Recursive Estimation of Rigid Body Motions
Final Report Abstract
Estimating rigid body motions plays a fundamental role in many applications. A rigid body motion includes both rotation and translation in 3D space, entails six degrees of freedom, and can be described by an element of the special Euclidean group SE(3), which inherently has a nonlinear and periodic group structure. Conventional esti- mation approaches work in a locally linearized space, which inherently limits their accuracy for large uncertainties and fast motions. This project established a unified on-manifold Bayesian filtering paradigm for topology-adaptive rigid body motion estimation based on unit dual quaternions with the following key contributions. • Parametric on-manifold filtering schemes were developed using directional statistics. Manually configurable deterministic samples and progressive filtering methods were proposed for enhanced estimation performance.• A novel parametric method for modeling uncertain unit dual quaternions was proposed. It allows probabilistic interpretation of correlated rotations and translations and served as the basis for a unit dual quaternion filter proposed for SE(3) estimation. • Novel grid-based quaternion filtering schemes were established for nonlinear SO(3) estimation in a non-parametric manner. • Unscented particle filtering schemes were established on the manifold of quaternions and dual quaternions for nonlinear SO(3) and SE(3) estimations, respectively. • A novel sample reduction approach was proposed that adapts to the manifold of dual quaternions. The proposed paradigm is innovative, self-contained, and provides a solid theoretical foundation for practical rigid body estimation.
Publications
- Nonlinear Progressive Filtering for SE(2) Estimation. In Proceedings of the 21st International Conference on Information Fusion (Fusion 2018), Cambridge, United Kingdom, July 2018
Li, Kailai, Gerhard Kurz, Lukas Bernreiter and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/ICIF.2018.8455231) - Simultaneous Localization and Mapping Using a Novel Dual Quaternion Particle Filter. In Proceedings of the 21st International Conference on Information Fusion (Fusion 2018), Cambridge, United Kingdom, July 2018
Li, Kailai, Gerhard Kurz, Lukas Bernreiter and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/ICIF.2018.8455347) - Geometry-Driven Deterministic Sampling for Nonlinear Bingham Filtering. In Proceedings of the 2019 European Control Conference (ECC 2019), Naples, Italy, June 2019
Li, Kailai, Daniel Frisch, Benjamin Noack and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/ECC.2019.8796102) - Geometry-Driven Stochastic Modeling of SE(3) States Based on Dual Quaternion Representation. In Proceedings Intelligent of the 2019 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2019), Taipei, Republic of China, May 2019
Li, Kailai, Florian Pfaff and Uwe D. Hanebeck
(See online at https://doi.org/10.1109/ICPHYS.2019.8780254) - Dual Quaternion Sample Reduction for SE(2) Estimation. In Proceedings of the 23rd International Conference on Information Fusion (Fusion 2020), Virtual, July 2020
Li, Kailai, Florian Pfaff and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/FUSION45008.2020.9190388) - Grid-Based Quaternion Filter for SO(3) Estimation. In Proceedings of the 2020 European Control Conference (ECC 2020), Virtual, May 2020
Li, Kailai, Florian Pfaff and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/ECC51009.2020.9143723) - Unscented Dual Quaternion Particle Filter for SE(3) Estimation. IEEE Control Systems Letters, 5(2):647–652, April 2021
Li, Kailai, Florian Pfaff and Uwe D. Hanebeck
(See online at https://doi.org/10.1109/LCSYS.2020.3005066)
