Since this uses reaction wheels, if you consistently push it in the same direction isn't it possible for the wheels to hit their max velocity and then be unable to correct anymore? In the video at least for the 2d version, it looks like the cube intentionally overshoots the balancing point so it can use gravity to let it get the reaction wheels back to 0, maybe they use that same method with the 3d one.
Pretty cool. Kind of funny that they have all the parts for a gyroscope inside of the cube, but are basically using the exact opposite method for balancing.
You are correct, if you constantly hold it offset from its balance point, the wheels will spin up until they saturate and it falls over.
The overshooting of the balance point isn't intentional, but a byproduct of the "learning control" employed to improve the jump. Brake residue alters the stopping ability of the brakes (and thus the duration of the energy transfer into the cube's body), and a slightly offset center of mass affects the location of the balance point. In successive attempts at jumping up the energy of the wheels is altered to compensate for these effects, if it undershoots once, likely it will overshoot the next time as it "hones in" on the correct settings. Once the jump is close enough to the balance point, the control switches from open-loop "jump" into closed-loop "balance" to stabilize the cube around the balance point.
The wheels are actively controlled by the motors, so it's not gravity that is slowing the wheels down, rather the moment that is required to stabilize the cube's body. There is also friction in the system, so some energy is always lost and thus the wheel rotational rates will tend to zero around the balance point.
Pretty cool. Kind of funny that they have all the parts for a gyroscope inside of the cube, but are basically using the exact opposite method for balancing.