24-354 General Robotics - Spring Midterm 2002

Final

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

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

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

· You must attempt all five problems

· 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 (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 Ө₂ to achieve the given position and orientation.

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