## Final

### 24-354 General Robotics Fall-02. Prof. Howie Choset

#### ·        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 Ө1 having joint limits of 0<Ө1<359.9 and Ө2 having no joint limits. Draw the path on the figure. Note: Ө1 is the first joint angle, and Ө2 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 (xb,ybb).   Given an arbitrary position and orientation x, y, z, α, and β, derive the inverse kinematics to solve for the required xb, yb, Өb, d1, and Ө2 to achieve the given position and orientation.

Top View                                                        Front View

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