Continuum Robots

Soft-bodied organisms such as octopuses and elephant trunks exhibit remarkable morphological adaptability, dynamically reconfiguring body shape and stiffness, and flexibly adjusting their control strategies to enable versatile behaviors. Inspired by these biological systems, various soft robots have emerged in recent decades, featuring diverse materials, stiffnesses, and morphologies tailored to specific tasks. Despite substantial advances in the materials and structural designs of soft robots, developing a generalizable control framework capable of rapid adaptation across diverse configurations remains a long-standing challenge. Existing controllers are limited to fixed configurations, demanding laborious configuration-specific remodelling and policy redesign for new configurations. Here, we introduce a generalizable control system that enables rapid adaptation across diverse soft robot configurations via reinforcement learning in a shared linear Koopman embedding space. By encoding robot dynamics into this embedding space, our method decouples control policies from specific morphologies, allowing real-time, model-free policy adaptation across diverse configurations without retraining from scratch. We validate our system across 33 distinct robot configurations. Our system achieves a 75 times reduction in transfer samples across configurations, while sustaining robust performance under high-speed motion, heavy payloads, and multiactuator faults, and achieving real-world skills previously unattainable in soft robotics. This work establishes a unified and adaptable control paradigm for diverse soft robot configurations, bridging mechanical reconfigurability with control flexibility, and may offer broader insights for generalizable control in complex physical systems.

Soft, growing vine robots extend through tip eversion, a mechanism that enables navigation through cluttered environments. However, integrating cameras and other sensors at the tip is uniquely challenging because the material forming the tip is constantly renewed as the robot grows. This continual material turnover, combined with friction between internal layers, added tip weight, and fabric constriction, complicates sensor and tool mounting. These limitations hinder the deployment of vine robots for inspection and search tasks, where rapid growth while carrying tip-mounted sensors is essential. In this work, we present a triangular roller tip mount that reduces internal resistance during growth by rolling rather than sliding against the robot body. The design was refined through iterative failure analysis, enabling, for the first time, consistent eversion on a TPU-coated ripstop nylon vine robot. To quantitatively evaluate mount performance, we introduce a custom testbed that isolates tip mounting effects by measuring tail tension during eversion. Comparative experiments across multiple mount variants, including prior designs, show that our triangular roller mount achieves the lowest tail tension and most repeatable growth performance. These results establish both a validated tip mount design and a repeatable benchmarking framework for advancing sensor and tool integration in soft growing robots. CAD for the mount and testbed is available at: https://sprout-mitll.github.io/tip_mounts/.

Vision-Language Action (VLA) models continue to face challenges such as slow inference speed and difficulty performing fine-grained motion adjustments, limiting their widespread adoption in industry. While the Real-Time Action Chunking (RTAC) algorithm has been proposed to address these bottlenecks, bridging the gap between the algorithm provided in pseudocode to a stable, real-world deployment on a low-cost robotic arm remains a challenge. In this work, we present a complete system-level implementation of RTAC tailored for a low-cost robotic manipulation system. We advance beyond the original high-level pseudocode by optimizing the threading implementation for the policy inference and control pipeline, reducing end-to-end latency and improving responsiveness without modifying the underlying policy. We evaluate this system on tasks involving the manipulation of agricultural produce, specifically garlic bulbs and walnuts. Experimental results demonstrate that our custom threading implementation significantly improves control stability and speed compared to the base implementation of RTAC.

Soft robotics is increasingly explored in artistic contexts, where tactile interaction provides audiences with embodied engagement beyond visual or auditory signals. This work presents an interactive installation that maps semantic emotion analysis of narrative text into variable stiffness of soft pneumatic modules. A natural language model identifies two dominant emotions from a predefined set of six, driving the inflation of seven hexagonally arranged soft actuators. The central actuator represents the primary emotion, while the surrounding ones express the secondary. We develop and mechanically characterize silicone actuators, called soft modules, featuring a thin membrane layer, demonstrating how this morphological control expands the achievable stiffness range while preserving simplicity and low-cost fabrication. A user study with ten participants further evaluates how multisensory coupling of stiffness and LEDs intensity influences emotional perception. The results suggest that stiffness modulation accompanied by color change can support emotionally meaningful and engaging tactile interaction in soft robotic installations.

Soft wearable robotic systems have emerged as a promising solution for assisting individuals with reduced hand function. This paper presents SoFiE, a modular soft finger exoskeleton designed to assist index-finger flexion during grasping tasks. The proposed system is primarily fabricated using 3D-printed flexible materials, enabling a lightweight, low-profile, and modular design. Actuation is achieved through a tendon-driven mechanism powered by a compact DC motor, while passive extension is provided by a compliant conductive spring. This element, termed StretchSense, also functions as a proprioceptive sensor by exhibiting resistance changes under deformation. Furthermore, a novel tactile sensing approach, MagSense, is introduced, using a magnet and magnetometer pair embedded in a soft fingertip structure to estimate contact force and object compliance. The system is fully untethered and controlled by an embedded microcontroller. In addition, actuator-level sensing through motor encoder feedback enables estimation of the system state, providing a foundation for safe and adaptive control strategies. Experimental validation demonstrates the capability of the system to provide reliable pose estimation, distinguish between materials with different stiffness, and generate distinct sensor signatures across different grasping tasks. This paper details the design, fabrication, and sensing concepts of the proposed exoskeleton as a proof of concept toward modular, soft, and assistive wearable robotics.

