Daily Papers

The AKSZ formalism is a construction of topological field theories where the target spaces are differential graded symplectic manifolds. In this paper, we describe an analogue of the AKSZ formalism where the target spaces are differential graded contact manifolds. We show that the space of fields inherits a weak contact structure, and we construct a solution to the analogue of the classical master equation, defined via the Jacobi bracket. In the n=1 case, we recover the Jacobi sigma model, and in the n=2 case, we obtain three-dimensional topological field theories associated to Courant-Jacobi algebroids.

Dexterous manipulation with multi-fingered robot hands promises human-level dexterity, but collecting large-scale dexterous robot hand data remains difficult. Learning from human demonstrations has emerged as a scalable alternative to robot teleoperation, providing strong priors on object interaction and contact strategies. Recent sim-to-real RL methods incorporate such priors, but often (i) omit rewards that explicitly incentivize precise contact, yielding weak real-world performance, and/or (ii) generalize poorly to unseen object instances. We propose DemoMimic (Dexterous Motion Mimic), a policy that manipulates objects by focusing on their geometry local to the contact points. Its contact-centric rewards encourage precise contact and improve sim-to-real consistency, yielding a single real-world policy that transfers across objects of varying shape, scale, mass, and friction wherever local contact structure is preserved. Real-world ablations show that DemoMimic achieves 71% success across 16 objects, four tasks, and two robot-hand embodiments, with the smallest sim-to-real drop compared to baselines.

We present the PLATO Hand, a dexterous robotic hand with a hybrid fingertip that combines a rigid fingernail, embedded distal phalanx, and compliant pulp to shape contact behavior during manipulation. By mechanically organizing how contact is initiated, supported, and transmitted at the fingertip, this structure creates stable and task-relevant contact conditions across diverse object geometries and grasp orientations. We develop a strain-energy-based bending--indentation model to guide the fingertip design and to explain how material stiffness and contact geometry govern deformation partitioning within the fingertip. Experiments show improved pinch stability, improved fingernail-mediated dorsal-contact force transmission and proprioceptive observability, and successful execution of edge-sensitive manipulation tasks, including paper singulation, card picking, and orange peeling. These results show that coupling a mechanically structured contact interface with a force-motion-transparent finger mechanism provides a principled approach to precise manipulation. Our project page is at: https://platohand.github.io

Contact-rich manipulation requires estimating forces, slip and contact geometry that can remain ambiguous in scene images. Optical tactile sensors provide both visual observations of the contact surface and mechanical measurements, yet learning from these signals raises two challenges: representing contact beyond appearance and transferring its benefits to a policy that does not require fingertip observations at deployment. We introduce HapticWAM, a world-action model that combines heterogeneous tactile encoding, structured contact prediction and teacher-student distillation. Its teacher encodes gel images together with deformation, shear, distributed forces, resultant wrench and derived contact state into a frozen video backbone. Rather than predicting tactile pixels alone, the model jointly generates actions and a contact package describing future events and mechanics. Anticipatory Contact Coupling uses the previously imagined package to condition attention, preserving a contact-related input when direct tactile observations are unavailable. Haptic-Imagination Distillation transfers both contact futures and action predictions to a student that retains the generative contact head but removes its fingertip input branches. On a real-world setup, across three contact-rich pick-and-place tasks, HapticWAM Student achieves a 77% per-task mean success rate (41 of 50 starts, 82% pooled), reaching 95% on one of the tasks, outperforming the evaluated teacher and baseline configurations.

Whole-body motion tracking policies turn a humanoid into a robust control interface: the teleoperator---or an upstream model---only supplies a coarse movement intent, while the low-level policy keeps the robot balanced and physically feasible. Existing trackers deliver this interface only on flat ground: trained in empty scenes, they never learn how contact with terrain and objects reshapes their dynamics, and they attempt to teach the policy to balance under any command by continually enlarging the reference-motion corpus, which stops working once feasible behaviors become environment-dependent. We present GigaBrain-WBC-0.5, the first Behavior World Model (BWM) for humanoid whole-body control. Rather than a purely reactive tracker, we train a causal Transformer to jointly predict its next action, next state, and the distribution over its next latent behavior command, so the network that acts also models how the environment shapes what it can do next. An automatic terrain-annotation pipeline recovers full 3D contact geometry from retargeted motion, enabling terrain annotation at the scale of existing motion datasets. The predicted distribution is reused at deployment to detect implausible commands online and retract them onto learned behaviors, so the robot attempts tasks in a "best-effort" manner. The result is a unified policy that takes real-time command, interacts with environment, and stays robust to implausible commands, falls, and disturbances. GigaBrain-WBC-0.5 achieves the highest success rate across all four regimes among three large-scale tracker baselines: 81.3% on terrain interaction (4.3x the strongest baseline), 83.1% under implausible commands, and 99.3% fall recovery (16.8x the strongest baseline). Hardware trials show robust interaction under missing supports and disturbances; the Unitree G1 checkpoint transfers to the Maker L01 robot with simple fine-tuning.

Single molecule junctions exhibit dynamic structural configurations that strongly influence their electronic and thermoelectric properties. Here, we combine conductance (G) and Seebeck coefficient (S) measurements using the novel AC based scanning tunnelling microscope break junction technique to probe the real-time evolution of oligo(phenylene ethynylene) molecular junctions. We show that most junctions undergo configuration changes that lead to notable changes in S while G remains nearly constant. Density functional theory and quantum transport simulations link these observations to variations in contact geometry and charge transfer at the molecule electrode interface. Our results demonstrate that simultaneous G and S measurements enable direct access to the dynamic reconfiguration of single molecule junctions and offer design insights for thermoelectric molecular devices and new routes for increasing single molecule junction stability.

