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Recursive Estimation of Rigid Body Motions

Subject Area Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
Term from 2016 to 2020
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 325035548
 
Final Report Year 2020

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.

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