Increasing interest in deep-sea operations and resources motivates the development of ecologically sensitive but environmentally durable robots. Dielectric elastomer actuator artificial muscles are good candidates for powering such systems due to their pressure and temperature tolerance and soft makeup, but they are difficult to integrate with robotic systems. This work presents an autonomous robotic platform: the CORE, capable of driving six artificial muscles while sensing visual and spatial information. To validate the platform, we developed the Cuttlebot - a cuttlefish-inspired robot that swims in three dimensions using undulatory fin locomotion. The Cuttlebot has four primary artificial muscles in its fins in addition to a tentacle-inspired soft gripper. The robot was evaluated in a series of tethered and untethered swimming tests, demonstrating a top speed of 2.5 centimeters per second translation and 10 degrees per second rotation. Furthermore, the CORE system was capable of driving specialized control signals into the artificial muscles to controllably output force and torque in six axes. This work provides a platform for developing complex, bio-inspired swimming robots for ocean exploration and monitoring, laying the foundation with our leading example: the Cuttlebot.

Robot-Assisted Minimally Invasive Surgery (RAMIS) enhances surgeon dexterity, with newer platforms leveraging haptic feedback to further improve performance. Such force information has broader potential to inform performance assessment, tactile localization, and surgical autonomy. This motivates the need for accessible approaches to integrating force sensing into RAMIS tools. This work presents a method for integrating a six-axis commercial force sensor into the distal end of a standard cable-driven surgical instrument, enabling end-effector force measurement while preserving the original mechanical functionality of the device. The proposed design emphasizes reproducibility and accessibility for research applications, requiring no specialized manufacturing tools. A transformer neural network integrates force sensor measurements with robot state information to aid estimation of applied forces at the end-effector, compensating for internal cable forces arising from actuation. Our proposed approach achieved normalized errors below 6%, and generalized to unseen conditions better than purely proximal data-driven sensing approaches. High internal cable forces caused sensor saturation and reduced axial force observability, which can degrade performance along the tool's major axis and under higher load conditions. Given current levels of performance, the balance of system integrability and performance enables applications and research into timely topics of haptic feedback, skill assessment, and force-informed autonomy in RAMIS. Videos and code are available at https://enhanced-telerobotics.github.io/shaft_force_sensing/.

Bimanual coordination is essential for many real-world manipulation tasks, yet learning bimanual robot policies is limited by the scarcity of bimanual robots and datasets. Single-arm robots, however, are widely available in research labs. Can we leverage them to train bimanual robot policies? We present MonoDuo, a framework for learning bimanual manipulation policies using single-arm robot demonstrations paired with human collaboration. MonoDuo collects data by teleoperating a single-arm robot to perform one side of a bimanual task while a human performs the other, then swapping roles to cover both sides. RGB-D observations from a wrist-mounted and fixed camera are augmented into synthetic demonstrations for target bimanual robots using state-of-the-art hand pose estimation, image and point cloud segmentation, and inpainting. These synthetic demonstrations, grounded in real robot kinematics, are used to train bimanual policies. We evaluate MonoDuo on five tasks: box lifting, backpack packing, cloth folding, jacket zipping, and plate handover. Compared to approaches relying solely on human bimanual videos, MonoDuo enables zero-shot deployment on unseen bimanual robot configurations, achieving success rates up to 70%. With only 25 target robot demonstrations, few-shot finetuning further boosts success rates by 65-70% over training from scratch, demonstrating MonoDuo's effectiveness in efficiently transferring knowledge from single-arm robot data to bimanual robot policies.

We present a hybrid robotic skin that combines electrical impedance tomography (EIT) with pneumatic tactile sensing to improve force reconstruction capability. The developed robotic skin is fabricated entirely by 3D printing and spray coating, making it affordable and easy to build. A Tikhonov-regularized inverse reconstruction, paired with per-pad pneumatic calibration, enables accurate large-area tactile sensing with a simple measurement scheme. For validation, we conducted load-cell indentation experiments; the results showed consistent force reconstruction across locations within a pad. Compared with an EIT-only baseline, sensitivity non-uniformity was also reduced, with the coefficient of variation decreasing from 0.31 to 0.14, indicating that the proposed approach addresses a longstanding limitation of EIT. We further demonstrated chest-mounted integration on a humanoid robot and found that the pneumatic signals remained reliable across diverse contact scenarios, including multiple simultaneous contacts on the same sensing pad. These results indicate a practical path toward accurate, scalable whole-body tactile sensing in real robotic systems.

This paper presents a magnet-based robotic skin that integrates a multilayer soft lattice with distributed Hall-effect sensor arrays and a tactile super-resolution model. External contact forces are converted to magnetic field changes by embedded permanent magnets, and the lattice spreads these changes across the sensing domain. This gives each sensor a large, overlapping receptive field and enables a large sensing area with minimal blind spots. Lattice parameters are tunable, enabling joint adjustment of mechanical compliance and transduction characteristics. An implicit modeling workflow and selective laser sintering (SLS) 3D printing support rapid fabrication of conformal, high-complexity structures. A convolutional neural network trained on experimental measurements estimates contact location and normal force in real time. Experiments validate localization accuracy and indicate scalability to larger surfaces, suggesting applicability to whole-body robotic skin and safe human-robot interaction.

