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Spiraling Robot

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I have a robot that is setup so that when I set the wheels going at the same speed in opposite directions the robot spins in a circle but the center of the axle does not move. The wheels are separated by 100 cm and I would like to write an algorithm to make the robot travel in an archemedian spiral (eg. r = theta) for searching a field. your help is much appreciated.

Whats the question?

Basically I have a robot with two wheels and I would like the center of the axle of the two wheels to travel on a path that looks like the path in the image below.

Hint: As the robot spirals outward, the curve becomes closer to a straight path.
Hint2: How do you make the robot go in a circle? How about a larger circle? Then a straight line.
Figure that out and you are 80% there.

That is exactly how I started the problem, but then I came upon a math problem that I need help with. Here is the setup:

Let MAX_SPEED be the max speed of the wheel in either direction.

I set the right wheel to spin at a speed of SPEED_RIGHT = MAX_SPEED
Then I realized that the speed of the left wheel describes the radius of the robot.
I thought of the following situations:

Then the robot will spin with a radius of 0, the center of the spin being in the center of the axle.

Then the robot will spin with a radius of HALF_AXLE_LENGTH, the center of the spin being where the left wheel touches the ground.

Then the robot will spin with a radius of INFINITY, the center of the spin being undefined.

Then I had to make a function of time that would increase the left wheel speed from -1 to +1, but I still am not sure of the function I should use to do this increase. When I solved this problem originally I made an algorithm that adjusts the wheel speed, but the algorithm requires a lot of calculations. Does anyone know of a function of time that could help me? Maybe an algorithm that relates SPEED_LEFT with radius?


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