# Preface

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In the last two decades, there has been a tremendous surge of activity in robotics, both at in terms of research and in terms of capturing the imagination of the general public as to its seemingly endless and diverse possibilities. This period has been accompanied by a technological maturation of robots as well, from the simple pick and place and painting and welding robots, to more sophisticated assembly robots for inserting integrated circuit chips onto printed circuit boards, to mobile carts for parts handling and delivery. Several areas of robotic automation have now become "standard" on the factory floor and, as of the writing of this book, the field is on the verge of a new explosion to areas of growth involving hazardous environments, minimally invasive surgery, and micro electro-mechanical mechanisms.

Concurrent with the growth in robotics in the last two decades has been the development of courses at most major research universities on various aspects of robotics. These courses are taught at both the undergraduate and graduate levels in computer science, electrical and mechanical engineering, and mathematics departments, with different emphases depending on the background of the students. A number of excellent textbooks have grown out of these courses, covering various topics in kinematics, dynamics, control, sensing, and planning for robot manipulators.

Given the state of maturity of the subject and the vast diversity of students who study this material, we felt the need for a book which presents a slightly more abstract (mathematical) formulation of the kinematics, dynamics, and control of robot manipulators. The current book is an attempt to provide this formulation not just for a single robot but also for multifingered robot hands, involving multiple cooperating robots. It grew from our efforts to teach a course to a hybrid audience of electrical engineers who did not know much about mechanisms, computer scientists who did not know about control theory, mechanical engineers who were suspicious of involved explanations of the kinematics and dynamics of garden variety open kinematic chains, and mathematicians who were curious, but did not have the time to build up lengthy prerequisites before beginning a study of robotics.

It is our premise that abstraction saves time in the long run, in return for an initial investment of effort and patience in learning some mathematics. The selection of topics---from kinematics and dynamics of single robots, to grasping and manipulation of objects by multifingered robot hands, to nonholonomic motion planning---represents an evolution from the more basic concepts to the frontiers of the research in the field. It represents what we have used in several versions of the course which have been taught between 1990 and 1993 at the University of California, Berkeley, the Courant Institute of Mathematical Sciences of New York University, the California Institute of Technology, and the Hong Kong University of Science and Technology (HKUST). We have also presented parts of this material in short courses at the Universita di Roma, the Center for Artificial Intelligence and Robotics, Bangalore, India, and the National Taiwan University, Taipei, Taiwan.

The material collected here is suitable for advanced courses in robotics consisting of seniors or first- and second-year graduate students. At a senior level, we cover Chapters 1--4 in a twelve week period, augmenting the course with some discussion of technological and planning issues, as well as a laboratory. The laboratory consists of experiments involving on-line path planning and control of a few industrial robots, and the use of a simulation environment for off-line programming of robots. In courses stressing kinematic issues, we often replace material from Chapter 4 (Robot Dynamics) with selected topics from Chapter 5 (Multifingered Hand Kinematics). We have also covered Chapters 5--8 in a ten week period at the graduate level, in a course augmented with other advanced topics in manipulation or mobile robots.

The prerequisites that we assume are a good course in linear algebra at the undergraduate level and some familiarity with signals and systems. A course on control at the undergraduate level is helpful, but not strictly necessary for following the material. Some amount of mathematical maturity is also desirable, although the student who can master the concepts in Chapter 2 should have no difficulty with the remainder of the book.

We have provided a fair number of exercises after Chapters 2--8 to help students understand some new material and review their understanding of the chapter. A toolkit of programs written in Mathematica for solving the problems of Chapters 2 and 3 (and to some extent Chapter 5) have been developed and are described in Appendix B. We have studiously avoided numerical exercises in this book: when we have taught the course, we have adapted numerical exercises from measurements of robots or other "real" systems available in the laboratories. These vary from one time to the next and add an element of topicality to the course.

The one large topic in robotic manipulation that we have not covered in this book is the question of motion planning and collision avoidance for robots. In our classroom presentations we have always covered some aspects of motion planning for robots for the sake of completeness. For graduate classes, we can recommend the recent book of Latombe on motion planning as a supplement in this regard. Another omission from this book is sensing for robotics. In order to do justice to this material in our respective schools, we have always had computer vision, tactile sensing, and other related topics, such as signal processing, covered in separate courses.

The contents of our book have been chosen from the point of view that they will remain foundational over the next several years in the face of many new technological innovations and new vistas in robotics. We have tried to give a snapshot of some of these vistas in Chapter 9. In reading this book, we hope that the reader will feel the same excitement that we do about the technological and social prospects for the field of robotics and the elegance of the underlying theory.

Richard Murray |
Berkeley, August 1993 |