Continuum Robot Control

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Overview

Continuum robot control aims to move a flexible robot’s tip or regulate its whole-body shape despite underactuation, deformation, and contact with the environment. Approaches range from Cosserat-rod and piecewise-constant-strain models with model-predictive or visual-servo control to learned dynamics, Koopman models, and reinforcement-learning policies. Camera-based and embedded sensing support feedback in settings such as surgical navigation, cluttered manipulation, locomotion, and aerial interaction, while safety controllers help manage collisions. A central challenge is balancing physically accurate models and reliable state estimation with the speed needed for real-time control, especially under contact, changing payloads, and sim-to-hardware transfer.

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71 papers4 papers in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

Mar 4, 2026

Modeling and Control of a Pneumatic Soft Robotic Catheter Using Neural Koopman Operators

Catheter-based interventions are widely used for the diagnosis and treatment of cardiac diseases. Recently, robotic catheters have attracted attention for their ability to improve precision and stability over conventional manual approaches. However, accurate modeling and control of soft robotic catheters remain challenging due to their complex, nonlinear behavior. The Koopman operator enables lifting the original system data into a linear "lifted space", offering a data-driven framework for predictive control; however, manually chosen basis functions in the lifted space often oversimplify system behaviors and degrade control performance. To address this, we propose a neural network-enhanced Koopman operator framework that jointly learns the lifted space representation and Koopman operator in an end-to-end manner. Moreover, motivated by the need to minimize radiation exposure during X-ray fluoroscopy in cardiac ablation, we investigate open-loop control strategies using neural Koopman operators to reliably reach target poses without continuous imaging feedback. The proposed method is validated in two experimental scenarios: interactive position control and a simulated cardiac ablation task using an atrium-like cavity. Our approach achieves average errors of 2.1 +- 0.4 mm in position and 4.9 +- 0.6 degrees in orientation, outperforming not only model-based baselines but also other Koopman variants in targeting accuracy and efficiency. These results highlight the potential of the proposed framework for advancing soft robotic catheter systems and improving catheter-based interventions.

Yiyao Yue, Noah Barnes, Lingyun Di +4

Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD, USA. · Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA. · Department of Mechanical Engineering, University of Maryland, College Park, MD, USA.

Robotic Endovascular InterventionContinuum Robot ControlSoft RoboticsKoopman Operator Learning
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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 ControlVision-Based Robot ControlContinuum Robot Shape EstimationRobotic ManipulationRobot Dynamics Learning
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Feb 22, 2026

3D Shape Control of Extensible Multi-Section Soft Continuum Robots via Visual Servoing

In this paper, we propose a novel vision-based control algorithm for regulating the whole body shape of extensible multisection soft continuum manipulators. Contrary to existing vision-based control algorithms in the literature that regulate the robot's end effector pose, our proposed control algorithm regulates the robot's whole body configuration, enabling us to leverage its kinematic redundancy. Additionally, our model-based 2.5D shape visual servoing provides globally stable asymptotic convergence in the robot's 3D workspace compared to the closest works in the literature that report local minima. Unlike existing visual servoing algorithms in the literature, our approach does not require information from proprioceptive sensors, making it suitable for continuum manipulators without such capabilities. Instead, robot state is estimated from images acquired by an external camera that observes the robot's whole body shape and is also utilized to close the shape control loop. Traditionally, visual servoing schemes require an image of the robot at its reference pose to generate the reference features. In this work, we utilize an inverse kinematics solver to generate reference features for the desired robot configuration and do not require images of the robot at the reference. Experiments are performed on a multisection continuum manipulator demonstrating the controller's capability to regulate the robot's whole body shape while precisely positioning the robot's end effector. Results validate our controller's ability to regulate the shape of continuum robots while demonstrating a smooth transient response and a steady-state error within 1 mm. Proof-of-concept object manipulation experiments including stacking, pouring, and pulling tasks are performed to demonstrate our controller's applicability.

