SoRoMoX: Fast, Differentiable, and Parallelizable Soft Robot Models

Reduced-order models based on Cosserat-rod theory are now well established, and modeling theory is no longer the primary bottleneck in soft-robot control. Their implementations, however, do not support the differentiable, GPU-parallel, and control-oriented workflows that underpin advanced rigid-robotics applications. Here, we fill this gap with SoRoMoX (Soft Robot Models in JAX), a fully numerical, JIT-compilable Python/JAX framework. SoRoMoX implements articulated, Piecewise Constant Strain, and Variable Strain models through a unified, control-ready interface that provides inertia matrices, gravitational and elastic forces, Jacobians, and their derivatives. To our knowledge, it is the first rod/strain-based soft-robot modeling framework that runs directly on GPUs and is end-to-end differentiable with respect to states, inputs, and parameters. Sequential CPU rollouts are up to 18.1x faster than state-of-the-art alternatives, while GPU-parallel rollouts increase throughput by up to 234.6x. This performance enables workflows that were previously impractical or impossible: static-equilibrium system identification with 66% lower marker RMSE; residual-force learning with a further 64% reduction; computed-torque tracking with RMSE reduced by a factor of approximately 500 relative to model-free PD; control-gain optimization with up to 62% lower loss than untuned gains; safety-constrained control using high-order control barrier functions to keep the peak contact force within a prescribed 5 N bound, compared with 33.5 N without the safety constraint; and reinforcement-learning policy training up to 7x faster than a CPU PyElastica discrete-rod baseline through massively parallel rollouts.

From Digital to Physical Reservoir Computing: Co-Optimizing Soft Robotic Reservoirs via Dynamics Matching

Soft robotic substrates are promising for Physical Reservoir Computing (PRC) because their compliant nonlinear dynamics can provide temporal memory, high-dimensional state transformations, and efficient inference. However, physical reservoirs are often adopted as-is rather than pretrained or co-optimized, potentially limiting soft robotic PRC performance relative to digital reservoirs. We investigate whether a physical reservoir can instead be pretrained against high-performing digital reference dynamics. Our formulation jointly optimizes physical parameters, a diffeomorphic physical-reference state map, and feedforward-feedback control using a differentiable physical model and an acceleration-level equation-error objective that avoids temporal integration. As a proof of concept, we instantiate the formulation with simulated soft robots, a Random Oscillators Network (RON) reference, and parallel multi-start gradient descent. We evaluate the optimized reservoirs on classification (sMNIST and ADIAC) and forecasting (Mackey-Glass and Lorenz96) tasks across four reservoir dimensions. Compared with unoptimized soft robot reservoirs, the optimized reservoirs achieve a mean relative improvement of 33.7% across all tasks and datasets, while remaining close to the digital reference. These results demonstrate the feasibility of dynamics-level co-optimization for the simulated soft robotic reservoirs considered here.

A Model-Based Decoupling Strategy for Proprioception and Contact Sensing in an Architected Soft Manipulator

Soft continuum robots require embedded sensing for proprioception and contact detection, yet integrating sensors into sparse, highly deformable architected structures remains challenging. We present a model-based strategy that decouples proprioceptive and contact signals from a common set of fluidic pressure sensors embedded in a soft architected segment. Each segment of the Innervated Trimmed Helicoid (ITH) contains six air channels routed in a localized zigzag pattern along the circumference. With only three principal kinematic degrees of freedom (axial compression, bending in x, bending in y), the six pressure readings form an overdetermined system. A piecewise constant curvature model maps pressures to shape, and Huber regression identifies outlier channels whose residuals indicate external contact. On a single ITH segment, this approach achieves proprioceptive shape estimation with a relative bending error of 0.11 +/- 0.02 and a contact detection rate of 97% across 178 trials. We integrate eight ITH segments into Air-Helix, a tendon-driven soft continuum manipulator, and present exploratory whole-arm demonstrations that include tactile teaching by demonstration, admittance-controlled force regulation, and tactile object reconstruction. The results suggest that localized fluidic innervation combined with model-based redundancy resolution is a practical path toward concurrent proprioception and contact sensing in architected soft robots.

Set-Supervised Diffusion Policy: Learning Action-Chunking Diffusion through Corrections

Diffusion policies have recently emerged as a powerful framework for robotic manipulation. However, like other behavior cloning methods, they remain vulnerable to distributional shift, often requiring human-in-the-loop interventions to correct failures during deployment. These interactions naturally provide paired supervision in the form of the robot's undesired actions and the human teacher's corrective actions. Yet existing data aggregation pipelines and standard behavior cloning losses largely ignore this negative signal from undesired actions, leading to overfitting to teacher's actions and an increasing reliance on costly expert data. To address this limitation, we propose Set-Supervised Diffusion Policy (SDP), a novel learning framework that utilizes contrastive action-chunk data to train diffusion policies from human corrections. From paired positive and negative action-chunks, SDP constructs a set of desired action-chunks and designs a training pipeline that encourages the diffusion policy to align with the set. Through extensive experiments across multiple robotic manipulation tasks, we demonstrate that SDP consistently improves policy performance, with particularly strong gains in robustness to noisy data. Moreover, SDP induces high-quality aggregated datasets, enabling more efficient and reliable policy learning from human-in-the-loop corrections. Our code is available at https://set-supervised-diffusion-policy.github.io/.

