4 ms·
I don't think the constraint is like normalization. Consider a platform with https://en.wikipedia.org/wiki/Omni_wheel https://en.wikipedia.org/wiki/Omni_wheel
by gugagore 5y ago
I don't think the constraint is like normalization.
Consider a platform with https://en.wikipedia.org/wiki/Omni_wheel https://en.wikipedia.org/wiki/Omni_wheel
There are 3 degrees of freedom for rigid bodies in the plane. If you have four wheels, then there is a constraint.
Associate with each wheel a unit vector along the direction it can impart force, perpendicular to the direction that it imparts no force. Now take a vector indicating the velocity you want to travel in (ignore rotation for simplicity).
To figure out how the velocity of each wheel, take the dot product of that wheel's unit vector with the target vector.
To see that normalization doesn't play in the constraint in the omniwheel case, note that any valid assignment of wheel velocities is still valid if you scale it up or down.
I think the case here is more complicated because it's not a euclidean space. There are poles. I believe underlyingly my analogy holds, though, if you think about manifolds and tangent spaces.
- Animats 5y agoI don't think the constraint is like normalization. Yes, this is different. I was thinking of a 3DOF trackball setup. There are 3DOF trackballs (you can both roll and twist) where a big trackball rests on three small ball-bearing balls. Two of those balls each have 2 axes of rotation sensing; one is just an idler. It's all friction-based; no gear teeth. So you have four incremental data signals coming out, which resolve to the three motions a sphere can do. That approach is homogeneous; no position of the trackball is special.