Homework 5
16-311 Introduction to Robotics
Prof. Howie Choset

• (50%) Group: Lab 4 - Low-level mobile base control.

• (50%) Individual: Answer the following questions.

  
  Figure 1

  • Refer to Figure 1 for the following questions:
    • Convolve each of the following with the source image in Figure 1.
      • [1 -1]

      • [1 1 1 -1 -1 -1]

      Plot the results using a computer. Label the graphs with the input, filter, and output in bracket notation, similar to this:
      
      input: [1 2 3 4 5 6]
      filter: [0 1]
      output: [0 2 3 4 5 6]

    • In a one dimensional environment what does the convolution mask [1, -1] do? (This convolution mask is different from the one in class. We know this, but if you understand the process of convolution this will not be a problem.)

    • How is the effect of the mask [1, 1, 1, -1, -1, -1] different?

    • If you wished to detect only the indicated edge, how would you post process the output of the convolution of the original signal with the [1, 1, 1, -1, -1, -1] mask?

  • Convolve the following image with the given filters.
    image:
    • [ 5 5 5 9 9 9 8 7 6 5 -5 0 0 0 0 ]
      
    
    filters:
    • [ -1 1 ]
      
    • [ 1 -1 ]
      
    • [ 1 0 0 1 ]
      
    • [ 1 0 0 -1 ]
      
    You may deal with the edges as you wish (padding with zeros, using nearest neighbor, and cropping are all valid).
    Plot the results using a computer. Label the graphs with the input, filter, and output as before.

  • For the closed loop response in Figure 2, draw the resulting response if the proportional gain were increased. Describe in a few words what happens.

    
    Figure 2
    

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    Some clarifications:
  • You don't have to use a computer if you don't want to. You can choose to draw the signal on a piece of paper, and the convolved signal below it.
  • If you decide to use a computer, you can discretize the signal in Figure 1 (eg [0 0 0 0 0 1 1 1 1 1] for a step function). Just ensure that the shape of the signal looks similar to Figure 1.
  • Make sure to keep the x-axis aligned (and scaled the same way) in your answers (i.e. if there is a spike, or any other feature) in your convolved image at a certain position, we will look at the original signal (that you drew) at the same position to check if it's right)

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    Turn in:

    Submit hardcopy for individual assignment at the beginning of class.

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  Last updated 2/9/09 by Somchaya Liemhetcharat