<s>
In	O
robotics	O
and	O
motion	O
planning	O
,	O
kinodynamic	B-Application
planning	I-Application
is	O
a	O
class	O
of	O
problems	O
for	O
which	O
velocity	O
,	O
acceleration	O
,	O
and	O
force/torque	O
bounds	O
must	O
be	O
satisfied	O
,	O
together	O
with	O
kinematic	O
constraints	O
such	O
as	O
avoiding	O
obstacles	O
.	O
</s>
<s>
developed	O
the	O
first	O
polynomial-time	B-Algorithm
approximation	I-Algorithm
schemes	I-Algorithm
(	O
PTAS	O
)	O
for	O
the	O
problem	O
.	O
</s>
<s>
More	O
recently	O
,	O
many	O
practical	O
heuristic	B-Algorithm
algorithms	I-Algorithm
based	O
on	O
stochastic	O
optimization	O
and	O
iterative	O
sampling	O
were	O
developed	O
,	O
by	O
a	O
wide	O
range	O
of	O
authors	O
,	O
to	O
address	O
the	O
kinodynamic	B-Application
planning	I-Application
problem	O
.	O
</s>
<s>
These	O
techniques	O
for	O
kinodynamic	B-Application
planning	I-Application
have	O
been	O
shown	O
to	O
work	O
well	O
in	O
practice	O
.	O
</s>
<s>
However	O
,	O
none	O
of	O
these	O
heuristic	B-Algorithm
techniques	O
can	O
guarantee	O
the	O
optimality	O
of	O
the	O
computed	O
solution	O
(	O
i.e.	O
,	O
they	O
have	O
no	O
performance	O
guarantees	O
)	O
,	O
and	O
none	O
can	O
be	O
mathematically	O
proven	O
to	O
be	O
faster	O
than	O
the	O
original	O
PTAS	O
algorithms	O
(	O
i.e.	O
,	O
none	O
have	O
a	O
provably	O
lower	O
computational	O
complexity	O
)	O
.	O
</s>
