Cover: Mobile Robots, Second Edition by Gerald Cook, Feitian Zhang

IEEE Press
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IEEE Press Editorial Board
Ekram Hossain, Editor in Chief

David Alan Grier      Andreas Molisch    Diomidis Spinellis

Donald Heirman     Saeid Nahavandi    Sarah Spurgeon

Elya B. Joffe       Ray Perez          Ahmet Murat Tekalp

Xiaoou Li            Jeffrey Reed

Mobile Robots

Navigation, Control and Sensing, Surface Robots and AUVs

Second Edition

Gerald Cook

George Mason University

Feitian Zhang

George Mason University

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Gerald Cook

To my heavenly Father for leading me to a vocation that has brought me a lifetime of joy and happiness.

To my wife, Nancy Anne, for her encouragement and support of all my endeavors throughout my career.

To my two adult sons, Bo and Ford, for their continued encouragement and interest in my work.

To my mother, Rose Boyer Cook, who as a single parent of four provided so abundantly for our needs.

Feitian Zhang

To my wife, Mi Zhou, and our children, Andy and Lisa, for bringing me strength and joy that encourage me throughout my career.

To my parents, Guangbo Zhang and Dongmei He, for their unconditional love and support all the time.


A number of experiences and acquaintances have contributed to this project. The Countermine Branch of the Science Division of the Night Vision Electronic Sensors Directorate (NVESD), United States Army played a particularly important role through its sponsorship of related research. This research effort had as its objective the detection and geo‐registration of landmines through the use of vehicular mounted sensors. The nature of the problem required that a broad set of tools be brought to bear. These required tools included a vehicle model, sensor models, coordinate transformations, navigation, state estimation, probabilistic decision making, and others. Much of the required technology had previously existed. The contribution here was to bring together these particular bodies of knowledge and combine them so as to meet the objectives. This led to several interesting years of interaction with NVESD and other researchers in this area of applied research.

Afterwards, it was realized that the work could be cast in a more general framework, leading to a set of notes for a second‐year graduate course in Mobile Robots. A course on modern control and one on random processes are the required prerequisites. This course was taught several times at George Mason University, and numerous revisions and additions resulted as well as a set of problems at the end of each chapter. Finally, the notes were organized more formally with the result being the first edition of this book.

I would like to express my appreciation to some of the individuals who have influenced and encouraged me in the writing of this book. These include Kelly Sherbondy, my research sponsor at NVESD, former colleague Guy Beale, department chairman Andre Manitius, former student Patrick Kreidl, industrial associate Bill Pettus, collaborator at the Naval Research Laboratory Jay Oaks, former students Smriti Kansal and Shwetha Jakkidi who were part of the NVESD project, and the many other students who have attended my classes and provided me with inspiration over the years.

Gerald Cook

The major addition to the second edition of this book includes modeling and control of autonomous underwater vehicles (AUVs), which exhibits unique complex three‐dimensional dynamics. The materials are mainly based on my PhD research project on design, modeling, and control of a novel underwater vehicle named gliding robotic fish that is essentially a hybrid of underwater glider and robotic fish. The research, sponsored by National Science Foundation (NSF), aimed to develop an autonomous platform for aquatic environmental monitoring through fundamental understanding and effective control of gliding robotic fish, which eventually led to generalized modeling and control approaches for AUVs written in this book. I would like to acknowledge and thank my PhD advisor Xiaobo Tan, my collaborators Hassan Khalil at Michigan State University and Fumin Zhang at Georgia Institute of Technology for their enormous support and insightful guidance in the research project, and my colleague Gerald Cook for motivating and encouraging me in co‐writing the second edition of this book.

Feitian Zhang

The following is a suggested schedule for teaching a one‐semester course from this book.

  1. Kinematic Models for Mobile Robots: 0.5 weeks.
  2. Mobile Robot Control: 1.5 weeks.
  3. Robot Attitude: 1.0 week.
  4. Robot Navigation: 2.0 weeks.
  5. Application of Kalman Filtering: 1.5 weeks.
  6. Remote Sensing: 1.5 weeks.
  7. Target Tracking Including Multiple Targets with Multiple Sensors: 1.0 week.
  8. Obstacle Mapping and Its Application to Robot Navigation: 1.0 week.
  9. Operating a Robotic Manipulator: 1.0 week.
  10. Remote Sensing via UAVs: 0.5 weeks.
  11. Dynamics Modeling of AUVs: 1.0 week.
  12. Control of AUVs: 1.5 week.

