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

### Due at beginning of class on Wednesday, Feb. 14th

• (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

• For the sample environment in Figure 3, draw the resulting path from the wavefront planner (in the continuous domain, ie. not with pixels) for the mobile robot using the L1 metric. Remember to take into account the configuration space of the robot.

Print out (or recreate with a computer) multiple copies of the figure, and submit the following:
• One copy showing the configuration space.
• One copy showing the wavefronts (you don't have to draw every single one, just a representative amount)
• One copy showing the resulting path(s). Figure 3

• For the configuration space generated from the previous problem, implement either the Bug1 or Bug2 planner to trace a path from start to goal.

### Turn in:

Hand in hard copy in class.

Last updated 2/6/8 by Howie Choset