A Mathematical Introduction to Robotic Manipulation_Murray

تاريخ التسجيل : 22/11/2009

Introduction
In the last twenty years, our conception and use of robots has evolved
from the stuff of science fiction films to the reality of computer-controlled
electromechanical devices integrated into a wide variety of industrial environments.
It is routine to see robot manipulators being used for welding
and painting car bodies on assembly lines, stuffing printed circuit boards
with IC components, inspecting and repairing structures in nuclear, undersea,
and underground environments, and even picking oranges and
harvesting grapes in agriculture. Although few of these manipulators
are anthropomorphic, our fascination with humanoid machines has not
dulled, and people still envision robots as evolving into electromechanical
replicas of ourselves. While we are not likely to see this type of robot in
the near future, it is fair to say that we have made a great deal of progress
in introducing simple robots with crude end-effectors into a wide variety
of circumstances. Further, it is important to recognize that our impatience
with the pace of robotics research and our expectations of what
robots can and cannot do is in large part due to our lack of appreciation
of the incredible power and subtlety of our own biological motor control
systems.
1 Brief History
The word robot was introduced in 1921 by the Czech playwright Karel
Capek in his satirical play R. U. R. (Rossum’s Universal Robots), where
he depicted robots as machines which resembled people but worked tirelessly.
In the play, the robots eventually turn against their creators and
annihilate the human race. This play spawned a great deal of further science
fiction literature and film which have contributed to our perceptions
of robots as being human-like, endowed with intelligence and even personality.
Thus, it is no surprise that present-day robots appear primitive when compared with the expectations created by the entertainment industry.
To give the reader a flavor of the development of modern robotics,
we will give a much abbreviated history of the field, derived from the accounts
by Fu, Gonzalez, and Lee [35] and Spong and Vidyasagar [110].
We describe this roughly by decade, starting from the fifties and continuing
up to the eighties.
The early work leading up to today’s robots began after World War
II in the development of remotely controlled mechanical manipulators,
developed at Argonne and Oak Ridge National Laboratories for handling
radioactive material. These early mechanisms were of the master-slave
type, consisting of a master manipulator guided by the user through a
series of moves which were then duplicated by the slave unit. The slave
unit was coupled to the master through a series of mechanical linkages.
These linkages were eventually replaced by either electric or hydraulic
powered coupling in “teleoperators,” as these machines are called, made
by General Electric and General Mills. Force feedback to keep the slave
manipulator from crushing glass containers was also added to the teleoperators
in 1949.
In parallel with the development of the teleoperators was the devel-
opment of Computer Numerically Controlled (CNC) machine tools for
accurate milling of low-volume, high-performance aircraft parts. The
first robots, developed by George Devol in 1954, replaced the master
manipulator of the teleoperator with the programmability of the CNC
machine tool controller. He called the device a “programmed articulated
transfer device.” The patent rights were bought by a Columbia University
student, Joseph Engelberger, who later founded a company called
Unimation in Connecticut in 1956. Unimation installed its first robot in
a General Motors plant in 1961. The key innovation here was the “programmability”
of the machine: it could be retooled and reprogrammed
at relatively low cost so as to enable it to perform a wide variety of
tasks. The mechanical construction of the Unimation robot arm represented
a departure from conventional machine design in that it used an
open kinematic chain: that is to say, it had a cantilevered beam structure
with many degrees of freedom. This enabled the robot to access a large
workspace relative to the space occupied by the robot itself, but it created
a number of problems for the design since it is difficult to accurately
control the end point of a cantilevered arm and also to regulate its stiffness.
Moreover, errors at the base of the kinematic chain tended to get
amplified further out in the chain. To alleviate this problem, hydraulic
actuators capable of both high power and generally high precision were
used for the joint actuators.
The flexibility of the newly introduced robots was quickly seen to be
enhanced through sensory feedback. To this end, Ernst in 1962 developed
a robot with force sensing which enabled it to stack blocks. To our
knowledge, this system was the first that involved a robot interacting
with an unstructured environment and led to the creation of the Project
MAC (Man And Computer) at MIT. Tomovic and Boni developed a pressure
sensor for the robot which enabled it to squeeze on a grasped object
and then develop one of two different grasp patterns. At about the same
time, a binary robot vision system which enabled the robot to respond to
obstacles in its environment was developed by McCarthy and colleagues
in 1963. Many other kinematic models for robot arms, such as the Stanford
manipulator, the Boston arm, the AMF (American Machine and
Foundry) arm, and the Edinburgh arm, were also introduced around this
time. Another novel robot of the period was a walking robot developed
by General Electric for the Army in 1969. Robots that responded to
voice commands and stacked randomly scattered blocks were developed
at Stanford and other places. Robots made their appearance in Japan
through Kawasaki’s acquisition of a license from Unimation in 1968.
