Problem 5 of Homework
Problem 5 of Homework
Problem 5 of Homework
Why so hard getting
convergence?
Consider two trajectories.
A very small difference in just one of
our parameters accounts for a large
difference in terminal
position/orientation
A very small difference in just one of
our parameters accounts for a large
difference in terminal
position/orientation
A very small difference in just one of
our parameters accounts for a large
difference in terminal
position/orientation
A very small difference in just one of
our parameters accounts for a large
difference in terminal
position/orientation
Notice that for quite a while the two
trajectories remain close together.
This high sensitivity after a longer
interval to small changes is
characteristic of many nonlinear
systems.
1. True or False: “Kinematics” is principally concerned
with the internal torques that act upon the various
robotic members.
2. True or False: The “homogeneous transformation
matrix” is a 3x3 matrix.
3. True or False: Elements of the “direction-cosine
matrix” or “rotation matrix” can be determined with
knowledge of three Euler-angle values.
1. True or False: “Kinematics” is principally concerned
with the internal torques that act upon the various
robotic members.
2. True or False: The “homogeneous transformation
matrix” is a 3x3 matrix.
3. True or False: Elements of the “direction-cosine
matrix” or “rotation matrix” can be determined with
knowledge of three Euler-angle values.
1. True or False: “Kinematics” is principally concerned
with the internal torques that act upon the various
robotic members.
2. True or False: The “homogeneous transformation
matrix” is a 3x3 matrix.
3. True or False: Elements of the “direction-cosine
matrix” or “rotation matrix” can be determined with
knowledge of three Euler-angle values.
1. True or False: “Kinematics” is principally concerned
with the internal torques that act upon the various
robotic members.
2. True or False: The “homogeneous transformation
matrix” is a 3x3 matrix.
3. True or False: Elements of the “direction-cosine
matrix” or “rotation matrix” can be determined with
knowledge of three Euler-angle values.
4. True or False: The angular velocity of a robot’s
end-most member, if it is referred to the
coordinate system that is fixed to that rigid
member, is always zero.
5. True or False: The angular velocity of a robot’s
end-most member, if it is measured with respect
to the coordinate system that is fixed to that rigid
member, is always zero.
6. True or False: The kinetic energy at any moment
of a robot’s end-most member depends only upon
the velocity of that member’s mass center with
respect to an inertial coordinate system, provided
that member is rigid.
4. True or False: The angular velocity of a robot’s
end-most member, if it is referred to the
coordinate system that is fixed to that rigid
member, is always zero.
5. True or False: The angular velocity of a robot’s
end-most member, if it is measured with respect
to the coordinate system that is fixed to that rigid
member, is always zero.
6. True or False: The kinetic energy at any moment
of a robot’s end-most member depends only upon
the velocity of that member’s mass center with
respect to an inertial coordinate system, provided
that member is rigid.
4. True or False: The angular velocity of a robot’s
end-most member, if it is referred to the
coordinate system that is fixed to that rigid
member, is always zero.
5. True or False: The angular velocity of a robot’s
end-most member, if it is measured with respect
to the coordinate system that is fixed to that rigid
member, is always zero.
6. True or False: The kinetic energy at any moment
of a robot’s end-most member depends only upon
the velocity of that member’s mass center with
respect to an inertial coordinate system, provided
that member is rigid.
4. True or False: The angular velocity of a robot’s
end-most member, if it is referred to the
coordinate system that is fixed to that rigid
member, is always zero.
5. True or False: The angular velocity of a robot’s
end-most member, if it is measured with respect
to the coordinate system that is fixed to that rigid
member, is always zero.
6. True or False: The kinetic energy at any moment
of a robot’s end-most member depends only upon
the velocity of that member’s mass center with
respect to an inertial coordinate system, provided
that member is rigid.
7. True or False: For two different Cartesian coordinate
systems, there are 12 possible sets of Euler angles
that may be used to specify the relative orientations
of those frames.
8. True or False: Nonholonomic robots’ forward
kinematics may be expressed in terms of differential
relations but not algebraic relations between the
internal rotations and the robot’s external position.
9.True or False: If we manage to return a holonomic
robot’s internal rotations to the same angles that
were taught to achieve a given pose, then, provided
the robot’s members remain rigid, the robot will
return to that same pose.
10.True or False: According to the Denevit-Hartenberg
convention, for member i-1, qi is positive about the
Zi axis in accordance with the right-hand rule.
7. True or False: For two different Cartesian coordinate
systems, there are 12 possible sets of Euler angles
that may be used to specify the relative orientations
of those frames.
8. True or False: Nonholonomic robots’ forward
kinematics may be expressed in terms of differential
relations but not algebraic relations between the
internal rotations and the robot’s external position.
9.True or False: If we manage to return a holonomic
robot’s internal rotations to the same angles that
were taught to achieve a given pose, then, provided
the robot’s members remain rigid, the robot will
return to that same pose.
10.True or False: According to the Denevit-Hartenberg
convention, for member i-1, qi is positive about the
Zi axis in accordance with the right-hand rule.
7. True or False: For two different Cartesian coordinate
systems, there are 12 possible sets of Euler angles
that may be used to specify the relative orientations
of those frames.
8. True or False: Nonholonomic robots’ forward
kinematics may be expressed in terms of differential
relations but not algebraic relations between the
internal rotations and the robot’s external position.
9.True or False: If we manage to return a holonomic
robot’s internal rotations to the same angles that
were taught to achieve a given pose, then, provided
the robot’s members remain rigid, the robot will
return to that same pose.
10.True or False: According to the Denevit-Hartenberg
convention, for member i-1, qi is positive about the
Zi axis in accordance with the right-hand rule.
7. True or False: For two different Cartesian coordinate
systems, there are 12 possible sets of Euler angles
that may be used to specify the relative orientations
of those frames.
