Figure out pendulum dynamics

[declanoller]

Doesn't actually need to match Pendulum-v0, but they need to be able to simulate the non-hardware version of Pendulum-raas and expect that it'll work about the same when they use it with the hardware version.

This involves setting the torque, making sure the velocity is in a reasonable range, etc.

[declanoller]

Some updates:

I did a test to get a sense of the power of the torque. To do this, I ran const_tests.py in the raas-experiments repo, which basically sets the torque, waits a second for it to normalize, then takes the observation at that angle, sweeping through ranges [-2, 2] and then [2, -2].

The first thing is that we can see it has some hysteresis:

Also looking at it, you can see (in long flat regions) that it probably has lots of static friction, which I'm guessing is causing the hysteresis.

This may not be a huge deal, hysteresis probably won't matter when it's swinging around a bunch. But it could make it a bit tricky to match our simulation version to.

the other thing to thing about is the angle. In openAI gym's Pendulum env, the upright angle (i.e., the goal) is theta = 0, and the position when it's down is -pi and pi. Our motor controller by default sets the down (i.e., hanging with no torque) position.

So our motor_controller.py has angles: down = 0/2pi, increase to top = pi. To make this equivalent with openAI gym, which has: down = -pi/pi, increase to top = 0, I think it should make sense to just say theta = theta_motor - np.pi. So I've edited PendulumEnv.py to reflect that, but someone check my math.

[philzook58]

We calculated the dynamics from the spec of the motors, however they only have "rated torque" which is a technical term for continuously deliverable torque at rated speed. We probably care more about stall torque which is a larger number.
Declan has some new measurements that approximate the appropriate torque number at ~ 10x the calculation based on "rated torque"

These are resonance curves