Killough Center of Rotation

[Ether]

In case anyone reading this thread is interested, here's an explanation how the omni rotation equations were derived. Scroll to the bottom of the list of attachments.

[gpetilli]

All,

I have updated the xls to use Ether's algorithm and a cleaner user interface.

Ether,

I think I duplicated your calculations, and I get the same final wheel speed results, but the intermediate alpha angle results for the rear wheels don't look appropriate to me. I have checked the equations several times and I think they match yours. Do they look correct to you?

[Ether]

Originally Posted by gpetilli

All,

I have updated the xls to use Ether's algorithm and a cleaner user interface.

Ether,

I think I duplicated your calculations, and I get the same final wheel speed results,

Yes, except for the (8,12.25) center of rotation test case. You have a division-by-zero error. You need to put a wrapper around Excel's atan2 function to test the XY input parameters and return a value of zero if both X and Y are zero. That will fix it.

but the intermediate alpha angle results for the rear wheels don't look appropriate to me.

What about them doesn't look appropriate? You do realize they are in radians, right?

I have checked the equations several times and I think they match yours. Do they look correct to you?

They don't match mine. You've got a cosine in there. The equations I posted don't have a cosine anywhere.

Are they correct? They seem to be, for the test cases you have run. Whether or not they are equivalent for all test cases would require further review. If you want to put together a labeled diagram explaining your equations similar to what I posted¹ I'd be happy to review it.


¹attachment "omni rotation derivation of equations" in this CD-media paper contains figures and a working Octave script showing the equations.

[gpetilli]

Added div0 checks. Hopefully final version.