In 1973, the first language for programming robot motion, called
WAVE, was developed at Stanford to enable commanding a robot with
high-level commands. About the same time, in 1974, the machine tool
manufacturer Cincinnati Milacron, Inc. introduced its first computercontrolled
manipulator, called The Tomorrow Tool (T3), which could lift
a 100 pound load as well as track moving objects on an assembly line.
Later in the seventies, Paul and Bolles showed how a Stanford arm could
assemble water pumps, and Will and Grossman endowed a robot with
touch and force sensors to assemble a twenty part typewriter. At roughly
the same time, a group at the Draper Laboratories put together a Remote
Center Compliance (RCC) device for part insertion in assembly.
In 1978, Unimation introduced a robot named the Programmable Universal
Machine for Assembly (PUMA), based on a General Motors study.
Bejczy at Jet Propulsion Laboratory began a program of teleoperation
for space-based manipulators in the mid-seventies. In 1979, the SCARA
(Selective Compliant Articulated Robot for Assembly) was introduced in
Japan and then in the United States.
As applications of industrial robots grew, different kinds of robots
with attendant differences in their actuation methods were developed.
For light-duty applications, electrically powered robots were used both
for reasons of relative inexpensiveness and cleanliness. The difficulty with
electric motors is that they produce their maximum power at relatively
high speeds. Consequently, the motors need to be geared down for use.
This gear reduction introduces friction, backlash, and expense to the design
of the motors. Consequently, the search was on to find a way of
driving the robot’s joints directly without the need to gear down its electric
motors. In response to this need, a direct drive robot was developed
at Carnegie Mellon by Asada in 1981.
In the 1980s, many efforts were made to improve the performance
of industrial robots in fine manipulation tasks: active methods using
feedback control to improve positioning accuracy and program compliance,
and passive methods involving a mechanical redesign of the arm.
It is fair to say, however, that the eighties were not a period of great
innovation in terms of building new types of robots. The major part of
the research was dedicated to an understanding of algorithms for control,
trajectory planning, and sensor aggregation of robots. Among the
first active control methods developed were efficient recursive Lagrangian
and computational schemes for computing the gravity and Coriolis force
terms in the dynamics of robots. In parallel with this, there was an effort
in exactly linearizing the dynamics of a multi-joint robot by state feedback,
using a technique referred to as computed torque. This approach,
while computationally demanding, had the advantage of giving precise
bounds on the transient performance of the manipulator. It involved exact
cancellation, which in practice had to be done either approximately or
adaptively. There were may other projects on developing position/force
control strategies for robots in contact with the environment, referred to
as hybrid or compliant control. In the search for more accurately controllable
robot manipulators, robot links were getting to be lighter and to
have harmonic drives, rather than gear trains in their joints. This made
for flexible joints and arms, which in turn necessitated the development
of new control algorithms for flexible link and flexible joint robots.
The trend in the nineties has been towards robots that are modifiable
for different assembly operations. One such robot is called Robotworld,
manufactured by Automatix, which features several four degree of freedom
modules suspended on air bearings from the stator of a Sawyer
effect motor. By attaching different end-effectors to the ends of the modules,
the modules can be modified for the assembly task at hand. In
the context of robots working in hazardous environments, great strides
have been made in the development of mobile robots for planetary exploration,
hazardous waste disposal, and agriculture. In addition to the
extensive programs in reconfigurable robots and robots for hazardous environments,
we feel that the field of robotics is primed today for some
large technological advances incorporating developments in sensor and actuator technology at the milli- and micro-scales as well as advances
in computing and control. We defer a discussion of these prospects for
robotics to Chapter 9.
2 Multifingered Hands and Dextrous Ma-
nipulation
The vast majority of robots in operation today consist of six joints which
are either rotary (articulated) or sliding (prismatic), with a simple “endeffector”
for interacting with the workpieces. The applications range from
pick and place operations, to moving cameras and other inspection equipment,
to performing delicate assembly tasks involving mating parts. This
is certainly nowhere near as fancy as the stuff of early science fiction, but
is useful in such diverse arenas such as welding, painting, transportation
of materials, assembly of printed circuit boards, and repair and inspection
in hazardous environments.
