My project only ever achieved partial success, never quite performing to the level intended. Here's a breakdown:
Once spun up to speed, the suitcase will at first appear normal. Any motion parallel to the suitcase (i.e. forward/backward/up/down) will exert no torque on the suitcase and it will thus behave completely normally. However, if one tries to rotate the suitcase horizontally (vertical axis of rotation), this requires exerting a torque in the vertical direction. As shown in the above diagram, with a large angular momentum outwards, away from the demonstrator, exerting a vertical torque will result in an angular momentum angled upwards, tilting the suitcase. This is shown in the video below.
This project is sufficient as a proof of concept / prototype, but its performance and reliability are poor in its current design.
The main issue comes from the motors, which are designed for RC aircraft and spinning lightweight propellers very quickly. The high mass flywheels have a moment of inertia which is too large for the motors to properly accelerate. When the electromagnets inside the motor "fire" for the first time, the flywheel barely moves at all. This results in it not being in the correct location when the magnets "fire" a second time. Most of the time, the flywheel will twitch back and forth randomly due to this improper timing. While I was able to get it to function, I was only able to do so with one of my three speed controllers, and thus only one motor (each motor is controlled by an electronic speed controller, ESC). I ordered more ESCs of a different brand and none of them could fire at the proper timing to get the flywheels going.
A secondary issue is that the flywheels have a danger of slipping off the motor's shafts. When precessing, there is a very large torque applied to the flywheel by the motor, but NOT along the shaft's axis of rotation. Over time, this can pull the flywheel off the shaft, which would result in total destruction of the suitcase.
I believe a design similar to this one would be a better bet, for a number of reasons: