Continuum Robot Shape Estimation

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16 papers4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Sep 30, 2026

Magnetic based In-situ Self 3D Pose Estimation for a Modular Soft Tendon-Driven Continuum Robot via IMU-Fusion

Continuum robots are well suited for gentle manipulation because of their inherent compliance and ability to adapt to complex environments. However, their continuously deformable structure makes accurate configuration estimation challenging, particularly when external vision systems are unavailable or obstructed. In this work, we present an embedded pose sensing framework that combines inertial measurement units (IMUs) and active magnetic fields to estimate the robot configuration without relying on external cameras. The angular measurements from the IMU and magnetic-field references are fused to improve local orientation estimation and reduce accumulated orientation error during operation. This pose sensing scheme achieves an update rate of 16.7~Hz, allowing real-time feedback. The proposed system is experimentally validated through closed-loop control, where the estimated robot configuration is used to maintain the end-effector at a desired position while interacting with an object. These results demonstrate the potential of distributed magnetic--inertial sensing for real-time pose estimation and closed-loop control of continuum robots.

Zheng Cao, Guo Ning Sue, Xiangyun Bu +3

Carnegie Mellon University

Continuum Robot Control Robot State Estimation Continuum Robot Shape Estimation Soft Robotics Multimodal Sensor Fusion

Sep 24, 2026

Reduced Cartesian Kinetostatics for Tendon-Driven Continuum Robots: Residual-Stabilized Full-Shape Propagation

Many planning and control tasks for tendon-driven continuum robots (TDCRs) require the complete Cartesian backbone geometry. We present a reduced Cartesian framework for planar, axially compressible TDCRs that propagates equilibrium configurations along prescribed tendon-force and tendon-displacement trajectories. The backbone is represented by two global position fields. Following exact variation, a Taylor-Galerkin reduction condenses prescribed spatial properties and distributed loads into offline moment vectors, yielding analytic reduced residuals and Jacobians without online spatial quadrature or numerical differentiation. Analytical differentiation and residual correction yield first-order rate systems requiring one fixed-dimensional linear solve per rate evaluation after initial equilibrium alignment on a regular branch. Across four simulated cases covering variable tendon routing, nonuniform geometry, axial compression, and their combined effects, the propagated Cartesian shapes and distributed strains closely match pointwise geometrically variable-strain (GVS) equilibrium solutions. Residual correction suppresses propagation drift across the tested step sizes while adding only about 0.98% to the mean update time of uncorrected Euler. The proposed method requires 0.508 ms per update on average, approximately 11 times faster than pointwise GVS solves. Displacement-driven experiments yield a maximum normalized mean backbone position error of 1.02% and a maximum end-effector position error of 0.28%. These results support efficient and accurate Cartesian full-shape prediction along prescribed actuation paths.

Ke Wu, Fangju Yang, Xiaohui Zhang +3

Continuum Robot Shape Estimation Continuum Robot Control Tendon-Driven Actuation Reduced-Order Modeling

Sep 21, 2026

Estimation and Control of Tensegrity Manipulator Kinematics based on Strut Inclination Angles

Unlike conventional rigid-link robots defined by discrete joints, continuum robots pose a fundamental challenge for expressing their complex continuous bending configurations for closed-loop control. Several modelling approaches have been proposed for conventional continuum robots, but tensegrity-based continuum robots remain largely open. Moreover, many of these approaches assume a continuous elastic backbone and are therefore not directly applicable to tensegrity manipulators, whose bodies are networks of rigid struts and tensioned cables. This work presents a reduced-order model for shape and posture control of a tensegrity-based continuum manipulator. The manipulator is modelled as a serially connected parallel-link mechanism. The proposed method is formulated as an optimization problem that uses geometric constraints of the tensegrity structure together with information from the Inertial Measurement Unit (IMU) sensors embedded in the strut elements. To the best of our knowledge, this work presents the first experimental demonstration of a real-time IMU-based shape estimation method on a full-scale tensegrity manipulator and demonstrates posture control using a simple Proportional-Integral (PI) controller. The results show that the proposed method can estimate the shape of both single-module tensegrity structures and multi-module tensegrity manipulators from arbitrary static configurations and achieve desired postures.

