Problem 5 of Homework

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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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• True or False Kinematics is principally
  concerned with the internal torques that act upon
  the various robotic members.
• 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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• True or False Kinematics is principally
  concerned with the internal torques that act upon
  the various robotic members.
• 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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• True or False Kinematics is principally
  concerned with the internal torques that act upon
  the various robotic members.
• 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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• True or False Kinematics is principally
  concerned with the internal torques that act upon
  the various robotic members.
• 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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• True or False The angular velocity of a robots
  end-most member, if it is referred to the
  coordinate system that is fixed to that rigid
  member, is always zero.
• True or False The angular velocity of a robots
  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 robots end-most member depends only
  upon the velocity of that members mass center
  with respect to an inertial coordinate system,
  provided that member is rigid.

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• True or False The angular velocity of a robots
  end-most member, if it is referred to the
  coordinate system that is fixed to that rigid
  member, is always zero.
• True or False The angular velocity of a robots
  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 robots end-most member depends only
  upon the velocity of that members mass center
  with respect to an inertial coordinate system,
  provided that member is rigid.

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• True or False The angular velocity of a robots
  end-most member, if it is referred to the
  coordinate system that is fixed to that rigid
  member, is always zero.
• True or False The angular velocity of a robots
  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 robots end-most member depends only
  upon the velocity of that members mass center
  with respect to an inertial coordinate system,
  provided that member is rigid.

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• True or False The angular velocity of a robots
  end-most member, if it is referred to the
  coordinate system that is fixed to that rigid
  member, is always zero.
• True or False The angular velocity of a robots
  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 robots end-most member depends only
  upon the velocity of that members mass center
  with respect to an inertial coordinate system,
  provided that member is rigid.

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• 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.
• 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
  robots external position.
• 9.True or False If we manage to return a
  holonomic robots internal rotations to the same
  angles that were taught to achieve a given pose,
  then, provided the robots 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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• 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.
• 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
  robots external position.
• 9.True or False If we manage to return a
  holonomic robots internal rotations to the same
  angles that were taught to achieve a given pose,
  then, provided the robots 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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• 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.
• 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
  robots external position.
• 9.True or False If we manage to return a
  holonomic robots internal rotations to the same
  angles that were taught to achieve a given pose,
  then, provided the robots 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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• 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.
• 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
  robots external position.
• 9.True or False If we manage to return a
  holonomic robots internal rotations to the same
  angles that were taught to achieve a given pose,
  then, provided the robots 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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• 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.
• 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
  robots external position.
• 9.True or False If we manage to return a
  holonomic robots internal rotations to the same
  angles that were taught to achieve a given pose,
  then, provided the robots 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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In the 1990s 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 1990s 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 1990s 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 1990s 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. vi
sual servoing. simultaneous localization and
mapping.
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The Roomba robot is most closely identified
with behavior-based robotics. teach/repeat. vi
sual 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 childs
bedroom. human recognition in a movie theatre of
the objects in an image of a childs 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 childs
bedroom. human recognition in a movie theatre of
the objects in an image of a childs 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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Problem 23
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ktrans2 (1/2) m2 rG2 . rG2
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rG2
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rG2
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