It is hoped that this book will also serve as a useful reference to those working in related areas. Because of the overriding objective described in the title of the book, the topics cut across traditional curricular boundaries to bring together material from several engineering disciplines. As a result, the book could be used for a course taught within electrical engineering, mechanical engineering, aerospace engineering, or possibly others. We would like to acknowledge here that MATLAB® is a registered trademark of The MathWorks, Inc. Also, please note, two of the videos referred to in Appendix A can be viewed at

About the Authors

Gerald Cook, ScD, is the Earle C. Williams Professor Emeritus of Electrical Engineering and past chairman of Electrical and Computer Engineering at George Mason University. He was previously Chairman of Electrical and Biomedical Engineering at Vanderbilt University and before that, Professor of Electrical Engineering at the University of Virginia. He is a Life Fellow of the Institute of Electrical and Electronics Engineers (IEEE), a former president of the IEEE Industrial Electronics Society and a former Editor in Chief of the IEEE Transactions on Industrial Electronics.

Feitian Zhang, PhD, is an Assistant Professor in the Department of Electrical and Computer Engineering at George Mason University. He received the Bachelor's and Master's degrees in Automatic Control from Harbin Institute of Technology in China, and the PhD degree in Electrical and Computer Engineering from Michigan State University. He was a Postdoctoral Research Associate in the Department of Aerospace Engineering at the University of Maryland prior to joining Mason. His research interests include robotics, control, artificial intelligence, and underwater vehicles.


I wish to take this opportunity to express my appreciation to Dr. Feitian Zhang for joining with me as Co‐Author in developing this second edition of Mobile Roots. He has demonstrated a high level of knowledge and skill in the area of autonomous underwater robots (AUVs) and adds a new dimension to the book with this contribution. It has been a pleasure working together on this project.

Mobile robots, as the name implies, have the ability to move around. They may travel on the ground, on the surface of bodies of water, under water, and in the air. This is in contrast with fixed‐base robotic manipulators that are more commonplace in manufacturing operations such as automobile assembly, aircraft assembly, electronic parts assembly, welding, spray painting, and others. Fixed‐base robotic manipulators are typically programmed to perform repetitive tasks with perhaps limited use of sensors, whereas mobile robots are typically less structured in their operation and likely to use more sensors.

As a mobile robot performs its tasks, it is important for its supervisor to maintain knowledge of its location and orientation. Only then can the sensed information be accurately reported and fully exploited. Thus navigation is essential. Navigation is also required in the process of directing the mobile robot to a specified destination. Along with navigation is the need for stable and efficient control strategies. The navigation and control operations must work together hand‐in‐hand. Once the mobile robot has reached its destination, the sensors can acquire the needed data and either store it for future transfer or report it immediately to the next level up. Thus, there is a whole system of functions required for effective use of mobile robots.

Mobile robots may be operated in a variety of different modes. One of these is the teleoperated mode in which a supervisor provides some of the instructions. Here sensors including cameras provide information from the robot to the supervisor that enables him or her to assess the situation and decide on the next course of action. The supervision may be very complete, leaving no decision making to the robot, or it may be at a high level only, leaving details to be worked out by algorithms residing on the robot. Some examples of this type of operation are the Mars rovers and the walking robots that descended down into the volcano on Mount Saint Helens in the state of Washington. Additional applications include the handling of hazardous materials such as nuclear waste or explosives and the search in war operations for explosives such as landmines. Other examples are unmanned air vehicles (UAVs) and AUVs that can be used for reconnaissance operations. The trajectory may be prespecified with the provision for intervention and redirection as the circumstances dictate.

One of the more interesting stories involving a teleoperated mobile robot took place in Prince William County, Virginia in the nineties. The police had a suspect cornered in an apartment house and decided that since he was armed they would send in their mobile robot. It was a tracked vehicle with a camera, an articulated manipulator, and a stun gun. Under the direction of a supervisor the robot was able to climb the stairs, open the apartment door, open a closet door, lift a pile of clothes off the suspect, and then stun him so that he could be apprehended. This served a very useful purpose and alleviated the need for the police officers to subject themselves to risk of injury or death.