Tufail Ahmad Bhat, Shuhei Ikemoto

Kyushu Institute of Technology, Japan

Robotic Control Tensegrity Robotics Robotics Continuum Robot Control Robot State Estimation Continuum Robot Shape Estimation

Sep 14, 2026

Tendon-Driven Continuum Robot with Modular Stiffness and In-Situ Self Pose Estimation

Continuum robots enable smooth shape morphing and safe interaction in confined environments. However, most existing systems are task-specific and depend on external sensing infrastructure, limiting their adaptability and real-world deployment. This paper presents a self-contained modular continuum robotic platform that combines mechanical reconfigurability with onboard pose estimation. The robot is constructed from interchangeable continuum joints with analytically precomputed stiffness, allowing rapid assembly and direct programming of the robot shape. Proprioceptive sensing is achieved using magnetic sensors and a modular learning-based framework, where a single model is trained per joint and reused across configurations. The system is experimentally validated in real world, demonstrating self-sensing capabilities and adaptation without external tracking.

Guo Ning Sue, Zheng Cao, Junzhe Hu +5

Carnegie Mellon University

Modular Robotics Robotics Robot State Estimation Robotic Perception Continuum Robot Design Continuum Robot Shape Estimation

Aug 26, 2026

Constraint-Aware Physics-Informed Neural Networks for Static Shape Estimation of Co-Manipulative Continuum Robots

Static shape estimation of co-manipulative continuum robots (CCRs) is challenging because the continuum arms and manipulated flexible object form a closed chain that must satisfy both static equilibrium and geometric loop-closure constraints. This paper presents a constraint-aware physics-informed neural network (PINN) for static shape estimation of a tendon-driven CCR modeled using the geometric variable strain formulation. The proposed method incorporates a projected static equilibrium residual and a configuration-level geometric residual to enforce the governing mechanics and closed-chain geometry. In simulation, the PINN is compared with a purely data-driven artificial neural network (ANN) under limited and noisy training data. With 140 samples and 50% label noise, the PINN reduces the relative configuration error, equilibrium residual, and closed-chain residual by 67.88%, 67.35%, and 88.06%, respectively. Using the full dataset, the PINN achieves 0.1597% relative configuration error with an inference time of 0.1773 ms, compared with 17.97 s for an iterative nonlinear solver. Experimental fine-tuning reduces the marker RMSE from 2.657 mm to 0.497 mm and increases R2 from -0.788 to 0.937. These results demonstrate accurate, physically consistent, and computationally efficient static shape estimation of closed-chain CCRs.

Rana Danesh, Pari Qarehdaghi, Farrokh Janabi-Sharifi

Continuum Robot Shape Estimation Deformable Shape Reconstruction Physics-Informed ML Robotic Manipulation

Aug 13, 2026

Capstan-driven Continuum Surgical Robot: Design, Modeling, and Perception

Shape and force sensing have long been critical bottlenecks in the development of compact capstan-driven continuum surgical robots, primarily due to the difficulty of obtaining cable tension information within the confined capstan assembly. To overcome these challenges, this paper presents an integrated design-modeling-sensing approach based on the concept of actuation-perception co-design. A compliant element is introduced into the motor mounting bracket of the drive system, enabling micro-deformation under the cable reaction force and thereby allowing real-time cable tension measurement without occupying the compact capstan space. To address the modeling complexity arising from unconventional joint configurations introduced by the spatial cable routing strategy, a parallel computation framework based on a multibody short-thick-beam model is proposed, which captures shear effects in short beam segments and synergistic multi-cable interactions while achieving real-time performance. Building on this framework, stable shape and force sensing is achieved by incorporating a proximal multi-axis force/torque sensor as an additional measurement anchor. Following this design-modeling-sensing framework, capstan-driven continuum surgical robots with single- and dual-segment configurations are developed. Experimental results validate the proposed framework in both single- and dual-segment continuum robots, demonstrating real-time tip pose estimation together with contact force and location perception. By enabling cable tension feedback without compromising the compact capstan architecture, the proposed framework makes integrated perception feasible for capstan-driven continuum surgical robots.

Gang Zhang, Yufu Qiu, Junyan Yan +3

Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong · School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China · state Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology (HUST), Wuhan, China +1

Continuum Robot Control Robot State Estimation Surgical Robotics Continuum Robot Design Continuum Robot Shape Estimation

Aug 5, 2026

Sliding Sensors: Configurable Confidence in State Estimation for Continuum Robots

Continuum robots often operate in uncertain environments, where accurate state estimation is essential for safe interactions. Estimate uncertainty is inherently spatially non-uniform: confidence varies depending on where measurements are available. Global estimation accuracy is not always the top priority, but rather achieving sufficient confidence at task-relevant locations along the robot. This extended abstract introduces mechanically reconfigurable sensing enabling uncertainty-shaping in state estimation for continuum robots. We present a concept hardware design demonstrating the feasibility of longitudinal translation of a sensor within a continuum robot. We demonstrate that state estimation confidence can be reconfigured by varying the sensor location, and show a reduction of full-body shape estimation errors when sliding the sensor back and forth over time, compared to a single fixed tip sensor.

