This is an improved version of my previous climber. It is much faster due to the strong motors. No sensors were used. If the walls would be perfectly parallel, it should continue to go up until the batteries run low.

Construction Tips
If you build this, be careful! Don't let it fall down while testing it for the first time. The two walls must be parallel to each other. If the walls are too close to each other your NXT will probably fall down, because there is no good balance.