Deformable

Manipulation involving rigid-deformable interactions, such as hanging clothes or dressing humans, is common in daily life, making it essential for household robots. Compared to single-object manipulation or interactions between rigid bodies, these tasks are particularly challenging due to the rich multi-point contacts and the complex dynamics of the deformable bodies during interaction. Therefore, object-centric representations such as 6D poses or structural points without task-specific information become insufficient for these interactions. In this work, we propose a hybrid correspondence-based representation tailored for rigid-deformable interactions. First, to capture intricate interaction information, we introduce structure-, task-, and interaction-aware sparse keypoints. The keypoints are generated based on the global structures of both rigid and deformable objects, and filtered by their local interaction contacts. However, tracking these sparse keypoints through the interaction remains difficult due to the high-dimensional dynamics of deformable objects. Therefore, we further construct dense correspondences on the deformable objects for accurate keypoint tracking throughout the manipulation. This hybrid design combines the advantages of both representations: sparse keypoints encode rich, task-specific information for fine-grained manipulation, while dense correspondences ensure efficient tracking and generalization to novel deformations, shapes, and scenarios. Together, they enable one-shot transfer to new tasks with minimal demonstrations. Extensive experiments demonstrate the effectiveness and broad applicability of our method.

Modeling continuous object deformation is important for many computer vision and robotics tasks, such as manipulation and simulation. Existing approaches rely on learning-based methods or physics simulators to model shape deformations. However, these approaches either use discrete time steps or are too computationally intensive for real-time applications. We present ODeform, a novel extension of Neural Ordinary Differential Equations to continuous 4D dynamics of deformable objects in 3D space. Our method transforms 3D point clouds and physical conditions (like material properties) into a unified latent space. By solving the resulting ordinary differential equations over time, we model deformations as continuous flows within this learned embedding, eliminating the need for discrete time steps while maintaining computational efficiency. We evaluate our approach on unseen physical parameter configurations, showing improved motion prediction accuracy over baseline methods. Our experiments further demonstrate a successful transfer to real 3D captured objects with novel shapes, along with effective interpolation and extrapolation of the learned dynamics. Our code and data will be made publicly available.

Video generation models achieve high visual quality but often struggle to generate physics-aware videos. Unlike rigid-body motion, which can be described by explicit trajectories or formulas, complex deformation dynamics remain challenging to synthesize. We observe that a lack of physical reasoning for localizing dynamic areas allows irrelevant regions to dilute the model's attention, leading to generation failure. In this paper, we propose DeforM, a reasoning-guided image-to-video generation framework that directs the model's focus toward physics-critical regions. To reason about and localize these critical regions, we introduce a VLM-guided physical reasoning module, DeforM-Reason, to identify target objects and generate spatial-temporal masks. For physical guidance, we develop two alternative strategies: DeforM-Free for training-free mechanism analysis and DeforM-Injection as a powerful training-based generator. Experimental results demonstrate that DeforM improves the realism of generated deformation scenarios, outperforming baseline models in both visual quality and physical consistency.

Dynamic scene reconstruction remains challenging due to the heterogeneous and spatially varying nature of real-world motion. Although recent 3D Gaussian Splatting methods have introduced diverse deformation formulations for dynamic novel view synthesis, each method typically relies on a single deformation model within its representation, which limits robustness across diverse dynamic scenarios. In this work, we study a fundamental problem-multi-deformation modeling for dynamic 3D Gaussian representations-under two distinct integration constraints that differ in when and how multiple deformation experts interact during training. From a Mixture-of-Experts (MoE) perspective, we view multi-deformation modeling as the problem of combining multiple specialized deformation models within a unified 3D representation. We first introduce Mixture of Deformation Experts (MoDE), which integrates multiple deformation experts directly into the deformable Gaussian Splatting pipeline through joint optimization. In MoDE, experts operate on a shared canonical Gaussian representation, enabling multi-deformation modeling without introducing additional training stages or modifying the original optimization schedule. In contrast, we further present Mixture of Experts for Dynamic Gaussian Splatting (MoE-GS) under a different integration constraint, where deformation experts are optimized independently and combined through a separate routing stage. As a result, expert interaction occurs over non-canonical Gaussian representations after individual optimization. Together, these two approaches provide alternative strategies for multi-deformation modeling, clarifying how integration constraints shape the design and behavior of deformation experts in dynamic 3D Gaussian representations. Our code is available at: https://github.com/cvsp-lab/MoE-GS-studio.