Ella Walsh, Spencer Teetaert, Eric Diller +2

University of Toronto Robotics Institute, Toronto, ON, Canada

Robotics Robot State Estimation Continuum Robot Shape Estimation Continuum Robot Design

Jun 28, 2026

Multi-Contact Force Estimation for Continuum Robots via Gaussian-Parameterized Factor Graphs

Continuum robots offer key advantages in navigating unstructured environments, but their safe operation requires accurate estimation of the external contact forces acting anywhere along the robot body. Estimating these forces at unknown locations is an ill-conditioned problem, particularly for multiple contacts. We propose a unified shape and force estimation framework formulated on a factor graph. By incorporating a Gaussian mixture force parameterization into a discretized probabilistic Cosserat rod model, we reduce the dimensionality of the unknown external forces and mitigate the ill-conditioning of node-wise force estimation. The framework fuses strain, tendon tension, and pose measurements to simultaneously estimate the robot's shape and external forces while accounting for modeling and sensor uncertainties. Numerical simulations demonstrate that the proposed method outperforms existing methods in terms of force location and magnitude estimation for both single and multi-contact scenarios. We further present a progressive variant that introduces basis functions on demand to estimate contact forces sequentially during a simulated confined-navigation task.

Aditya Prakash, Panagiotis Tsiotras

School of Aerospace Engineering Georgia Institute of Technology Atlanta, GA, USA

Contact Force Estimation Robot State Estimation Continuum Robot Shape Estimation

Jun 17, 2026

Shape Sensing of Continuum Robots using Direct Laser Writing

Continuum robots offer a promising approach for minimally invasive and natural-orifice surgical procedures due to their inherent compliance and dexterity. However, this flexibility also makes estimating the current shape of the robot challenging. Several approaches have been used to reconstruct the shape of these robots, including imaging, optical sensing, magnetic sensing, and resistive sensing. Strain sensors fabricated using direct laser writing (DLW) could provide an alternative sensing method. This technique involves using a laser to induce carbonization of certain polymers to create graphene patterns, such as strain sensors. In this paper, we demonstrate how a flexible continuum joint and a DLW sensor can be machined as one monolithic structure using the same laser and the same setup. The fabricated sensors are characterized using linear and nonlinear models, which are used to predict the joint angle with error as low as 1.76 degrees. Furthermore, we demonstrate how a DLW sensor can be used to implement closed-loop control in a robotic joint, achieving tracking error under 3 degrees.

Amber K. Rothe, Nidhi Malhotra, Jaydev P. Desai

Medical Robotics and Automation (RoboMed) Laboratory, Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA

Continuum Robot Control Continuum Robot Shape Estimation Soft Robotics

May 9, 2026

Continuum Robot Modeling with Action Conditioned Flow Matching

Predicting the shape of tendon driven continuum robots (TDCRs) at steady state from actuation remains challenging due to continuous deformation, complex tendon routing, compliance, friction, and fabrication variability. In this paper, we address this problem as kinematic self modeling conditioned on action. We present a lightweight 3D printed TDCR hardware platform and an RGB-D data collection pipeline with multiple cameras, and we learn a point cloud flow matching model that maps motor actuation states to the robot's settled 3D geometry. The model is trained from randomly sampled quasi static configurations and evaluated on test motor commands within the same TDCR design family and actuation range. We compare against prior 3D deformable object and robot self modeling approaches in both MuJoCo simulation and real hardware experiments. Experiments on simulated 2-, 3-, and 5-module TDCRs and real 2- and 3-module robots show improved shape prediction accuracy under CD and EMD metrics. We further show in simulation that the same conditional formulation generalizes to tip payload as a conditioning input, enabling payload conditioned steady-state shape prediction. These results demonstrate a data driven self modeling framework for quasi static TDCR geometry prediction.