Establishing a universal benchmark for tactile representation learning in robotic manipulation remains challenging due to the diversity of tactile sensor designs, data formats, and robot embodiments. Rather than seeking to establish such, we explore a scalable and promising direction for future development: egocentric vision paired with full-hand tactile data. To this end, we introduce HT-Bench, a large-scale multi-task benchmark for dexterous full-hand tactile sensing, comprising 10M RGB frames and 7.8M tactile frames collected across 226 tasks. HT-Bench evaluates tactile representations from three key perspectives: whether they encode meaningful contact geometry, whether they can align tactile observations with visual information, and whether they generalize to unseen tasks. To assess these capabilities, HT-Bench includes four tasks: fine-grained tactile similarity retrieval, masked tactile inpainting, vision-to-tactile synthesis, and multimodal tactile frame prediction. We further propose HandTouch, a vector-quantized vision--tactile encoder that learns tactile representations through progressive spatial, cross-modal, and temporal training. Across HT-Bench, HandTouch consistently outperforms representative tactile encoder baselines, improving Recall@5 on fine-grained tactile similarity retrieval from 74.65\% to 85.23\%, reducing RMSE on masked tactile inpainting from 0.022 to 0.010, and increasing OOD cIoU on vision-to-tactile synthesis from 0.628 to 0.705. These results demonstrate the effectiveness of HandTouch and suggest that large-scale egocentric full-hand tactile data provides a scalable basis for evaluating and advancing tactile representation learning in dexterous manipulation.

Tactile sensing provides contact information that can be difficult to infer from vision alone, but tactile hardware for dexterous hands has not converged to a common design. Dexterous hands differ in finger structure, contact surfaces, and sensor layouts, while simulated tactile signals still differ from measurements produced by physical sensors. These factors make it difficult to study visuo-tactile manipulation across diverse dexterous hands within a consistent experimental setting. We present Bench2Dex, a simulation benchmark for visuo-tactile bimanual manipulation across 12 dexterous hands. We adapt existing robot models with a shared simulated tactile interface that converts local contact geometry into image-like tactile observations. The interface provides a consistent observation format across different hand morphologies without attempting to reproduce the output of a specific physical tactile sensor. Bench2Dex includes 26 bimanual manipulation tasks that involve tool use, articulated-object interaction, and multi-stage manipulation, together with about 1.3K human-teleoperated demonstrations. The benchmark provides synchronized visual, tactile, proprioceptive, action, and object-state observations, together with executable task metrics. For robustness, we group seven perturbation types into invariance axis, where the correct action does not change, and equivariance axis, where the correct action changes together with the perturbation. We evaluate ACT, Diffusion Policy, pi0.5, and GR00T N1.5 on Bench2Dex and report their performance and failure modes. Bench2Dex is meant as a platform for studying visuo-tactile learning across dexterous hands. It does not assume that simulated tactile observations can replace real tactile sensing; it offers a shared setting for algorithm development while tactile hardware and simulation models are still evolving.

Recent advancements in vision-language-action (VLA) models have shown promise in robotic manipulation, yet they continue to struggle with long-horizon, multi-step tasks. Existing methods lack internal reasoning mechanisms that can identify task-relevant interaction cues or track progress within a subtask, leading to critical execution errors such as repeated actions, missed steps, and premature termination. To address these challenges, we introduce PALM, a VLA framework that structures policy learning around interaction-centric affordance reasoning and subtask progress cues. PALM distills complementary affordance representations that capture object relevance, contact geometry, spatial placements, and motion dynamics, and serve as task-relevant anchors for visuomotor control. To further stabilize long-horizon execution, PALM predicts continuous within-subtask progress, enabling seamless subtask transitions. Across extensive simulation and real-world experiments, PALM consistently outperforms baselines, achieving a 91.8% success rate on LIBERO-LONG, a 12.5% improvement in average length on CALVIN ABC->D, and a 2x improvement over real-world baselines across three long-horizon generalization settings.

Text-conditioned full-body human-object interaction (HOI) generation requires synthesizing human motion and object trajectories that match the input text while remaining precisely coordinated over time. Most methods represent the human and object as separate trajectories and predict the global human-object couplings. Learning this complex, dynamically changing relationship implicitly, however, often yields object drift, missed contact, and penetration. We introduce PAMI, a Part-Anchored Motion framework for Interaction generation. Inspired by the classic Hough Transform, our key idea is to localize object motion by letting body-part anchors vote for it: we express object motion relative to multiple body-part anchors and use PamiVAE to learn an interaction latent space, decoding frame-wise weights that aggregate these part-specific votes. Building on this representation, PAMI generates interactions in a coarse-to-fine hierarchy. PamiGen first generates a coarse human-object interaction from text in this structured latent space, and PamiRefiner then recursively resolves fine-grained contact geometry using a hybrid surface-sensing representation, combining long-range probes that capture overall body-part influence with short-range sensors that resolve detailed contacts near the object surface. Experiments on InterAct show that PAMI generates more faithful interactions and more accurate human-relative object motion than previous methods, achieving 14.5% higher contact recall than the previous state of the art. Extensive ablations validate the contributions of both the part-anchored voting representation and hybrid surface-sensing refinement.

