>A lot of those movements are there to zero out the axes so that each movement starts from a known good position and orients itself against the camera. Usually there's a switch that, for example, senses when the body goes all the way to the bottom, which is the origin for the whole positioning system.
Ideally the "zeroing" should be done once when the robot "wakes up" or only once in a while, and there should be digital encoders on all motors, the position should always be known within a tiny margin of error, and not enough to cause a problem for positioning. At least that's how I'd do it, I'm not sure how they built this thing.
It's always a trade-off! You could have more accurate sensors and motors that are more expensive, or you can have cheaper motors with no sensors and higher accumulated errors. Since this is more of a research project than a product, we went for a cheap robot with the slower-but-more-accurate approach.
Encoders are not that expensive and they don't have to be integrated into the motor. I've done this stuff before, it's not so costly and it really improves the entire system.
Ideally the "zeroing" should be done once when the robot "wakes up" or only once in a while, and there should be digital encoders on all motors, the position should always be known within a tiny margin of error, and not enough to cause a problem for positioning. At least that's how I'd do it, I'm not sure how they built this thing.