Screw-based feature constraint model and degeneracy analysis for robotic state estimation: Theory and experiments

Degeneracy caused by the repetition of geometric features remains a significant bottleneck in robotic state estimation systems like odometry and SLAM. To address this challenge, we propose a novel approach based on screw theory to model feature constraints and analyze degeneracy. Unlike conventional methods, our approach derives feature constraint representations via geometric operations rather than by derivative computations, and decouples the cost-function formulation, yielding a more robust and interpretable framework. Initially, a feature constraint model is formulated using the screw representation. Subsequently, a degeneracy analysis model and a judgment formula are presented, both grounded in screw theory and the feature constraint model. The proposed model inherently separates translational and helical degeneracy while accurately estimating environmental parameters, such as the position and pitch of the rotation axis, to reduce assessment errors, enable outlier rejection, and improve the robustness of degeneracy detection. A novel feature extraction and management method is proposed to improve computation efficiency and coverage of the feature in sparsely scanned scenarios. Simulations and real-world experiments show that our approach improves the robustness and accuracy of degeneracy detection while reducing the computation time by more than 70%. A dimensionless stability metric for the judgment formula is proposed, showing that our approach significantly outperforms existing state-of-the-art (SOTA) approaches by more than two orders of magnitude. To date, this study constitutes the first formal endeavor to conceptualize and systematically analyze the problem of helical degeneracy, providing a novel and rigorous perspective on the inherent challenges of robotic state estimation.