Anticipating how users will interact with their surroundings is essential for proactive systems that provide timely assistance in AR, VR, and embodied applications. Prior work typically forecasts hand-object interactions directly from historical observations, leaving intention and contact geometry implicit. However, similar observation histories can precede semantically or geometrically distinct futures. Inspired by behavioral evidence that gaze can provide early cues for underlying intention, we propose Gaze2HOI, a gaze-aware framework that formulates hand-object interaction forecasting as a hierarchical problem comprising intention inference, contact grounding, and coupled hand-object motion generation. Specifically, Gaze2HOI first weights gaze cues by fixation strength and recency, and uses them to modulate the visual representations of a vision-language model (VLM) through Temporal Gaze Saliency Modulation (TGSM), thereby reducing semantic ambiguity in intention inference. Subsequently, an Anticipatory Contact Grounding (ACG) module maps these structured intentions into explicit contact, support, and placement fields, effectively mitigating geometric ambiguity. Driven by these explicit conditions, a diffusion-based model jointly generates the 6-DoF object trajectories and future articulated motion of both hands. To evaluate Gaze2HOI, we further introduce EgoAIM, a phase-aware benchmark that organizes egocentric hand-object interactions into four phases defined by evolving hand-object relations and provides fine-grained intention annotations. Extensive experiments demonstrate that Gaze2HOI achieves state-of-the-art performance in both intention inference and motion forecasting, even approaching oracle-level end-to-end performance in specific interaction phases. Project page: https://gaze2hoi.github.io/.

VLA models encode visual observations as 2D patch tokens with no intrinsic geometric structure. We introduce GST-VLA with two contributions. First, the Gaussian Spatial Tokenizer (GST) converts frozen dense depth and frozen semantic patch features into N_g{=}128 anisotropic 3D Gaussian primitives, each parameterized by a metric residual mean μin R^3, log-scale covariance log σin R^3, and learned opacity αin (0,1). The covariance eigenstructure encodes local surface orientation, and opacity provides per-primitive geometric confidence, both inaccessible from scalar depth. Spatial attention pooling with learned queries concentrates the fixed token budget on geometrically salient regions rather than distributing uniformly. Second, 3D Depth-Aware Chain-of-Thought (DA-CoT) reasoning supervises four structured intermediate spatial thoughts, covering 3D object grounding, grasp affordance contact geometry, pairwise metric distances, and coarse SE(3) waypoints, as explicit generation targets in the training loss. A cross-attention sublayer at every VLM transformer block provides direct access to the raw 256-primitive Gaussian field during DA-CoT generation. A 300M-parameter flow-matching action expert with mixture-of-experts feedforward sublayers decodes 7-DoF delta action chunks via conditional ODE integration, conditioned on both VLM hidden states and DA-CoT outputs through dual cross-attention. Trained with composite L_flow + L_CoT + L_depth across three progressive stages, GST-VLA achieves 96.4% on LIBERO (+2.0%), and 80.2% on SimplerEnv (+5.4%). Ablations isolate the contribution of each GST component, each DA-CoT thought, and each training stage, confirming independent and synergistic gains concentrated on precision demanding tasks.

Teleoperation is a key approach for collecting high-quality, physically consistent demonstrations for robotic manipulation. However, teleoperation for dexterous manipulation remains constrained by: (i) inaccurate hand-robot motion mapping, which limits teleoperated dexterity, and (ii) limited tactile feedback that forces vision-dominated interaction and hinders perception of contact geometry and force variation. To address these challenges, we present TAG, a low-cost glove system that integrates precise hand motion capture with high-resolution tactile feedback, enabling effective tactile-in-the-loop dexterous teleoperation. For motion capture, TAG employs a non-contact magnetic sensing design that provides drift-free, electromagnetically robust 21-DoF joint tracking with joint angle estimation errors below 1 degree. Meanwhile, to restore tactile sensation, TAG equips each finger with a 32-actuator tactile array within a compact 2 cm^2 module, allowing operators to directly feel physical interactions at the robot end-effector through spatial activation patterns. Through real-world teleoperation experiments and user studies, we show that TAG enables reliable real-time perception of contact geometry and dynamic force, improves success rates in contact-rich teleoperation tasks, and increases the reliability of demonstration data collection for learning-based manipulation.

Video-Action Models (VAMs) leverage the broad visual dynamics captured by pre-trained video diffusion models, offering a promising path toward generalizable robot manipulation. However, RGB-only video rollouts are not directly actionable: they leave metric 3D motion, contact geometry, and fine-grained spatial constraints under-specified, making action grounding ambiguous. Meanwhile, scaling action supervision across diverse tasks and embodiments remains costly. We present PointAction, a framework that bridges video predictions to robot actions through explicit point-based 4D modeling. PointAction fine-tunes a foundation video generation model to jointly predict future RGB frames and dynamic 3D pointmaps, producing temporally consistent 3D motion of task-relevant scene geometry. These point dynamics serve as a structured, embodiment-agnostic action interface, which a diffusion-based action decoder maps to executable robot actions. By using metric 3D point dynamics as the interface between video prediction and control, PointAction reduces the ambiguity of RGB-only action grounding and supports transfer across tasks and embodiments with limited action supervision. Experiments show that PointAction achieves state-of-the-art 4D generation quality on robot scenes, outperforms existing baselines in simulation, and generalizes to two real robot arms unseen during pretraining.

World action models (WAMs) have recently shown promise in jointly modeling future observations and executable robot actions. However, most existing WAMs still operate in 2D video or latent spaces, where visually plausible rollouts miss the 3D spatial constraints and occluded contact geometry required for precise manipulation. While geometric foundation models offer strong priors for recovering dense 3D structure and motion from visual observations, forcing WAMs to predict the dense 4D representation introduces costly geometric decoding and slows down causal action generation. To address the trade-off, we present WAM4D, a fast 4D world action model that uses lightweight spatial register tokens as training-time future-depth readouts to transfer pretrained geometric priors into a causal video-action transformer, then removes the register branch for lightweight action inference. To prevent non-causal shortcuts, we further design causal mixture attention for the Mixture-of-Transformers (MoT) WAM backbone, defining modality-specific visibility among video, action, and geometry tokens. Comprehensive experiments on RoboTwin 2.0 and challenging real-world manipulation tasks show that WAM4D improves spatial consistency and achieves competitive action prediction while maintaining efficient inference.

