2009

The argument to the Zero Plane Map is a unit vector to give the direction of
the EE axis. Equivalently, when the EE slides along the EE axis, the solver
plane should be fixed. Therefore, the Zero Plane Map defines a vector field on
a sphere. Given a point on the sphere, it produces a tangential unit vector to
be interpreted as the normal to the zero plane.
1. Normal to the zero plane
Solver Plane Flipping
It is a mathematical fact that there does not exist a continuous vector field
on a sphere. No matter how hard you try, there will always be a point on the
sphere where neighboring vectors change dramatically. This is where the
solver plane will flip when the end effector axis approaches to it.
This is because, on one hand, the history independent requirement demands
us to assign a fixed vector to the singular point. On the other hand, no matter
what vector is assigned, it will be dramatically different from some vectors
assigned to the neighboring points.
Inverse Kinematics (IK) | 3399