Driving With Geometry
The XRP’s driving and turning functions can also be used to draw geometric patterns! By driving a set distance and turning by a certain angle several times, you can draw a shape with as many sides as you want.
Tip
To see the path your XRP has driven, you can place a dry-erase marker between the robot’s wheels and trace your pattern on a whiteboard.
To draw any polygon, you just need to know the size of the shape’s exterior angles, and you need to decide how long the sides should be. Then, you just have to drive straight with the distance of a side length and turn the number of degrees of the corresponding exterior angle. Repeat this until the shape is finished.
Triangle
For a triangle, the interior angles measure 60 degrees and the exterior angles measure 120 degrees. We can trace a triangle with side lengths of 30 cm by having our robot drive straight for 30 cm three times and turn 120 degrees in between each drive straight.
from XRPLib.defaults import *
differentialDrive.straight(30, 0.5)
differentialDrive.turn(120, 0.5)
differentialDrive.straight(30, 0.5)
differentialDrive.turn(120, 0.5)
differentialDrive.straight(30, 0.5)
Square
The process for tracing a square is similar to tracing a triangle. The interior angles are 90 degrees so the exterior angles are also 90 degrees. Keeping a side length of 30 cm, we can trace a square by programming our robot to drive straight for 30 cm four times and turn 90 degrees between each drive straight.
from XRPLib.defaults import *
drivetrain.straight(30, 0.5)
drivetrain.turn(90, 0.5)
drivetrain.straight(30, 0.5)
drivetrain.turn(90, 0.5)
drivetrain.straight(30, 0.5)
drivetrain.turn(90, 0.5)
drivetrain.straight(30, 0.5)
Polygons
We can generalize the procedure used to make a triangle and square to make any regular polygon; you just have to determine the exterior angle and choose a side length. However, for polygons with many sides, this process can get very tedious. Instead of repeating the same code multiple times, we can use a function to simplify the process.
First, lets determine what information the function needs. To trace a polygon, you need to determine the number of sides and the length of each side. We can create a function that takes these two values as an input. The function will drive the distance we give it, turn by the exterior angle, and then repeat that process as many times as there are sides in the shape. We can use a loop for this. The one problem is: how do we know the measure of the exterior angles? Fortunately, this can be easily calculated with this equation:
With the variable n representing the number of sides of your polygon, this equation determines the number of degrees of your polgyon’s exterior angles. With this information, you can now write a function to trace any regular polygon!
from XRPLib.defaults import *
def polygon(sideLength, numSides):
for i in range(int(numSides)):
differentialDrive.turn((360 / numSides), 0.5)
differentialDrive.straight(sideLength, 0.5)
Pinwheel
Now we know how to easily draw any polygon, but we can take it one step further and draw a polygon pinwheel. This pattern consists of several polygons extending out from a center point. Your XRP can execute this by tracing several polygons consecutively and turning slightly between each new polygon. A pinwheel of 3 squares should look something like this:
Programming this may seem like a daunting task, but it is actually quite simple. Every time you want to trace a piece of the pinwheel, you just need to call your polygon function from before and then turn your robot slightly. We can calculate the measure of this turn by dividing 360 degrees by the number of polygons we are tracing in order to keep even spacing between each polygon. Repeat this process as many times as there are polygons in the pinwheel, and your pattern will be finished!
from XRPLib.defaults import *
def pinwheel(sideLength, numSides, numShapes):
for i in range(numShapes):
polygon(sideLength, numSides)
drivetrain.turn(360 / numShapes, 0.5)