The increasing use of drones in human-centric applications highlights the need for designs that can survive collisions and recover rapidly, minimizing risks to both humans and the environment. We present HoLoArm, a quadrotor with compliant arms inspired by the nodus structure of dragonfly wings. This design provides natural flexibility and resilience while preserving flight stability, which is further reinforced by the integration of a Reinforcement Learning (RL) control policy that enhances both recovery and hovering performance. Experimental results demonstrate that HoLoArm can passively deform in any direction, including axial one, and recover within 0.3-0.6 s depending on the direction and level of the impact. The drone can survive collisions at speeds up to 7.6 m/s and carry a 540 g payload while maintaining stable flight. This work contributes to the morphological design of soft aerial robots with high agility and reliable safety, enabling operation in cluttered and human shared environments, and lays the groundwork for future fully soft drones that integrate compliant structures with intelligent control.

Soft pneumatic actuators are widely used in soft robotics because they can produce large motions while remaining compliant enough to interact safely with objects, environments, and the human body. However, their performance is not solely determined by pressure. Instead, the response depends on the way the actuator is built, including the shape of its chambers, the placement of reinforcements, the use of folds, material stiffness, and the constraints that guide its deformation. As the literature has expanded, it has become more difficult to determine which mechanism is most suitable for a given application and which reported results can be compared across studies. This review examines soft pneumatic actuators according to the design strategies used to generate four motion classes: linear, bending, twisting, and omnidirectional actuation. For each class, it analyzes the structural features that define the deformation path, including braid angle, fold geometry, fiber orientation, chamber arrangement, structural asymmetry, and internal constraint layers. It then discusses how the design choice affect motion output, force generation, air demand, repeatability, durability, fabrication difficulty, and robotic integration. The review further identifies key conditions that must be considered when selecting or comparing actuators, including pressure, loading condition, actuator size, pneumatic supply, and hysteresis This approach helps explain why actuators with similar motion outputs may differ substantially in design requirements, pneumatic demand, and practical suitability. It also highlights the design priorities needed for compact, efficient, repeatable, and deployable soft pneumatic systems in wearable, biomedical, and mobile robotic applications.

This article presents a novel SOFA based finite element method for the soft body modeling and the corresponding dynamic simulation and control of a pneumatic morphing soft quadrotor. The proposed modeling preserves the physical interpretability and control structure of traditional quadrotor dynamics, while capturing the complex, time-varying behavior of pneumatically actuated soft arms. In SOFA, the soft pneumatically actuated arms are discretized as a tetrahedral mesh following an elastic material law that produces internal forces adequate to the real dynamic behavior of the body. Pneumatic actuation governed by both periodic and error-based control signals is applied within the internal cavities to analyze the morphing capability. Finally, a proportional-integral controller is proposed to study the controlled dynamic behavior and morphing capabilities of the pneumatic arm, wherein the pneumatic actuation to the soft arm is controlled to achieve the desired target position. The simulation results show the effectiveness of the proposed novel modeling framework and the related controller design.

Soft mobile robots have emerged as a promising area of research with potential applications in various disciplines including but not limited to search-and-rescue, service, surveillance, explorations, and manufacturing. In this article, we provide a comprehensive review of the current state of soft mobile robot research, focusing on wheelless terrestrial locomotive systems. We include past and present developments in locomotion strategies, actuation methods, modeling approaches, and control systems. Further, we identify key research challenges that must be overcome to enable the widespread adoption of soft mobile robots in various applications. Overall, this article provides a valuable resource for researchers and practitioners interested in the field of soft mobile robots and soft robotics.

Continuum robots enable dexterous manipulation in constrained environments, but require accurate and efficient models for real-time manipulation and control. Traditional physics-based models can be computationally expensive and may suffer from inaccuracies due to unmodeled effects, while current learning-based methods often generalize poorly beyond the specific robot on which they are trained. We present a formulation of surrogate modeling for tendon-driven continuum robots as an operator learning problem that maps robot design parameters and tendon actuation inputs to resulting configurations. This formulation enables a single trained model to generalize across a large class of robot designs. We develop four novel neural operator architectures--two based on Deep Operator Networks (DeepONets) and two based on Fourier Neural Operators (FNOs)--and train them on simulation data to predict robot configurations. All architectures achieve good accuracy while allowing for fast and accurate generalization across designs. Our results demonstrate that operator learning provides an effective and generalizable surrogate for continuum robot mechanics in the design space, enabling fast modeling for control, planning, and design optimization in surgical and industrial applications.

Developing dynamic models for tendon-driven continuum robots is challenging due to their nonlinear, high-dimensional, and friction-dominated dynamics. This paper presents a comparative study of data-driven system identification methods, including N4SID, ARX, and SINDYc, for modeling a tendon-actuated continuum robot with rolling joints developed at CERN. Despite the high number of joints of the robot, experimental analysis reveals that a two-degree-of-freedom dynamic model can accurately capture the system dynamics, owing to strong kinematic dependencies between the joints. The models are validated against experimental data, and used in the design of a model predictive controller, demonstrating their feasibility for real-time control.

