Midterm: Introduction to Robotics 16-311
Fall 2005
1hr
15 mins, use one 8.5 x 11 cheat sheet
Name:
Team:
Problem #1 [25 pts]
(a) Draw the generalized Voronoi diagram for the configuration space for the square shaped robot in the orientation shown. [20 pts]
(b) Draw the
shortest path with respect to the L2 metric between the start and goal
locations shown. [5 pts]
Extra
Problem #2 [15 pts]
The following describes two convolution scenarios.
- Convolve a signal with the mask [-1 1] and then convolve the result again with the same mask [-1 1].
- Convolve a signal with the mask [ -1 2 -1].
(a) Is the result the same or different? [5 pts]
(b) Why? [5 pts]
(c) What algebraic operation does convolving with the mask [-1 2 -1] do? [5 pts]
Problem #3 [9 pts]
(a) How many DOF does a circular robot which can translate and rotate on some point other than its center have? [3 pts]
(b) How many DOF does a robot with a fixed base and 3 revolute joints have? [3 pts]
(c) What is the dimension of the configuration space for a robot which can only translate and has a boom on it that can rotate? [3 pts]
Problem #4 [30 pts]
A 1 DOF prismatic joint is a linear DOF, which as its name suggests, provides motion along a line. Think of it as a telescoping arm. The robot below has a revolute joint with angle θ at the base, which rotates a prismatic joint with length s whose range of motion is 0 to 100 cm. The base joint has no limits. The robot is shown in its initial position.
There are 3 obstacles: two point obstacles at (0,50) and (0,-50), and a curved quarter circular wall with radius 75 cm.
Pick a metric and draw the shortest path with respect to that metric. Draw the end position in the workspace along with 2 intermediate points on the shortest path.
Workspace:
Configuration Space
Problem #5 [21 pts]
Draw a line to match the resulting signal with the corresponding mask that was used to convolve the original signal.
Original signal:
|
|
|
|
|
|
|
|
|
