Modeling and predicting the motion of soft robots remains challenging due to their infinite-dimensional and highly nonlinear dynamics. A promising direction is to learn dynamics directly from high-dimensional sensory streams. Yet, standard RGB cameras suffer from motion blur, making it challenging to capture fast transients and biasing learning toward steadystate behaviors. Here, we turn to event-based cameras, which provide asynchronous, high-frequency visual information better suited to capturing dynamic deformations. We propose a learning architecture that encodes two-channel event frames from a DVS sensor through a convolutional autoencoder while jointly learning a compact latent representation of the robot's dynamics. Within this space, we test several latent models, including a novel spiking-harmonic latent oscillator network (snLON), in which spiking neurons capture the event structure of the data stream and drive a latent Oscillator Network that represents the underlying mechanical dynamics. Validated in both simulation and real-world experiments, the proposed framework predicts long-horizon soft-robot motion with high accuracy and consistency from a single initial event frame and control sequence.

Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific, interpretable low-dimensional dynamics directly from data. We propose a methodology that combines a linear autoencoder with symbolic regression to derive such models. The linear autoencoder provides a consistent latent embedding for configurations, velocities, accelerations, and inputs, enabling the sparse identification of nonlinear dynamics (SINDy) to operate in a compact, physics-aligned space. A multi-phase, hybrid-aware training scheme ensures coherent latent coordinates across contact transitions. We focus our validation on quadruped jumping—a representative, challenging, yet contained scenario in which a principled template model is especially valuable. The resulting symbolic dynamics outperform the state-of-the-art handcrafted actuated spring-loaded inverted pendulum (aSLIP) baseline in simulation and hardware across multiple robots and jumping modalities.

Soft robots, compared to rigid robots, possess inherent advantages, including higher degrees of freedom, compliance, and enhanced safety, which have contributed to their increasing application across various fields. Among these benefits, adaptability is particularly noteworthy. In this article, adaptability in soft robots is categorized into external and internal adaptability. External adaptability refers to the robot’s ability to adjust, either passively or actively, to variations in environments, object properties, geometries, and task dynamics. Internal adaptability refers to the robot’s ability to cope with internal variations, such as manufacturing tolerances or material aging, and to generalize control strategies across different robots. As the field of soft robotics continues to evolve, the significance of adaptability has become increasingly pronounced. In this review article, we summarize various approaches to enhancing the adaptability of soft robots, including design, sensing, and control strategies. Additionally, we assess the impact of adaptability on applications such as surgery, wearable devices, locomotion, and manipulation. We also discuss the limitations of soft robotics adaptability and prospective directions for future research. By analyzing adaptability through the lenses of implementation, application, and challenges, this article aims to provide a comprehensive understanding of this essential characteristic in soft robotics and its implications for diverse applications.

Designing accurate yet reliable tracking controllers with tight performance guarantees for Lagrangian systems is challenging due to nonlinear modeling uncertainties and conservative stability criteria. This article proposes a structure-preserving projector-based tracking control law for uncertain Euler-Lagrange (EL) systems using physically consistent Lagrangian-Gaussian Processes (LGPs). We leverage the uncertainty quantification of the LGP for adaptive feedforward-feedback balancing. In particular, an accurate probabilistic guarantee for exponential stability is derived by leveraging matrix analysis results and ideas from contraction analysis, where the benefit of the proposed controller is proven and shown in the closed-form expressions for convergence rate and radius. Extensive numerical simulations not only demonstrate the controller's efficacy based on a two-link and a soft robotic manipulator, but also all theoretical results are explicitly analyzed and validated.

