and using dynamical systems in learning control laws, trajectory planning, and methods for compliant and force control . Features for teaching in each chapter: applications, which range from arm manipulators to whole-body control of humanoid robots; pencil-and-paper and programming exercises; lecture videos, slides, and MATLAB code examples available on the author’s website . an eTextbook platform website offering protected material[EPS2] for instructors including solutions.

Book Biologically Inspired Control of Humanoid Robot Arms

Download or read book Biologically Inspired Control of Humanoid Robot Arms written by Adam Spiers and published by Springer. This book was released on 2016-05-19 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates a biologically inspired method of robot arm control, developed with the objective of synthesising human-like motion dynamically, using nonlinear, robust and adaptive control techniques in practical robot systems. The control method caters to a rising interest in humanoid robots and the need for appropriate control schemes to match these systems. Unlike the classic kinematic schemes used in industrial manipulators, the dynamic approaches proposed here promote human-like motion with better exploitation of the robot’s physical structure. This also benefits human-robot interaction. The control schemes proposed in this book are inspired by a wealth of human-motion literature that indicates the drivers of motion to be dynamic, model-based and optimal. Such considerations lend themselves nicely to achievement via nonlinear control techniques without the necessity for extensive and complex biological models. The operational-space method of robot control forms the basis of many of the techniques investigated in this book. The method includes attractive features such as the decoupling of motion into task and posture components. Various developments are made in each of these elements. Simple cost functions inspired by biomechanical “effort” and “discomfort” generate realistic posture motion. Sliding-mode techniques overcome robustness shortcomings for practical implementation. Arm compliance is achieved via a method of model-free adaptive control that also deals with actuator saturation via anti-windup compensation. A neural-network-centered learning-by-observation scheme generates new task motions, based on motion-capture data recorded from human volunteers. In other parts of the book, motion capture is used to test theories of human movement. All developed controllers are applied to the reaching motion of a humanoid robot arm and are demonstrated to be practically realisable. This book is designed to be of interest to those wishing to achieve dynamics-based human-like robot-arm motion in academic research, advanced study or certain industrial environments. The book provides motivations, extensive reviews, research results and detailed explanations. It is not only suited to practising control engineers, but also applicable for general roboticists who wish to develop control systems expertise in this area.

Book Mastering Robot dynamics

Download or read book Mastering Robot dynamics written by Cybellium Ltd and published by Cybellium Ltd. This book was released on with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Embark on an Enlightening Journey to "Mastering Robot Dynamics" In a world driven by automation and robotics, mastering the intricacies of robot dynamics is pivotal for creating advanced robotic systems that move with precision and intelligence. "Mastering Robot Dynamics" is your ultimate guide to navigating the complex world of robot motion, control, and manipulation. Whether you're an engineer, researcher, robotics enthusiast, or student, this book equips you with the knowledge and skills needed to excel in designing and controlling sophisticated robotic mechanisms. About the Book: "Mastering Robot Dynamics" takes you on a transformative journey through the intricacies of robot motion and control, from foundational concepts to advanced techniques. From kinematics and dynamics to trajectory planning and real-time control, this book covers it all. Each chapter is meticulously designed to provide both a deep understanding of the principles and practical applications in real-world robotic scenarios. Key Features: · Foundational Understanding: Build a solid foundation by comprehending the core principles of robot dynamics, including kinematics, inertia, and motion equations. · Robot Kinematics: Explore forward and inverse kinematics, understanding how robots move and calculating joint configurations. · Robot Dynamics: Dive into the study of forces, torques, and motion equations, learning how robots interact with their environments. · Trajectory Planning: Master the art of planning robot paths and trajectories, considering constraints and optimizing motion sequences. · Sensors and Perception: Gain insights into sensor integration, perception systems, and how robots interact with the world through feedback. · Motion Control: Learn about different types of control strategies, from PID control to advanced techniques like model predictive control. · Collision Avoidance: Understand methods for detecting and avoiding collisions, ensuring safety and reliability in robot operations. · Robot Manipulation: Explore techniques for manipulating objects, including grasp planning, manipulation tasks, and robotic arms. · Challenges and Trends: Discover challenges in robot dynamics, from sensor noise to complex control algorithms, and explore emerging trends shaping the future of robotics. Who This Book Is For: "Mastering Robot Dynamics" is designed for engineers, researchers, robotics enthusiasts, students, and anyone passionate about robotics. Whether you're aiming to enhance your skills or embark on a journey toward becoming a robotics expert, this book provides the insights and tools to navigate the complexities of designing and controlling robotic systems. © 2023 Cybellium Ltd. All rights reserved. www.cybellium.com

Book Robot Dynamics And Control

    Book Details:
  • Author : Mark W Spong
  • Publisher : John Wiley & Sons
  • Release : 2008-08-04
  • ISBN : 9788126517800
  • Pages : 356 pages

Download or read book Robot Dynamics And Control written by Mark W Spong and published by John Wiley & Sons. This book was released on 2008-08-04 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. It provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. The book includes many worked examples, examples illustrating all aspects of the theory, and problems.

