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It seems like pitch angle could be computed from just gyro data, which uses 2 gyros.

However, isn't pitch computed from acceleration rather than gyro data?

pitch = 180 * arctan (accelerationX/sqrt(accelerationY*accelerationY + accelerationZ*accelerationZ))/PI

where no gyro data is needed. So how could a copter be balanced with just gyro data?

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It depends on the type of gyro. The cheap and available electronic gyros produce a signal proportional to the rotation speed. You don't get absolute angles. Even if you started stationary and level, then integrated from there, the answer would be useless in a just a few seconds due to offset drift.

Some gyros are more accurate, but cost much more. Other gyros use a spinning flywheel as a reference and do produce angle signals, but those are also much more expensive, not to mention heavier and larger. NASA can afford to put them on spacecraft and commercial jetliners used to use them for long over-water hauls where there weren't navigation beacons, but you're not going to put one on your copter. Even then, the mechanical gyros drift over time too.

In the end, inertial navigation fundamentally relies on integration to find position, so has a ever-increasing error envelope with time. This is one reason the astronauts on the way to the moon and back had to do regular position fixes from star sightings and the like. The inertial navigation provided the immediate position and orientation, but the accumulated drift had to be occasionally reset from absolute measurements using other methods.

In the case of cheap MEMs gyros (the only kind you can reasonably put on your copter) they are really only good to tell you the angular velocity. The absolute vertical direction is determined by measuring the gravity vector, and you can measure the absolute angle about the vertical axis with a Hall effect magnetometer.

Nowadays, of course you use GPS for absolute location. It doesn't tell you orientation, but once you're moving you can find heading from multiple GPS readings. GPS is used for the long term data, and inertial navigation only to fill in the short term information that is too detailed for GPS.

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