In robotics, there exists drive-trains that can move omni-directionally (that is in any direction). These come in many shapes and sizes, but most come in a three wheel or four wheel configuration, to keep things simple lets assume three wheels.
These drives are made possible by what is know as an omni-wheel, that is a wheel with casters along it which allows power to be applied in the direction the wheel spins, but not in the direction perpendicular to the wheel.
You can think of the "power" direction as having a lot of friction, and of course the part that rolls with the wheel, while the "slip" of the casters provides a very low friction, non-powered direction.
I come from a programming background, not physics but I want to better understand the physics at work here. So let's look at a simplified picture:
I know that friction and the center of mass are important factors. That's about it.
So my question is, given a direction (green arrow), can a set of forces (red arrows) be calculated such that they equal the overall resulting force. IE, given blue and green can you calculate the various red forces?