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

As urban waste volumes escalate and labor shortages intensify, automated waste sorting systems are becoming a necessity. However, current robotic solutions often struggle with the 3D perception and manipulation of transparent, deformable, or cluttered objects. This work introduces ROBOCYCLE, an autonomous dual-arm robotic recycling platform designed to meet the recycling standards of the Tokyo metropolitan area. Our approach integrates multi-view RGB-D perception, transformer-based instance segmentation using RF-DETR, and 6-DoF grasp planning via the Anygrasp SDK. By processing segmentated point clouds, the system generates robust candidate poses for irregular and deformable waste. The system achieved a 90.3% grasp success rate and 84.3% overall task success rate, effectively performing complex coordinated tasks such as unscrewing PET bottle caps. The proposed platform offers a scalable solution for autonomous waste management in real-world human environments.

Gaussian splatting (GS) has garnered significant attention in VR/AR and digital content creation due to its explicit parameterization and efficient rendering capabilities. However, existing GS-based methods for deformable objects face two key limitations: (i) illumination is erroneously baked into textures, causing physically inconsistent responses under dynamic deformations and lighting changes; (ii) snapshot-based reconstruction restricts post-reconstruction material editing. To address these challenges, we propose Deformable and Relightable GS (DR-GS), a unified Gaussian framework that integrates physically-based inverse rendering, relighting, and deformation-aware manipulation. Through explicitly disentangling geometry, illumination, and material representations, DR-GS overcomes the limitations of static snapshots, resolving unrealistic appearance under varying conditions while enabling post-reconstruction parameter editing. Extensive experiments show that DR-GS achieves leading visual quality across static reconstruction, dynamic deformation, and relighting, reliably preserving reflections and specular highlights on glossy surfaces. It further establishes a fully decoupled geometry-illumination-material pipeline, enabling high-quality 3D asset creation and comprehensive post-editing.

Demonstration augmentation is proposed for cost-efficient data acquisition, but existing methods are fundamentally limited in deformable manipulation due to two challenges: (1) the state space is high-dimensional with physics-induced constraints, making valid configurations impossible to reach via low-dimensional pose perturbations; and (2) trajectory transfer is non-equivariant, as material points no longer move rigidly together under deformation. We present DeformGen, a dynamics-based augmentation framework that achieves topological diversity for deformable objects. For the state challenge, DeformGen expands the valid state distribution by applying localized physical disturbances and forward-simulating the dynamics to obtain topology-coherent, physically plausible deformable states. For the trajectory challenge, DeformGen transfers source manipulation trajectories via deformation-field warping, which lifts per-particle displacements into a continuous spatial function to adapt the end-effector trajectory consistently with the deformed geometry. In this way, our method jointly augments the state distribution and its associated manipulation behavior. Experiments on high-fidelity deformable manipulation benchmarks show that DeformGen generally improves policy learning compared with training on the original demonstrations alone and with rigid-style augmentation baselines.

Deformable linear objects (DLOs) such as wires, cables, and ropes are common in robotic manipulation tasks, yet simulating them with both visual realism and physical accuracy remains challenging. Existing visual simulation methods typically rely on procedural geometric primitives that lack physically grounded deformation behavior, while physics-based approaches with robot learning support often approximate DLOs as rigid-link chains or generic soft bodies, failing to accurately capture the bending, twisting, and shear mechanics of slender elastic structures. In this work, we introduce DeformX, a co-simulation framework that integrates a dedicated Cosserat rod physics engine with NVIDIA Isaac Sim, enabling DLO simulations that are both physically faithful and visually realistic. Our Cosserat rod engine simulates the dynamics and self-collisions of DLOs, and contact interactions with arbitrary free-form meshes. To achieve high-fidelity visualization, we employ mesh skinning to map discrete rod deformations onto imported CAD models. To the best of our knowledge, DeformX is the one of the first frameworks for DLO simulation that unifies realistic visualization, principled physics, and compatibility with robot learning pipelines. We demonstrate its versatility across synthetic data generation and policy learning for DLO manipulation, and validate visual and physical fidelity through comparisons against real-world experiments. Notably, fine-tuning Segment Anything Model 3 (SAM3) on DeformX-generated data yields a 10.2% mAP@75 improvement in real-image wire segmentation, and a rope-swinging policy trained entirely in DeformX achieves a mean target-hitting error of 6.6 cm on a UR5e manipulator in real-world trials, highlighting its strong sim-to-real transfer capability.

