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.

An evolutionary model of animats with VLM-based subjective evaluation

In this study, we propose a framework that incorporates subjective evaluations provided by a Vision-Language Model (VLM) into the fitness evaluation and selection processes of a genetic algorithm. As the target of evolution, we employ virtual soft robots with flexible morphologies and locomotion and present the VLM with sequence images representing the locomotion of two individuals. Selection is performed via pairwise comparisons based on subjective evaluation terms such as adorably and weirdly. The outcomes of these comparisons are used as selection pressure within the genetic algorithm, enabling the simultaneous evolution of morphology and locomotion. Experimental results demonstrate that subjective selection by the VLM accelerates population convergence compared to random selection, while also giving rise to distinctive morphologies and motions corresponding to each evaluation term. An auxiliary experiment with human participants further showed that, although individual pairwise choices only partly agreed with the VLM selections, the resulting morphological and locomotion tendencies were qualitatively similar and repeated human evaluations imposed noticeable fatigue. Moreover, the observation that similar evolutionary outcomes emerged across different evaluation terms suggests that the VLM does not apply these terms in a purely literal manner but instead decomposes them into multiple internal evaluation criteria when making judgments. This work visualizes the evolutionary process through which subjective linguistic expressions are mapped onto embodied phenotypes and provides a foundational framework for analyzing the structure of subjective judgment in VLMs. The proposed approach is expected to contribute to new developments in evolutionary computation and artificial life research based on subjective evaluation.

Deep learning-based prediction of time-resolved adhesive forces in viscoelastic Hertzian contacts

Fast prediction of the response of adhesive soft viscoelastic contacts represents a current challenge in soft robotics and for gripping and manipulation tasks. Determining the complete time-resolved force trajectory requires full numerical simulations, whose computational cost is strongly parameter-dependent, making them impractical for real-time application or design-optimization loops. In this work, we overcome this limitation by training a scalar-conditioned, stateful, sequence-to-sequence deep learning model to predict the full force evolution from a prescribed displacement history for both short- and long-range adhesion regimes. The data set spans four orders of magnitude in loading and unloading rates and includes varied dwell times, with the Tabor parameter ranging from $0.2$ to $3.2$. To enable learning across these heterogeneous time scales, we introduce a fixed-measurement-step (FMS) representation that converts variable-length trajectories into fixed-length sequences while preserving their physical-time information. Different architectures were trained, including long short-term memory (LSTM) networks, temporal convolutional neural (TCN) networks, and time-distributed dense layers with three different Tabor-conditioning mechanisms. The models were compared using global waveform and error metrics. We found that the best-performing model has an LSTM architecture with concatenated conditioning, which achieves a held-out mean-squared error of $5.0\times10^{-4}$, a median pull-off-force error of $\approx2.2\%$, and a median hysteresis error of $\approx1.1\%$. For the held-out protocols, the model predicts a complete force trajectory with a median inference time of $0.16$ s. The model is tested across unseen parameter combinations and against analytical limiting cases, providing a rapid surrogate for repeated numerical evaluations with potential use in control-oriented applications.

A Continual Learning Framework for Adaptive Control of Modular Soft Robots

Soft robots have attracted significant attention in applications such as medical intervention, rehabilitation, and robotic manipulation due to their inherent compliance, flexibility, and high degrees of freedom. Modular soft robots (MSRs), composed of multiple interconnected segments, represent an emerging class of robotic systems with highly deformable and reconfigurable structures capable of performing complex tasks. However, designing controllers for MSRs remains challenging due to their nonlinear dynamics, modeling complexity, and hyper-redundant nature. Existing approaches typically require controllers to be retrained from scratch whenever the robot morphology changes. In this work, we address these challenges through a continual learning inspired control framework capable of incrementally adapting to changes in robot morphology while preserving previously acquired knowledge. Specifically, the proposed framework enables the controller to sequentially learn new MSR configurations without forgetting previously learned ones. In addition, for MSRs with fixed configurations, the same framework can be employed in a distributed manner to learn module-specific dynamics, enabling localized control and improved precision. The proposed approach is validated through closed-loop trajectory tracking experiments in simulation using a tendon-driven soft robot, as well as on a real-world three-module pneumatic soft robotic arm. Furthermore, we demonstrate the adaptive capabilities of the framework through a reaching experiment in which the controller selectively activates only the necessary modules to reach a virtual target position, thereby reducing computational overhead.

THREAD: Trajectory Planning for Hybrid Rigid-Soft Manipulators with Environment-Aware Diffusion

Manipulation in confined environments, such as threading a manipulator through narrow apertures, remains a fundamental challenge, especially for conventional rigid robots. Hybrid rigid-soft manipulators offer promise but face two compounding planning challenges: backbone shapes feasible in free space become infeasible under environmental contact, and planning rigid and soft segments independently ignores their kinematic coupling. We present THREAD, the first diffusion-based trajectory planner for hybrid manipulation, learning a generative prior over physically realizable backbone trajectories conditioned on local environment geometry, with physics-inspired losses encoding curvature, smoothness, and collision constraints jointly across both segments. Trained in simulation, THREAD achieves 92.4% task success with 5x fewer collisions than the strongest baseline. We show cross-embodiment real-world transfer with minimal online updates, successfully threading through apertures as small as 1.3x the soft segment diameter.

Damage Adaptation in Seconds for Architected Materials

Adaptation to damages and in-situ physical repairs is essential for long-term robot autonomy, yet challenging outside of narrowly defined and well-anticipated bounds. In this work we proprioceptively adapt to catastrophic damage in soft-actuated systems in under one minute. Architected materials are well equipped for adaptation: actuator failure occurs gradually rather than acutely, and damage can be described in a low-dimensional, discrete coordinate space. Surprisingly, latent damage representations plus a simple yet robust ensemble method is sufficient for adapting to unseen damage in real-time. Moreover, we identify conditions under which exponential sample complexity collapses to linear sample complexity for learned representations of architected materials, a concrete advantage over rigid components or continuum soft mechanisms. We demonstrate LEAP, our method for adaptive proprioception, via a tracing task for a 6DoF soft wrist based on Handed Shearing Auxetic (HSA) actuators. Our algorithm is able to adapt to cuts, burns, and actuator repairs, enabling simulation-free real-time adaptation that is critical for realizing the promise of soft robots outside the lab. Videos and more information are available at https://murpheylab.github.io/leap.