Jiong Lin, Jinchen Ruan, Hod Lipson

Department of Mechanical Engineering, Columbia University, New York, NY, USA

3D Shape Generation Point Cloud Generation Continuum Robot Control Tendon-Driven Actuation Continuum Robot Shape Estimation Soft Robotics

Apr 17, 2026

Factor Graph-Based Shape Estimation for Continuum Robots via Magnus Expansion

Reconstructing the shape of continuum manipulators from sparse, noisy sensor data is a challenging task, owing to the infinite-dimensional nature of such systems. Existing approaches broadly trade off between parametric methods that yield compact state representations but lack probabilistic structure, and Cosserat rod inference on factor graphs, which provides principled uncertainty quantification at the cost of a state dimension that grows with the spatial discretization. This letter combines the strength of both paradigms by estimating the coefficients of a low-dimensional Geometric Variable Strain (GVS) parameterization within a factor graph framework. A novel kinematic factor, derived from the Magnus expansion of the strain field, encodes the closed-form rod geometry as a prior constraint linking the GVS strain coefficients to the backbone pose variables. The resulting formulation yields a compact state vector directly amenable to model-based control, while retaining the modularity, probabilistic treatment and computational efficiency of factor graph inference. The proposed method is evaluated in simulation on a 0.4 m long tendon-driven continuum robot under three measurement configurations, achieving mean position errors below 2 mm for all three scenarios and demonstrating a sixfold reduction in orientation error compared to a Gaussian process regression baseline when only position measurements are available.

Lorenzo Ticozzi, Patricio A. Vela, Panagiotis Tsiotras

School of Aerospace Engineering · School of Electrical and Computer Engineering

Factor Graph Optimization Robotics Robot State Estimation Continuum Robot Shape Estimation

Mar 8, 2026

ACCURATE: Arbitrary-shaped Continuum Reconstruction Under Robust Adaptive Two-view Estimation

Accurate reconstruction of arbitrary-shaped long slender continuum bodies, such as guidewires, catheters and other soft continuum manipulators, is essential for accurate mechanical simulation. However, existing image-based reconstruction approaches often suffer from limited accuracy because they often underutilize camera geometry, or lack generality as they rely on rigid geometric assumptions that may fail for continuum robots with complex and highly deformable shapes. To address these limitations, we propose ACCURATE, a 3D reconstruction framework integrating an image segmentation neural network with a geometry-constrained topology traversal and dynamic programming algorithm that enforces global biplanar geometric consistency, minimizes the cumulative point-to-epipolar-line distance, and remains robust to occlusions and epipolar ambiguities cases caused by noise and discretization. Our method achieves high reconstruction accuracy on both simulated and real phantom datasets acquired using a clinical X-ray C-arm system, with mean absolute errors below 1.0 mm.

Yaozhi Zhang, Shun Yu, Yugang Zhang +1

Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai, China

3D Reconstruction Continuum Robot Shape Estimation Deformable Shape Reconstruction Multi-View 3D Reconstruction

Mar 8, 2026

Cable-driven Continuum Robotics: Proprioception via Proximal-integrated Force Sensing

Micro-scale continuum robots face significant limitations in achieving three-dimensional contact force perception, primarily due to structural miniaturization, nonlinear mechanical, and sensor integration. To overcome these limitations, this paper introduces a novel proprioception method for cable-driven continuum robots based on proximal-integrated force sensing (i.e., cable tension and six-axis force/torque (F/T) sensor), inspired by the tendon-joint collaborative sensing mechanism of the finger. By integrating biomechanically inspired design principles with nonlinear modeling, the proposed method addresses the challenge of force perception (including the three-dimensional contact force and the location of the contact point) and shape estimation in micro-scale continuum robots. First, a quasi-bionic mapping between human tissues/organs and robot components is established, enabling the transfer of the integrated sensing strategy of tendons, joints, and neural feedback to the robotic system. Second, a multimodal perception strategy is developed based on the structural constraints inherent to continuum robots. The complex relationships among mechanical and material nonlinearities, robot motion states, and contact forces are formulated as an optimization problem to reduce the perception complexity. Finally, experimental validation demonstrates the effectiveness of the proposed method. This work lays the foundation for developing safer and smarter continuum robots, enabling broader clinical adoption in complex environments.