Most existing vision-language manipulation research targets rigid robotic arms, whose fixed morphology limits adaptability in cluttered or confined spaces. Soft robotic arms offer an appealing alternative due to their deformability, but confront challenges such as unreliable proprioception and distributed low-level actuation. To investigate these challenges, we introduce \ManiSoft, a benchmark for vision-language manipulation with soft arms. ManiSoft features a tailored simulator that couples realistic soft-body dynamics with contact-rich interactions via an elastic force constraint. On this basis, ManiSoft defines four tasks, each highlighting distinct aspects of deformable control, from basic end-effector coordination to obstacle avoidance. To support policy training and evaluation, \ManiSoft{} includes an automated pipeline that generates $6{,}300$ diverse scenes and corresponding expert trajectories. To produce high-quality trajectories at scale, we first employ a high-level planner to decompose each task into a sequence of waypoints, followed by a low-level reinforcement learning policy that generates torque commands to track waypoints. Benchmarking three representative policy models shows relatively promising results in clean scenes but substantial performance drop under randomization. Visualization analysis indicates that failures stem primarily from inaccurate visual estimation of proprioceptive state and limited exploitation of deformability for adaptive obstacle avoiding. We anticipate ManiSoft to serve as a valuable testbed, bridging the gap between rigid and soft arms in the context of vision-language manipulation. Out codes and datasets are released at https://buaa-colalab.github.io/ManiSoft.

The growing adoption of lattice-based structures in soft robotics creates a need for advanced sensing solutions capable of monitoring their global deformation, particularly compression and extension. In this work, we address this challenge by introducing a novel optical sensor based on two patterned waveguides arranged in an ellipsoidal geometry. This Bidirectional Optical sensor for Actuation Tracking (BOAT) is seamlessly co-printed with a lattice structure actuated by an embedded pneumatic artificial muscle (PAM), and its performance is assessed. During PAM elongation or contraction, the bending of the embedded BOAT waveguides induces output signal variations that enable a clear discrimination between compression and extension states. The designs of both each specific waveguide structure (by surface patterning) and of the sensorized lattice-based unit embedding two BOATs are supported by numerical simulations. Experimental calibration over 100 consecutive pressure cycles ranging from +50 kPa to $-$40 kPa demonstrates a highly repeatable response, allowing a reliable distinction between extension and compression. Finally, sensor feedback is used to implement a digital shadow, enabling continuous synchronization between the whole sensorized unit and its virtual counterpart. These results establish BOAT as a powerful and reliable approach for deformation monitoring in soft lattice-based robotic systems.

Robotic cloth folding is a challenging task, particularly when considering dynamic folding tasks, which aim at folding cloth by fast motions that leverage its dynamics. When subject to such fast motions, the complexity of cloth dynamics hinders both system identification and planning of folding trajectories, resulting in a difficult simulation-to-reality transfer when using physical models of cloth. Compared to the dexterity that humans exhibit when performing folding tasks, robotic approaches usually employ small garments with quite rigid dynamics, and are either too slow, or fast but imprecise, requiring several attempts to achieve a reasonably good fold. In this paper, we tackle these challenges by generating fast folding trajectories with a novel model predictive controller, integrating physics-based simulation of cloth dynamics and efficient, kernel-based Koopman operator regression. Koopman operator regression, an increasingly popular machine learning technique for nonlinear system identification, is used to obtain a linear model for the cloth being folded. Such a surrogate model, trained with data from a high-fidelity, physics-based cloth simulator, can then be employed within a suitable model predictive control algorithm, in place of the costly, nonlinear one, to efficiently generate folding trajectories to be executed by a robotic manipulator. Both in simulated and real-robot experiments, we show how the linearization supplied by the Koopman operator-based model can be employed to efficiently generate fast folding trajectories to unseen poses, without sacrificing folding accuracy.

Flexible endoscopic robots enable minimally invasive access through natural orifices, but their control accuracy is limited by configuration-dependent hysteresis in the tendon-sheath mechanisms (TSMs). Tendon-sheath friction and tendon elasticity induce a systematic discrepancy between the proximal actuation input and distal output, and this discrepancy varies with the insertion tube configuration. To address this challenge, this paper proposes the Self-Sensing Tendon Loop (SSTL), a double-pass tendon loop routed through the insertion tube and wrapped around a distal pulley, and returned to the proximal end. The loop structure allows both the input and output tensions of the SSTL to be measured proximally, thereby providing an input-output tension profile without requiring distal force or fiber-optic sensors. Because the SSTL shares the same routing path as the actuation TSM, the two TSMs exhibit strongly correlated hysteresis behaviors. From the SSTL tension profile, a learning-based mapping estimates the configuration-dependent hysteresis parameters of the actuation TSM, which are then used by a feedforward controller to compensate for actuation hysteresis. We validate the proposed method by tracking actuation tendon tension under three different insertion tube configurations. Across sinusoidal and random trajectories, the proposed method reduces average RMSE by 88.1% compared with the uncompensated baseline, achieving 97.8% of the performance of direct identification, which requires direct measurement of the input and output tension profile of the actuation TSM.

This paper presents a reproducible and physically feasible dynamic parameter identification framework for CRANE-X7, a low-cost robot arm driven by modular smart actuators. To improve practical identifiability, products of inertia are removed according to approximate link symmetry, reducing the rigid-body model from 65 to 39 base parameters. Identification motions are hand-designed from structured single-joint and adjacent-joint primitives under practical joint-range limits. The proposed pipeline combines preprocessing, inverse-dynamics-regressor-based ordinary least squares (OLS), conditional semidefinite-programming (SDP) projection for feasibility recovery, and closed-loop input error (CLIE) refinement. Candidate solutions from 40 structured trajectories are analyzed in a common principal component analysis (PCA) space to select a statistically central representative model. Because statistical centrality alone does not ensure physical acceptability, the selected model is finally screened by an all-pose positive-definiteness audit of the inertia matrix and, when necessary, corrected by a localized post-CLIE SDP rescue step. Experiments show that the parameter cloud becomes progressively more concentrated from OLS to SDP and CLIE, while the final accepted model preserves high predictive accuracy on held-out validation motions. These results demonstrate a practical route to statistically coherent and physically feasible dynamic models for low-cost robot platforms.

