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

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.