So I’m thinking of doing a 6 motor 6 wheel drive (just so the motors can be direct and I can run turbo gearing with the least friction to avoid burning), and I was thinking about how the placement of the two extra wheels would affect the center of rotation on the robot.
On four wheels, a robot’s center of rotation is obviously the intersection of the wheels’ diagonals, but on a six wheel drive, do the middle two wheels play a role at all?
Initially I thought no because I thought that the center of rotation is dependent on the outer bounds of the things rotating (the wheels in this case), which wouldn’t change from 4 to 6 wheels on my bot, but now I’m not sure, and I couldn’t find much clarification on the matter.
Cut a paper square, find its center, pin it by the center to another piece of paper and trace the corners and mid-side (supposed wheel locations) while turning it around the pin. This will represent the distance traveled by each wheel for given amount of rotation.
But in fact, part of that distance, in the case of corner wheels, is traveled through the side-rolling action of the omniwheel rubber cylinders, which would require a little deeper, vector-based analysis.
If I was building that, I’d try 4 omniwheels in the corners and 2 normal/traction wheels in the middle. That would well define your turning point while preventing your robot being pushed around from the side (common weakness of simple 4-omni drivebases).
You can also, for the sake of the test, attach encoders to all the axles and compare the readings (straight move to see the difference between omni and traction, turn to observe the effect of different wheel trajectory).
That is not actually the case. It depends on a number of factors: wheel types (all omniwheels, some omniwheels and some grips, etc.), the center of mass, what wheels are driven, and how the wheels are aligned (tank, some rotating like a car, etc.). As a basic rule of thumb and assuming all perfect omniwheels, a spin turn will happen around the center of mass.
Assuming the same wheel type and an even weight distribution, I meant.
Also slight update, I did some math and the center of rotation does in fact change (in my case towards the rear of the robot as the middle wheels are farther back), but this may actually be a blessing in disguise as the pull towards the back of the bot may counteract the uneven weight distribution when holding a mobile goal in the front.
EDIT: The theory I did to arrive at my conclusion:
