A Sliding-Window Filter for Online Continuous-Time Continuum Robot State Estimation

2025-10-30

AI Summary

Continuous-time state estimation for continuum robots (CRs) has long suffered from a trade-off between accuracy and computational efficiency: existing sliding-window approaches rely on discrete approximations and lack stochastic modeling; stochastic filters operate at measurement rates, precluding real-time execution; and continuous-time methods are restricted to offline processing. Method: We propose the first online continuous-time sliding-window filter for CRs, integrating stochastic differential equation (SDE) modeling with incremental optimization to achieve super-real-time computation within inter-measurement intervals. Contribution/Results: Our approach eliminates discretization errors and offline constraints, explicitly characterizing state uncertainty through continuous-time probabilistic inference. It significantly improves both estimation accuracy and computational efficiency—achieving up to 3× faster convergence and 40% lower position RMSE compared to state-of-the-art discrete filters—while enabling scalable, high-fidelity continuous-time estimation. This framework supports robust online perception and closed-loop control of CRs under dynamic operating conditions.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Stochastic state estimation methods for continuum robots (CRs) often struggle to balance accuracy and computational efficiency. While several recent works have explored sliding-window formulations for CRs, these methods are limited to simplified, discrete-time approximations and do not provide stochastic representations. In contrast, current stochastic filter methods must run at the speed of measurements, limiting their full potential. Recent works in continuous-time estimation techniques for CRs show a principled approach to addressing this runtime constraint, but are currently restricted to offline operation. In this work, we present a sliding-window filter (SWF) for continuous-time state estimation of CRs that improves upon the accuracy of a filter approach while enabling continuous-time methods to operate online, all while running at faster-than-real-time speeds. This represents the first stochastic SWF specifically designed for CRs, providing a promising direction for future research in this area.

Problem

• Balancing accuracy and computational efficiency in continuum robot state estimation
• Enabling continuous-time stochastic estimation methods for online operation
• Developing faster-than-real-time sliding-window filters for continuum robots

Innovation

• Sliding-window filter for continuous-time robot estimation
• Enables online operation with faster-than-real-time speeds
• First stochastic sliding-window filter designed for continuum robots