16-311 Midterm Spring 2006

Name:______________________

There are eleven questions below. Each is worth 10 points.

You must choose ten questions to answer and cross out the other question.

(10 points) Is the following planner complete? Explain why or why not.

Planner steps:
1. Move towards the goal in a straight line.












(10 points) For each of the following tell what kind of path optimality is guaranteed:

1. Voronoi diagram
   
   
2. Visibility graph
   
   
3. Wavefront planner
   
   
4. Trapezoidal decomposition
   
   

(10 points) Convolve the following input and mask. Give the output in the same bracket notation. Show your work.

• Input: [ 0 1 2 3 4 4 4 0 0 3 3 3 2 1 0 ]
• Mask: [ -1 1 ]
  
  
  
  
  
  
  
  

(10 points) What mathematical operation is being performed by the mask in Question 3?






(10 points) If you convolved the following image with the given mask, what would you expect to see?



• Image:
  
• Mask:

  | -1 -1 -1 |
  |  0  0  0 |
  |  1  1  1 |
  









(10 points)Give an example of a sensor which has resistance as its output.






(10 points)Describe a software method for debouncing a switch. Give one negative consequence of using this method.





(8 and 9)
The following diagram shows the workspace for a two joint manipulator.
The first joint angle is &Theta₁ and the second is &Theta₂
The triangles are obstacles.


(10 points) Draw the configuration space on the diagram below.




(10 points) On your configuration space diagram, show the shortest path between the two given points.

(10 points) Draw the Generalized Voronoi Diagram for the following Workspace:



(10 points) A camera is used to take a photograph of a student who is 1.8 m tall. The student stands 2.7 m in front of the camera. The image height on the film is 6.7 cm. What is the focal length of the camera? Show your work.

Did you remember to cross out one question?