<s>
Any-angle	B-General_Concept
path	I-General_Concept
planning	I-General_Concept
algorithms	O
are	O
pathfinding	B-Algorithm
algorithms	O
that	O
search	O
for	O
a	O
Euclidean	O
shortest	O
path	O
between	O
two	O
points	O
on	O
a	O
grid	O
map	O
while	O
allowing	O
the	O
turns	O
in	O
the	O
path	O
to	O
have	O
any	O
angle	O
.	O
</s>
<s>
More	O
traditional	O
pathfinding	B-Algorithm
algorithms	O
such	O
as	O
A*	B-Protocol
either	O
lack	O
in	O
performance	O
or	O
produce	O
jagged	O
,	O
indirect	O
paths	O
.	O
</s>
<s>
A*	B-Protocol
with	O
an	O
8-connected	O
discrete	O
grid	O
graph	O
(	O
2D	O
;	O
26	O
for	O
the	O
3D	O
triple	O
cubic	O
graph	O
)	O
is	O
very	O
fast	O
,	O
but	O
only	O
looks	O
at	O
paths	O
in	O
45-degree	O
increments	O
.	O
</s>
<s>
The	O
advantage	O
is	O
that	O
all	O
optimizations	O
of	O
grid	O
A*	B-Protocol
like	O
jump	B-Algorithm
point	I-Algorithm
search	I-Algorithm
will	O
apply	O
.	O
</s>
<s>
A	O
visibility	O
graph	O
with	O
all	O
the	O
grid	O
points	O
can	O
be	O
searched	O
with	O
A*	B-Protocol
for	O
the	O
optimal	O
solution	O
in	O
2D	O
space	O
.	O
</s>
<s>
An	O
any-angle	B-General_Concept
path	I-General_Concept
planning	I-General_Concept
algorithm	O
aims	O
to	O
produce	O
optimal	O
or	O
near-optimal	O
solutions	O
while	O
taking	O
less	O
time	O
than	O
the	O
basic	O
visibility	O
graph	O
approach	O
.	O
</s>
<s>
So	O
far	O
,	O
five	O
main	O
any-angle	B-General_Concept
path	I-General_Concept
planning	I-General_Concept
algorithms	O
that	O
are	O
based	O
on	O
the	O
heuristic	O
search	O
algorithm	O
A*	B-Protocol
have	O
been	O
developed	O
,	O
all	O
of	O
which	O
propagate	O
information	O
along	O
grid	O
edges	O
:	O
</s>
<s>
Field	B-General_Concept
D*	I-General_Concept
(	O
FD*	O
)	O
and	O
3D	O
Field	B-General_Concept
D*	I-General_Concept
-	O
Dynamic	O
pathfinding	B-Algorithm
algorithms	O
based	O
on	O
D*	O
that	O
use	O
interpolation	O
during	O
each	O
vertex	O
expansion	O
and	O
find	O
near-optimal	O
paths	O
through	O
regular	O
,	O
nonuniform	O
cost	O
grids	O
.	O
</s>
<s>
Field	B-General_Concept
D*	I-General_Concept
therefore	O
tries	O
to	O
solve	O
the	O
weighted	O
region	O
problem	O
and	O
3D	O
Field	B-General_Concept
D*	I-General_Concept
the	O
corresponding	O
three-dimensional	O
problem	O
.	O
</s>
<s>
Multi-resolution	O
Field	B-General_Concept
D*	I-General_Concept
–	O
Extension	O
of	O
Field	B-General_Concept
D*	I-General_Concept
for	O
multi-resolution	O
grids	O
.	O
</s>
<s>
Theta*	B-Algorithm
-	O
Uses	O
the	O
same	O
main	O
loop	O
as	O
A*	B-Protocol
,	O
but	O
for	O
each	O
expansion	O
of	O
a	O
vertex	O
,	O
there	O
is	O
a	O
line-of-sight	O
check	O
between	O
and	O
the	O
successor	O
of	O
,	O
.	O
</s>
<s>
AP	O
Theta*	B-Algorithm
is	O
an	O
optimization	O
of	O
Theta*	B-Algorithm
that	O
uses	O
angle-propagation	O
to	O
decrease	O
the	O
cost	O
of	O
performing	O
line-of-sight	O