Joint-Embedding Predictive Architectures (JEPAs) learn world models by predicting in representation space rather than reconstructing pixels, making them a natural backbone for latent model predictive control from offline demonstration logs. JEPA-style training optimizes short-horizon latent prediction, whereas planning requires a multi-step ranking of imagined futures by goal progress. Prior JEPA planners often inherit that ranking from embedding geometry, typically latent Euclidean distance, which arises as a byproduct of representation learning rather than as a progress cost mined from the logs. We propose temporal-distance JEPA (TD-JEPA), which retains the LeWM encoder--predictor backbone and mines a directed temporal cost from reward-free trajectories: same-trajectory step order supplies positive targets, cross-trajectory pairs act as heuristic negatives, and a rollout-consistency term matches the planner horizon. The mined supervision serves two roles: as the deployed planning cost when progress is topological, and as a representation signal that improves Euclidean planning when contact geometry dominates. Under locked evaluation, deploying the mined cost raises Two-Room success to 100.0% versus LeWM's 97.4%, while shared Euclidean planning on the same temporally trained checkpoint raises OGB-Cube by 14.2 points over LeWM and improves Push-T. Against LeWM and the concurrent RC-aux baseline under locked evaluation, TD-JEPA matches or exceeds both methods on every environment. Ablations show that the directed head, cross-trajectory negatives, and rollout consistency each contribute. TD-JEPA narrows the train--plan gap for JEPA world-model planners by discovering temporal progress structure in offline logs and co-designing cost form with plan-time deployment. Code is available at https://github.com/HKBU-KnowComp/TD-JEPA.

World action models jointly learn to forecast world dynamics and predict robot actions, such that the learned internal world dynamics guide accurate actions. Existing approaches typically represent the world as RGB frames or latent counterparts while predicting actions as end-effector poses or joint angles, but they often struggle to capture the 3D spatial structure and contact geometry central to dexterous manipulation. We introduce Point World Action Model (PointWAM), a 3D world action model that decomposes the world into a scene (i.e., environment) and hands (i.e., actor), and jointly forecasts both as 3D point trajectories within a shared space-time coordinate frame. This explicit, disentangled representation enables effective pre-training on large-scale human demonstration videos without requiring any task-specific object or keypoint selection. Given a colored point cloud and a language instruction, PointWAM predicts how the scene and hands co-evolve in 3D space over time, then retargets the forecast hand motion to robot actions. Pre-training on human videos improves average DexJoCo success by 56.9 percentage points, and scene-trajectory supervision adds 10.9 points over forecasting the hands alone. With both, PointWAM surpasses the prior state of the art on ten DexJoCo tasks by 11.7 points and outperforms strong VLAs on a real robot.

Monocular videos of human manipulation provide abundant dexterous demonstrations, yet reconstructing hand-object interaction from a single view and transferring it to robot hands remain difficult, limiting their direct use for robot execution. Prior methods either require task-specific RL training, limiting scalability, or assume clean motion-capture trajectories and thus cannot operate directly on video. We present OmniHOI, a pipeline that turns an RGB video of hand-object interaction into an interaction-faithful trajectory on dexterous hands. The key idea is to enforce physical consistency using the evidence available at each stage: image evidence during reconstruction, contact geometry during retargeting, and dynamics during physics-in-the-loop refinement. Each stage optimizes the corresponding representation directly, correcting errors before they propagate downstream or must be absorbed by a learned policy. Across 150 motion-capture trajectories transferred to each of five dexterous hands with 6 to 22 DoF, we achieve 39-89% success, compared with at most 31% for prior transfer methods. On 60 monocular video clips, we achieve 53% success, compared with 28% for the best prior video-to-robot pipeline. Its trajectories also execute on a real bimanual robot across diverse tasks.

Handheld devices have opened up unprecedented opportunities to collect large-scale, high-quality demonstrations efficiently. However, existing systems often lack robust tactile sensing or reliable pose tracking to handle complex interaction scenarios, especially for bimanual and contact-rich tasks. In this work, we propose ViTaMIn-B, a more capable and efficient handheld data collection system for such tasks. We first design DuoTact, a novel compliant visuo-tactile sensor built with a flexible frame to withstand large contact forces during manipulation while capturing high-resolution contact geometry. To enhance the cross-sensor generalizability, we propose reconstructing the sensor's global deformation as a 3D point cloud and using it as the policy input. We further develop a robust, unified 6-DoF bimanual pose acquisition process using Meta Quest controllers, which eliminates the trajectory drift issue in common SLAM-based methods. Comprehensive user studies confirm the efficiency and high usability of ViTaMIn-B among novice and expert operators. Furthermore, experiments on four bimanual manipulation tasks demonstrate its superior task performance relative to existing systems. Project page: https://chuanyune.github.io/ViTaMIn-B_page/

