<s>
In	O
computer	O
animation	O
and	O
robotics	O
,	O
inverse	B-General_Concept
kinematics	I-General_Concept
is	O
the	O
mathematical	O
process	O
of	O
calculating	O
the	O
variable	O
joint	O
parameters	O
needed	O
to	O
place	O
the	O
end	O
of	O
a	O
kinematic	B-Application
chain	I-Application
,	O
such	O
as	O
a	O
robot	O
manipulator	O
or	O
animation	O
character	O
's	O
skeleton	O
,	O
in	O
a	O
given	O
position	O
and	O
orientation	O
relative	O
to	O
the	O
start	O
of	O
the	O
chain	O
.	O
</s>
<s>
Inverse	B-General_Concept
kinematics	I-General_Concept
is	O
also	O
used	O
to	O
recover	O
the	O
movements	O
of	O
an	O
object	O
in	O
the	O
world	O
from	O
some	O
other	O
data	O
,	O
such	O
as	O
a	O
film	O
of	O
those	O
movements	O
,	O
or	O
a	O
film	O
of	O
the	O
world	O
as	O
seen	O
by	O
a	O
camera	O
which	O
is	O
itself	O
making	O
those	O
movements	O
.	O
</s>
<s>
This	O
occurs	O
,	O
for	O
example	O
,	O
where	O
a	O
human	O
actor	O
's	O
filmed	O
movements	O
are	O
to	O
be	O
duplicated	B-Application
by	I-Application
an	I-Application
animated	I-Application
character	I-Application
.	O
</s>
<s>
In	O
robotics	O
,	O
inverse	B-General_Concept
kinematics	I-General_Concept
makes	O
use	O
of	O
the	O
kinematics	O
equations	O
to	O
determine	O
the	O
joint	O
parameters	O
that	O
provide	O
a	O
desired	O
configuration	O
(	O
position	O
and	O
rotation	O
)	O
for	O
each	O
of	O
the	O
robot	O
's	O
end-effectors	O
.	O
</s>
<s>
Inverse	B-General_Concept
kinematics	I-General_Concept
transforms	O
the	O
motion	O
plan	O
into	O
joint	O
actuator	B-Algorithm
trajectories	O
for	O
the	O
robot	O
.	O
</s>
<s>
Once	O
a	O
vehicle	O
's	O
motions	O
are	O
known	O
,	O
they	O
can	O
be	O
used	O
to	O
determine	O
the	O
constantly-changing	O
viewpoint	O
for	O
computer-generated	O
imagery	O
of	O
objects	O
in	O
the	O
landscape	O
such	O
as	O
buildings	O
,	O
so	O
that	O
these	O
objects	O
change	O
in	O
perspective	B-Architecture
while	O
themselves	O
not	O
appearing	O
to	O
move	O
as	O
the	O
vehicle-borne	O
camera	O
goes	O
past	O
them	O
.	O
</s>
<s>
The	O
movement	O
of	O
a	O
kinematic	B-Application
chain	I-Application
,	O
whether	O
it	O
is	O
a	O
robot	O
or	O
an	O
animated	O
character	O
,	O
is	O
modeled	O
by	O
the	O
kinematics	O
equations	O
of	O
the	O
chain	O
.	O
</s>
<s>
Forward	O
kinematics	O
uses	O
the	O
joint	O
parameters	O
to	O
compute	O
the	O
configuration	O
of	O
the	O
chain	O
,	O
and	O
inverse	B-General_Concept
kinematics	I-General_Concept
reverses	O
this	O
calculation	O
to	O
determine	O
the	O
joint	O
parameters	O
that	O
achieve	O
a	O
desired	O
configuration	O
.	O
</s>
<s>
Inverse	B-General_Concept
kinematics	I-General_Concept
is	O
an	O
example	O
of	O
the	O
kinematic	O
analysis	O
of	O
a	O
constrained	O
system	O
of	O
rigid	O
bodies	O
,	O
or	O
kinematic	B-Application
chain	I-Application
.	O
</s>
<s>
While	O
analytical	O
solutions	O
to	O
the	O
inverse	B-General_Concept
kinematics	I-General_Concept
problem	O
exist	O
for	O
a	O
wide	O
range	O
of	O
kinematic	B-Application
chains	I-Application
,	O
computer	O
modeling	O
and	O
animation	O
tools	O
often	O
use	O
Newton	O
's	O
method	O
to	O
solve	O
the	O
non-linear	O
kinematics	O
equations	O
.	O
</s>
<s>
Inverse	B-General_Concept
kinematics	I-General_Concept
is	O
important	O
to	O
game	O
programming	O
and	O
3D	O
animation	O
,	O
where	O
it	O
is	O
used	O
to	O
connect	O
game	O
characters	O
physically	O
to	O
the	O
world	O
,	O
such	O
as	O
feet	O
landing	O
firmly	O
on	O
top	O
of	O
terrain	O
(	O
see	O
for	O
a	O
comprehensive	O
survey	O
on	O
)	O
.	O
</s>
<s>
An	O
animated	O
figure	O
is	O
modeled	O
with	O
a	O
skeleton	O
of	O
rigid	O
segments	O
connected	O
with	O
joints	O
,	O
called	O
a	O
kinematic	B-Application
chain	I-Application
.	O
</s>
<s>
The	O
inverse	B-General_Concept
kinematics	I-General_Concept