Gang Zhang, Junyan Yan, Jibiao Chen +1

Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong · Curve Robotics Limited, Hong Kong · Shun Hing Institute of Advanced Engineering and Multi-Scale Medical Robotics Center, Hong Kong

Contact Force Estimation Continuum Robot Shape Estimation Robotic Perception Tactile Sensing Soft Robotics

Mar 2, 2026

Shape-Interpretable Visual Self-Modeling Enables Geometry-Aware Continuum Robot Control

Continuum robots possess high flexibility and redundancy, making them well suited for safe interaction in complex environments, yet their continuous deformation and nonlinear dynamics pose fundamental challenges to perception, modeling, and control. Existing vision-based control approaches often rely on end-to-end learning, achieving shape regulation without explicit awareness of robot geometry or its interaction with the environment. Here, we introduce a shape-interpretable visual self-modeling framework for continuum robots that enables geometry-aware control. Robot shapes are encoded from multi-view planar images using a Bezier-curve representation, transforming visual observations into a compact and physically meaningful shape space that uniquely characterizes the robot's three-dimensional configuration. Based on this representation, neural ordinary differential equations are employed to self-model both shape and end-effector dynamics directly from data, enabling hybrid shape-position control without analytical models or dense body markers. The explicit geometric structure of the learned shape space allows the robot to reason about its body and surroundings, supporting environment-aware behaviors such as obstacle avoidance and self-motion while maintaining end-effector objectives. Experiments on a cable-driven continuum robot demonstrate accurate shape-position regulation and tracking, with shape errors within 1.56% of image resolution and end-effector errors within 2% of robot length, as well as robust performance in constrained environments. By elevating visual shape representations from two-dimensional observations to an interpretable three-dimensional self-model, this work establishes a principled alternative to vision-based end-to-end control and advances autonomous, geometry-aware manipulation for continuum robots.

Peng Yu, Xin Wang, Ning Tan

School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China.

Continuum Robot Control Vision-Based Robot Control Continuum Robot Shape Estimation Robotic Manipulation Robot Dynamics Learning

Feb 27, 2026

Evaluating Accuracy of Vine Robot Shape Sensing with Distributed Inertial Measurement Units

Soft, tip-extending vine robots are well suited for navigating tight, debris-filled environments, making them ideal for urban search and rescue. Sensing the full shape of a vine robot's body is helpful both for localizing information from other sensors placed along the robot body and for determining the robot's configuration within the space being explored. Prior approaches have localized vine robot tips using a single inertial measurement unit (IMU) combined with force sensing or length estimation, while one method demonstrated full-body shape sensing using distributed IMUs on a passively steered robot in controlled maze environments. However, the accuracy of distributed IMU-based shape sensing under active steering, varying robot lengths, and different sensor spacings has not been systematically quantified. In this work, we experimentally evaluate the accuracy of vine robot shape sensing using distributed IMUs along the robot body. We quantify IMU drift, measuring an average orientation drift rate of 1.33 degrees/min across 15 sensors. For passive steering, mean tip position error was 11% of robot length. For active steering, mean tip position error increased to 16%. During growth experiments across lengths from 30-175 cm, mean tip error was 8%, with a positive trend with increasing length. We also analyze the influence of sensor spacing and observe that intermediate spacings can minimize error for single-curvature shapes. These results demonstrate the feasibility of distributed IMU-based shape sensing for vine robots while highlighting key limitations and opportunities for improved modeling and algorithmic integration for field deployment.

Alexis E. Laudenslager, Antonio Alvarez Valdivia, Nathaniel Hanson +1

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana, USA. · Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts, USA

Continuum Robot Shape Estimation Robot State Estimation Soft Robotics

Feb 26, 2026

Performance and Experimental Analysis of Strain-based Models for Continuum Robots

Although strain-based models have been widely adopted in robotics, no comparison beyond the uniform bending test is commonly recognized to assess their performance. In addition, the increasing effort in prototyping continuum robots highlights the need to assess the applicability of these models and the necessity of comprehensive performance evaluation. To address this gap, this work investigates the shape reconstruction abilities of a third-order strain interpolation method, examining its ability to capture both individual and combined deformation effects. These results are compared and discussed against the Geometric-Variable Strain approach. Subsequently, simulation results are experimentally verified by reshaping a slender rod while recording the resulting configurations using cameras. The rod configuration is imposed using a manipulator displacing one of its tips and extracted through reflective markers, without the aid of any other external sensor -- i.e. strain gauges or wrench sensors placed along the rod. The experiments demonstrate good agreement between the model predictions and observed shapes, with average error of 0.58% of the rod length and average computational time of 0.32s per configuration, outperforming existing models.

Annika Delucchi, Vincenzo Di Paola, Andreas Müller +1

Department of Mechanical, Energy, Management and Transportation Engineering (DIME), University of Genova, Italy · Institute of Robotics, Johannes Kepler University (JKU) Linz, Austria

Continuum Robot Shape Estimation Robotics Deformable Shape Reconstruction