Abhinav Gandhi, Shou-Shan Chiang, Cagdas D. Onal +1

Robotics Engineering Department, Worcester Polytechnic Institute 100 Institute Rd, Worcester, MA 01609, USA

Continuum Robot ControlVision-Based Robot ControlSoft Robotics
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Feb 21, 2026

Systematic Analysis of Coupling Effects on Closed-Loop and Open-Loop Performance in Aerial Continuum Manipulators

This paper investigates two distinct approaches to the dynamic modeling of aerial continuum manipulators (ACMs): the decoupled and the coupled formulations. Both open-loop and closed-loop behaviors of a representative ACM are analyzed. The primary objective is to determine the conditions under which the decoupled model attains accuracy comparable to the coupled model while offering reduced computational cost under identical numerical conditions. The system dynamics are first derived using the Euler--Lagrange method under the piecewise constant curvature (PCC) assumption, with explicit treatment of the near-zero curvature singularity. A decoupled model is then obtained by neglecting the coupling terms in the ACM dynamics, enabling systematic evaluation of open-loop responses under diverse actuation profiles and external wrenches. To extend the analysis to closed-loop performance, a novel dynamics-based proportional-derivative sliding mode image-based visual servoing (DPD-SM-IBVS) controller is developed for regulating image feature errors in the presence of a moving target. The controller is implemented with both coupled and decoupled models, allowing a direct comparison of their effectiveness. The open-loop simulations reveal pronounced discrepancies between the two modeling approaches, particularly under varying torque inputs and continuum arm parameters. Conversely, the closed-loop experiments demonstrate that the decoupled model achieves tracking accuracy on par with the coupled model (within subpixel error) while incurring lower computational cost.

Niloufar Amiri, Shayan Sepahvand, Iraj Mantegh +1

Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada · Aerospace Research Center, National Research Council of Canada (NRC), Montreal, QC H3T 2B2, Canada

Continuum Robot ControlAerial ManipulationDynamical Systems
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Feb 20, 2026

Infinite-Dimensional Closed-Loop Inverse Kinematics for Soft Robots via Neural Operators

For fully actuated rigid robots, kinematic inversion is a purely geometric problem, efficiently solved by closed-loop inverse kinematics (CLIK) schemes that compute joint velocities to position the robot body in space. For underactuated soft robots, however, not all configurations are attainable through control action, making kinematic inversion extremely ill-posed. Extensions of CLIK address this by introducing end-to-end mappings from actuation to task space for the controller to operate on, but typically assume finite dimensions of the underlying virtual configuration space. In this work, we formulate CLIK in the infinite-dimensional domain to reason about the entire soft robot shape while solving tasks, thereby skipping intermediate approximation steps. We do this by composing an actuation-to-shape map with a shape-to-task map, deriving the differential end-to-end kinematics via an infinite-dimensional chain rule, and thereby obtaining a Jacobian-based CLIK algorithm. Since complex soft-robot models are rarely available in closed form, and neither the actuation-to-shape mapping nor its Jacobian can typically be obtained analytically, we propose to learn it using differentiable neural operator networks. We first present an analytical study on a constant-curvature segment, and then apply the neural version of the algorithm to a three-fiber soft robotic arm whose underlying model relies on morphoelasticity and active filament theory.

Carina Veil, Moritz Flaschel, Ellen Kuhl +1

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA · Institute of Applied Mechanics, Friedrich-Alexander-Universität Erlangen–Nürnberg, 91058 Erlangen, Germany · Cognitive Robotics Department, Delft University of Technology, 2628 Delft, The Netherlands

Inverse KinematicsContinuum Robot ControlSoft Robotics
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Feb 18, 2026

Dynamic Modeling and MPC for Locomotion of Tendon-Driven Soft Quadruped

SLOT (Soft Legged Omnidirectional Tetrapod), a tendon-driven soft quadruped robot with 3D-printed TPU legs, is presented to study physics-informed modeling and control of compliant legged locomotion using only four actuators. Each leg is modeled as a deformable continuum using discrete Cosserat rod theory, enabling the capture of large bending deformations, distributed elasticity, tendon actuation, and ground contact interactions. A modular whole-body modeling framework is introduced, in which compliant leg dynamics are represented through physically consistent reaction forces applied to a rigid torso, providing a scalable interface between continuum soft limbs and rigid-body locomotion dynamics. This formulation allows efficient whole-body simulation and real-time control without sacrificing physical fidelity. The proposed model is embedded into a convex model predictive control framework that optimizes ground reaction forces over a 0.495 s prediction horizon and maps them to tendon actuation through a physics-informed force-angle relationship. The resulting controller achieves asymptotic stability under diverse perturbations. The framework is experimentally validated on a physical prototype during crawling and walking gaits, achieving high accuracy with less than 5 mm RMSE in center of mass trajectories. These results demonstrate a generalizable approach for integrating continuum soft legs into model-based locomotion control, advancing scalable and reusable modeling and control methods for soft quadruped robots.

