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

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... 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.