It seems my robot is Jewish.

It's Tuesday, and we all know what that means: I've finished my work for this week. So, I've been doing math.

Specifically, robot math. (And no, I don't mean ROBOT + ROBOT = EVIL ROBOT ARMY.)

You may remember my holonomic drive design. It can move in any direction without turning, sure, but I knew that its maximum speed would be different in different directions, in the way the speed of light isn't.

My reasoning was thus: a wheel can exert force best in the direction it's driven — in a car, for example, that'd be "forward or backwards." Since the omni-wheels on the robot are frequently dragged side-to-side by the other wheels, as well, they can't always give their all. The robot can exert the most force — and thus move fastest, barring other influences — when any two of its wheels are moving at top speed. (If all three move at top speed, it spins in place.)

I tend to think visually, so I wanted to get this idea into graph form. The visual representation is simple: for each direction from a central point, shade outwards according to how fast the bot can move in that direction. (Mathematically speaking, this is a polar inequality bounded by a set of three linear equations, one for each wheel.)

Well, here's the amusing bit:


The solution — the maximum speed, given limits on the speed of each wheel — is the shaded hexagon. But boy, was it odd to see my calculator slowly drawing a shield-of-David before it shaded the center.

The wheels are indicated by the fat dots around the circle there. So, if you note the locations of the points on the hexagon, you'll see my suspicion was correct: the robot moves fastest when being driven toward or away from any one wheel, meaning that wheel is stationary while the other two spin at top speed.

Yay!