机器人学基础：力学与控制（第三版）英文原版

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"《机器人学导论》第三版英文版，由John J. Craig撰写，是电气与计算机工程系列的一部分，内容覆盖了机器人学的基础到高级主题，包括机械和控制方面的知识。" 本书深入介绍了机器人学的关键概念和技术，分为13章，详细阐述了以下几个重要知识点： 1. **介绍**：这一部分可能涵盖机器人学的基本定义、历史以及在现代社会中的应用，为后续章节的学习奠定基础。 2. **空间描述和变换**：这一章讲解了如何在三维空间中描述和操作机器人，包括坐标系的转换、向量和矩阵的操作等基础知识。 3. **操纵器动力学**：讨论了机器人关节和连杆的运动学，包括笛卡尔坐标和关节坐标下的描述，以及如何推导和理解机器人运动链的几何关系。 4. **逆动力学**：这部分涉及求解逆运动学问题，即给定末端执行器的位置和方向，如何确定各关节的运动参数。 5. **雅可比矩阵**：雅可比矩阵关联了关节速度和末端执行器速度，同时也用于计算静态力和力矩，对于理解和设计机器人的控制策略至关重要。 6. **操纵器动力学**：涵盖了机器人动力学模型的建立，包括惯性、摩擦、驱动和约束力的分析，以及如何利用这些信息进行动态建模和控制。 7. **轨迹生成**：研究如何规划机器人的平滑路径，避免碰撞和优化运动性能。 8. **操纵器机制设计**：讨论了机器人结构设计的原则，如连杆的布局、自由度的选择，以及如何平衡机械效率和灵活性。 9. **线性控制**：介绍了适用于操纵器的线性控制理论，如PID控制、状态反馈等，以及它们在实际机器人系统中的应用。 10. **非线性控制**：深入探讨非线性控制策略，如滑模控制和自适应控制，以应对机器人系统的非线性特性。 11. **力控制**：讲述如何实现对机器人执行器力和扭矩的精确控制，这对于精细操作和交互任务至关重要。 12. **机器人编程语言和系统**：涵盖了机器人操作系统（ROS）和其他编程框架，以及如何编写和执行机器人程序。 13. **离线编程系统**：讨论了机器人程序的离线生成，如基于计算机图形学的方法和仿真技术。书后附录包括三角恒等式、角度设定约定和一些逆运动学公式，以及部分练习题的答案，为读者提供了进一步学习和自我检验的资源。《机器人学导论》第三版是深入理解机器人技术的宝贵教材，适合工程学生、研究人员和专业工程师作为参考书籍。通过阅读本书，读者可以掌握机器人学的核心概念，从而能够设计、分析和控制各种机器人系统。

8 Chapter 1

Introduction

FIGURE 1

9 A

World

War I biplane with a pilot and a rear gunner The rear gunner

mechanism is subject to

the

problem of singular positions.

enemy plane is

spotted at azimuth one o'clock and elevation 25 degrees!

The gunner trains his stream of bullets on the enemy plane and tracks its motion so

as to hit it with a continuous stream of bullets for as long as

possible. He succeeds

and thereby downs the enemy aircraft.

A second enemy plane is seen at azimuth one o'clock and elevation 70 degrees!

The gunner orients his gun and begins firing. The enemy plane is moving so as to

obtain a higher and higher elevation relative to the gunner's plane. Soon the enemy

plane is passing nearly overhead. What's this? The gunner is no longer able to keep

his stream of bullets trained on the enemy plane! He found that, as the enemy plane

flew overhead, he was required to change his azimuth at a very high rate. He was

not able to swing his gun in azimuth quickly enough, and the enemy plane

escaped!

In the latter scenario, the lucky enemy pilot was saved by a singularity!

The

gun's orienting mechanism, while working well over most of its operating range,

becomes less than ideal when the gun is directed straight upwards or nearly so. To

track targets that pass through the position directly overhead, a very fast motion

around the azimuth axis is required. The closer the target passes to the point directly

overhead, the faster the gunner must turn the azimuth axis to track the target. If

the target flies directly over the gunner's head, he would have to spin the gun on

its

azimuth axis at infinite speed!

Should the gunner complain to the mechanism designer about this problem?

Could a better mechanism be designed to avoid this problem? It turns out that

you really can't avoid the problem very easily. In fact, any

two-degree-of-freedom

orienting mechanism that has exactly two rotational joints cannot avoid having

this problem. In the case of this mechanism, with the stream of bullets directed

Section 1.2

The mechanics and control of mechanical manipulators

straight

up, their direction aligns with the axis of rotation of the azimuth rotation.