Breastfeeding is essential for infant nutrition, but the increasing number of women returning to work before weaning highlights the need for efficient and comfortable milk expression methods. Traditional breast pumps rely solely on vacuum suction, which can cause discomfort, tissue damage, and longer extraction times compared to natural nursing. This study aims to develop a breast pump that better mimics the biomechanics of infant breastfeeding to improve comfort and efficiency. We investigated two actuator designs–membrane and soft pleated–integrated into the breast shield to replicate infant sucking. The pleated actuator proved most effective, offering a wide range of expansion and contraction. Unlike traditional pumps, vacuum is applied through radial expansion, allowing the nipple to widen rather than elongate, closely simulating infant tongue movements. The breast shield was fabricated using additive manufacturing with soft, elastic materials, enabling complex geometries and varied stiffness. The prototype was tested against a commercial pump using an artificial breast phantom. Results suggest this design can enhance milk output, reduce pumping time, and improve user comfort. By merging soft robotics with biological insights, our approach offers a promising alternative to conventional breast pumps.

Industrial robotics demands significant energy to operate, making energy-reduction methodologies increasingly important. Strategies for planning minimum-energy trajectories typically involve solving nonlinear optimal control problems (OCPs), which rarely cope with real-time (RT) requirements. In this article, we propose a paradigm for generating near minimum-energy trajectories for manipulators by learning from optimal solutions. Our paradigm leverages a residual learning approach, which embeds boundary conditions (BCs) while focusing on learning only the adjustments needed to steer a standard solution to an optimal one. Compared to a computationally expensive OCP-based planner, our paradigm achieves 87.3% of the performance near the training dataset and 50.8% far from the dataset, while being two to three orders-of-magnitude faster.

Segmenting gas bubbles in multiphase flows is a critical yet unsolved challenge in numerous industrial settings, from metallurgical processing to maritime drag reduction. Traditional approaches — and most recent learning-based methods — assume near-spherical shapes, limiting their effectiveness in regimes where bubbles undergo deformation, coalescence, or breakup. This complexity is particularly evident in air lubrication systems, where coalesced bubbles form amorphous and topologically diverse patches. In this work, we revisit the problem through the lens of modern vision foundation models. We cast the task as a transfer learning problem and demonstrate, for the first time, that a fine-tuned Segment Anything Model (SAM v2.1) can accurately segment highly non-convex, irregular bubble structures using as few as 100 annotated images.

Soft robots' ability to safely navigate complex environments motivates the development of algorithms for accurate environmental interaction assessment, enabling greater autonomy. Specifically, strain-based shape and force estimation of continuum robots with embedded soft sensors poses an open challenge mainly owing to continuous softness, anisotropic deformation, and non-linear properties. Mathematical description of deformable soft bodies and accurate estimation of external forces are crucial for achieving controllable and intelligent behaviors of these robots. In this paper, a kinetostatic strain-based modeling for rod-driven soft robots (RDSR) with embedded stretch sensors is proposed, which incorporates local strains, actuation variables, and external interactions. The strain model enables full shape estimation of the robot and prediction of strain variations in soft bodies. Building on this, we develop a force estimator based on predicted and measured sensor and actuator lengths to evaluate 3D external forces, accounting for both orthogonal and tangential components relative to the backbone. Moreover, we introduce a methodology using a novel ellipsoid representation to handle tangential forces that may become insensitive in certain singular configurations. This estimator allows us to either disregard such forces when they do not influence deformation or estimate them when they become observable. Our simulations and experiments demonstrate how this approach can be used to analyze the robot's configuration and successfully estimate external forces. Finally, it is demonstrated that when the continuum arm follows trajectories with higher strain sensitivity, tangential force estimation is significantly improved.

Recent advances in machine learning have begun to embed oscillatory network principles within neural architectures, aiming to enhance computational efficiency and robustness in time-series regression. Building on these developments, we take a step toward applying such principles to the learning of physical dynamics. We introduce Neural Linear Oscillator Networks (nLON): a vision-based framework that extracts compact latent representations of complex motion directly from image sequences. A convolutional autoencoder encodes position and velocity into a low-dimensional manifold, whose temporal evolution is governed by coupled linear mechanical oscillators driven by a linear combination of the inputs. This strong structural prior not only promotes sample efficiency and interpretability but also guarantees that the learned model remains a mechanical, Wiener-type system. From this formulation, we derive closed-loop controllers that ensure stable regulation. We focus on soft robots-systems whose nonlinear, continuous, and high-dimensional dynamics make them both a challenging and ideal testbed for our approach. Using tentacle robots in high-fidelity simulations and real-world experiments, we validate that our framework delivers accurate long-horizon predictions and consistently surpasses state-of-the-art baselines, achieving superior structural fidelity and final-step accuracy. Finally, we leverage the learned dynamics for model-based control, demonstrating in simulation that the resulting scheme achieves robust and reliable tracking.

