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White Paper: Swivel Angle of the HI IK Solver 433
No rmally, the preferred pose is the one when the
solver is first assigned. So, the plane on which one
lays the joints corresponds to the horizontal plane
here. Rule A makes sure that the chain w ill stay on
theplaneifonemovesthegoalontheplane.
Rule B means that, w hen you move the go al along
the great circle vertical to the equator, the chain
w ill stay vertical, except when it passes through the
poles, which are the singular points of this map.
Pa re nt S pa ce
So far, we have described things as if the whole
world comprises only IK elements. In practice,
theIKchainandgoalmightsitatpointsof
separate transformation hierarchies. Ultimately,
we need to map the position of the end effector
that is described in the world to a point on the
sphere. Depending how the sphere is mounted
relative to the end effector position, the readings
of latitude and longitude are different. The parent
transformation space that this sphere is to be
placed in is called the Swivel Angle Parent Space,
or Parent Space when the context is clear.
The parent space has to be invariant with regard
to the IK parameters. Right now, we provide two
choices:
•
Start Joint—TheSwivelAngleParentSpaceis
thesameastheparentspaceoftheStartJoint.
•
IK Goal—The Swivel Angle Parent Space is the
parent space of the IK Goal.
Example 1
If both the start joint and the goal are rooted
directly at the world, the choice of Parent Space
does not give rise to any difference. In the
following example, the start joint is parented to
object A.
The IK chain is parented (via the start joint) at objec t A .
Assume this is the pose when the IK solver is
assigned. So, this is the preferred pose. The plane
on that the joints are laid out is the horizontal
plane of the (Zero Plane Map) sphere.
• A: Parent Space is Start Joint. In this case, the
sphere is parented to A. If A is rotated about
the drawn axis, the sphere is rotated together
w ith it. The goal is in a separate transformation
hierarchy. I t stays in place, and the end effector
sticks to it because of the IK solution. Since the
(plane) normal is fixed to the sphere, it rotates
w ith A, too. Therefore, the whole chain appears
to be rotated together with the parent object.
• B: Parent Space is IK Goal. Suppose that the
goal is parented to the world. In this case, the
sphere is parented to the world and, hence,
stays fixed. Since the normal is fixed to the
sphere, the chain will appear stationary when
Aisrotated.
Example 2
In the following example, we look at a case where
there exists a rotation in the parent space when the
IK solver is assigned.