A passive monolithic compliant grasping mechanism that works based on the eversion of an elastically deformable bistable shell is conceptualized. It comprises grasping arms made of beam segments that work in conjunction with the everting shell. The grasper is capable of picking up a stiff object of any shape up to a maximum size and weight. The bistable shell everts upon contact with the object to enable the grasping arms envelop the object forming an enclosure. The mechanism then stays in that configuration until it is actuated again to turn the shell back to its original configuration and thereby opening the enclosure to release the object. The stiffness of the arms decides the payload of the mechanism. The size of the arms decides the largest object that can be grasped and held. The arms have distributed compliance so that they can conform to the shape of the object without applying undue force on it.

Learning-based surrogates for partial differential equations have recently matched the accuracy of classical solvers while achieving orders-of-magnitude speedups, predominantly in fluid settings and structured geometries. In contrast, robust surrogates for deformable solids remain underexplored, despite the presence of nonlinear elasticity, plasticity, and transient behavior that challenge standard architectures. We introduce a multigrid graph neural network for solid mechanics that couples an encoder-processor-decoder backbone with a physics-informed coarsening strategy. Instead of downsampling via geometric heuristics, our method scores nodes using a residual-based measure of local physical activity and preferentially retains regions of high strain or stress concentration, allocating multiscale capacity where it is most needed. This preserves long-range interactions through hierarchical message passing while improving stability over long rollouts. We evaluate on multiple datasets covering linear, nonlinear, and transient regimes, and observe consistent gains in accuracy and rollout stability compared to standard sampling baselines. Our results highlight the importance of physics-informed coarsening for scalable surrogate modeling in solid mechanics.

Monocular 3D shape recovery is fundamental to geometric understanding, yet achieving robust generalization across arbitrary viewpoints and unseen object categories remains a significant challenge. In this paper, we present a generalizable deformation learning framework that reconstructs 3D objects by explicitly deforming a category-level shape template to match the target observation. To address complex shape variations between the template and the target, we introduce a geometry-guided feature modeling mechanism. This process first enriches foundation features with template topology to yield a geometry-aware representation, which is then explicitly correlated with the target observation to guide precise deformation. Furthermore, to bridge the disparity between the fixed template and arbitrary target views, we propose a view-adaptive feature aggregation module. This module leverages multi-view template features and their corresponding camera poses to enrich the canonical template representation, ensuring robust feature alignment regardless of the target's perspective. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art methods in handling large shape variations and diverse viewpoints, exhibiting strong generalization to novel categories and effectively supporting downstream real-world dexterous robotic manipulation tasks. Project homepage: https://GODeform.github.io/

We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.

Manipulating fragile deformable containers, such as disposable plastic cups filled with liquid, demands real-time grip-force adaptation within an extremely narrow force margin: insufficient force causes slip, while excessive force irreversibly deforms the thin wall. Existing approaches struggle to achieve such force-sensitive manipulation tasks. We propose a noise-statistics-based calibration-driven reflex control paradigm with vision-based tactile sensing: by analyzing the sensor's intrinsic noise characteristics (via a brief static-hold-and-unload protocol), we directly derive all controller thresholds, eliminating external force calibration, trial-and-error manual tuning, or material-specific physical models. Instantiating this paradigm, we present TactileReflex, a three-channel closed-loop controller that extracts three image-level proxies, shear intensity ($S_y$), contact intensity ($F_n$), and center of pressure ($C$), from dual visuo-tactile sensors and drives prioritized reflex channels at ~12 Hz for slip suppression, weight-adaptive release, and force protection. Each channel closes the loop directly on its proxy via noise-derived thresholds. Ablation demonstrates that only the full three-channel system is able to prevent irreversible container deformation (5/5 success vs. at most 1/5 for partial configurations). In a dynamic pouring task, fixed-effort baselines fail in all 10 attempts due to pose drift, while TactileReflex achieves 9/10 success across two water volumes. As a self-contained and interpretable controller, TactileReflex can serve as a plug-and-play safety layer beneath high-level manipulation pipelines, including haptic-free VR teleoperation and vision-language-action (VLA) policies.