Soft robots enable safe and adaptive interaction with their environment, but still face major challenges in detecting contact during manipulation. This paper presents a low-cost vision-based setup designed to obtain groundtruth contact areas of soft manipulators without requiring the embedding of sensors into their structure. The platform uses an external camera and controlled lighting to capture the contact interface under different materials and configurations. Three segmentation methods, HSV thresholding, the Segment Anything Model (SAM 2.1), and a CNN with a VGG16 encoder, were compared for performance. Among them, optimized HSV thresholding achieved the best balance between accuracy and simplicity, with a Dice score of 0.97 and a mean error of 8% on reference tests. The proposed setup provides a practical and reproducible method to study contact formation in soft robotics and a reproducible method for obtaining ground-truth data for tactile sensing and control.

Soft robots, with their compliant and underactuated nature, pose significant challenges for real-time shape regulation. Practical implementations of these methods often rely on fully-actuated approximations, over-looking the underactuated nature of these continuum structures. This study experimentally validates model-based controllers through collocated control that explicitly address underactuation, incorporating gravity cancellation and elasticity compensation to outperform conventional PD/PID approaches. A new multi-segment soft robot with a passively actuated segment has been designed, enabling experimental validation and providing strong evidence of the controllers’ effectiveness. The work bridges theory and practice, offering a practical framework for real-time shape regulation applicable to diverse soft robotic systems.

Robots operating alongside people, particularly in sensitive scenarios such as aiding the elderly with daily tasks or collaborating with workers in manufacturing, must guarantee safety and cultivate user trust. Continuum soft manipulators promise safety through material compliance, but as designs evolve for greater precision, payload capacity, and speed, and increasingly incorporate rigid elements, their injury risk resurfaces. In this letter, we introduce a comprehensive High-Order Control Barrier Function (HOCBF) + High-Order Control Lyapunov Function (HOCLF) framework that enforces strict contact force limits across the entire soft-robot body during environmental interactions. Our approach combines a differentiable Piecewise Cosserat-Segment (PCS) dynamics model with a convex-polygon distance approximation metric, named Differentiable Conservative Separating Axis Theorem (DCSAT), based on the soft robot geometry to enable real-time, whole-body collision detection, resolution, and enforcement of the safety constraints. By embedding HOCBFs into our optimization routine, we guarantee safety, allowing, for instance, safe navigation in operational space under HOCLF-driven motion objectives. Extensive planar simulations demonstrate that our method maintains safety-bounded contacts while achieving precise shape and task-space regulation. This work thus lays a foundation for the deployment of soft robots in human-centric environments with provable safety and performance.

Motor imagery (MI), an important category in electroencephalogram (EEG) research, often intersects with scenarios demanding low energy consumption, such as portable medical devices and isolated environment operations. Traditional deep learning (DL) algorithms, despite their effectiveness, are characterized by significant computational demands accompanied by high energy usage. As an alternative, spiking neural networks (SNNs), inspired by the biological functions of the brain, emerge as a promising energy-efficient solution. However, SNNs typically exhibit lower accuracy than their counterpart convolutional neural networks (CNNs). Although attention mechanisms successfully increase network accuracy by focusing on relevant features, their integration in the SNN framework remains an open question. In this work, we combine the SNN and the attention mechanisms for the EEG classification, aiming to improve precision and reduce energy consumption. To this end, we first propose a noniterative leaky integrate-and-fire (NiLIF) neuron model, overcoming the gradient issues in traditional SNNs that use iterative LIF neurons for long time steps. Then, we introduce the sequence-based attention mechanisms to refine the feature map. We evaluated the proposed noniterative SNN with attention (NiSNN-A) model on two MI EEG datasets, OpenBMI and BCIC IV 2a. Experimental results demonstrate that: 1) our model outperforms other SNN models by achieving higher accuracy and 2) our model increases energy efficiency compared with the counterpart CNN models (i.e., by 2.13 times) while maintaining comparable accuracy.

