I'm trying to figure out the distance travelled at the articulation point of a turning vehicle with 4 driven wheels (each wheel houses a motor and can all rotate at different RPMs). If this isn't a suitable place for such a question, please let me know if there's a better exchange/forum for it.
This is a work-related odometry calculation problem used in a larger analytic, not something "just for the sake of doing it" (I wish!), so I unfortunately don't have anyone academic to turn to for assistance/grading etc.
- The distance from the articulation point to the front axle, $l_1$,
- The distance from the articulation point to the rear axle, $l_2$ ($l_1$ != $l_2$),
- The length of each axle, $l_a$,
- The articulation angle, γ,
- The RPM of each wheel, and
- The diameter of each wheel.
I have a timeseries of RPM/articulation angle data with a 2Hz sampling rate, but if I can get some help with the general equations, I'm more than comfortable doing this bit.
I've done similar instant centre problems with non-articulated vehicles in the past, but my uni years are now a fair bit behind me and these days I spend most of my time programming, so my engineering skills are a bit rusty. Unfortunately, "reasonable" accuracy is important here (still making allowable assumptions such as disregarding slip, etc) so I can't use the assumption of linear distance. Any help would be very much appreciated!