《现代机器人学：力学、规划与控制》详解

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《Modern Robotics: Mechanics, Planning, and Control》是一本由Kevin M. Lynch和Frank C. Park编著的经典机械臂学习教材，首次出版日期为2017年5月。该书以现代机器人技术为核心，全面探讨了机械系统的力学、规划与控制。书中特别关注了三种类型的机器人：串联机器人（open chains）、并联机器人（closed chains）以及轮式机器人，这些是理解机器人运动学和动力学的基础。在动力学建模部分，作者采用旋量理论，这是一种高效的数学工具，能够简洁地表达三维空间中的运动和旋转。旋量理论对于处理机器人关节运动、姿态变化以及力矩分析等方面具有显著优势，使得复杂系统的行为更加易于理解和分析。章节2详细介绍了配置空间的概念，这是机器人运动分析的关键概念。首先，作者阐述了刚体和机器人的自由度（degrees of freedom），区分了它们各自的特点。刚体自由度指的是其在三维空间中的独立移动和旋转方式，而机器人自由度则考虑了关节和机械结构的约束。接着，Grübler's Formula被引入，这是一个用于计算机器人可能运动模式的公式，它对设计和分析机器人的运动范围有重要作用。配置空间的讨论进一步深入，包括配置空间的拓扑和表示方法。配置空间拓扑关注的是空间中的连通性和可达性，即机器人可以实际到达的所有位置和姿态构成的空间结构。配置空间的表示则涉及如何将这些抽象概念转化为实际操作中的坐标系和参数化形式，这对于实现路径规划和控制算法至关重要。《Modern Robotics: Mechanics, Planning, and Control》是一本深度讲解机械臂技术的权威著作，不仅涵盖了基础知识，如机械结构、运动学和动力学，还提供了旋量理论的实用应用，有助于读者全面掌握机器人系统的理论基础和实践技能。对于机械臂爱好者、研究人员和工程师来说，这是一本不可或缺的学习资源。

xiv Preface

simple and elegant geometric interpretation that lies at the heart of what they

are calculating.

The breakthrough that makes the techniques of classical screw theory ac-

cessible to a more general audience arrived in th e early 1980’s, when Roger

Brockett showed how to mathematically describe kinemat i c chains in terms of

the Lie group structure of the rigid-body motions [20]. This discovery allowed

one, among other things, to re-invent screw theory simply by ap pealing to basic

linear algebra and linear di↵erential equations. With this “modern screw the-

ory” the powerful tools of modern di↵erential geometry can be brought to bear

on a wide-ranging collection of robotics problems, some of whi ch we ex p l ore

here, others of which are covered i n the excellent but more advanced graduate

textbook by Murray, Li and Sastry [122].

As the ti tl e indicates, this book covers what we feel to be the fundamentals

of robot mechanics, together with the basics of planning and control. A thor-

ough treatment of all the chapters would likely take two semesters, par t i cul ar l y

when coupled with programming assignments or experiments with robots. The

contents of Chapters 2-6 const i t u t e the minimum essentials, and these topics

should probably be covered in sequence.

The in st r uct or can then selectively choose content from the remaining chap-

ters. At Seoul National University, the unde rgr adu at e course M2794.0027 Intro-

duction to Robotics covers, in one semester, Chapters 2-7 and parts of Chapters

10, 11, and 12. At Northwestern, ME 449 Robotic Manipulation cover s, in an 11-

week quarter, Chapters 2-6 and 8, then t ou ches on di↵erent topics in Chapters

9-13 dep en di n g on the interests of the students and instructor. A course focus-

ing on the kinematics of robot arms and wheeled vehicles could cover chapters

2-7 and 13, while a course on kinematics and motion planning could addition-

ally include Chapters 9 and 10. A course on the mechanics of manipulation

would cover Chapters 2-6, 8, and 12, while a course on robot control would

cover Chapters 2-6, 8, 9, and 11. If the instructor prefers to avoid dynamics

(Chapter 8), the basics of robot control (Chapters 11 and 13) can be covered by

assuming control of velocity at each actuator, not forces and torques. A cour se

focusing only on motion planning could cover Chapters 2 and 3, Chapter 10 in

depth (possibly supplemented by research papers or other references cited in

that chapter), and Chapter 13.

To hel p the instructor choose which topics to teach and to help the student

keep track of what she has learned, we have inclu ded a summary at the end of

each chapter and a summary of important notation and formulas used through-

out the book (Appendix A). For those whose primary interest in t hi s text is

as an introductory r ef eren ce, we have attempted to provide a reasonably com-

prehensive, though by no means exhaustive, set of references and bibliographic

Preface xv

notes at the end of each chap t er. S ome of the exercises provided at t h e end of

each chapter extend the basic results covered in the book, and for those who

wish to probe fu rt h er, these should be of some interest in their own right. Some

of the more advanced material in the book can be used to support independ ent

study projects.

Another important component of the book is the software, which is written

to reinforce the concept s in the book an d to make the formulas operational. The

software was developed primari ly by Kevin ’ s ME 449 students at Northwestern

and is freely downloadable from http://modernrobotics.org. Video lectures

that accompany the textbook will also be available at the website. The intent

of the video content is to “ﬂip” the classroom. Students watch the brief lectures

on their own time, rewinding and rewatching as needed, and class time is fo-

cused more on collaborative problem-solving. This way, the professor is present

when the students are applying the material and discoveri ng the gaps in their

understanding, creating th e opportun i ty for i nteractive mini-lectures addressing

the concepts that need most reinforcing. We believe that the added value of

the professor i s greatest in this interactive role, not in delivering a lecture the

same way it was delivered the previous year. This approach has worked wel l for

Kevin’s introduction to mechatronics course, http://nu32.org.

Video content is generated using the Lightboard, http://lightboard.info,

created by Michael Peshkin at Northwestern University. We thank him for

sharing this convenient and e↵ective tool for creating instruct i onal v i deos.

We have also found the V-REP robot simulation software to be a valuable

supplement to the book and its software. This simulation software allows stu-

dents to interactively explore the kinemat i cs of robot arm s and mobile manipu-

lators and to animate trajectories that are th e result of exercises on kinematics,

dynamics, and control.

While this book presents our own perspective on how to introduce t h e fun-

damental topics in ﬁrst courses on robot mechanics, planning, and control, we

acknowledge the excellent textbooks that already exist and that have served

our ﬁeld well. Among these, we would like to mention as particularl y inﬂuential

the books by Murray, Li, and Sastry [122]; Craig [32]; Spong, Hutchinson, and

Vidyasagar [ 177] ; Siciliano, Sciavicco, Villani, and Oriolo [171] ; Mason [109];

Corke [30]; and the motion planning books by Latombe [80], LaValle [83], and

Choset, Lynch, Hut chinson, Kantor, Burgard, Kavraki, and Thrun [27]. In ad-

dition, the Handbook of Robotics [170], edited by Siciliano and Khatib with

a multimedia extension edited by Kr¨oger (http://handbookofrobotics.org),

is a landmark in our ﬁeld, collecting the perspectives of hundreds of leading

researchers on a huge variety of topics relevant to modern robotics.

It is our pleasure to acknowledge the many people who have been the sources

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