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The Advantage of "Robot Math"

Team engineering notebook page shows sketches of the goals and destinations to the left with descriptions and calculations to the right. Each diagram is described in detail explaining the purpose of the calculation and how that informs the next steps.
A team applies math to plan a route in their engineering notebook.

The Advantage of "Robot Math"

Robotics teams that effectively use math concepts, like proportional reasoning and scale, usually have the upper hand in competitions. When these teams form alliances with others during the competition, they can quickly make changes, like mapping out a new path or determining the correct motor rotation values for their autonomous programs. Knowing the math behind the changes can save valuable time. Teams then use that time to make other physical or program changes to their robots that can increase their chances of winning. Using "robot math" like proportional reasoning and scale can definitely maximize a team's performance.

In the image above, the team is using the actual measurements of the field that VEX provided to calculate the distances between different locations on the field. They then calculate the shortest distance from a particular location to the planned destination. These are particularly important calculations for moving the robot accurately during the autonomous program.

Motivate Discussion icon Motivate Discussion - Applying Math to Scale

Q: Why would you use "robot math" instead of guessing and checking?
A: Guessing and checking takes too much time. Plus, if you use math to determine how to adjust your robot or its program, you can apply changes to your numbers/values systematically instead of guessing and checking each new value.

Q: You are drawing out the VEX V5 competition field on paper. The actual dimensions are just under 12 x 12 feet as the perimeter of the interior of the field is 11.7 by 11.7 feet. You want to scale it down so that 1 foot is represented by 10 millimeters (mm). The drawing size/actual size ratio is 10 mm/ 1 foot. What is the scaled down drawing dimensions?
A: The scaled dimensions are 117 mm by 117 mm.

Math explanation:

Proportions show that two ratios are equal.

Two ratio examples are equal. Each side is identical. The first ratio reads 'drawing size over actual size' and the second ratio reads 'drawing size over actual size'.

For the ratio on the left, we are using the ratio that the drawing is is 10 mm but the actual size is 1 foot.

  • Notice the drawing size is in the numerator and the actual size is in the denominator. It is important to keep these the same for both ratios so that they remain equal.
  • Since we know that the actual size of the competition field is 11.7 feet, we will put this in the denominator in the second ratio.
  • The drawing size of the competition field will go in the numerator, but we do not know this size yet, we need to calculate. So, for now we will put the variable X there.

Two ratios are equal. The first ratio reads 'ten millimeters over one foot' and the second ratio reads 'the variable X over eleven point seven feet'.

To solve for X, the unknown drawing size of the brick building, we can use the method of cross multiplication.

The two ratios are shown the same as before, but now there are arrows indicating cross multiplication. Again, the first ratio reads 'ten millimeters over one foot' and the second ratio reads 'the variable X over eleven point seven feet'.

Using cross multiplication gives us the following. The next step is to solve for the unknown drawing size of the competition field designated by X.

The result of the cross multiplication is an equation of 'one hundred and seventeen millimeters multiplied by one foot is equal to one foot multiplied by the variable X'.

To solve for X, we must undo the multiplication of 1 foot times X by dividing both sides by 1 foot.

This equation is similar to the one we had in the last step, but now both sides are divided by one foot. It now reads 'one hundred and seventeen millimeters multiplied by one foot divided by one foot is equal to one foot multiplied by the variable X divided by one foot'.

Notice when dividing both sides by 1 foot, the units of foot cancel on the left and right sides of the equal sign, leaving just millimeters (mm) on the left side.

The equation is the same as the last step, but all of the 'foot' terms are crossed out. It now reads 'one hundred and seventeen millimeters is equal to the variable X'.

Simplifying further, we see the right side reduces to just our unknown drawing size of the competition field, represented by the variable X.

  • On the left side, we are left with 117 mm. Thus, the unknown drawing size of the competition field is 117 mm.

The final result is an equation defining the variable X. It reads 'the variable X is equal to one hundred and seventeen millimeters'.

Q: The perimeter of the exterior of the competition field is 11.9 by 11.9 feet. What are the scaled down dimensions of the exterior of the field so that you can add them to the drawing that you already have for the interior?
A: The dimensions are 119 mm by 119 mm using the same process as above.

Extend Your Learning icon Extend Your Learning - Scaling a Competition Field

Create a scaled drawing of this year's VEX Robotics Competition Field. The following is an example picture of the 2019-2020 Tower Takeover Field but images of the current year's field are available at this link.

Top-down view of the 2019-2020 Tower Takeover game field, featuring cylindrical towers, cubes, and team alliance stations.

Beginning students might use an image of the competition field, like this one, and figure out the scale based on the actual measurements provided by VEX and the measurements within the image.
Experienced students could create their own scaled drawings of this year's field based on the dimensions provided by VEX.
Advanced students could create their scaled drawing of the field and then iterate (plan, test, and refine) an autonomous program.

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