An Overview of the Burer-Monteiro Method for Certifiable Robot Perception

TL;DR

This paper reviews the Burer-Monteiro method's application in certifiable robot perception, highlighting its efficiency in solving semidefinite relaxations for global optimization, and provides practical guidance for practitioners.

Contribution

It consolidates existing literature on BM in perception, clarifies the role of LICQ, and shares practical insights for real-time certifiable perception applications.

Findings

BM reduces computational costs in semidefinite programming

LICQ is crucial for certifiable perception methods

Practical considerations improve BM implementation in robotics

Abstract

This paper presents an overview of the Burer-Monteiro method (BM), a technique that has been applied to solve robot perception problems to certifiable optimality in real-time. BM is often used to solve semidefinite programming relaxations, which can be used to perform global optimization for non-convex perception problems. Specifically, BM leverages the low-rank structure of typical semidefinite programs to dramatically reduce the computational cost of performing optimization. This paper discusses BM in certifiable perception, with three main objectives: (i) to consolidate information from the literature into a unified presentation, (ii) to elucidate the role of the linear independence constraint qualification (LICQ), a concept not yet well-covered in certifiable perception literature, and (iii) to share practical considerations that are discussed among practitioners but not thoroughly covered in the literature. Our general aim is to offer a practical primer for applying BM towards certifiable perception.