机器人学入门：力学与控制探索

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"Introduction to Robotics Mechanics and Control" 这本书的标题是"Introduction to Robotics Mechanics and Control"，这是一本关于机器人的英文书籍，涵盖了机器人学的基础知识，包括机械原理和控制技术。作者通过与专家John J. Craig的对话，揭示了进入机器人行业的路径以及这一领域的吸引力。在描述中，作者Peter I. Corke提到了他如何被机器人吸引，并决定将其作为职业生涯的起点。他的哥哥在高中时期制作了一个简单的机器人，这个经历激发了他对机器人的兴趣。在11年级时，他自己设计了一个拥有四个自由度（DoF）的机械臂机器人，还配备了光敏细胞作为“眼睛”和录音机，使机器人能够说话。然而，在大学期间，他暂时放下了对机器人的热情，认为在现实世界中以机器人技术为生可能并不实际。但五年后，当他发现机器人在制造业中变得越来越普遍时，他决定投身于机器人领域。从标签"Robotics Mechanics and Control"可以推断，这本书将深入探讨机械设计、动力学、运动学和控制系统等主题。这些是构建和控制机器人所必需的基本概念。机械部分可能涉及关节设计、传动机制和结构稳定性；控制部分则可能涵盖PID控制器、轨迹规划、传感器融合以及机器人操作系统（ROS）的基础知识。在部分内容中，虽然没有直接提供具体的技术细节，但我们可以推测书中会讨论到如何从个人爱好发展成为专业领域，以及教育背景如何为进入机器人行业做准备。John J. Craig提到他去RP（可能是Rensselaer Polytechnic Institute，一所知名的工程学院）学习，并专注于与机器人相关的领域。 "Introduction to Robotics Mechanics and Control"这本书将为读者提供一个全面的视角，从基础理论到实际应用，深入理解机器人学的各个方面，包括机械设计和控制系统的设计，同时也分享了专业人士如何进入并在这个快速发展领域的职业经验。对于那些对机器人技术感兴趣，无论是为了学术研究还是职业发展，这本书都是一个宝贵的资源。

Section 1.2

The mechanics

and

control of mechanical

manipulators

joint space to Cartesian space is needed. These days, however, it is rare to find an

industrial

robot

that

lacks this basic inverse kinematic algorithm.

The inverse kinematics problem is

not

as simple as the forward kinematics

one. Because the kinematic equations are nonlinear, their solution is

not

always

easy (or even possible) in a closed form. Also, questions about the existence of a

solution and about multiple solutions arise.

Study of these issues gives one an appreciation for what the human mind and

nervous system are accomplishing when we, seemingly without conscious thought,

move and manipulate objects with our arms and hands.

The existence or nonexistence of a kinematic solution defines the

workspace

of a given manipulator. The lack of a solution means that the manipulator cannot

attainthe desired position and orientationbecauseit lies outside of the manipulator's

workspace.

Velocities, static forces, singularities

In addition to dealing with static positioning problems, we may wish to analyze

manipulators in motion. Often, in performing velocity analysis of a mechanism, it is

convenient to define a matrix quantity called the

Jacobian of the manipulator. The

Jacobian specifies a

mapping from velocities in joint space to velocities in Cartesian

space. (See Fig. 1.8.)

The

nature of this mapping changes as the configuration of

the manipulator varies.

certain points, called singularities, this mapping is

not

invertible.

understanding of the phenomenonis important to designers and users

of manipulators.

Consider the

rear

gunner in a World War

I-vintage

biplane fighter plane

(illustrated in Fig. 1.9). While the pilot flies the plane from the front cockpit, the

rear

gunner's

job

is to shoot at enemy aircraft. To perform this task, his gun is mounted

in a mechanism

that

rotates about two axes, the motions being called azimuth and

elevation. Using these two motions (two degrees of freedom), the gunner can direct

his stream of bullets in any direction he desires in the upper hemisphere.

FIGURE

1.8: The geometrical relationship between joint rates and velocity of the

end-effector can be described in a matrix called the Jacobian.

Section 1.2

The mechanics and control

mechanical manipulators 9

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

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

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.f 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 expected/(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 control 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

mechanical manipulators 11

FIGURE

1.11: 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.

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 more

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

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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