Hi,
Here is the VEX IQ robot which can climb the sofa:
I made it with my daughter. It take about one month of thinking and experimenting. We tryed different schemes, but this is the only one which really works.
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Nicely done! The folding rack gear is a very cool idea for giving the bot a boost! And I really like that you accomplished it with only 4 motors.
I built my own climbing bot a while ago. No video, but a photo is attached. (Search on Avatar III, and you’ll see a very similar bot in action.) My bot used 6 motors and worm gears to operate the “arms.” Each arm was geared independently and could turn a complete circle, but due to the weight, I needed a 60:1 gear ratio to lift the front. The back was lighter, so I got by with something like a 36:1 there. As you can see, I also used tank treads. The arms were attached to free spinning gears that I drilled out. This let me put them on the same axles as the drive motors for the tank treads. It worked pretty well and could right itself if flipped over. I was ultimately able to drive up and over an overturned Vex IQ storage bin, but no way my bot could have tackled the sofa. Super job!
The bot has been created for the precisely formulated task: climb the sofa :). So, I think its not so universal. There five motors, because the rack is two-sided, and use two motors. We created it with wheels initially, but they were too ugly, and sliped on the sofa surface, so we replaced them with tank treads (which even more compact).
Weight is really important, and so, gear ratios and overall frame construction. As can be seen we used stabilizer shaft, because the frame is not strong enough.
Free spinning gears are cool. I have to order another gear pack gor that 
Very cool!
Great job done so far. Thank you for the TY link.