Another possible mode is autonomous operation. Here the robot operates without external inputs except those inputs obtained through its sensors. Often there is a random element to the motion with sensors for collision avoidance and/or signal seeking. One example of this type of operation was the miniature solar‐powered lawn mowers at the CIA in Langley, Virginia. These mobile robots were the size of a dinner plate and had razor sharp blades. The courtyard in which they worked was quite smooth with well‐defined boundaries. Each robot could move in a random direction until hitting an obstacle at which time it switched to a new direction. Another example of this autonomous robotic behavior is a swimming‐pool cleaner. This device moves about the pool sucking up any debris on the bottom of the pool and causing it to be pumped into the filtration system. The motion of the mobile robot seems to be somewhat random with the walls of the pool providing a natural boundary. Similar devices exist for vacuuming homes or offices.

A very exciting and recent example of an underwater semi‐autonomous vehicle was the crossing of the Atlantic Ocean, from the coast of New Jersey to the coast of Spain, by the deep‐sea glider Scarlet. This 8‐ft long, 135 lb, unmanned vehicle was the product of a research team at Rutgers University and Teledyne Webb Research. The voyage took 221 days, extended over 4,600 miles, and provided data on the water temperature and salinity as a function of depth. The glider was powered by a battery that alternately pumped water out of the front portion of the vehicle to cause it to rise and took on water to cause it to dive. The battery could also be shifted forward or backward to modify the weight distribution and thereby adjust the glide angle. As the glider dove or climbed, its hydrodynamic wings gave it forward motion in much the same manner as that of a toy airplane glider dropped from a second floor window. It was equipped with a rudder for steering. Normally it traveled down to a depth of 600 ft below the surface of the ocean and then up to within 60 ft of the surface. A few times per day it would surface to get a GPS fix on its position, make radio contact with its supervisor and obtain a new way‐point to head toward. Apparently the vehicle was equipped with an inertial measurement device that would provide heading information while underwater. (Washington Post, Tuesday, December 15, 2009, health and science Section pages E1 and E6.) As was mentioned, an important application of AUVs such as this is data collection of variables such as water temperature and salinity as a function of location, including depth.

Examples of mobile robots in manufacturing facilities include wheeled vehicles used for material transfer from one work station to another. Here a line painted on the floor may designate the path for the mobile robot to follow. Optical sensors sense the boundaries of the line and give commands to the steering system to cause the mobile robot to follow along the track. Schemes such as this can also be used for mobile robots whose assignment is to perform inventory checks or security checks in a large facility such as a warehouse. Here the path for the mobile robot is specified and the sensors acquire and store the required information as the robot makes its rounds.

There are two basic types of steering used by mobile robots operating on the ground. For both of these types of steering, the mobile robot may have one or two front wheels. One type is front‐wheel steering much like that of an automobile. This type of steering presents interesting challenges to the controller, because it yields a nonzero turning radius. This radius is limited by the length of the robot and the maximum steering angle.

The other type of steering involves independent wheel control for each side. By rotating the left and right wheels in opposite directions at the same speed, the robot can be made to turn while in place, i.e., at a zero turning radius. Tracked vehicles use this same type of differential‐drive steering strategy, there often referred to as skid steering.

Examples of mobile robots also include, as we mentioned earlier, AUVs such as underwater gliders, whose diverse applications range from oil/gas exploration and environmental monitoring to search and rescue and national harbor security. Due to the complex interaction between surrounding fluid and AUVs, hydrodynamics play an important role in determining vehicle dynamics which exhibits high nonlinearity. In addition, AUVs operate in open water environments typically in a truly three‐dimensional trajectory. Therefore, it is essential to establish the dynamic model of AUVs and further investigate how to control AUV’s dynamic motions given the unique propulsion and steering mechanisms such as buoyancy adjustment and control surfaces (e.g., a rudder or an elevator).

The objectives of this book are to serve as a textbook for a one‐semester graduate course on wheeled surface robots as well as AUVs and also to provide a useful reference for one interested in these fields. The book presumes knowledge of modern control and random processes. Exercises are included with each chapter. Prior facility with digital simulation of dynamic systems is very helpful but may be developed as one takes the course. The material lends itself well to the inclusion of a course project if one desires to do so.