Autonomous contact-based micromanipulation is challenging because surface and interfacial interactions at the microscale are difficult to model accurately, limiting the use of conventional model-based control and sim-to-real learning. We present a closed-loop sim-to-real reinforcement learning (RL) approach for microfiber shape control on a surface. The central idea is to train geometric shape regulation in a simplified frictionless simulator and rely on real-time visual feedback during deployment to iteratively correct the observed effects of unmodeled surface interactions. An RL policy trained entirely in simulation is transferred directly to a physical dual-gripper micromanipulation system operating at 40 Hz, without retraining or domain adaptation. Using silk microfibers as a testbed, the policy achieves a mean point-wise shape error of 270 $\pm$ 80 $μ$m across twenty-four diverse initial configurations. Across nine specimens covering all combinations of three fiber diameters (50, 80, and 120 $μ$m) and three manipulated lengths (10 mm, 15mm, and 20 mm), the same policy achieves sub-millimeter final shape error without any retraining or retuning. These results show that a policy learned in a simplified simulator can achieve repeatable real-world microfiber shape regulation under surface contact, provided that the task-relevant effects of the sim-to-real mismatch remain observable and correctable within the closed feedback loop.

Simulation-ready physical 3D assets have emerged as a promising direction owing to their broad applicability in downstream tasks. However, most existing 3D generation methods either neglect physical properties or are limited to a single asset category, e.g., rigid, deformable, or articulated objects. To address these limitations, we introduce PhysX-Omni, a unified framework for simulation-ready physical 3D generation across diverse asset types. Specifically, we develop a novel and efficient geometry representation tailored for Vision-Language Models, which directly encodes high-resolution 3D structures without compression, significantly improving generation performance. In addition, we construct the first general simulation-ready 3D dataset, PhysXVerse, covering diverse indoor and outdoor categories. Furthermore, to comprehensively and flexibly evaluate both generative and understanding capabilities in the wild, we propose PhysX-Bench, which encompasses six key attributes: geometry, absolute scale, material, affordance, kinematics, and function description. Extensive experiments with conventional metrics and PhysX-Bench show that PhysX-Omni performs strongly in both generation and understanding. Moreover, additional studies further validate the potential of PhysX-Omni for applications in simulation-ready scene generation and robotic policy learning. We believe PhysX-Omni can significantly advance a wide range of downstream applications, particularly in embodied AI and physics-based simulation.

State Space Models (SSMs) have emerged as a powerful and efficient alternative to Transformers, demonstrating linear-time complexity and exceptional sequence modeling capabilities. However, their application to vision tasks remains challenging. First, existing vision SSMs largely depend on manually designed fixed scanning methods to flatten image patches into sequences, which imposes predefined geometric structures and increases the complexity. Second, the broader adoption of vision SSMs is hindered in domains that require query-based interactions between distinct information streams. This is a result of the inherently causal and self-referential nature of SSMs designed for 1D sequence modeling tasks. This fusion mechanism is indispensable for critical perception tasks such as multi-view 3D fusion. To address these limitations, we propose Deformba, a context adaptive method that dynamically augments the spatial structural information while maintaining the linear complexity of SSMs. Deformba also allows multi-modal fusion like cross attention. To demonstrate the effectiveness and general applicability of Deformba, we test its performance on general 2D vision tasks such as image classification, object detection, and segmentation, as well as 3D vision tasks like BEV perception. Extensive experiments show that Deformba achieves strong performance across various visual perception benchmarks.