Visual policies learned from human videos, teleoperation, and robot demonstrations offer scalable motion priors, but often fail in contact-rich manipulation, where success significantly depends on local force and contact geometry. Tactile sensing provides these complementary signals, yet tactile data remain costly to collect and hard to generalize across sensors, robots, and tasks. We introduce OmniTacTune, a policy-agnostic real-world RL pipeline that adapts tactile feedback to pretrained visual policies through residual correction. OmniTacTune uses a two-stage design: it first bootstraps tactile-aware learning from autonomous base-policy rollouts, then learns a lightweight tactile residual policy through online interaction. Extensive experiments show that OmniTacTune generalizes across diverse contact-rich tasks, visual base policies, and tactile representations. Across four real-world contact-rich tasks, it improves visual base policies from 5-40% success to 85-100% within 40-80 minutes, demonstrating an efficient path for adapting tactile feedback to scalable visual robot policies. Project page: https://colinyu1.github.io/omnitactune-site/

Learning humanoid-object interaction requires coordinating whole-body balance, locomotion, and dexterous hand contact to control both robot and object motion. Human demonstrations provide examples of coordinated interaction, but transferring these behaviors to humanoid robots requires learning how to establish and maintain effective contacts under different embodiments and dynamics. We present Weave, a unified framework for learning whole-body dexterous humanoid-object interaction from captured human demonstrations. Weave first converts captured human-object interactions into executable robot-object references through contact-aware retargeting and approach-motion completion. At its core is a contact- and geometry-aware policy that jointly commands 29 body joints and 12 actuated finger joints across multiple objects and interaction sequences. Evaluation across nine objects yields a 92.5% success rate on trained interactions and, without any additional training, 65.0% on sequences never seen during training. We additionally release ~9,000 physically executed rollouts spanning ~23 hours, providing robot-object trajectories with contact annotations for downstream interaction-policy learning and physically consistent HOI motion generation. Project website: https://xiaohu-art.github.io/Weave/

Text-to-image and personalized editing models now synthesize high-fidelity single-subject images with ease. Yet placing multiple named people into shared contact actions such as embrace, carry, or grapple still exposes major failures: fused limbs, invented extremities, and interpenetrating bodies. Existing evaluations largely overlook these anatomical and geometric issues, and VLM-as-a-judge checklists often saturate on Interaction while the errors remain obvious to humans. We introduce MPIE-Bench, a 2,500-sample benchmark of video-mined editing triplets spanning 405 scenes, 14 interaction categories, and four contact densities (C0-C3). We also propose MPIE-Eval, whose two new axes score contact-time geometry from a frozen public multi-person mesh reconstruction. Anatomy asks whether every human-like mass is explained by a complete set of reconstructed bodies, and Interaction asks whether the penetration and surface distance between those bodies match the contact the instruction asked for. Across ten editors, mesh Anatomy tops out at 0.65 and mesh Interaction at 0.72 on two different models, so no single editor is strong on both, while VLM checklists rate the same images above 0.95. A five-rater study confirms that both axes track human judgement more closely than a zero-shot VLM judge, and the rankings hold under ablation of every weight and threshold.

Learning-based simulation of multi-object rigid-body dynamics remains difficult because contact is discontinuous and errors compound over long horizons. Most existing methods remain tied to mesh connectivity and vertex-level message passing, which limits their applicability to mesh-free inputs such as point clouds and leads to high computational cost. Efficiently modeling high-fidelity rigid-body dynamics from mesh-free representations, therefore, remains challenging. We introduce RigidFormer, an object-centric Transformer-based model that learns mesh-free rigid-body dynamics with controllable integration step sizes. RigidFormer reasons at the object level and advances each object through compact anchors; Anchor-Vertex Pooling enriches these anchors with local vertex features, retaining contact-relevant geometry without dense vertex-level interaction. We propose Anchor-based RoPE to inject anchor geometry into attention while respecting the unordered nature of objects and anchors: object-token processing is permutation-equivariant, and the mean-pooled anchor descriptor is invariant to anchor reindexing while preserving shape extent. RigidFormer further enforces rigidity by projecting updates onto the rigid-body manifold using differentiable Kabsch alignment. On standard benchmarks, RigidFormer outperforms or matches mesh-based baselines using point inputs, runs faster, generalizes to unseen point resolutions and across datasets, and scales to 200+ objects; we also show a preliminary extension to command-conditioned articulated bodies by treating body parts as interacting object-level components.

Generalizing tool manipulation requires both semantic planning and precise physical control. Modern generalist robot policies, such as Vision-Language-Action (VLA) models, often lack the physical grounding required for contact-rich tool manipulation. Conversely, existing contact-aware policies that leverage tactile or haptic sensing are typically instance-specific and fail to generalize across diverse tool geometries. Bridging this gap requires learning representations that are both semantically transferable and physically grounded, yet a fundamental barrier remains: diverse real-world tactile data are prohibitive to collect at scale, while direct zero-shot sim-to-real transfer is challenging due to the complex nonlinear deformation of soft tactile sensors. To address this, we propose Semantic-Contact Fields (SCFields), a unified 3D representation that fuses visual semantics with dense extrinsic contact estimates, including contact probability and force. SCFields is learned through a two-stage Sim-to-Real Contact Learning Pipeline: we first pre-train on large-scale simulation to learn geometry-aware contact priors, then fine-tune on a small set of real data pseudo-labeled via geometric heuristics and force optimization to align real tactile signals. The resulting force-aware representation serves as the dense observation input to a diffusion policy, enabling physical generalization to unseen tool instances. Experiments on scraping, crayon drawing, and peeling demonstrate robust category-level generalization, significantly outperforming vision-only and raw-tactile baselines. Project page: https://kevinskwk.github.io/SCFields/.

