I agree - it was a fun lesson and very interesting. I have not given much thought to MEMS gyroscopes before this. I enjoyed the video you posted - Cabe. It simplified the concept for me and I can visualize its application more clearly.
Be careful with the low cost MEMS gyros. They suffer both from drift and large zero rate outputs. This means that if you continuously take readings when the device is not in motion, the MEMS gyro will say you have turned a full circle after an hour or so. They can be fun used measuring motion on one plane, but for 3 dimensional movement the calculations involved in figuring out where you are are beyond the wit of an embedded micro-controller. (not to mention the capabilities of some engineers - it's not the simple like an accelerometer)
Gyros, like all instruments come in different grades. For the short term RC-style stabilization mentioned in the video, noise and bias of a gyro don't make much difference and can be compensated for. However if you are navigating a plane full of passengers across the country - it's a much more complex requirement as you noted requiring a different grade of instrument.
I doubt that they are beyond the microcontroller. Most calculations like this break down to very simple expressions when properly discretized. However, doing that analysis may well be beyond most programmers who are trying to tell the microcontroller what to do.
The algorithms for 3 dimensional position calculations can be found in application notes, but they involve matrix multiplications and basic controllers like PIC and M0 are not up to the job, not if they are controlling motors at the same time. Factoring in all the errors a MEMS gyro is capable of and you realize it's not really useful for navigation. In practical terms, there is no way you will accurately follow a corkscrew motion with these sensors.
I'd be a little careful about saying no. Often enough, people put constraints on these things that are way beyond what is necessary. For example, you added the "controlling motors" constraint. I've done real time adaptive servo position control with a PIC that was also monitoring a half dozen inputs. It is all in when and how often you do the tasks. Reading the encoder (a very simple task) has to be very fast, or you will miss counts. The inner loop of the servo control has to be in the 100 to 1000 Hz range. The adaptivity can be done in the 1 to 10 Hz range.
Reading a gyro has to be very fast. Compensation can be slower. Navigation can be much slower. A 3D matrix-vector multiply is only 9 multiplies and six additions. That isn't much, especially if you have some hardware help to do it (which some PICs do). If you had to do that at 100 kHz, that would be beyond a PIC, but I doubt that you do.
Having said that. the inherent errors in a MEMs gyro will cause them to drift. You will need other input to compensate for that. But that is not a processor limitation. An array of high speed DSPs would have the same problem.
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