## Final

**24-354 General Robotics **

**Fall****-02. Prof. Howie Choset**

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You have 1 hour and 30 minutes to complete the
exam.

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Please write all answers either on the exam or
in a blue book

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You must attempt all *five* problems

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Good Luck

**Problem #1** (25 points)

(a.) (10 points) For the following *configuration
space*, draw a trapezoidal decomposition and a Boustrophedon decomposition.

(b.) (10 points) For each method, superimpose the
adjacency graph on your drawing.

(c.) (5 points) If you were to use the decomposition
to determine a coverage path, comment on the significant features of each path
and explain why they are different.

Trapeziodal

Boustrophedon

Spare for work

** **

** **

**Problem #2** (25 points)

(a.) (15 points) Given the following workspace (*with
robot shown at start configuration*) and configuration space, use the
Wavefront planner with the L2 metric to find a path in configuration space from
the start configuration to the goal configuration, subject to Ө_{1}
having joint limits of 0<Ө_{1}<359.9 and Ө_{2}
having no joint limits. Draw the path on the figure. Note: Ө_{1}
is the first joint angle, and Ө_{2} is the second joint angle.

(b.) (10 points) Draw five intermediate
configurations between the start and goal configurations, and show their
location in the configuration space.

**Problem #3** (20 points)

For the two link,
prismatic-revolute manipulator shown below, assign coordinate frames and derive
the Denavit Hartenberg parameters.

**Problem #4** (5 points)

Robotics can be broken down into various classes of
sub-categories. Pick three
sub-categories that together encompass the robotics field and define them.

**Problem #5** (25 points)

(a.)(20
points) We’ve taken the manipulator of
problem 3, rotated it, and affixed it to a planar, 3-DOF mobile base (x_{b},y_{b},Ө_{b}). Given an arbitrary position and orientation x,
y, z, α, and β, derive the inverse kinematics to solve for the
required x_{b}, y_{b}, Ө_{b}, d_{1, }and
Ө_{2} to achieve the given position and orientation.

Top
View Front
View

(b.)(5
points) What is the configuration space
of this 5-DOF robot.