problem	O
computes	O
the	O
joint	O
angles	O
for	O
a	O
desired	O
pose	O
of	O
the	O
figure	O
.	O
</s>
<s>
Therefore	O
,	O
inverse	B-General_Concept
kinematics	I-General_Concept
is	O
used	O
in	O
computer-aided	O
design	O
systems	O
to	O
animate	O
assemblies	O
and	O
by	O
computer-based	O
artists	O
and	O
animators	O
to	O
position	O
figures	O
and	O
characters	O
.	O
</s>
<s>
Movement	O
of	O
one	O
element	O
requires	O
the	O
computation	O
of	O
the	O
joint	O
angles	O
for	O
the	O
other	O
elements	O
to	O
maintain	O
the	O
joint	B-Algorithm
constraints	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
inverse	B-General_Concept
kinematics	I-General_Concept
allows	O
an	O
artist	O
to	O
move	O
the	O
hand	O
of	O
a	O
3D	O
human	O
model	O
to	O
a	O
desired	O
position	O
and	O
orientation	O
and	O
have	O
an	O
algorithm	O
select	O
the	O
proper	O
angles	O
of	O
the	O
wrist	O
,	O
elbow	O
,	O
and	O
shoulder	O
joints	O
.	O
</s>
<s>
A	O
method	O
of	O
comparing	O
both	O
forward	O
and	O
inverse	B-General_Concept
kinematics	I-General_Concept
for	O
the	O
animation	O
of	O
a	O
character	O
can	O
be	O
defined	O
by	O
the	O
advantages	O
inherent	O
to	O
each	O
.	O
</s>
<s>
Modern	O
digital	O
creation	O
packages	O
(	O
DCC	O
)	O
offer	O
methods	O
to	O
apply	O
both	O
forward	O
and	O
inverse	B-General_Concept
kinematics	I-General_Concept
to	O
models	O
.	O
</s>
<s>
An	O
analytic	O
solution	O
to	O
an	O
inverse	B-General_Concept
kinematics	I-General_Concept
problem	O
is	O
a	O
closed-form	O
expression	O
that	O
takes	O
the	O
end-effector	O
pose	O
as	O
input	O
and	O
gives	O
joint	O
positions	O
as	O
output	O
,	O
.	O
</s>
<s>
Analytical	O
inverse	B-General_Concept
kinematics	I-General_Concept
solvers	O
can	O
be	O
significantly	O
faster	O
than	O
numerical	O
solvers	O
and	O
provide	O
more	O
than	O
one	O
solution	O
,	O
but	O
only	O
a	O
finite	O
number	O
of	O
solutions	O
,	O
for	O
a	O
given	O
end-effector	O
pose	O
.	O
</s>
<s>
Many	O
different	O
software	O
products	O
(	O
Such	O
as	O
FOSS	B-Application
programs	O
IKFast	O
and	O
)	O
are	O
able	O
to	O
solve	O
these	O
problems	O
quickly	O
and	O
efficiently	O
using	O
different	O
algorithms	O
such	O
as	O
the	O
FABRIK	O
solver	O
.	O
</s>
<s>
One	O
issue	O
with	O
these	O
solvers	O
,	O
is	O
that	O
they	O
are	O
known	O
to	O
not	O
necessarily	O
give	O
locally	O
smooth	O
solutions	O
between	O
two	O
adjacent	O
configurations	O
,	O
which	O
can	O
cause	O
instability	O
if	O
iterative	O
solutions	O
to	O
inverse	B-General_Concept
kinematics	I-General_Concept
are	O
required	O
,	O
such	O
as	O
if	O
the	O
IK	O
is	O
solved	O
inside	O
a	O
high-rate	O
control	O
loop	O
.	O
</s>
<s>
There	O
are	O
many	O
methods	O
of	O
modelling	O
and	O
solving	O
inverse	B-General_Concept
kinematics	I-General_Concept
problems	O
.	O
</s>
<s>
The	O
most	O
flexible	O
of	O
these	O
methods	O
typically	O
rely	O
on	O
iterative	B-Algorithm
optimization	I-Algorithm
to	O
seek	O
out	O
an	O
approximate	O
solution	O
,	O
due	O
to	O
the	O
difficulty	O
of	O
inverting	O
the	O
forward	O
kinematics	O
equation	O
and	O
the	O
possibility	O
of	O
an	O
empty	O
solution	O
space	O
.	O
</s>
<s>
The	O
Jacobian	O
inverse	O
technique	O
is	O
a	O
simple	O
yet	O
effective	O
way	O
of	O
implementing	O
inverse	B-General_Concept
kinematics	I-General_Concept
.	O
</s>
<s>
A	O
line	B-Algorithm
search	I-Algorithm
should	O
be	O
used	O
to	O
scale	O
this	O
to	O
an	O
acceptable	O
value	O
.	O
</s>
<s>
The	O
inverse	B-General_Concept
kinematics	I-General_Concept
problem	O
can	O
also	O
be	O
approximated	O
using	O
heuristic	O
methods	O
.	O
</s>
<s>
The	O
heuristic	O
algorithms	O
have	O
low	O
computational	O
cost	O
(	O
return	O
the	O
final	O
pose	O
very	O
quickly	O
)	O
,	O
and	O
usually	O
support	O
joint	B-Algorithm
constraints	I-Algorithm
.	O
</s>