Book Dynamics and Control of Robotic Manipulators with Contact and Friction

Download or read book Dynamics and Control of Robotic Manipulators with Contact and Friction written by Shiping Liu and published by John Wiley & Sons. This book was released on 2019-02-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the friction, contact and impact on robot control and force feedback mechanism Dynamics and Control of Robotic Manipulators with Contact and Friction offers an authoritative guide to the basic principles of robot dynamics and control with a focus on contact and friction. The authors discuss problems in interaction between human and real or virtual robot where dynamics with friction and contact are relevant. The book fills a void in the literature with a need for a text that considers the contact and friction generated in robot joints during their movements. Designed as a practical resource, the text provides the information needed for task planning in view of contact, impact and friction for the designer of a robot control system for high accuracy and long durability. The authors include a review of the most up-to-date advancements in robot dynamics and control. It contains a comprehensive resource to the effective design and fabrication of robot systems and components for engineering and scientific purposes. This important guide: Offers a comprehensive reference with systematic treatment and a unified framework Includes simulation and experiments used in dynamics and control of robot considering contact, impact and friction Discusses the most current tribology methodology used to treat the multiple–scale effects Contains valuable descriptions of experiments and software used Presents illustrative accounts on the methods employed to handle friction in the closed loop, including the principles, implementation, application scope, merits and demerits Offers a cohesive treatment that covers tribology and multi-scales, multi-physics and nonlinear stochastic dynamics control Written for graduate students of robotics, mechatronics, mechanical engineering, tracking control and practicing professionals and industrial researchers, Dynamics and Control of Robotic Manipulators with Contact and Friction offers a review to effective design and fabrication of stable and durable robot system and components.

Book Robotics Research

Download or read book Robotics Research written by Cédric Pradalier and published by Springer Science & Business Media. This book was released on 2011-05-02 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of papers presented at the 14th International Symposium of Robotic Research (ISRR). ISRR is the biennial meeting of the International Foundation of Robotic Research (IFRR) and its 14th edition took place in Lucerne, Switzerland, from August 31st to September 3rd, 2009. As for the previous symposia, ISRR 2009 followed up on the successful concept of a mixture of invited contributions and open submissions. Half of the 48 presentations were therefore invited contributions from outstanding researchers selected by the IFRR officers, and half were chosen among the 66 submissions after peer review. This selection process resulted in a truly excellent technical program which, we believe, featured some of the very best of robotic research. Out of the 48 presentations, the 42 papers which were finally submitted for publication are organized in 8 sections that encompass the major research orientations in robotics: Navigation, Control & Planning, Human-Robot Interaction, Manipulation and Humanoids, Learning, Mapping, Multi-Robot Systems, and Micro-Robotics. They represent an excellent snapshot of cutting-edge research in robotics and outline future directions.

Book Robotics and Automation Handbook

Download or read book Robotics and Automation Handbook written by Thomas R. Kurfess and published by CRC Press. This book was released on 2018-10-03 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the capability and utility of robots has increased dramatically with new technology, robotic systems can perform tasks that are physically dangerous for humans, repetitive in nature, or require increased accuracy, precision, and sterile conditions to radically minimize human error. The Robotics and Automation Handbook addresses the major aspects of designing, fabricating, and enabling robotic systems and their various applications. It presents kinetic and dynamic methods for analyzing robotic systems, considering factors such as force and torque. From these analyses, the book develops several controls approaches, including servo actuation, hybrid control, and trajectory planning. Design aspects include determining specifications for a robot, determining its configuration, and utilizing sensors and actuators. The featured applications focus on how the specific difficulties are overcome in the development of the robotic system. With the ability to increase human safety and precision in applications ranging from handling hazardous materials and exploring extreme environments to manufacturing and medicine, the uses for robots are growing steadily. The Robotics and Automation Handbook provides a solid foundation for engineers and scientists interested in designing, fabricating, or utilizing robotic systems.

