Fast Continuum Robot Shape and External Load State Estimation on SE(3)

2026-01-08

arXiv.org

AI Summary

This work addresses the challenge that existing continuum robot state estimation methods struggle to simultaneously model actuation inputs and external loads while lacking a unified spatiotemporal state representation. We propose the first general framework on the SE(3) manifold that jointly fuses tendon tensions, external wrenches, boundary conditions, and arbitrary backbone measurement uncertainties, enabling spatiotemporal state estimation through temporal priors. Leveraging a discrete Cosserat rod model, we formulate the problem as a factor graph and solve it efficiently via batch sparse nonlinear optimization. Simulations demonstrate real-time kinematic and distributed load estimation for tendon-driven robots, while experiments on a concentric tube surgical robot achieve high-accuracy end-effector force and shape estimation, highlighting its potential for surgical palpation.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Previous on-manifold approaches to continuum robot state estimation have typically adopted simplified Cosserat rod models, which cannot directly account for actuation inputs or external loads. We introduce a general framework that incorporates uncertainty models for actuation (e.g., tendon tensions), applied forces and moments, process noise, boundary conditions, and arbitrary backbone measurements. By adding temporal priors across time steps, our method additionally performs joint estimation in both the spatial (arclength) and temporal domains, enabling full \textit{spacetime} state estimation. Discretizing the arclength domain yields a factor graph representation of the continuum robot model, which can be exploited for fast batch sparse nonlinear optimization in the style of SLAM. The framework is general and applies to a broad class of continuum robots; as illustrative cases, we show (i) tendon-driven robots in simulation, where we demonstrate real-time kinematics with uncertainty, tip force sensing from position feedback, and distributed load estimation from backbone strain, and (ii) a surgical concentric tube robot in experiment, where we validate accurate kinematics and tip force estimation, highlighting potential for surgical palpation.

Problem

• continuum robot
• state estimation
• external load
• SE(3)
• Cosserat rod

Innovation

• continuum robot
• state estimation on SE(3)
• spacetime estimation
• factor graph optimization
• external load sensing