Saumya Karan, Neerav Maram, Suraj Borate +1

IIT Gandhinagar, Department of Electrical Engineering, Gujarat, India · Sreenidhi Institute of Science and Technology, Department of Electronics and Computer Engineering, Telangana, India

Quadruped LocomotionSoft RoboticsContinuum Robot ControlModel Predictive Control
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Feb 18, 2026

MarUco: A Markerless 6D Pose Estimation Framework for Closed-Loop Control of Surgical Continuum Manipulators

Flexible endoscopic continuum manipulators offer high dexterity and access to complex anatomy, but nonlinear hysteresis limits feedforward control accuracy. Closed-loop control can compensate for these errors but requires accurate six-degree-of-freedom (6D) end-effector pose feedback. We present MarUco, a markerless 6D pose estimation framework for closed-loop control using only stereo vision during operation. A photorealistic pseudo-rigid-body simulation pipeline generates large-scale annotated training data without manual labeling. A multifeature fusion network integrates masks, keypoints, heatmaps, and bounding boxes from both stereo views to estimate an initial pose, followed by a learned single-pass render-and-compare module that refines the pose without iterative optimization. Kinematics-free hand-eye calibration estimates camera-to-robot-base extrinsics, and self-supervised adaptation uses unlabeled real stereo pairs to mitigate sim-to-real pose error. Across 1,000 real samples, MarUco achieves translation and rotation errors of 0.78 ±\pm 0.50 mm and 3.07 ±\pm 1.25°, respectively, with a total processing time of 52.4 ms per stereo pair. In closed-loop experiments over eight reference paths, MarUco achieves a mean terminal translation error of 1.8 mm, an 88% reduction relative to uncompensated open-loop control. To the best of our knowledge, this is the first markerless position-based visual servoing framework for continuum manipulators.

Junhyun Park, Chunggil An, Myeongbo Park +3

Department of Robotics and Mechatronics Engineering, DGIST, Daegu 42988, Republic of Korea · AI Research Lab, DEEPNOID, Seoul, Republic of Korea

Object Pose EstimationContinuum Robot ControlVision-Based Robot ControlSurgical Robotics
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Feb 16, 2026

Real-time Monocular 2D and 3D Perception of Endoluminal Scenes for Controlling Flexible Robotic Endoscopic Instruments

Endoluminal surgery offers a minimally invasive option for early-stage gastrointestinal and urinary tract cancers but is limited by surgical tools and a steep learning curve. Robotic systems, particularly continuum robots, provide flexible instruments that enable precise tissue resection, potentially improving outcomes. This paper presents a visual perception platform for a continuum robotic system in endoluminal surgery. Our goal is to utilize monocular endoscopic image-based perception algorithms to identify position and orientation of flexible instruments and measure their distances from tissues. We introduce 2D and 3D learning-based perception algorithms and develop a physically-realistic simulator that models flexible instruments dynamics. This simulator generates realistic endoluminal scenes, enabling control of flexible robots and substantial data collection. Using a continuum robot prototype, we conducted module and system-level evaluations. Results show that our algorithms improve control of flexible instruments, reducing manipulation time by over 70% for trajectory-following tasks and enhancing understanding of surgical scenarios, leading to robust endoluminal surgeries.

Ruofeng Wei, Kai Chen, Yui Lun Ng +7

Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China. · Department of Mechanical Engineering, The University of Hong Kong, China. · Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, and also with the Department of Mechanical Engineering, The University of Hong Kong.

