  We consider the problem of robotic planning under uncertainty in this paper.
This problem may be posed as a stochastic optimal control problem, a solution
to which is fundamentally intractable owing to the infamous "curse of
dimensionality". Hence, we consider the extension of a "decoupling principle"
that was recently proposed by some of the authors, wherein a nominal open-loop
problem is solved followed by a linear feedback design around the open-loop,
and which was shown to be near-optimal to second order in terms of a "small
noise" parameter, to a much wider range of noise levels. Our empirical evidence
suggests that this allows for tractable planning over a wide range of
uncertainty conditions without unduly sacrificing performance.
