Decoupling stochastic optimal control problems for efficient solution: insights from experiments across a wide range of noise regimes

TL;DR

This paper extends a decoupling approach for stochastic optimal control in robotic planning, enabling efficient solutions across diverse noise regimes by combining open-loop planning with feedback design, maintaining near-optimal performance.

Contribution

It generalizes a decoupling principle to handle a broader spectrum of noise levels, improving tractability and robustness in stochastic robotic planning.

Findings

Decoupling approach remains effective across various noise regimes.

Near-optimal performance is maintained with the extended method.

Empirical results validate the approach's robustness and efficiency.

Abstract

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.