Ben Berkowitz

16-311 Introduction to Robotics

Homework 1:

The iRobot PackBot:

The iRobot PackBot is a mobile robotic platform designed for bomb disposal, checkpoint and inspection tasks.

The PackBot is controlled remotely by a human operator using a radio or tethered control box.

The robot senses using four cameras, temperature sensors, accelerometers, an inclinometer, a compass and magnetometers to direct itself and aid in bomb detection.

Using these sensor inputs and the direction of the human operator the PackBot is able to process commands and plan its actions using a Onboard Mobile Pentium PC.

Based on these plans the PackBot can perform actions such as inspecting vehicles and disabling bombs using its eight degree of freedom manipulator arm and gripper and its mobile base.

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Homework 2:

Rube Goldberg Machine:

Group 4: Ben Berkowitz, David Andrews, Chin-Chiang Tseng

Components:

Measuring Tape:

Ramp with Pool Ball:

Pivoting Shoe:

Hinged Block of Wood:

Spray can, Candle, String:

Baking soda and Vinegar:

Balloon:

Energy Transfers:

1: The measuring tape is released, pulling down on the string and raising the ramp.

2: The change in the ramp angle causes the pool ball to roll down the ramp.

3: The pool ball strikes the shoe counterweight, causing the shoe to pivot downwards.

4: The shoe kicks the block of wood, causing it to swing downwards.

5: The block of wood hits the spray can, causing it to spray a flammable mist.

6: The flammable mist is ignited by the candle, creating a cloud of flames which melts the string.

7: The broken string causes the bottle to swing downwards mixing the baking soda and vinegar.

8: The gas created from the baking soda and vinegar blows the balloon into the air, causing it to sputter around the room.

VIDEO!!!!

GRwebpage1_files\MVI_1094.avi

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Homework 3:

Vision Lab:

Image 1: Mona Lisa

Contrasted:

Histogram:

Binary with threshold of 70:

Image2: Letter D

Contrasted:

Histogram:

Binary with threshold of 22:

Image 3: Tractor Maintenance

Contrasted:

Histogram:

Binary with threshold of 175:

Part 2:

1. Assume we have a digital image I (2D, discrete) representing a 3D scene. Let's choose some particular pixel P (not on an edge or corner). This pixel might be corrupted with noise, so we want to take an average of P and its neighbors and use that value instead of P's stored value.
   Formally, we want: , where and N is the total number of pixels in the neighborhood (including P).
1. Come up with a 3x3 mask (corresponding to an 8-connected neighborhood) that implements the average operator.

1/9	1/9	1/9
1/9	1/9	1/9
1/9	1/9	1/9

2. Now perform this procedure (multiply pixel's neighborhood by mask and add) for each pixel in the image. What popular image processing operator have we just applied?

We have just applied convolution on the image.

3. Have we lost information? Can you recreate the original image from the "mean image" we've just generated? If so, how? If not, why not?

By applying convolution on the image we have lost information because we have smoothed out the pixel variation across the image.

You cannot recreate the original image because there is no way of knowing which pixels contributed to the overall average.

4. Above, we weighted the actual pixel's contribution just as much as its neighbors' contributions. However, the neighbors might have different values not because of noise, but because they are actually storing information for a different region in 3D space. Propose a different 3x3 mask that performs a weighted average, with larger weight on the actual pixel (i.e., the pixel we want to replace). Recall that the weights in a weighted average must sum to one.

1/16	1/16	1/16
1/16	1/2	1/16
1/16	1/16	1/16

2. On the surface of Mars, Pathfinder identifies a Martian with its stereographic vision system (Figure 2).

The Martian's face is 50 pixels to the left of the center of the display in the left camera, and 40 pixels to the left of the centerline in the right camera.

The resolution of the camera display is 72 pixels per inch. The cameras are 12.5 inches apart, and have a focal length of half an inch.

How far is the Martian from Pathfinder?

Figure 2

α = Tan^-1( (50/72) / (1/2) ) = 54.246°

β = Tan^-1( (40/72) / (1/2) ) = 48.013°

1) h_α / h_β = α / β = 1.130

2) h_α + h_β = 12.5 in

1, 2) h_α / (12.5 - h_α) = α / β;

h_α = 12.5 x 1.130 - h_α x 1.130;

h_α( 1 + 1.130) = 14.125

h_α = 6.631

D = h_α / Tan(α)

D = 6.631 / ( (50/72) / (1/2) )

D = 4.774 in

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Homework 4:

Convolution:

Mask 1:

-1	0	1
-1	0	1
-1	0	1

Mask 2:

-1	-1	0	1	1
-1	-1	0	1	1
-1	-1	0	1	1
-1	-1	0	1	1
-1	-1	0	1	1

Mask 3:

-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1
-1	-1	-1	-1	0	1	1	1	1

Image 1:

Image 1 convolved with Mask 1:

Image 1 convolved with Mask 2:

Image 1 convolved with Mask 3:

Image 2:

Image 2 convolved with Mask 1:

Image 2 convolved with Mask 2:

Image 2 convolved with Mask 3:

• (a) What do these masks do to the input image?

The masks perform vertical edge detection on the input image, with white pixels corresponding to areas of steep positive slope and black areas corresponding to areas of steep negative slopes

• (b) What are the advantages of using a small mask? Why would you want to use a large mask?

By using a smaller mask you get a crisper image and lose less information due to averaging. You would want to use a larger mask if you have a noisy image and want to minimize the noise from interfering with convolution.

• (c) Suppose you wanted to identify the horizon in images at sea. What mask might you use to do this?

To do this I would use a horizontal edge detection mask such as:

-1	-1	-1	-1	-1
-1	-1	-1	-1	-1
0	0	0	0	0
1	1	1	1	1
1	1	1	1	1

Homework 4 Code:

GRwebpage1_files\HW4.c