Statistical Linearization for Robust Motion Planning

TL;DR

This paper introduces a statistical linearization approach to simplify robust motion planning under uncertainties, transforming it into a deterministic problem with constraints, and demonstrates its effectiveness through space vehicle descent simulations.

Contribution

The paper presents a novel application of statistical linearization to reformulate robust motion planning as a deterministic control problem with error estimates and controllability analysis.

Findings

Efficient deterministic reformulation of robust motion planning.

Error bounds and controllability results established.

Successful numerical experiments on space vehicle descent.

Abstract

The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal control has enabled particularly accurate formulations of the problem. Nevertheless, despite interesting progresses, these problem formulations still require expensive numerical computations. In this paper, we start bridging this gap by leveraging statistical linearization. Specifically, through statistical linearization we reformulate the robust motion planning problem as a simpler deterministic optimal control problem subject to additional constraints. We rigorously justify our method by providing estimates of the approximation error, as well as some controllability results for the new constrained deterministic formulation. Finally, we apply our method to the powered descent of a space vehicle, showcasing the consistency and efficiency of our approach through numerical experiments.