alt Hacker NewsThis already exists- there's a class of robot called "meltybrains" which spin the whole robot using one or more wheel, detect the speed of spinning with a gyro and modulate the speed of the wheels at different points in its' rotation in order to create translational movement. Since they effectively put all the weight allowance into the "weapon" they can be very effective. The additional complexity means that they are hard to get working reliably in chaotic combat conditions. A team called "Project liftoff" had some serious success though.
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Meltybrains are still wheeled robots even if they use the wheels in a novel way.
If you could develop a self-starting top capable of remote controlled translational movement you would get non-wheeled weight bonuses up to 2x in most competitions.
I saw Project Liftoff in person, that little death-frisbee? Looked like they have two points of contact with the floor, which is probably just better design.
And now that I think a bit further, I might just be imagining a more complicated version of one of those crabwalk spinny metal ones..