Where do I learn more about this feedback mechanism?
It depends on the kind of feedback. You can have absolute or relative feedback. Relative would be, for example, to use an encoder on each wheel to find out how much it has turned. Absolute would be using a compass to know exactly what direction the vehicle is facing at any time.
Purely from a physics perspective, considering an ideal environment, how do I derive a relation between rpm and the steering angle?
If you know how much each wheel has turned then it is really just simple trigonometry. You have two arcs that are the same proportion around the circumference of two circles. The circles must have the same centre point. Well, I say "simple" - that's a relative term. And of course it depends if you are moving like a car (i.e., turning while moving forwards) or like a tank (turning on the spot) as to whether such calculations are particularly meaningful.
But then of course that's only if you actually know the RPM. Which requires feedback.
There is no easy relationship between PWM and the angle turned. This is because PWM does not define the RPM:
- PWM defines the current
- The current defines the torque
- The torque defines the acceleration (and ultimately maximum speed) under different loads and conditions.
Those loads and conditions change depending on lots of factors. With no way to change the angles of the wheels they will need to slip on the surface as you turn. That adds friction and varies depending on both the speed at which you turn, the angle you turn through, and the surface you are driving on at the time. A high friction surface will both increase the power transfer and at the same time require more power to turn. A sharper turn angle will slip more and require more power to overcome the friction.
It's a very complex relationship with far too many variables. Which is why cars have steering mechanism to change the angle of the wheels, and some vehicles have rear-wheel steering as well to change the angle of the rear wheels to reduce slip and friction (such as the Porsche 911 and many large heavy vehicles), and why London cabs use "Ackermann" steering which gives each wheel a different angle while turning to increase the angle the vehicle can turn through so it can turn in the road easier.
So all in all if you want to know what direction you are pointing at any time, although it's harder to interface with and use, and may be a little more expensive, a compass or other absolute rotation sensor is the way to go.
If you want to turn to a specific angle, (or turn through a specific angle, which is just a relative change between two specific angles) then it's a case of "move a bit" then "see what angle I'm at" then "move a bit more" and "see what angle I'm at".
You could either use a simplistic approach where you always move in discrete steps, or use a PID to calculate what would be a good amount to turn to get you closer and closer to the desired angle depending on how far you turned last time.