Quadrupedal jumping has been intensively investigated in recent years. Still, realizing controlled jumping with soft landings remains an open challenge due to the complexity of the jump dynamics and the need to perform complex computations during the short time. This work tackles this challenge by leveraging trajectory optimization and behavior cloning. We generate an optimal jumping motion by utilizing dual-layered coarse-to-refine trajectory optimization. We combine this with a variable impedance control approach to achieve soft landing. Finally, we distill this computationally heavy jumping and landing policy into an efficient neural network via behavior cloning. Extensive simulation experiments demonstrate that, compared to classic model predictive control, the variable impedance control ensures compliance and reduces the stress on the motors during the landing phase. Furthermore, the neural network can reproduce jumping and landing behavior, achieving at least a 97.4% success rate. Hardware experiments confirm the findings, showcasing explosive jumping with soft landings and on-the-fly evaluation of the control actions.

Obtaining dynamic models of continuum soft robots is central to the analysis and control of soft robots, and researchers have devoted much attention to the challenge of proposing both data-driven and first-principle solutions. Both avenues have, however, shown their limitations; the former lacks structure and performs poorly outside training data, while the latter requires significant simplifications and extensive expert knowledge to be used in practice. This paper introduces a streamlined method for learning low-dimensional, physicsbased models that are both accurate and easy to interpret. We start with an algorithm that uses image data (i.e., shape evolutions) to determine the minimal necessary segments for describing a soft robot's movement. Following this, we apply a dynamic regression and strain sparsification algorithm to identify relevant strains and define the model's dynamics. We validate our approach through simulations with various planar soft manipulators, comparing its performance against other learning strategies, showing that our models are both computationally efficient and 25x more accurate on out-of-training distribution inputs. Finally, we demonstrate that thanks to the capability of the method of generating physically compatible models, the learned models can be straightforwardly combined with model-based control policies.

The existing model-based control strategies for tendon-driven continuum soft robots neglect the dynamics of the actuation system. Nevertheless, such dynamics have an important impact on the closed-loop performance. This work analyzes the influence of the actuation dynamics in tendon-driven continuum soft robots performing trajectory-tracking tasks. To this end, we use singular perturbation (SP) theory to design controllers that account for such dynamics. We provide the analytical formulation of the SP controllers and their in-depth experimental validation. Additionally, we use high-and low-stiffness tendons to experimentally compare the performance of the proposed SP controllers against traditional feedback control schemes that disregard the actuation dynamics. The experimental results show that SP controllers outperform the approaches that neglect the actuation dynamics by reducing oscillations and achieving lower errors without relying on high gains. Furthermore, it is shown that neglecting the actuation dynamics may lead to instability when the tendons have a low stiffness coefficient.

Model-based manipulation of deformable objects has traditionally dealt with objects while neglecting their dynamics, thus mostly focusing on very lightweight objects at steady state. At the same time, soft robotic research has made considerable strides toward general modeling and control, despite soft robots and deformable objects being very similar from a mechanical standpoint. In this work, we leverage these recent results to develop a control-oriented, fully dynamic framework of slender deformable objects grasped at one end by a robotic manipulator. We introduce a dynamic model of this system using functional strain parameterizations and describe the manipulation challenge as a regulation control problem. This enables us to define a fully model-based control architecture, for which we can prove analytically closed-loop stability and provide sufficient conditions for steady state convergence to the desired state. The nature of this work is intended to be markedly experimental. We provide an extensive experimental validation of the proposed ideas, tasking a robot arm with controlling the distal end of six different cables, in a given planar position and orientation in space.