A Modal-Space Formulation for Momentum Observer Contact Estimation and Effects of Uncertainty for Continuum Robots

TL;DR

This work addresses dynamic contact estimation for continuum robots with variable curvature by extending the generalized momentum observer (GMO) to a modal-space representation of curvature and combining it with real-time shape sensing. It introduces a modal-space dynamics model, a constrained wrench-estimation framework, and an uncertainty analysis to characterize reachability and detectability under state errors, validating the approach with simulations and experiments that compare GMO to the joint force/torque deviation (JFD) method. Major contributions include the modal-space GMO formulation, a constrained optimization-based wrench estimator, and a first exploration of state-uncertainty effects on estimation performance, plus a preliminary extension to multi-segment robots. The results show improved robustness to sensor noise and state uncertainty in the x-direction and demonstrate practical potential for safe human-robot collaboration in large-scale continuum robots, with implications for active safety in ISCRs.

Abstract

Contact detection for continuum and soft robots has been limited in past works to statics or kinematics-based methods with assumed circular bending curvature or known bending profiles. In this paper, we adapt the generalized momentum observer contact estimation method to continuum robots. This is made possible by leveraging recent results for real-time shape sensing of continuum robots along with a modal-space representation of the robot dynamics. In addition to presenting an approach for estimating the generalized forces due to contact via a momentum observer, we present a constrained optimization method to identify the wrench imparted on the robot during contact. We also present an approach for investigating the effects of unmodeled deviations in the robot's dynamic state on the contact detection method and we validate our algorithm by simulations and experiments. We also compare the performance of the momentum observer to the joint force deviation method, a direct estimation approach using the robot's full dynamic model. We also demonstrate a basic extension of the method to multisegment continuum robots. Results presented in this work extend dynamic contact detection to the domain of continuum and soft robots and can be used to improve the safety of large-scale continuum robots for human-robot collaboration.

Figures (13)

• Figure 1: A collaborative robot for cooperative manipulation in confined spaces using continuum segments. Contact detection and wrench estimation is a key component of ensuring worker safety during human-robot interaction. Robot sensory skin as described in Abah2022_sensor_disk
• Figure 2: (a) Actuation tendons and passive shape sensing strings whose lengths are used to calculate $\mathbf{c}$. The figure is reproduced with permission from Orekhov2023_shape_sensing.(b) Cross section of the robot showing the backbone arc length coordinate $s$, the local backbone frame $\{T(s)\}$, and the robot base frame $\{T(0)\}$.
• Figure 3: Continuum robot actuation unit: Motor with rotor inertia $J_{m}$, gearhead with inertia $J_{gh}$ and reduction ratio $R_{gh}$, pinion with inertia $J_p$ about the center of rotation, gear with inertia $J_g$ about the center of rotation, shaft and capstan with combined inertia $J_c$. The gear and pinion have a reduction ratio of $R_{gp}$.
• Figure 4: Continuum segment cross section showing the terms used to calculate the joint friction
• Figure 5: Simulated vs. measured continuum segment tip positions after calibration: Experimental tip $x$ position, simulated tip $x$ position, experimental tip $y$ position, simulated tip $y$ position, experimental tip $z$, simulated tip $z$ position.