Once a Space Elevator goes into operation, there will be lifters traveling both up and down the ribbon. If we don’t want to have them travel in an asynchronous manner, we’ll have to figure out some way to have lifters pass each other (one going up and the other going down) while both are on the ribbon. Lifters designed now cannot do this – they clamp to the ribbon, enveloping both sides of it (or all four sides of it, if you want to count the ribbon edges). I’ve toyed with the idea of suggesting this as one of the challenges to be met in future Space Elevator games; i.e. you have to have two lifters on the tether simultaneously, one going up and one going down, and they have to be able to pass each other without causing problems.
Today I came across a video of another kind of climber, one that could, perhaps, crawl up on just one side of the ribbon. You can find a video of it in action here. It’s battery powered (I think), and doesn’t seem to be designed to carry anything, but it’s a step in the right direction. Funding for this is being provided by DARPA.