My info was very helpful. I could have suggested a bipedal robot but that has humongous sensor feedback and control system requirements which are more than likely over your head. A robot with 4 legs is much easier to stabilize. As far as a power supply, the only way to have power on an untethered robot (which is what I assume you want since cords aren't cool) is to use a battery.
No one is going spend time dreaming up design ideas for you if you have not shown an attempt to get started on your own.
you can get help but you have to put some energy too.
try explaining what this step climber is supposed to do.
what size of steps, what size of payload, what speed...?
is this a toy walker, transport for dissabled, or something to move
bricks or bags of cement in a place with no room for crane...?
which part of project you need help with?