Clay sculpting is a nuanced, artistic task involving dexterous manipulation with long-horizon planning to achieve high-level goals. As a robotics problem, we formulate clay sculpting as a shape-to-shape matching challenge. Prior deformable object manipulation work either requires retraining a policy per goal or relies on dynamics models which represent state as sparse point clouds which do not capture important clay features, such as textures, well. We present a method for modeling the dynamics of deformable materials and planning for robotic sculpting in a representation that is visually-aligned, capturing lighting and texture features. With three different deformable materials and various end-effectors, we demonstrate that our dynamics model is comparable in performance to the state-of-the-art with the added benefit of being compatible with visual planning. Our actions are represented as parametrized pushes into clay with a single end-effector, which proved to be suitable for long-horizon (>100 actions) clay relief sculptures. Lastly, we show the benefits of planning in a visually-aligned representation, but also provide analysis providing evidence as to why this representation is challenging to plan in compared to 3D representations.

World models for deformable objects should recover not only geometry and appearance, but also underlying physical dynamics, interaction grounding, and material behavior. Learning such a model from real videos is challenging because deformable linear, planar, and volumetric objects evolve under high-dimensional deformation, noisy interactions, and complex material response. The model must therefore infer a physical state from visual observations, roll it forward under new interactions, and render the resulting dynamics with high visual fidelity. We present DeformMaster, a video-derived interactive physics-neural world model that turns real interaction videos into an online interactive model of deformable objects within a unified dynamics-and-appearance framework. DeformMaster preserves structured physical rollout while using a neural residual to compensate for unmodeled effects, grounds sparse hand motion as distributed compliant actuator for hand-continuum interaction, represents material response with spatially varying constitutive experts, and drives high-fidelity 4D appearance from the predicted physical evolution. Experiments on real-world deformable-object sequences demonstrate DeformMaster's ability to roll out future dynamics and render dynamic appearance, outperforming state-of-the-art baselines while supporting novel action rollout, material-parameter variation, and dynamic novel-view synthesis. Project page: https://can-lee.github.io/deformmaster-web/

Reliable real-time 3D shape sensing is essential for robust control and interpretation of deformable systems during motion. Existing vision-based approaches require line-of-sight and complex instrumentation, limiting operation in occluded and space-constrained settings. Here, we introduce a scalable, skin-like sensor that reconstructs its continuous 3D deformation in real time from distributed strain measurements. The device embeds a 2D array of mirror-stacked, printed oxidized eutectic gallium-indium (o-EGaIn) strain gauges within an elastomeric film to measure off-neutral-axis strains. Combined with a mechanics-informed observation model and a fast optimization routine, the system estimates local curvature, elongation, offset, and orientation under concurrent stretching, bending, and indentation, enabling reconstruction of complex surfaces. A 5-by-5 array with a 12 mm pitch achieves a mean surface reconstruction error of 0.62 mm with 0.1s latency across all tested scenarios. When conforming to complex surfaces, the sensor provides fast 3D shape mapping of the underlying geometry. Demonstrations involving palm gesturing, finger indentation, and contact-induced balloon deformation highlight utility for epidermal motion tracking, haptic interaction, and intraoperative monitoring.

Accurate CT-MRI registration of the cervical spine is essential for preoperative planning because this region is anatomically complex,highly variable,and vulnerable to injury of the vertebral arteries and spinal cord. However,cervical CT-MRI registration remains underexplored,particularly for rigid-deformable hybrid modeling,and the lack of high-quality annotated multimodal data further limits progress. To address these challenges, we construct and release a comprehensively annotated CT-MRI dataset, R-D-Reg, and propose MSR, a rigid-deformable hybrid registration framework for complex joint structures. Specifically, MSR includes a rigid registration module for independent local rigid alignment of individual vertebrae and a deformable registration module with an MSL block that combines Mamba-based global modeling and Swin Transformer-based local modeling through adaptive gating. The rigid and deformable deformation fields are then fused to generate a hybrid field that better preserves local anatomical consistency. The code and dataset are publicly available at https://github.com/ssc1230609-spec/MSR-registration.

Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum. In this work, we propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction. Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum. We train our network in an unsupervised fashion using a physics-based loss, and we show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role.