  We consider the problem of robotic planning under uncertainty. This problem
may be posed as a stochastic optimal control problem, complete solution to
which is fundamentally intractable owing to the infamous curse of
dimensionality. We report the results of an extensive simulation study in which
we have compared two methods, both of which aim to salvage tractability by
using alternative, albeit inexact, means for treating feedback. The first is a
recently proposed method based on a near-optimal "decoupling principle" for
tractable feedback design, wherein a nominal open-loop problem is solved,
followed by a linear feedback design around the open-loop. The second is Model
Predictive Control (MPC), a widely-employed method that uses repeated
re-computation of the nominal open-loop problem during execution to correct for
noise, though when interpreted as feedback, this can only said to be an
implicit form. We examine a much wider range of noise levels than have been
previously reported and empirical evidence suggests that the decoupling method
allows for tractable planning over a wide range of uncertainty conditions
without unduly sacrificing performance.