calculations	O
to	O
.	O
</s>
<s>
Lazy	O
Theta*	B-Algorithm
is	O
another	O
optimization	O
of	O
Theta*	B-Algorithm
that	O
uses	O
lazy	O
evaluation	O
to	O
reduce	O
the	O
number	O
of	O
line-of-sight	O
calculations	O
by	O
delaying	O
the	O
line-of-sight	O
calculations	O
for	O
each	O
node	O
from	O
when	O
it	O
is	O
explored	O
to	O
when	O
it	O
is	O
expanded	O
.	O
</s>
<s>
Incremental	B-Algorithm
Phi*	O
is	O
an	O
incremental	B-Algorithm
,	O
more	O
efficient	O
variant	O
of	O
Theta*	B-Algorithm
designed	O
for	O
unknown	O
2D	O
environments	O
.	O
</s>
<s>
Strict	O
Theta*	B-Algorithm
and	O
Recursive	O
Strict	O
Theta*	B-Algorithm
improves	O
Theta*	B-Algorithm
by	O
restricting	O
the	O
search	O
space	O
to	O
Taut	O
Paths	O
introduced	O
by	O
ANYA	O
.	O
</s>
<s>
Like	O
Theta*	B-Algorithm
,	O
This	O
is	O
an	O
algorithm	O
that	O
returns	O
near-optimal	O
paths	O
.	O
</s>
<s>
Block	B-General_Concept
A*	I-General_Concept
-	O
Generates	O
a	O
local	O
distance	O
database	O
containing	O
all	O
possible	O
paths	O
on	O
a	O
small	O
section	O
of	O
the	O
grid	O
.	O
</s>
<s>
There	O
are	O
also	O
A*	B-Protocol
-based	O
algorithm	O
distinct	O
from	O
the	O
above	O
family	O
:	O
</s>
<s>
Hybrid	O
A*	B-Protocol
is	O
an	O
extension	O
of	O
A*	B-Protocol
that	O
considers	O
two	O
additional	O
dimension	O
representing	O
vehicle	O
state	O
,	O
so	O
that	O
the	O
paths	O
are	O
actually	O
possible	O
.	O
</s>
<s>
Besides	O
,	O
for	O
search	O
in	O
high-dimensional	O
search	O
spaces	O
,	O
such	O
as	O
when	O
the	O
configuration	O
space	O
of	O
the	O
system	O
involves	O
many	O
degrees	O
of	O
freedom	O
that	O
need	O
to	O
be	O
considered	O
(	O
see	O
Motion	O
planning	O
)	O
,	O
and/or	O
momentum	B-Algorithm
needs	O
to	O
be	O
considered	O
(	O
which	O
could	O
effectively	O
double	O
the	O
number	O
of	O
dimensions	O
of	O
the	O
search	O
space	O
;	O
this	O
larger	O
space	O
including	O
momentum	B-Algorithm
is	O
known	O
as	O
the	O
phase	O
space	O
)	O
,	O
variants	O
of	O
the	O
rapidly-exploring	B-General_Concept
random	I-General_Concept
tree	I-General_Concept
(	O
RRT	O
)	O
have	O
been	O
developed	O
that	O
(	O
almost	O
surely	O
)	O
converge	O
to	O
the	O
optimal	O
path	O
by	O
increasingly	O
finding	O
shorter	O
and	O
shorter	O
paths	O
:	O
</s>
<s>
Informed	O
RRT*	O
improves	O
the	O
convergence	O
speed	O
of	O
RRT*	O
by	O
introducing	O
a	O
heuristic	O
,	O
similar	O
to	O
the	O
way	O
in	O
which	O
A*	B-Protocol
improves	O
upon	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Any-angle	B-General_Concept
path	I-General_Concept
planning	I-General_Concept
are	O
useful	O
for	O
robot	B-General_Concept
navigation	I-General_Concept
and	O
real-time	O
strategy	O
games	O
where	O
more	O
optimal	O
paths	O
are	O
desirable	O
.	O
</s>
<s>
Hybrid	O
A*	B-Protocol
,	O
for	O
example	O
,	O
was	O
used	O
as	O
an	O
entry	O
to	O
a	O
DARPA	O
challenge	O
.	O
</s>
