If you meant vertical is along the wall, it's no problem. But if you meant your robot will climb up the wall, it's quite difficult, but not really impossible.
Your wall should be glass. If it's as rough as normal wall, it's quite difficult to climb up.
but if it's glass, there are many projects on it.
You should build your robot as a cross. There should be 2 "feet" on each segment.
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O is your feet
As this design, your robot may climb up, move to left or right "ON" the wall.
You should use a hydraulic system on your robot. To move up or down on the wall, firstly, 2 middle feet are powered, and 2 side feet are free. You may use a DC motor to move the 2 side feet up. After that, make them powered. Free the 2 middle feet, than move up. Continue this loop, to move your robot up and down. It's similar to moving left or right.