Book Inverse Dynamics Control in Robotics Applications

Download or read book Inverse Dynamics Control in Robotics Applications written by Krzysztof Piotr Jankowski and published by Trafford. This book was released on 2004 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents both the foundations and implementation aspects of the inverse dynamics control, and examines how the solution of the inverse dynamics problem can be used for the development of controllers for selected engineering applications. The inverse dynamics control approach is directly related to the solution of the inverse dynamics problem considered in analytical mechanics. Having the specified motion and the desired properties of the resulting system, the control inputs that ensure the realization of these control objectives are to be found. By appropriately inverting the dynamic model of the plant to be controlled, a control law can be constructed which cancels the nonlinear part of the dynamics, decouples the interactions between the regulated variables, and specifies the time characteristics of the decay of the task errors. The constrained system formalism is used throughout the book and its usefulness for inverse dynamics formulation is established. The capability of the inverse dynamics controller to enforce the execution of prescribed motion of the system and at the same time to control the interaction forces with the environment is demonstrated. A new approach for the task space decomposition needed for hybrid position/force control is developed, motivated by constrained system formalism and linear algebra methods. The application of the inverse dynamics control is illustrated for several exemplary mechanical systems and for a wide variety of robotic systems; including robots constrained by the environment, robots with flexible joints, multiple robot arms, etc. Pure nonlinear inverse dynamics control is considered, as well as its robust version, and the approximate solutions to the problem. The results of numerical simulations and real-time experiments are presented to support the analytical developments. More than 200 literature sources are referred to in the book. Many mechanical systems considered in engineering practice are dynamically similar to the class of systems considered in this book. The new applications for inverse dynamics solutions arise in such fields as high precision robot manipulator control, flight control, biomechanics, vehicle control, and in many related areas. Therefore, the book can be of interest to specialists involved in developing control laws for a large variety of mechanical systems.

Book Robust Robotic Manipulation for Effective Multi contact and Safe Physical Interactions

Download or read book Robust Robotic Manipulation for Effective Multi contact and Safe Physical Interactions written by Mikael Daniel Gabriel Jorda and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Robots are complex systems, at the intersection of numerous engineering domains. The goal of many researchers is to build a fully capable and safe robot that can work and assist humans in their daily lives. To reach these goals, the complex robotic systems must be separated in different subsystem components such as perception, world understanding, navigation, manipulation, interfaces and interaction. These subsystems need to be safe and robust in order to synergistically work together. In particular, a reliable and general robot manipulation framework for free space and contact tasks is required for robots to become useful in new environments. In this thesis, we aim at developing a theoretical and practical foundation for safe and robust robotic manipulation, involving multiple simultaneous physical interactions with complex and unknown environments. We start with the well known operational space control framework: a task-oriented control methodology that enables task dynamic decoupling and hierarchical control structures. After reviewing the operational space control theory for controlling a robot task and posture, we present a series of practical considerations for its robust implementation on real hardware platforms. The integration in this framework of constraints such as joint limits and obstacles is then discussed, and a method to react safely to unexpected contacts on the robot structure during operations is proposed. These constraints are handled as control objectives in the control hierarchy, using artificial potential fields to generate repulsive forces and dynamically consistent projections to ensure an independent control of the constraints and task objectives. This systematic treatment of constraints at the control level enables a robust, autonomous execution of complex tasks in changing environments. This framework was extended over the years to consider underactuated robots in arbitrary contact situations. This resulted in a comprehensive formulation to the problem of controlling a high-dimensional robotic system involving complex tasks subject to various constraints, obstacles, balance and multiple contacts. Contacts are essential for robot manipulation. On the one hand, parts of the robot tasks involve physical interactions that need to be controlled precisely. On the other hand, further contacts are required on underactuated systems in order to enable the robot motion and guarantee its balance. In addition, contacts between the robot and the environment are subject to geometric and friction constraints that need to be addressed by the control framework. Therefore, in this thesis, the operational space whole-body control framework is completed to enable a systematic treatment of multi-contact scenarios. A virtual linkage model separates the contact forces into three sets. The resultant forces allow the robot to compensate for its underactuation. The task contact forces are controlled to their desired values. The internal forces provide a way to satisfy geometric and friction constraints. A method using barrier functions is proposed to specify a set of internal forces that ensure the robot's balance and contact stability. Even when the desired contact forces are correctly specified, their control remains a challenge. Indeed, the fast and discontinuous closed loop dynamics of stiff physical interactions leads to instabilities in robot force control. Therefore, we adapt a time domain passivity approach to guarantee the stability of explicit force controllers. This results in an increased robustness and safety for robotic systems in multiple contact scenarios. To develop effective interfaces for human-robot collaboration, we also study haptic robot teleoperation. Haptic devices provide an intuitive interface to remotely control robots and combine the high-level cognitive autonomy of humans with the autonomous manipulation capabilities of robots. The goal of haptic robot control is to maximize the transparency between the human operator and the robot environment. It means that the robot environment should be felt by the human as if they were directly interacting with it, and the human commands should be executed precisely by the robot. Transparency is very challenging to achieve when communication delays are present in the system, which occurs systematically when there is a significant physical distance between the controlled robot and its human operator. To address this challenge, we propose a new paradigm for performing haptic-robot control. Instead of relying on a global feedback loop, the new method establishes two autonomous controllers acting on the robot and the haptic device, interfaced via a dual-proxy model. The dual-proxy is a bridge between the local controllers. It generates appropriate motion and force inputs that are consistent with the task physical interactions. The model relies on the exchange of position, contact, and environment geometry information, avoiding the limitations caused by a direct force feedback between robot and haptic device in conventional teleoperation. To estimate the environment contact geometry in real-time, we also design a new perception algorithm that enables a fully autonomous implementation of the dual-proxy model. The performance of all the control methods presented in this thesis are evaluated via simulations and hardware experimental validation. Combining these methods together results in a robust, safe and generic manipulation control framework for complex robots in interaction with uncertain environments. Such framework is one of the key components for a complete and fully capable robotic system.