In this paper, we discuss a novel continuum robot design that enables the online tuning of the magnetic response at its tip. The proposed method allows for the change of both effective magnetic direction and intensity, introducing steering DOF without the need to control the external fields. This is unattainable with classical designs, which rely on fixed internal magnetic content and steer solely under the effect of a controllable magnetic field. The proposed robot design can be used in both controllable and fixed magnetic fields, potentially widening the clinical applicability of these robots. We experimentally show a max tip deflection of 33.8 mm from the resting state (23 % of the length of the robot). We discuss a model based on modified beam theory that captures the mechanical behavior of the continuum robot, with a mean absolute tip tracking error of 1.86 mm (1.2 % of the length) and maximum errors of less than 4.8 mm (3.2 % of the length) for all experimental points.

This paper presents a motion analysis framework for an athlete wearing sport-specific flexible prosthesis based on the soft-rigid hybrid-link system. Such a motion analysis is a challenging problem because we need to consider the interaction force between the rigid human skeleton system and a flexible prosthesis. However, most of human musculoskeletal models are based on the computation framework of a rigid-body multi-link system. Recently in soft robotics research field, fast and efficient modeling methods were developed for a flexible rod deformation, which allows us to build a hybrid-link system that integrates rigid-link and soft-bodies in a unified formulation. We apply inverse kinematics of the hybrid-link system to motion reconstruction from a motion captured data, and also present the estimation of the joint torques and ground reaction force by inverse dynamics. Through a human subject experiment, we show that the inverse dynamics achieved approximately 12% error on the ground reaction force estimation. Furthermore, we provide the muscle force estimation considering muscle amputation and interaction force with the prosthesis leg deformation.

Positive-negative pressure regulation is critical to soft robotic actuators, enabling large motion ranges and versatile actuation modes. However, achieving high-performance regulation across both pressure polarities remains challenging due to asymmetric inflation-deflation dynamics, valve nonlinearities, and switching-induced flow disturbances. This paper presents BiPneu, a scalable and cost-efficient multi-channel bipolar-pressure pneumatic system for soft robots that enables wide-range, accurate, and responsive pressure regulation while providing seamless compatibility with high-level software ecosystems. A dual-mode sliding-mode controller (DM-SMC) with hysteresis-supervised mode selection is proposed based on a hybrid electro-pneumatic model. Extensive simulation and experiments demonstrate the superior performance of DM-SMC in tracking step and sinusoidal pressure references compared with both advanced model predictive controllers and well-tuned PID controllers. Experimental results show average absolute errors of 1.44 kPa in multi-step tests and 4.23 kPa in sinusoidal tracking, corresponding to reductions of 11.9% and 35.6% relative to PID control, along with improved control effort, valve switching rate, and transient response. Robustness of DM-SMC is further verified on a bellow actuator with pressure-dependent volume. Finally, BiPneu's capability is demonstrated via two soft robotic examples, quick ball-maneuvering with a soft parallel manipulator and real-time finite element method (FEM)-based teleoperation of a soft bellows actuator.

Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate representation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as alternatives with superior accuracy; however, they often overlook known mechanics, require large training datasets, and typically discard shape estimation of the robot. We present a physics-informed neural network (PINN) for kinematic modeling of a 6-DoF CTR with three pre-curved tubes that embeds the Cosserat rod differential equations and learns from few-shot observational data, balancing physics priors with data-driven fitting. PINN enables full-state estimation of shape, twist angle, torsional strain, bending moment, and orientation. Benchmark tests show a mean shape error below 1% of the robot length and accurately recovered other kinematic states, outperforming a purely physics-based Cosserat rod model baseline while using a minimal training set. The resulting model is also computationally efficient and robust, making it well-suited for real-time control applications.

Follow-the-leader (FTL) motion exploits the unique morphology of continuum robots (CRs) to navigate confined spaces by having the body retrace the path of the tip. While extensively studied, existing FTL methods typically assume a fixed base or a single degree-of-freedom insertion mechanism, limiting their applicability to practical systems in which CRs are mounted on robotic manipulators with fully actuated SE(3) base pose. This paper presents a sampling-based motion planner for FTL motion of manipulator-mounted CRs that jointly considers robot configuration and base pose. The key idea is to decouple global shape search from base pose determination by computing the base pose through a closed-form geometric construction, thereby avoiding iterative optimization during online planning. The approach supports general forward models and enables efficient planning by shifting the majority of computation offline. We establish theoretical guarantees including resolution complete shape search and converging tip tracking throughout waypoint traversal and interpolation. Experiments on 120 simulated paths over 3 test classes demonstrate 0% tip error and 1.9% mean shape deviation (w.r.t. robot length) at 100% success rate. We validate the practicality of our approach on a 6-DOF tendon-driven CR mounted on a serial manipulator. Code and visualization available at https://continuumroboticslab.github.io/sb-ftl-cr-planner/.

Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical Archard and Greenwood-Williamson models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target friction laws, with only a few asperities in unit cells. The predicted designs are strictly validated against high-fidelity Boundary Element Method (BEM) simulations. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for discovering functional tribological surfaces.

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.

In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert principle, which governs the motion of dynamical systems, is preserved by construction in the absence of external forces. This allows learning physically consistent models that overcome erroneous drift in the system's energy, thereby providing stable long-term predictions. At the core of our approach lie linear operators for Gaussian process conditioning, constructed from discrete forced Euler-Lagrange equations and variational discretization schemes. Thereby and unlike prior work, the method enables learning dynamics from discrete position snapshots, i.e., without access to a system's velocities or momenta. This is particularly relevant for a large class of practical scenarios where only position measurements are available, for instance, in motion capture or visual servoing applications. We demonstrate the data-efficiency and generalization capabilities of the LGPs in various synthetic and real-world case studies, including a real-world soft robot with hysteresis. The experimental results underscore that the LGPs learn physically consistent dynamics with uncertainty quantification solely from sparse positional data and enable stable long-term predictions.

We introduce an elastic-driven self-folding approach that fabricates robots directly from flat 3D-printed conductive PLA nets. Elastic bands routed through printed hooks store energy that folds the sheet into programmed 3D geometries, while the flat state allows accurate placement of electronics and magnets before deployment. The same substrate doubles as electrodes for capacitive touch and supports a reusable platform I/O palette with Hall sensors and eccentric rotating mass (ERM) motors for docking detection and vibration actuation. We also derive a closed-form folding model that balances hinge stiffness with elastic band moment to predict equilibrium fold angles; experiments validate the model and yield a design map linking hinge thickness, band size, and hook spacing to target angles. Using this workflow we realize multiple polyhedral modules and demonstrate three applications: a cube that highlights the potential of self-folding for scalable modular robot collectives, a deployable gripper, and a tendon-driven finger. The method is low cost, stimulus-free, and integrates actuation and sensing.

In this paper, we design feedback control laws for soft robots modelled using the Cosserat rod, which is spatially discretised using the Piecewise Constant Strain (PCS) approach. The PCS approach transforms the nonlinear PDEs describing the Cosserat rod to a system of nonlinear ODEs. This simplification results in a model describing soft robots which is similar to the serial rigid-link manipulators. We design feedback control laws for the quasi-static PCS model by using external wrenches as control inputs. The control laws are designed based on state-feedback linearisation in strain and task spaces. An extensive set of numerical results demonstrates the performance of the control laws for end-effector trajectory tracking and shape control of soft robots.

Reliable estimation of neuromuscular activation is a key enabler for adaptive and personalized control in wearable robotics. However, surface electromyography (EMG) remains difficult to deploy robustly outside laboratory settings due to electrode sensitivity, signal non-stationarity, and strong subject dependence. In this work, we propose an adaptive IMU-to-EMG learning framework that reconstructs continuous muscle activation envelopes from wearable inertial measurements across heterogeneous movement conditions. The approach combines a Transformer encoder with Gaussian Error Gated Linear Units (GEGLU-Transformer) to enhance cross-subject generalization and enable rapid subject-specific personalization. Under a strict leave-one-subject-out (LOSO) protocol on a multi-condition lower-limb biomechanics dataset, the proposed architecture achieves r = 0.706 +/- 0.139 and R^2 = 0.474 +/- 0.208 without subject-specific adaptation. With only 0.5% adaptation data, performance increases to r = 0.761 +/- 0.030 and R^2 = 0.559 +/- 0.047, demonstrating rapid adaptation and early performance saturation. These results support attention-based architectures combined with lightweight adaptation as a practical and scalable alternative to direct EMG sensing for real-world wearable robotic applications.

3D-printed artificial skins are a scalable approach to whole-body tactile and proximity coverage, but prior implementations have been limited to unimodal sensing and rigid materials. To improve the practical usability of 3D-printed artificial skins, we present a hybrid time-of-flight (ToF) and self-capacitance (SC) sensing skin that demonstrates multi-modal sensing integration, soft compliant coverings for impact absorption and pressure sensing, and a streamlined electrical interface between printed conductive traces and external electronics. We show that combining ToF and SC modalities enables contact detection, scene reconstruction, and pressure-correlated tactile responses with the compliant covering by deploying six artificial skin units with 40 sensing elements over an FR3 robot arm.

Haptic feedback has been a long-missed feature in robotic-assisted surgery, one that would allow surgeons to perceive tissue properties and apply controlled forces during delicate procedures. Although commercial robotic systems have begun to integrate haptic technologies, their high costs limit accessibility for training and research purposes. To address this gap, we extend our previously developed low-cost robotic surgery training setup, RoboScope, by incorporating a wrist-mounted force/torque (F/T) sensor for haptic feedback training. Wrist-mounted sensing avoids many challenges associated with tip-mounted sensors but introduces additional non-contact forces, such as gravity, sensor bias, installation offsets, and associated torques, which compromise measurement accuracy. In this paper, we propose a robust real-time compensation method based on recursive least squares (RLS). This method eliminates the need for dataset collection and frequent recalibration while adapting to changing operating conditions. Experimental validation demonstrates that the proposed approach achieves over 95% error reduction in non-contact force compensation and more than 91% in non-contact torque compensation, significantly outperforming existing methods. These results highlight the potential of our approach for providing reliable haptic feedback in robotic surgery training and research.

