A Near-Optimal Separation Principle for Nonlinear Stochastic Systems Arising in Robotic Path Planning and Control

TL;DR

This paper introduces a near-optimal separation principle for nonlinear stochastic systems in robotic path planning, enabling tractable control design by combining open-loop trajectory optimization with feedback control under small noise assumptions.

Contribution

It proposes a novel separation principle for nonlinear stochastic systems that simplifies control design while maintaining near-optimal performance, diverging from traditional estimation-control separation.

Findings

Provides a tractable control design approach with quantifiable near-optimality.

Derives a trajectory-optimized linear quadratic regulator for stochastic nonlinear systems.

Validates the separation principle under small noise assumptions.

Abstract

We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which yields a tractable design that is quantifiably near-optimal. We exhibit a "separation" principle under a small noise assumption consisting of the optimal open-loop design of nominal trajectory followed by an optimal feedback law to track this trajectory, which is different from the usual effort of separating estimation from control. As a corollary, we obtain a trajectory-optimized linear quadratic regulator design for stochastic nonlinear systems with Gaussian noise.