Tribot swerve

[Andrew Schreiber]

Originally Posted by Ben Martin

Offhand, I can think of a few considerations:
- Looks like the side length would be ~37 in. for an equilateral triangle. This could make passing through a 36" door difficult if the bumpers are on (we have a hard time doing this with 28" robots with bumpers as is)
- You have ~23% less total volume available to you with the triangle configuration than the square configuration (with maxed out dimensions and an equilateral triangle).
These two items would dissuade me from pushing it in most cases, but in a game where space constraints are not an issue and you need wide pickups, I could see this configuration being useful.

http://i.imgur.com/nw7BGa8.jpg

Again, three wheels doesn't mean 3 sides. But for a demo there's no real reason to build more structure than is required to mount the modules.


One thing to be aware of is that you DO have a smaller contact patch. So for years where your CG is higher you may want to avoid 3 wheel swerves. see BBS 2010, the last of their 3 wheel swerves. Was actually retrofited in the off season to have 4 modules.


The thing I found interesting was the post about how you want 1 steering wheel up front. Every 3 wheel bot I've seen that has a denoted front (meaning, not 148 in 2008) has had 2 steering wheels up front and a steering wheel in back (16 various years, 67 in 2005). Id be willing to bet that was a function of not wanting to intake over a module? Not sure.

[Aren Siekmeier]

Originally Posted by Andrew Schreiber

One thing to be aware of is that you DO have a smaller contact patch.

This sort of depends on what you mean by "smaller." Turns out the the forward back or side to side direction (versus diagonally) is actually less stable than any direction for 3 wheels. I crunched some numbers on this a bit ago: suppose you have a unit circlecircle of diameter 1 available as your frame perimeter, and you need to fit your contact points on this circle. To simplify things (and because it's almost always at least approximately true), the contacts are evenly spaced around the circle. How many do you want? We start by quantifying "stability," as you have, by the distance across the contact polygon in a given direction. In some directions this will be maximized (corner to corner) and in others it will be minimized (side to side). Below is a plot of these maximum and minimum moments for 3 wheels all the way up to 10 (could easily go higher, but honestly?).



The odd numbers have the smallest spread between max and min, so they are maybe more stable when looking at all directions combined. But the even numbers actually achieve the max in a particular direction, since you can actually go from corner to corner on a diameter. So while in certain directions, 4 wheels is less stable (side to side), in others it is the most stable (corner to corner). But when do you ever push or accelerate in the corner to corner direction?

Remember that this is comparing 3 vs. 4 vs 5 wheels (etc.) on the same circle (for the sake of having some sort of control). You could possibly get more out of a 3 wheel since you can make a triangle with longer legs instead of keeping the entire frame inside the circle, but then the shape of the frame is getting more awkward.

[Aren Siekmeier]

For fun: here's the same figure, but this time instead of keeping the contact points on a circle of diameter 1 (with the idea of having a circular frame perimeter), we make the convex contact polygon have perimeter π (the perimeter of a circle of diameter 1). This way, the frame is no bigger than it needs to be to house the wheels, and gets the wheels as far apart as possible.

Edit: oops, my spreadsheet was sort of a mess, so there was an error in this calculation. I've updated the figure below.


Now that we are taking full advantage of the contact shape and getting the wheels further apart with the same frame perimeter, the 3 wheel configuration is actually better than the 4 wheel, with much lower spread between min and max, and much much higher minimum moment. (The max moment for 4 wheel is still the best, but is pretty unusual that anyone is ever tipping in that direction.) It actually gets worse as you approach a continuum of contact points all along a circle (n=infinity).

However, the circular (or near circular) frame would arguably be better than a triangle when you are worried about getting out of t-bones, pins, tight spots, etc., so the other figure should not be forgotten.