Absolute Positioning System Help

[Tom Bottiglieri]

I am in the process of creating a robot absolute positioning system, such as stangPS, and was wondering if any teams or programmers could help me with a few concepts.

I am keeping track of robot x and y values (relative to the origin at bottom left of field, field would be quadrant 1 on a Cartesian plane) in integer variables, and trying to keep track of the robots 2d position. I understand how I can increment these value by keeping track of distance traveled with shaft encoders and a yaw gyro. But, my theory only works with straight line movement. Heres why:

When the robot moves straight from its starting position, I could increase the x variable with the distance traveled. Then if I turn and drive a distance I could find the y and x value of change by taking the sin and cosine of the angle I turned, multiplied by the distance of that line traveled (hypotenuse of a right triangle).

But, I am totally stuck on how to code this for arcing robot movement. The robot does not always travel in a linear fashion, and I am not sure how to compensate for this.

Has anyone ever used the same method as I am, and know what to do to solve my problem?