Book Robot Force Control

Download or read book Robot Force Control written by Bruno Siciliano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the fundamental requirements for the success of a robot task is the capability to handle interaction between manipulator and environment. The quantity that describes the state of interaction more effectively is the contact force at the manipulator's end effector. High values of contact force are generally undesirable since they may stress both the manipulator and the manipulated object; hence the need to seek for effective force control strategies. The book provides a theoretical and experimental treatment of robot interaction control. In the framework of model-based operational space control, stiffness control and impedance control are presented as the basic strategies for indirect force control; a key feature is the coverage of six-degree-of-freedom interaction tasks and manipulator kinematic redundancy. Then, direct force control strategies are presented which are obtained from motion control schemes suitably modified by the closure of an outer force regulation feedback loop. Finally, advanced force and position control strategies are presented which include passivity-based, adaptive and output feedback control schemes. Remarkably, all control schemes are experimentally tested on a setup consisting of a seven-joint industrial robot with open control architecture and force/torque sensor. The topic of robot force control is not treated in depth in robotics textbooks, in spite of its crucial importance for practical manipulation tasks. In the few books addressing this topic, the material is often limited to single-degree-of-freedom tasks. On the other hand, several results are available in the robotics literature but no dedicated monograph exists. The book is thus aimed at filling this gap by providing a theoretical and experimental treatment of robot force control.

Book Human   Robot Interaction

Download or read book Human Robot Interaction written by Dan Zhang and published by Cambridge Scholars Publishing. This book was released on 2020-08-19 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces state-of-the-art technologies in the field of human-robot interactions. It details advances made in this field in recent decades, including dynamics, controls, design analysis, uncertainties, and modelling. The text will appeal to graduate students, practitioners and researchers in the fields of robotics, computer and cognitive science, and mechanical engineering.

Book CONTROL SYSTEMS  ROBOTICS AND AUTOMATION     Volume XXII

Download or read book CONTROL SYSTEMS ROBOTICS AND AUTOMATION Volume XXII written by Heinz D. Unbehauen and published by EOLSS Publications. This book was released on 2009-10-11 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Encyclopedia of Control Systems, Robotics, and Automation is a component of the global Encyclopedia of Life Support Systems EOLSS, which is an integrated compendium of twenty one Encyclopedias. This 22-volume set contains 240 chapters, each of size 5000-30000 words, with perspectives, applications and extensive illustrations. It is the only publication of its kind carrying state-of-the-art knowledge in the fields of Control Systems, Robotics, and Automation and is aimed, by virtue of the several applications, at the following five major target audiences: University and College Students, Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.

Book Modelling and Control of Robot Manipulators

Download or read book Modelling and Control of Robot Manipulators written by Lorenzo Sciavicco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental and technological topics are blended uniquely and developed clearly in nine chapters with a gradually increasing level of complexity. A wide variety of relevant problems is raised throughout, and the proper tools to find engineering-oriented solutions are introduced and explained, step by step. Fundamental coverage includes: Kinematics; Statics and dynamics of manipulators; Trajectory planning and motion control in free space. Technological aspects include: Actuators; Sensors; Hardware/software control architectures; Industrial robot-control algorithms. Furthermore, established research results involving description of end-effector orientation, closed kinematic chains, kinematic redundancy and singularities, dynamic parameter identification, robust and adaptive control and force/motion control are provided. To provide readers with a homogeneous background, three appendices are included on: Linear algebra; Rigid-body mechanics; Feedback control. To acquire practical skill, more than 50 examples and case studies are carefully worked out and interwoven through the text, with frequent resort to simulation. In addition, more than 80 end-of-chapter exercises are proposed, and the book is accompanied by a solutions manual containing the MATLAB code for computer problems; this is available from the publisher free of charge to those adopting this work as a textbook for courses.