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

We introduce CRISP, a method that recovers simulatable human motion and scene geometry from monocular video. Prior work on joint human-scene reconstruction relies on data-driven priors and joint optimization with no physics in the loop, or recovers noisy geometry with artifacts that cause motion tracking policies with scene interactions to fail. In contrast, our key insight is to recover convex, clean, and simulation-ready geometry by fitting planar primitives to a point cloud reconstruction of the scene, via a simple clustering pipeline over depth, normals, and flow. To reconstruct scene geometry that might be occluded during interactions, we make use of human-scene contact modeling (e.g., we use human posture to reconstruct the occluded seat of a chair). Finally, we ensure that human and scene reconstructions are physically-plausible by using them to drive a humanoid controller via reinforcement learning. Our approach reduces motion tracking failure rates from 55.2\% to 6.9\% on human-centric video benchmarks (EMDB, PROX), while delivering a 43\% faster RL simulation throughput. We further validate it on in-the-wild videos including casually-captured videos, Internet videos, and even Sora-generated videos. This demonstrates CRISP's ability to generate physically-valid human motion and interaction environments at scale, greatly advancing real-to-sim applications for robotics and AR/VR.

Dense hand contact estimation requires both high-level semantic understanding and fine-grained geometric reasoning of human interaction to accurately localize contact regions. Recently, multi-modal large language models (MLLMs) have demonstrated strong capabilities in understanding visual semantics, enabled by vision-language priors learned from large-scale data. However, leveraging MLLMs for dense hand contact estimation remains underexplored. There are two major challenges in applying MLLMs to dense hand contact estimation. First, encoding explicit 3D hand geometry is difficult, as MLLMs primarily operate on vision and language modalities. Second, capturing fine-grained vertex-level contact remains challenging, as MLLMs tend to focus on high-level semantics rather than detailed geometric reasoning. To address these challenges, we propose ContactPrompt, a training-free and zero-shot approach for dense hand contact estimation using MLLMs. To effectively encode 3D hand geometry, we introduce a detailed hand-part segmentation and a part-wise vertex-grid representation that provides structured, localized geometric information. To enable accurate and efficient dense contact prediction, we develop a multi-stage structured contact reasoning with part conditioning, progressively bridging global semantics and fine-grained geometry. Therefore, our method effectively leverages the reasoning capabilities of MLLMs while enabling precise dense hand contact estimation. Surprisingly, the proposed approach outperforms previous supervised methods trained on large-scale dense contact datasets without requiring any training. The codes will be released.

Nonprehensile manipulation is essential for manipulating objects that are too thin, large, or otherwise ungraspable in the wild. To sidestep the difficulty of contact modeling in conventional modeling-based approaches, reinforcement learning (RL) has recently emerged as a promising alternative. However, previous RL approaches either lack the ability to generalize over diverse object shapes, or use simple action primitives that limit the diversity of robot motions. Furthermore, using RL over diverse object geometry is challenging due to the high cost of training a policy that takes in high-dimensional sensory inputs. We propose a novel contact-based object representation and pretraining pipeline to tackle this. To enable massively parallel training, we leverage a lightweight patch-based transformer architecture for our encoder that processes point clouds, thus scaling our training across thousands of environments. Compared to learning from scratch, or other shape representation baselines, our representation facilitates both time- and data-efficient learning. We validate the efficacy of our overall system by zero-shot transferring the trained policy to novel real-world objects. Code and videos are available at https://sites.google.com/view/contact-non-prehensile.

We introduce a novel framework that utilizes the internal weight activations of modern Large Language Models (LLMs) to construct a metric space of languages. Unlike traditional approaches based on hand-crafted linguistic features, our method automatically derives high-dimensional vector representations by computing weight importance scores via an adapted pruning algorithm. Our approach captures intrinsic language characteristics that reflect linguistic phenomena. We validate our approach across diverse datasets and multilingual LLMs, covering 106 languages. The results align well with established linguistic families while also revealing unexpected inter-language connections that may indicate historical contact or language evolution. The source code, computed language latent vectors, and visualization tool are made publicly available at https://github.com/mshamrai/deep-language-geometry.

Contact-rich dexterous manipulation with multi-finger hands remains an open challenge in robotics because task success depends on multi-point contacts that continuously evolve and are highly sensitive to object geometry, frictional transitions, and slip. Recently, tactile-informed manipulation policies have shown promise. However, most use tactile signals as additional observations rather than modeling contact state or how their action outputs interact with low-level controller dynamics. We present Contact-Grounded Policy (CGP), a visuotactile policy that grounds multi-point contacts by predicting coupled trajectories of actual robot state and tactile feedback, and using a learned contact-consistency mapping to convert these predictions into executable target robot states for a compliance controller. CGP consists of two components: (i) a conditional diffusion model that forecasts future robot state and tactile feedback in a compressed latent space, and (ii) a learned contact-consistency mapping that converts the predicted robot state-tactile pair into executable targets for a compliance controller, enabling it to realize the intended contacts. We evaluate CGP using a physical four-finger Allegro V5 hand with Digit360 fingertip tactile sensors, and a simulated five-finger Tesollo DG-5F hand with dense whole-hand tactile arrays. Across a range of dexterous tasks including in-hand manipulation, delicate grasping, and tool use, CGP outperforms visuomotor and visuotactile diffusion-policy baselines.

In a typical video conferencing setup, it is hard to maintain eye contact during a call since it requires looking into the camera rather than the display. We propose an eye contact correction model that restores the eye contact regardless of the relative position of the camera and display. Unlike previous solutions, our model redirects the gaze from an arbitrary direction to the center without requiring a redirection angle or camera/display/user geometry as inputs. We use a deep convolutional neural network that inputs a monocular image and produces a vector field and a brightness map to correct the gaze. We train this model in a bi-directional way on a large set of synthetically generated photorealistic images with perfect labels. The learned model is a robust eye contact corrector which also predicts the input gaze implicitly at no additional cost. Our system is primarily designed to improve the quality of video conferencing experience. Therefore, we use a set of control mechanisms to prevent creepy results and to ensure a smooth and natural video conferencing experience. The entire eye contact correction system runs end-to-end in real-time on a commodity CPU and does not require any dedicated hardware, making our solution feasible for a variety of devices.