Functional magnetic composites capable of large deformation, load bearing, and multifunctional motion are essential for next-generation adaptive soft robots. Here, we present muscle-inspired magnetic actuators (MMA), additively manufactured from a thermoplastic/permanent magnet polyurethane/Nd2Fe14B (TPU/MQP-S) composite using laser powder bed fusion (LPBF). By tuning the laser-energy scale between 1.0 and 3.0, both mechanical stiffness and magnetic response are precisely controlled: the tensile strength increases from 0.28 to 0.99 MPa while maintaining 30-45% elongation at break. This process enables the creation of 0.5 mm-thick flexural hinges, which reversibly bend and fold under moderate magnetic fields without damage. Two actuator types are reported showing the system versatility. The elongated actuator with self-weight of 1.57 g, magnetized in its contracted state, achieves linear contraction under a 500 mT field, lifting 50 g (32x its own weight) and sustaining performance over at least 50 cycles. Equipped with anisotropic frictional feet, it supports movement of a magnetic crawling robot that achieves up to 100% locomotion success on textured substrates. The expandable actuator exhibits reversible opening and closing under a 300 mT field, reliably grasping and releasing different objects, including soft berries and rigid 3D printed geometries. It can also anchor in a tube while holding suspended 50 g loads. This work demonstrates a LPBF-based strategy to program both stiffness and magnetization within a single material system, enabling remotely driven, reconfigurable, and fatigue-resistant soft actuators. The approach opens new possibilities for force controlled, multifunctional magnetic soft robots for adaptive gripping, locomotion, and minimally invasive manipulation of biomedical tools.

Dielectric elastomer actuators (DEAs) have garnered extensive attention especially in soft robotic applications over the past few decades owing to the advantages of lightweight, large strain, fast response and high energy density. However, because the DEAs suffer from nonlinear elasticity, inherent viscoelastic creep, hysteresis and vibrational dynamics, the modeling, control and self-sensing of DEAs are challenging, thereby hindering the practical applications of DEAs. In order to address these challenges, numerous studies have been conducted. In this review, various physics-based modeling methods and phenomenological modeling methods for predicting the electromechanical response of DEAs are presented and discussed. Different control methods for DEAs are reviewed, which are classified into open-loop feedforward control, feedback control, feedforward-feedback control and adaptive feedforward control. Physics-based self-sensing methods and data-driven self-sensing methods for reconstructing the DEA displacement without the need for additional sensors are discussed. Finally, the existing problems and new opportunities for the further studies are summarized.

Vine-inspired robots achieve large workspace coverage through tip eversion, enabling safe navigation in confined and cluttered environments. However, their deployment in free space is fundamentally limited by low axial stiffness, poor load-bearing capacity, and the inability to retain shape during and after steering. In this work, we propose a reconfigurable pneumatic joint (RPJ) architecture that introduces discrete, pressure-tunable stiffness along the robot body without compromising continuous growth. Each RPJ module comprises symmetrically distributed pneumatic chambers that locally increase bending stiffness when pressurized, enabling decoupling between global compliance and localized rigidity. We integrate the RPJs into a soft growing robot with tendon-driven steering and develop a compact base station for mid-air eversion. System characterization and experimental validation demonstrate moderate pressure requirements for eversion, as well as comparable localized stiffening and steering performance to layer-jamming mechanisms. Demonstrations further show that the proposed robot achieves improved shape retention during bending, reduced gravitational deflection under load, cascading retraction, and reliable payload transport up to 202 g in free space. The RPJ mechanism establishes a practical pathway toward structurally adaptive vine robots for manipulation-oriented tasks such as object sorting and adaptive exploration in unconstrained environments.

Continuum robots are well suited for navigating confined and fragile environments, such as vascular or endoluminal anatomy, where contact with surrounding structures is often unavoidable. While controlled contact can assist motion, unfavorable contact can degrade controllability, induce kinematic singularities, or introduce safety risks. We present a contact-aware planning approach that evaluates contact quality, penalizing hazardous interactions, while permitting benign contact. The planner produces kinematically feasible trajectories and contact-aware Jacobians which can be used for closed-loop control in hardware experiments. We validate the approach by testing the integrated system (planning, control, and mechanical design) on anatomical models from patient scans. The planner generates effective plans for three common anatomical environments, and, in all hardware trials, the continuum robot was able to reach the target while avoiding dangerous tip contact (100% success). Mean tracking errors were 1.9 +/- 0.5 mm, 1.2 +/- 0.1 mm, and 1.7 +/- 0.2 mm across the three different environments. Ablation studies showed that penalizing end-of-continuum-segment (ECS) contact improved manipulability and prevented hardware failures. Overall, this work enables reliable, contact-aware navigation in highly constrained environments.

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.

Co-design is a high-dimensional search problem in the robot morphology and control design space. Efficient search requires exploiting the structure shaped by their interaction. To understand this structure, we analyze the landscapes of soft locomotion and manipulation tasks. We identify three patterns consistent across regions of their co-design spaces: 1) Within a region, quality varies along a low-dimensional manifold, with minimal variation orthogonal to it, reducing the effective search space dimensionality. 2) In higher-quality regions, the variance in quality is spread across more dimensions, necessitating search to expand dimensionality as quality improves. 3) In higher-quality regions, quality varies along joint morphology-control dimensions, requiring search along them. Using these insights, we devise an efficient co-design algorithm that yields 36% better co-designs than state-of-the-art baselines. We examine their exploration patterns and show that these baselines required an order of magnitude more function evaluations to find co-designs of comparable quality. Finally, we ablate our algorithm to verify that exploiting the identified structure was the key to efficient co-design.