8. True or False: Nonholonomic robots’ forward
kinematics may be expressed in terms of differential
relations but not algebraic relations between the
internal rotations and the robot’s external position.
9.True or False: If we manage to return a holonomic
robot’s internal rotations to the same angles that
were taught to achieve a given pose, then, provided
the robot’s members remain rigid, the robot will
return to that same pose.
10.True or False: According to the Denevit-Hartenberg
convention, for member i-1, qi is positive about the
Zi axis in accordance with the right-hand rule.
7. True or False: For two different Cartesian coordinate
systems, there are 12 possible sets of Euler angles
that may be used to specify the relative orientations
of those frames.
8. True or False: Nonholonomic robots’ forward
kinematics may be expressed in terms of differential
relations but not algebraic relations between the
internal rotations and the robot’s external position.
9.True or False: If we manage to return a holonomic
robot’s internal rotations to the same angles that
were taught to achieve a given pose, then, provided
the robot’s members remain rigid, the robot will
return to that same pose.
10.True or False: According to the Denevit-Hartenberg
convention, for member i-1,
i
is positive about the Z
i
axis in accordance with the right-hand rule.
In the 1990’s a mobile robot was deployed in several
locations across the country as a test by the U.S. Dept. of
Veterans Affairs:
to assist in the harvest of tree-borne fruit.
to dispense gasoline autonomously at filling stations.
to deliver medicines autonomously in hospitals.
to secretly monitor U.S. veterans’ affairs.
In the 1990’s a mobile robot was deployed in several
locations across the country as a test by the U.S. Dept. of
Veterans Affairs:
to assist in the harvest of tree-borne fruit.
to dispense gasoline autonomously at filling stations.
to deliver medicines autonomously in hospitals.
to secretly monitor U.S. veterans’ affairs.
Early in the 1990’s one firm worried about the
imminent release of a Japanese robot that would:
autonomously deliver commercial-grade floor
maintenance.
dispense gasoline autonomously at filling stations.
deliver medicines autonomously in hospitals.
assist with the harvest of tree-borne fruit.
Early in the 1990’s one firm worried about the
imminent release of a Japanese robot that would:
autonomously deliver commercial-grade floor
maintenance.
dispense gasoline autonomously at filling stations.
deliver medicines autonomously in hospitals.
assist with the harvest of tree-borne fruit.
Robots that operate under the “teach-repeat”
mode are often taught using:
unemployed college professors.
a degree-jogging filament.
a teach pendant.
a robomaster.
Robots that operate under the “teach-repeat”
mode are often taught using:
unemployed college professors.
a degree-jogging filament.
a teach pendant.
a robomaster.
Teach-repeat relies upon:
the angular-position servomechanism of each joint rotation.
the rigidity of robots’ members.
the delivery of each workpiece to the prototype workpieces’
position/orientation in space.
All of the above.
Teach-repeat relies upon:
the angular-position servomechanism of each joint rotation.
the rigidity of robots’ members.
the delivery of each workpiece to the prototype workpieces’
position/orientation in space.
All of the above.
A large and largely unsuccessful effort to apply
calibrated vision to control robots in a nearly
workerless factory was attempted:
in the 1980s at IBM.
in the 1960s at Nissan.
in the 1990s at Boeing.
in the 1980s at GM.
A large and largely unsuccessful effort to apply
calibrated vision to control robots in a nearly
workerless factory was attempted:
in the 1980s at IBM.
in the 1960s at Nissan.
in the 1990s at Boeing.
in the 1980s at GM.
In 2004 a cry went out from the scientific
community to use a robot to:
monitor Antarctica for global warming.
service the Hubble telescope.
descend into Mt. St. Helens.
transport spent nuclear fuel into Yucca
Mountain.
In 2004 a cry went out from the scientific
community to use a robot to:
monitor Antarctica for global warming.
service the Hubble telescope.
descend into Mt. St. Helens.
transport spent nuclear fuel into Yucca
Mountain.
Visual Servoing makes extensive use of:
ultrasound sensors.
the matrix Jacobian.
nonholonomic degrees of freedom.
cheesecake.
Visual Servoing makes extensive use of:
ultrasound sensors.
the matrix Jacobian.
nonholonomic degrees of freedom.
cheesecake.
The Roomba robot is most closely identified with:
behavior-based robotics.
teach/repeat.
visual servoing.
simultaneous localization and mapping.
The Roomba robot is most closely identified with:
behavior-based robotics.
teach/repeat.
visual servoing.
simultaneous localization and mapping.
Which of the following is not an instance of the
“inverse problem”:
creating a Pixar movie scene from a
geometric/optical model of a child’s bedroom.
human recognition in a movie theatre of the
objects in an image of a child’s bedroom
presented on the screen.
identification of the flaws in a reactor vessel using
ultrasound responses.
solving a crime using fingerprints.
Which of the following is not an instance of the
“inverse problem”:
creating a Pixar movie scene from a
geometric/optical model of a child’s bedroom.
human recognition in a movie theatre of the
objects in an image of a child’s bedroom
presented on the screen.
identification of the flaws in a reactor vessel using
ultrasound responses.
solving a crime using fingerprints.
The intensity of light reflecting off a surface in any
given direction can be measured in:
Newtons per degree.
foot-candles per solid radian.
Watts per steradian.
Joules per angstrom.
The intensity of light reflecting off a surface in any
given direction can be measured in:
Newtons per degree.
foot-candles per solid radian.
Watts per steradian.
Joules per angstrom.
Problem 21
Problem 22
l
l
l
l
Problem 23
k
trans2
= (1/2) m
2
r
G2
.
r
G2
r
G2
=
r
G2
=
r
G2
=
r
G2
=