The term hand or end-effector is used to describe the interface between
the manipulator (arm) and the environment, out of anthropomorphic
intent. The vast majority of hands are simple: grippers (either two- or
three-jaw), pincers, tongs, or in some cases remote compliance devices.
Most of these end-effectors are designed on an ad hoc basis to perform
specific tasks with specific parts. For example, they may have suction
cups for lifting glass which are not suitable for machined parts, or jaws
operated by compressed air for holding metallic parts but not suitable
for handling fragile plastic parts. Further, a difficulty that is commonly
encountered in applications is the clumsiness of a six degree of freedom
robot equipped only with these simple hands. The clumsiness manifests
itself in:
1. A lack of dexterity. Simple grippers enable the robot to hold parts
securely but they cannot manipulate the grasped object.
2. A limited number of possible grasps resulting in the need to change
end-effectors frequently for different tasks.
3. Large motions of the arm are sometimes needed for even small motions
of the end-effector. Since the motors of the robot arm are
progressively larger away from the end-effector, the motion of the
earliest motors is slow and inefficient.
4. A lack of fine force control which limits assembly tasks to the most
rudimentary ones.
A multifingered or articulated hand offers some solutions to the problem
of endowing a robot with dexterity and versatility. The ability of a multifingered hand to reconfigure itself for performing a variety of different
grasps reduces the need for changing end-effectors. The large number
of lightweight actuators associated with the degrees of freedom of the
hand allows for fast, precise, and energy-efficient motions of the object
held in the hand. Fine motion force-control at a high bandwidth is also
facilitated for similar reasons. Indeed, multifingered hands are a truly
anthropomorphically motivated concept for dextrous manipulation: we
use our arms to position our hands in a given region of space and then
use our wrists and fingers to interact in a detailed and intricate way with
the environment. We preform our fingers into grasps which pinch, encircle,
or immobilize objects, changing grasps as a consequence of these
actions. One measure of the intelligence of a member of the mammalian
family is the fraction of its motor cortex dedicated to the control of its
hands. This fraction is discerned by painstaking mapping of the body
on the motor cortex by neurophysiologists, yielding a homunculus of the
kind shown in Figure 1.7. For humans, the largest fraction (30–40%) of the motor cortex is dedicated to the control of the hands, as compared
with 20–30% for most monkeys and under 10% for dogs and cats.
From a historical point of view, the first uses of multifingered hands
were in prosthetic devices to replace lost limbs. Childress [18] refers to
a device from 1509 made for a knight, von Berlichingen, who had lost
his hand in battle at an early age. This spring-loaded device was useful
in battle but was unfortunately not handy enough for everyday functions.
After the Berlichingen hand, numerous other hand designs have
been made from 1509 to the current time. Several of these hands are
still available today; some are passive (using springs), others are bodypowered
(using arm flexion control or shrug control). Some of the hands
had the facility for voluntary closure and others involuntary closure. Childress
classifies the hands into the following four types:
1. Cosmetic. These hands have no real movement and cannot be activated,
but they can be used for pushing or as an opposition element
for the other hand.
2. Passive. These hands need the manual manipulation of the other
(non-prosthetic) hand to adjust the grasping of the hand. These
were the earliest hands, including the Berlichingen hand.
3. Body powered. These hands use motions of the body to activate the
hand. Two of the most common schemes involve pulling a cable
when the arm is moved forward (arm-flexion control) or pulling
the cable when the shoulders are rounded (shrug control). Indeed,
one frequently observes these hands operated by an amputee using
shrugs and other such motions of her upper arm joints.
4. Externally powered. These hands obtain their energy from a storage
source such as a battery or compressed gas. These are yet to
displace the body-powered hands in prostheses.
Powered hand mechanisms came into vogue after 1920, but the greatest
usage of these devices has been only since the 1960s. The Belgrade
hand, developed by Tomovi´c and Boni [113], was originally developed for
Yugoslav veterans who had lost their arms to typhus. Other hands were
invented as limb replacements for “thalidomide babies.” There has been
a succession of myoelectrically controlled devices for prostheses culminating
in some advanced devices at the University of Utah [44], developed
mainly for grasping objects. While these devices are quite remarkable
mechanisms, it is fair to say that their dexterity arises from the visionguided
feedback training of the wearer, rather than any feedback mechanisms
inherent in the device per se.
As in the historical evolution of robots, teleoperation in hazardous or
hard to access environments—such as nuclear, underwater, space, mining,

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