This means that, at exactly this point, the azimuth rotation does not cause a

change in the direction of the stream of bullets. We know we need two degrees

of freedom to orient the stream of bullets, but, at this point, we have lost the

effective use of one of the joints. Our mechanism has become locally degenerate

at this location and behaves as if it only has one degree of freedom (the elevation

direction).

This kind of phenomenon is caused by what is called a singularity of the

mechanism. All mechanisms are prone to these difficulties, including robots. Just

as with the rear gunner's mechanism, these singularity conditions do not prevent

a robot arm from positioning anywhere within its workspace. However, they can

cause problems with motions of the arm in their neighborhood.

Manipulators do not always move through space; sometimes they are also

required to touch a workpiece or work surface and apply a static force. In this

case the problem arises: Given a desired contact force and moment, what set of

joint torques is required to generate them? Once again, the Jacobian matrix of the

manipulator arises quite naturally in the solution of this problem.

Dynamics

Dynamics is a huge field of study devoted to studying the forces required to cause

motion. In order to accelerate a manipulator from rest, glide at a constant end-

effector velocity, and finally decelerate to a stop, a complex set of torque functions

must be applied by the joint actuators.2 The exact form of the required functions of

actuator torque depend on the spatial and temporal attributes of the path taken by

the end-effector and on the mass properties of the links and payload, friction in the

joints, and so on. One method of controlling a manipulator to follow a desired path

involves calculating these actuator torque functions by using the dynamic equations

of motion of the manipulator.

Many of us have experienced lifting an object that is actually much lighter

than we

(e.g., getting a container of milk from the refrigerator which

we thought was full, but was nearly empty). Such a misjudgment of payload can

cause an unusual lifting motion. This kind of observation indicates that the human

control system is more sophisticated than a purely kinematic scheme. Rather, our

manipulation control system makes use of knowledge of mass and other dynamic

effects. Likewise, algorithms that we construct to

the motions of a robot

manipulator should take dynamics into account.

A second use of the dynamic equations of motion is in simulation. By refor-

mulating the dynamic equations so that acceleration is computed as a function of

actuator torque, it is possible to simulate how a manipulator would move under

application of a set of actuator torques. (See Fig. 1.10.) As computing power

becomes more and more cost effective, the use of simulations is growing in use and

importance in many fields.

In Chapter 6, we develop dynamic equations of motion, which may be used to

control or simulate the motion of manipulators.

2We use joint actuators as the generic term for devices that

power a manipulator—for example,

electric motors, hydraulic and pneumatic actuators, and muscles.

Section 1.2

The mechanics and control of mechanical manipulators

FIGURE 1.1 1: In order to move the end-effector through space from point A

to point

B, we must compute a trajectory for each joint to follow.

a useful robot, that can take two approaches: build a specialized

robot for

a specific

task, or build a universal robot

that

would able to perform a wide variety of tasks.

In the case of a specialized robot, some careful thinking will yield a solution for

how many joints are needed. For example, a specialized robot designed solely to

place electronic components on a flat circuit board does not need to have

than four joints. Three joints allow the position of the hand to attain

any position

in three-dimensional space, with a fourth joint added to allow the hand to rotate

the grasped component about a vertical axis. In the case of a universal robot, it is

interesting that fundamental properties of the physical world

we live in dictate the

"correct" minimum number of joints—that minimum number is six.

Integral to the design of the manipulator are issues involving the choice and

location of actuators, transmission systems, and internal-position (and sometimes

force) sensors. (See Fig. 1.12.) These and other design issues will be discussed in

Chapter 8.

Linear

position control

Some

manipulators are equipped with stepper motors or other actuators that

can

execute a desired trajectory directly. However, the vast majority of manipulators

are driven by actuators that supply a force or a torque to cause motion of the links.

In this case, an algorithm is needed to compute torques that will cause the desired

motion. The problem of dynamics is central to the design of such algorithms, but

does not in itself constitute a solution. A primary concern of a position

control

system

is to compensate automatically for errors in knowledge of the parameters

of a system and to suppress disturbances that tend to perturb the system from the

desired trajectory. To accomplish this, position and velocity sensors

are monitored

by the control

algorithm,

which computes torque commands for the actuators. (See

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