Uncertainty Quantification of Set-Membership Estimation in Control and Perception: Revisiting the Minimum Enclosing Ellipsoid

Autor:	Tang, Yukai, Lasserre, Jean-Bernard, Yang, Heng
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Computer Science - Robotics
Druh dokumentu:	Working Paper
Popis:	Set-membership estimation (SME) outputs a set estimator that guarantees to cover the groundtruth. Such sets are, however, defined by (many) abstract (and potentially nonconvex) constraints and therefore difficult to manipulate. We present tractable algorithms to compute simple and tight overapproximations of SME in the form of minimum enclosing ellipsoids (MEE). We first introduce the hierarchy of enclosing ellipsoids proposed by Nie and Demmel (2005), based on sums-of-squares relaxations, that asymptotically converge to the MEE of a basic semialgebraic set. This framework, however, struggles in modern control and perception problems due to computational challenges. We contribute three computational enhancements to make this framework practical, namely constraints pruning, generalized relaxed Chebyshev center, and handling non-Euclidean geometry. We showcase numerical examples on system identification and object pose estimation. Comment: Accepted to 6th Learning for Dynamics and Control (L4DC) as oral presentation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.15962 Zobrazit plný text záznamu View this record from Arxiv