<s>
A	O
rapidly	B-General_Concept
exploring	I-General_Concept
random	I-General_Concept
tree	I-General_Concept
(	O
RRT	O
)	O
is	O
an	O
algorithm	O
designed	O
to	O
efficiently	O
search	O
nonconvex	O
,	O
high-dimensional	O
spaces	O
by	O
randomly	O
building	O
a	O
space-filling	B-Algorithm
tree	I-Algorithm
.	O
</s>
<s>
They	O
easily	O
handle	O
problems	O
with	O
obstacles	O
and	O
differential	O
constraints	O
(	O
nonholonomic	O
and	O
kinodynamic	B-Application
)	O
and	O
have	O
been	O
widely	O
used	O
in	O
autonomous	O
robotic	O
motion	O
planning	O
.	O
</s>
<s>
An	O
RRT	O
can	O
also	O
be	O
considered	O
as	O
a	O
Monte-Carlo	B-Algorithm
method	I-Algorithm
to	O
bias	O
search	O
into	O
the	O
largest	O
Voronoi	B-Architecture
regions	I-Architecture
of	O
a	O
graph	O
in	O
a	O
configuration	O
space	O
.	O
</s>
<s>
Some	O
variations	O
can	O
even	O
be	O
considered	O
stochastic	O
fractals	B-Application
.	O
</s>
<s>
With	O
uniform	O
sampling	O
of	O
the	O
search	O
space	O
,	O
the	O
probability	O
of	O
expanding	O
an	O
existing	O
state	O
is	O
proportional	O
to	O
the	O
size	O
of	O
its	O
Voronoi	B-Architecture
region	I-Architecture
.	O
</s>
<s>
As	O
the	O
largest	O
Voronoi	B-Architecture
regions	I-Architecture
belong	O
to	O
the	O
states	O
on	O
the	O
frontier	O
of	O
the	O
search	O
,	O
this	O
means	O
that	O
the	O
tree	O
preferentially	O
expands	O
towards	O
large	O
unsearched	O
areas	O
.	O
</s>
<s>
For	O
a	O
general	O
configuration	O
space	O
C	O
,	O
the	O
algorithm	O
in	O
pseudocode	B-Language
is	O
as	O
follows	O
:	O
</s>
<s>
RRT	O
,	O
a	O
family	O
of	O
RRT-based	O
planners	O
aiming	O
to	O
generate	O
solutions	O
for	O
high-dimensional	O
systems	O
in	O
real-time	B-General_Concept
,	O
by	O
progressively	O
searching	O
in	O
lower-dimensional	O
subspaces	O
.	O
</s>
