A Practical SVD-based Ellipsoid Estimation Method for Active Modeling of Robotic Ureteroscope

Instead of the Kalman-type filters requiring strict assumption on noise distributions, the extended set membership filter (ESMF) only assumes unknown but bounded (UBB) noises, therefore is more practical and applicable for the active modeling of robotic ureteroscope. However, the ESMF calculation needs the ellipsoid analysis that usually suffers from numerical instability, especially during the real-time processing of sensory measurements, and may further result in the divergence of the whole control system. In this paper, we propose the singular value decomposition for ESMF to handle this problem. The ESMF is firstly introduced as a preknowledge. Then, a singular value decomposition-based extended set membership filtering algorithm (SVD-ESMF) is constructed based on the sequential processing technique. Finally, we verify the performance of the proposed algorithm combined with the active modeling method on a self-built robotic flexible ureteroscope platform. Compared with the normal ESMF algorithm, the SVD-ESMF successfully eliminates the influence of unstable points and guarantees the confidence of the estimated bounds.