Reconciling distributed compliance with high-performance control in continuum soft robotics

High-performance closed-loop control of truly soft continuum manipulators has remained elusive. Experimental demonstrations have largely relied on sufficiently stiff, piecewise architectures in which each actuated segment behaves as a distributed yet effectively rigid element, while deformation modes beyond simple bending are suppressed. This strategy simplifies modeling and control, but sidesteps the intrinsic complexity of a fully compliant body and makes the system behave as a serial kinematic chain, much like a conventional articulated robot. An implicit conclusion has consequently emerged within the community: distributed softness and dynamic precision are incompatible. Here we show this trade-off is not fundamental. We present a highly compliant, fully continuum robotic arm - without hardware discretization or stiffness-based mode suppression - that achieves fast, precise task-space convergence under dynamic conditions. The platform integrates direct-drive actuation, a tendon routing scheme enabling coupled bending and twisting, and a structured nonlinear control architecture grounded in reduced-order strain modeling of underactuated systems. Modeling, actuation, and control are co-designed to preserve essential mechanical complexity while enabling high-bandwidth loop closure. Experiments demonstrate accurate, repeatable execution of dynamic Cartesian tasks, including fast positioning and interaction. The proposed system achieves the fastest reported task-execution speed among soft robots. At millimetric precision, execution speed increases nearly fourfold compared with prior approaches, while operating on a fully compliant continuum body. These results show that distributed compliance and high-performance dynamic control can coexist, opening a path toward truly soft manipulators approaching the operational capabilities of rigid robots without sacrificing morphological richness.

Towards Terrain-Aware Safe Locomotion for Quadrupedal Robots Using Proprioceptive Sensing

Achieving safe quadrupedal locomotion in real-world environments has attracted much attention in recent years. When walking over uneven terrain, achieving reliable estimation and realising safety-critical control based on the obtained information is still an open question. To address this challenge, especially for low-cost robots equipped solely with proprioceptive sensors (e.g., IMUs, joint encoders, and contact force sensors), this work first presents an estimation framework that generates a 2.5-D terrain map and extracts support plane parameters, which are then integrated into contact and state estimation. Then, we integrate this estimation framework into a safety-critical control pipeline by formulating control barrier functions that provide rigorous safety guarantees. Experiments demonstrate that the proposed terrain estimation method provides smooth terrain representations. Moreover, the coupled estimation framework of terrain, state, and contact reduces the mean absolute error of base position estimation by 64.8%, decreases the estimation variance by 47.2%, and improves the robustness of contact estimation compared to a decoupled framework. The terrain-informed CBFs integrate historical terrain information and current proprioceptive measurements to ensure global safety by keeping the robot out of hazardous areas and local safety by preventing body-terrain collision, relying solely on proprioceptive sensing.

SENSE-STEP: Learning Sim-to-Real Locomotion for a Sensory-Enabled Soft Quadruped Robot

Robust closed-loop locomotion remains challenging for soft quadruped robots due to high-dimensional dynamics, actuator hysteresis, and difficult-to-model contact interactions, while conventional proprioception provides limited information about ground contact. In this paper, we present a learning-based control framework for a pneumatically actuated soft quadruped equipped with tactile suction-cup feet, and we validate the approach experimentally on physical hardware. The control policy is trained in simulation through a staged learning process that starts from a reference gait and is progressively refined under randomized environmental conditions. The resulting controller maps proprioceptive and tactile feedback to coordinated pneumatic actuation and suction-cup commands, enabling closed-loop locomotion on flat and inclined surfaces. When deployed on the real robot, the closed-loop policy outperforms an open-loop baseline, increasing forward speed by 41% on a flat surface and by 91% on a 5-degree incline. Ablation studies further demonstrate the role of tactile force estimates and inertial feedback in stabilizing locomotion, with performance improvements of up to 56% compared to configurations without sensory feedback.

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.

Segmenting the Complex and Irregular in Two-Phase Flows: A Real-World Empirical Study with SAM2

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.

A Survey on Soft Robot Adaptability: Implementations, Applications, and Prospects

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 paper, 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, 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 paper aims to provide a comprehensive understanding of this essential characteristic in soft robotics and its implications for diverse applications.