Many existing learning-based grasping approaches concentrate on a single embodiment, provide limited generalization to higher DoF end-effectors and cannot capture a diverse set of grasp modes. We tackle the problem of grasping using multiple embodiments by learning rich geometric representations for both objects and end-effectors using Graph Neural Networks. Our novel method - GeoMatch - applies supervised learning on grasping data from multiple embodiments, learning end-to-end contact point likelihood maps as well as conditional autoregressive predictions of grasps keypoint-by-keypoint. We compare our method against baselines that support multiple embodiments. Our approach performs better across three end-effectors, while also producing diverse grasps. Examples, including real robot demos, can be found at geo-match.github.io.

Vision-language-action policies may predict a transferable manipulation strategy yet fail to realize it reliably on the encountered object: objects compatible with the same grasp differ in geometry and compliance, and visual feedback degrades under closure occlusion. AgenticTactileVLA is presented as an execution-time supervisor that shifts part of object-specific adaptation from prediction to physical interaction. A fixed VLA provides the approach and hand targets; the supervisor decides whether to remain transparent, refine finger flexion, retain or release the corrected configuration, return control to the VLA for retry, or select a compliant hand-control regime. It uses finger-position and motor-effort feedback as proprioceptive contact evidence and requires neither tactile sensors nor VLA retraining. On a Unitree G1 with a BrainCo Revo2 hand, a randomized matched-block evaluation on five objects held out from VLA training yields 61.3% completion for the base VLA, 72.0% for unconditional close-to-stall control, and 84.0% for the supervisor under a shared budget; the gain is positive on every object and persists under moderate pose perturbations. Ablations show the gain is not explained by extended closure alone, and that selective triggering reduces correction episodes by 65.7% with no detected change in completion. A retention audit shows acceptance predicts retention in 88.9% of held-out cases, while compliant objects expose conservative false rejection. A thin-walled-cup study demonstrates contextual routing to compliant control, matching an always-compliant reference. These results suggest that contact-guided execution-time adaptation can improve the object-level generalization of a fixed VLA to held-out objects by adapting physical realization without object-specific retraining.

Current dexterous grasp planners primarily optimize for physical stability, focusing on whether an object can be grasped rather than how it should be grasped to support downstream functional tasks. However, conditioning grasp synthesis on specific human grasp taxonomies typically requires prohibitively expensive, object-annotated datasets. To address these limitations, we propose CoToGrasp, a novel generative framework that synthesizes diverse, stable grasps strictly conditioned on specific contact topologies. To bypass the data collection bottleneck, CoToGrasp is trained entirely in an object-agnostic manner. We introduce a feature-based canonical workspace that projects local object features into a unified gripper-centric domain, effectively decoupling the semantic functional intent from the arbitrary object geometry. By learning the intrinsic contact manifold of the gripper within this workspace, our model achieves zero-shot generalization to unseen objects at inference. Extensive evaluations on the large-scale DexGraspNet dataset demonstrate that CoToGrasp achieves state-of-the-art performance, outperforming existing taxonomy-guided planners. Finally, we demonstrate the physical viability and kinematic feasibility of our synthesized contact topologies on a physical robot platform. Code is available on our project website https://cea-list.github.io/cotograspweb/ .

Acquiring contact patterns between hands and nonrigid objects is a common concern in the vision and robotics community. However, existing learning-based methods focus more on contact with rigid ones from monocular images. When adopting them for nonrigid contact, a major problem is that the existing contact representation is restricted by the geometry of the object. Consequently, contact neighborhoods are stored in an unordered manner and contact features are difficult to align with image cues. At the core of our approach lies a novel hand-object contact representation called RUPs (Region Unwrapping Profiles), which unwrap the roughly estimated hand-object surfaces as multiple high-resolution 2D regional profiles. The region grouping strategy is consistent with the hand kinematic bone division because they are the primitive initiators for a composite contact pattern. Based on this representation, our Regional Unwrapping Transformer (RUFormer) learns the correlation priors across regions from monocular inputs and predicts corresponding contact and deformed transformations. Our experiments demonstrate that the proposed framework can robustly estimate the deformed degrees and deformed transformations, which makes it suitable for both nonrigid and rigid contact.

Understanding hand-object interaction from egocentric vision is essential for modeling how people physically engage with the surrounding world. Yet reasoning about physically grounded interaction requires estimating the forces acting on hands and objects, beyond localizing contact. We present EgoPHI, the first method that jointly estimates dense contact maps and 3D force distributions on hand and object meshes from a single monocular RGB image and object geometry. To address the lack of scalable ground-truth force annotations, we introduce a physics-based simulation pipeline that augments existing hand-object datasets with dense per-vertex force supervision. EgoPHI then learns dense 3D contact and force on interacting hand and articulated object meshes, extending vision-based force estimation beyond image-space or planar settings. Our evaluation on in-distribution and out-of-distribution benchmarks shows that EgoPHI improves force estimation over existing approaches while generalizing to unseen datasets. To evaluate sim-to-real transfer, we constructed two physical objects that capture dense object contact and force magnitude and used them to record a dataset of interactions from eight participants across diverse touch and grasp types. Our results demonstrate that EgoPHI recovers meaningful 3D contact and force distributions in simulated, out-of-distribution, and real-world settings, advancing egocentric hand-object understanding from contact localization toward physically grounded interaction reasoning.

