The ability for a robot to climb stairs or especially a ladder amazes just about everyone who sees it and rightfully so because it is just so complicated to achieve!
The robot must be made to balance itself and moves it weight up and perhaps back down the stairs without tilting too much to one side and falling.
Many people were amazed in the 1960s with a simple spring toy called a “slinky” which when placed at the top of a stair case it would proceed to unravel and walk itself down a the stairs a step at a time.
This was and is amazing to see but many people assumed that it would be easy to make a robot do the same thing but it is not.
We will all realize that a small lightweight toy can be made to do just about anything but when you are talking a full human sized heavy robot then that is a totally different story.
You can see some of the robots by Boston Dynamics able to go up and down stairs and dance and move along rough surfaces so they are certainly the ones to learn from and watch.
http://www.bostondynamics.com
Here are a special type of small wall climbing robots that are capable of climbing at an 85% off vertical wall. The 6 ounce robots with 2 wheels and a trailing tail can be thrown up onto a roof and will survive a fall from a several story fall. https://www.youtube.com/watch?v=OyalmPyDcis&list=PLa_gU2Ib52Hene7NjDsN7QkA6k-97E7MS