Intro to Robotics midterm solution

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Problem 5 of Homework

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Problem 5 of Homework

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Why so hard getting

convergence?

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Consider two trajectories.

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A very small difference in just one of

our parameters accounts for a large

difference in terminal

position/orientation

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A very small difference in just one of

our parameters accounts for a large

difference in terminal

position/orientation

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A very small difference in just one of

our parameters accounts for a large

difference in terminal

position/orientation

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A very small difference in just one of

our parameters accounts for a large

difference in terminal

position/orientation

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Notice that for quite a while the two

trajectories remain close together.

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This high sensitivity after a longer

interval to small changes is

characteristic of many nonlinear

systems.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Robots that operate under the “teach-repeat”
mode are often taught using:

unemployed college professors.

a degree-jogging filament.

a teach pendant.

a robomaster.

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Robots that operate under the “teach-repeat”
mode are often taught using:

unemployed college professors.

a degree-jogging filament.

a teach pendant.

a robomaster.

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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.

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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.

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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.

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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.

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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.

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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.

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Visual Servoing makes extensive use of:

ultrasound sensors.

the matrix Jacobian.

nonholonomic degrees of freedom.

cheesecake.

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Visual Servoing makes extensive use of:

ultrasound sensors.

the matrix Jacobian.

nonholonomic degrees of freedom.

cheesecake.

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The Roomba robot is most closely identified with:

behavior-based robotics.

teach/repeat.

visual servoing.

simultaneous localization and mapping.

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The Roomba robot is most closely identified with:

behavior-based robotics.

teach/repeat.

visual servoing.

simultaneous localization and mapping.

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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.

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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.

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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.

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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.

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Problem 21

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Problem 22

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l

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l

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l

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l

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Problem 23

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k

trans2

= (1/2) m

2

r

G2

.

r

G2

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r

G2

=

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r

G2

=

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r

G2

=

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r

G2

=

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