LIF-M: A Manifold-Based Approach for 3D Robot Localization in Unstructured Environments

Abstract

Accurate localization of robots in unstructured environments poses challenges due to low localization accuracy and local trajectory oscillation caused by complex feature points when using Euclidean-based filtering methods. In this study, we propose a novel 3D robot localization method named LIF-M that leverages a manifold-based approach in conjunction with an unscented Kalman filter (UKF-M). Additionally, a relocalization algorithm is designed to ensure localization stability. The proposed method addresses the limitations of conventional Euclidean-based filtering methods by incorporating manifold-based techniques, providing a more comprehensive representation of the complex geometric features. We introduce the manifold concept, where the relevant definition is defined and utilized within the LIF-M framework. By combining left and right invariants, we effectively reduce noise uncertainty, resulting in improved localization accuracy. Moreover, we employ sigma points as a matrix representation of the state points’ space in order to seamlessly transition between the matrix space and the vector representation of the tangent space. Experimental tests and error calculations were conducted to evaluate the performance of various algorithm frameworks, and the results demonstrated the importance of the manifold-based approach for accurate attitude estimation. Compared to the standard UKF, the manifold space equips LIF-M with better robustness and stability in unstructured environments.