If you watch this video, you can get a sense of how an elevator can operate in two dimensions. But, what I can't figure out is how it is driven.
If you consider a conventional elevator, there is a car and a counterweight connected by steel rope. The motor only has to oppose or resist the difference in weight between them (at most half the load, because it can be counterweighted to the car plus half its rated load). This limits the work the motor has to do when lifting the imbalance, and limits the energy it has to remove when lowering an imbalance. Also, the work is done by fixed equipment (typically at the top of the shaft) which doesn't contribute to the weight of the car.
But in the two-dimensional ropeless system, there is no counterwieght, the motor is part of the car (and adds to its weight), so has to drive all that weight going up, and get rid of all that energy going down. It also has to do it without risk of runaway/freefall. And, it shouldn't just burn off all that energy as heat (terribly inefficient). So my question is, how is it done?