This paper presents the design, modeling, and fabrication of 3D-printed, tendon-actuated continuum robots featuring a flexible, tapered backbone constructed from thermoplastic polyurethane (TPU). Our scalable design incorporates an integrated electronics base housing that enables direct tendon tension control and sensing via actuators and compression load cells. Unlike many continuum robots that are single-purpose and costly, the proposed design prioritizes customizability, rapid assembly, and low cost while enabling high curvature and enhanced distal compliance through geometric tapering, thereby supporting a broad range of compliant robotic inspection and manipulation tasks. We develop a generalized forward kinetostatic model of the tapered backbone based on Cosserat rod theory using a Newtonian approach, extending existing tendon-actuated Cosserat rod formulations to explicitly account for spatially varying backbone cross-sectional geometry. The model captures the graded stiffness profile induced by the tapering and enables systematic exploration of the configuration space as a function of the geometric design parameters. Specifically, we analyze how the backbone taper angle influences the robot's configuration space and manipulability. The model is validated against motion capture data, achieving centimeter-level shape prediction accuracy after calibrating Young's modulus via a line search that minimizes modeling error. We further demonstrate teleoperated grasping using an endoscopic gripper routed along the continuum robot, mounted on a 6-DoF robotic arm. Parameterized iLogic/CAD scripts are provided for rapid geometry generation and scaling. The presented framework establishes a simple, rapid, and reproducible pathway from parametric design to controlled tendon actuation for tapered, tendon-driven continuum robots manufactured using fused deposition modeling 3D printers.

This paper proposes SoftGM, an octopus-inspired distributed control architecture for segmented soft robotic arms that learn to reach targets in contact-rich environments using online obstacle discovery without assuming full obstacle geometry at the start of each episode. SoftGM formulates each arm section as a cooperative agent and represents the arm-environment interaction as a graph. SoftGM uses a two-stage graph attention message passing scheme following a Centralised Training Decentralised Execution (CTDE) paradigm with a centralised critic and decentralised actor. We evaluate SoftGM in a Cosserat-rod simulator (PyElastica) across three tasks that increase the complexity of the environment: obstacle-free, structured obstacles, and a wall-with-hole scenario. Compared with six widely used MARL baselines (IDDPG, IPPO, ISAC, MADDPG, MAPPO, MASAC) under identical information content and training conditions, SoftGM matches strong CTDE methods in simpler settings and achieves the best performance in the wall-with-hole task. Robustness tests with observation noise, single-section actuation failure, and transient disturbances show that SoftGM maintains comparable performance under non-ideal simulated conditions while keeping control effort bounded, suggesting that selective contact-relevant information routing improves resilience in the tested settings.

Equipping robotic systems with the capacity to generate $\textit{ex novo}$ hardware during operation extends physical adaptability. Unlike modular systems that rely on discrete component integration pre- or post-deployment, we envision physical adaptation through continuous in-body development via hardware synthesis. Drawing inspiration from circulatory systems that redistribute mass and function in biological organisms, we utilize fluidics to restructure the material interface, a capability currently unmatched in robotics. Here, we realize this proof-of-concept hardware generation through a vascularized robotic composite designed for programmable material synthesis, demonstrated via receptogenesis - the on-demand construction of sensors. By coordinating the fluidic transport of precursors with external localized UV irradiation, we drove an $\textit{in situ}$ photopolymerization that chemically reconstructed the vasculature from the inside out. This reaction converted precursors with photolatent initiator into a solid dispersion of UV-sensitive polypyrrole in PETG, establishing a sensing modality validated by a characteristic decrease in electrical impedance. The newly synthesized sensor closed a local control loop in real time to regulate wing flapping in a moth-inspired robotic demonstrator. Our work is a proof-of-concept materials basis for $\textit{ex novo}$ hardware generation in a vascularized composite - a step towards situated robots adapting to environmental cues.

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.

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.

This paper presents a quantitative comparison between centralised and distributed multi-agent reinforcement learning (MARL) architectures for controlling a soft robotic arm modelled as a Cosserat rod in simulation. Using PyElastica and the OpenAI Gym interface, we train both a global Proximal Policy Optimisation (PPO) controller and a Multi-Agent PPO (MAPPO) under identical budgets. Both approaches are based on the arm having $n$ number of controlled sections. The study systematically varies $n$ and evaluates the performance of the arm to reach a fixed target in three scenarios: default baseline condition, recovery from external disturbance, and adaptation to actuator failure. Quantitative metrics used for the evaluation are mean action magnitude, mean final distance, mean episode length, and success rate. The results show that there are no significant benefits of the distributed policy when the number of controlled sections $n\le4$. In very simple systems, when $n\le2$, the centralised policy outperforms the distributed one. When $n$ increases to $4< n\le 12$, the distributed policy shows a high sample efficiency. In these systems, distributed policy promotes a stronger success rate, resilience, and robustness under local observability and yields faster convergence given the same sample size. However, centralised policies achieve much higher time efficiency during training as it takes much less time to train the same size of samples. These findings highlight the trade-offs between centralised and distributed policy in reinforcement learning-based control for soft robotic systems and provide actionable design guidance for future sim-to-real transfer in soft rod-like manipulators.