Robotic EndoscopyRobotic PerceptionSurgical RoboticsContinuum Robot ControlObject Pose EstimationMonocular 3D Object Detection
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Feb 3, 2026

Soft Swing-up: Benchmarking Model-Based Optimal Control for Rigid-Soft Underactuated Systems

Continuum soft robots are inherently underactuated and subject to intrinsic input constraints, making dynamic control particularly challenging, especially in hybrid rigid-soft robots. While most existing methods focus on quasi-static behaviors, dynamic tasks such as swing-up require accurate exploitation of continuum dynamics. This has led to studies on simple low-order template systems that often fail to capture the complexity of real continuum deformations. Model-based optimal control offers a systematic solution; however, its application to rigid-soft robots is often limited by the computational cost and inaccuracy of numerical differentiation for high-dimensional models. Building on recent advances in the Geometric Variable Strain model that enable analytical derivatives, this work investigates three optimal control strategies for underactuated soft systems -- Direct Collocation, Differential Dynamic Programming, and Nonlinear Model Predictive Control -- to perform dynamic swing-up tasks. To address stiff continuum dynamics and constrained actuation, implicit integration schemes and warm-start strategies are employed to improve numerical robustness and computational efficiency. The methods are evaluated in simulation on three Rigid-Soft and high-order soft benchmark systems -- the Soft Cart-Pole, the Soft Pendubot, and the Soft Furuta Pendulum -- highlighting their performance and computational trade-offs.

Daniele Caradonna, Nikhil Nair, Anup Teejo Mathew +5

The BioRobotics Institute, Scuola Superiore Sant’Anna, Pisa, Italy · Department of Excellence in Robotics and AI, Scuola Superiore Sant’Anna, Pisa, Italy · Department of Cognitive Robotics, Delft University of Technology, 2628 CN Delft, The Netherlands +3

Robotic ControlModel Predictive ControlContinuum Robot ControlOptimal ControlSoft Robotics
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Dec 22, 2025

Collaborative Continuum Robots: A Survey from an Automation-System Perspective

Continuum robots (CRs), owing to their compact structure, inherent compliance, and flexible deformation, have been widely applied in various fields. By coordinating multiple CRs to form collaborative continuum robots (CCRs), task adaptability, flexibility and load capacity can be further improved, thus offering significant advantages. In recent years, interest in this emerging field has grown steadily within the continuum-robotics community. In this survey, a closed-loop task-execution architecture for CCRs is constructed from an automation-system perspective, clarifying the system-level logic that transforms target-task specifications into multi-CR collaborative execution. Based on this architecture, CCRs are classified into three representative collaboration modes, namely separated collaboration, assistance collaboration, and parallel collaboration. Research progress is then systematically summarized and analyzed in terms of key technologies, including multi-CR task allocation, structural design, modeling, motion planning methods, control strategies, and sensing mechanisms. Finally, research opportunities in key technologies and system integration challenges for real-world deployment are discussed, providing guidance for research and application of CCRs.

Xinyu Li, Qian Tang, Guoxin Yin +4

Multi-Robot CoordinationContinuum Robot ControlContinuum Robot Design
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Nov 10, 2025

Rapidly Learning Soft Robot Control via Implicit Time-Stepping

With the explosive growth of rigid-body simulators, policy learning in simulation has become the de facto standard for most rigid morphologies. In contrast, soft robotic simulation frameworks remain scarce and are seldom adopted by the soft robotics community. This gap stems partly from the lack of easy-to-use, general-purpose frameworks and partly from the high computational cost of accurately simulating continuum mechanics, which often renders policy learning infeasible. In this work, we demonstrate that rapid soft robot policy learning is indeed achievable via implicit time-stepping. Our simulator of choice, DisMech, is a general-purpose, fully implicit soft-body simulator capable of handling both soft dynamics and frictional contact. We further introduce delta natural curvature control, a method analogous to delta joint position control in rigid manipulators, providing an intuitive and effective means of enacting control for soft robot learning. To highlight the benefits of implicit time-stepping and delta curvature control, we conduct extensive comparisons across four diverse soft manipulator tasks against one of the most widely used soft-body frameworks, Elastica. With implicit time-stepping, parallel stepping of 500 environments achieves up to 6x faster speeds for non-contact cases and up to 40x faster for contact-rich scenarios. Finally, a comprehensive sim-to-sim gap evaluation--training policies in one simulator and evaluating them in another--demonstrates that implicit time-stepping provides a rare free lunch: dramatic speedups achieved without sacrificing accuracy.

Andrew Choi, Dezhong Tong, Xiaonan Huang

Horizon Robotics, Cupertino, CA, USA · Robotics Department at the University of Michigan, Ann Arbor, MI, USA

Robot Policy LearningRobotics SimulationContinuum Robot ControlSoft RoboticsDeformable Object Simulation
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