GRADES 9-12
CALIBRATING A ROVERBOT

BACKGROUND INFORMATION: If you are giving directions to a stranger to your town, you might say, "Go two blocks south, then one block west, and you'll be at your destination." The object of this lesson is to find out a way we can use directions like this to control robots. We start with motors for our robots for which we can specify how long they should be turned on. How can we convert time duration to distance traveled? We assume that the robot we have built travels at a constant speed while the motors are turned on. Mathematically we are assuming that distance is related linearly to time: distance = k * time where k is a constant of proportionality. We can determine k by gathering data from our robot. Ideally, we only need to run the robot one time and measure how far it traveled in a certain number of seconds. But we know that it is difficult to measure exactly how far the robot travels and we should gather more readings. Due to experimental errors in measurement and other causes, the data we gather may not lie exactly on a straight line. We can use data analysis tools to determine a linear regression line. This line is one for which the sum of the squares of the errors will be a minimum. The error at a time at which data was taken is the vertical distance between the line and the data point. Once we have a value to use for our calibration constant "k", we can use our time/distance relationship to predict the location of the robot after it travels for any time.