How does it steer? Do you steer a front wheel(s) or do you have some way to make the drive wheels turn at different speeds using one motor?
For your spiral, you need to calculate the radius at each moment of time and from that determine either the difference is wheel speeds or the steering angle.
For differential drive, calculate the different circumferences for the inner and outer wheels - that gives you the different speeds.
For steering by turning wheels, draw yourself a picture of how it turns and you should be able to sort out the trigonometry. http://en.wikipedia.org/wiki/Ackermann_steering_geometry