Contact-rich manipulation tasks in unstructured environments often require both haptic and visual feedback. However, it is non-trivial to manually design a robot controller that combines modalities with very different characteristics. While deep reinforcement learning has shown success in learning control policies for high-dimensional inputs, these algorithms are generally intractable to deploy on real robots due to sample complexity. We use self-supervision to learn a compact and multimodal representation of our sensory inputs, which can then be used to improve the sample efficiency of our policy learning. We evaluate our method on a peg insertion task, generalizing over different geometry, configurations, and clearances, while being robust to external perturbations. Results for simulated and real robot experiments are presented.

We present LYRIC, a generative flow-matching controller for language-driven physics-based contact-rich interaction control, that enables simulated characters to perform contact-rich whole-body object interactions from a free-form language instruction and a sparse terminal object goal. To obtain reliable expert trajectories from imperfect motion-capture references, a single tracking policy is trained using geometry-conditioned interaction rewards and relaxed reference tracking near hand-object contact. To guide interaction progress without prescribing a full-body kinematic reference, we factorize the controller into a task-level planner that predicts short-horizon object and humanoid-root trajectories, and an action generator that resolves whole-body motion and contacts in closed loop. After behavior cloning, we freeze the planner and post-tune the action generator on policy using the planner's predictions as stable supervision for intermediate task progression. In a controlled OMOMO evaluation, our tracker achieves 64.3% success compared with 53.2% for an InterMimic reimplementation, while a unified policy achieves 76.5% on the full OMOMO dataset. On the held-out split, LYRIC achieves 90.3% task success, compared with 74.2% for the strongest matched kinematic-planner baseline, with better semantic alignment and motion quality. Without retraining, the controller also supports test-time object-waypoint guidance. Qualitative results further demonstrate robust, natural contact-rich interactions and zero-shot transfer to novel object shapes. The webpage is available at https://neu-vi.github.io/LYRIC/

Reconstructing metrically accurate humans and their surrounding scenes from a single image is crucial for virtual reality, robotics, and comprehensive 3D scene understanding. However, existing methods struggle with depth ambiguity, occlusions, and physically inconsistent contacts. To address these challenges, we introduce PhySIC, a framework for physically plausible Human-Scene Interaction and Contact reconstruction. PhySIC recovers metrically consistent SMPL-X human meshes, dense scene surfaces, and vertex-level contact maps within a shared coordinate frame from a single RGB image. Starting from coarse monocular depth and body estimates, PhySIC performs occlusion-aware inpainting, fuses visible depth with unscaled geometry for a robust metric scaffold, and synthesizes missing support surfaces like floors. A confidence-weighted optimization refines body pose, camera parameters, and global scale by jointly enforcing depth alignment, contact priors, interpenetration avoidance, and 2D reprojection consistency. Explicit occlusion masking safeguards invisible regions against implausible configurations. PhySIC is efficient, requiring only 9 seconds for joint human-scene optimization and under 27 seconds end-to-end. It naturally handles multiple humans, enabling reconstruction of diverse interactions. Empirically, PhySIC outperforms single-image baselines, reducing mean per-vertex scene error from 641 mm to 227 mm, halving PA-MPJPE to 42 mm, and improving contact F1 from 0.09 to 0.51. Qualitative results show realistic foot-floor interactions, natural seating, and plausible reconstructions of heavily occluded furniture. By converting a single image into a physically plausible 3D human-scene pair, PhySIC advances scalable 3D scene understanding. Our implementation is publicly available at https://yuxuan-xue.com/physic.

General-purpose vision-language models (VLMs) bring broad knowledge and spatial reasoning to robot manipulation, yet existing systems either use them indirectly, to predict constraints or write programs, or give them a view of the scene rather than a world in which to act. We present World Action Agent (WAA), a multi-agent harness through which VLMs pilot robots with basic tools, making every decision within a visual action workspace. The workspace has three properties. Contact views, selected automatically from the scene geometry, present the scene around the current interaction. Action rehearsal turns each action into an editable proposal that the agent, alone or through an Imagination Agent, previews and revises against planning feedback before execution. In-view correction closes the loop between observation, rehearsal, and low-level execution, letting the agent remove residual offsets in the view where it observes them. Through the same workspace, WAA acquires embodied procedural knowledge in two ways: it evolves multimodal skills from expert videos and human teaching under evidence-based review and consults them through a Skill Agent, and its interaction traces train smaller VLMs to pilot the same harness. On LIBERO-Pro, WAA with skills evolved only from LIBERO-90 reaches a state-of-the-art 75.6% average success, outperforming end-to-end VLAs, code-as-policy agents, and a visual-harness baseline with the same backbone; the same skills remain effective on robosuite without further learning. Fine-tuning Qwen3.5-9B on harness traces raises its out-of-domain success from 1.7% to 43.3%.

We present DecoupledGaussian, a novel system that decouples static objects from their contacted surfaces captured in-the-wild videos, a key prerequisite for realistic Newtonian-based physical simulations. Unlike prior methods focused on synthetic data or elastic jittering along the contact surface, which prevent objects from fully detaching or moving independently, DecoupledGaussian allows for significant positional changes without being constrained by the initial contacted surface. Recognizing the limitations of current 2D inpainting tools for restoring 3D locations, our approach proposes joint Poisson fields to repair and expand the Gaussians of both objects and contacted scenes after separation. This is complemented by a multi-carve strategy to refine the object's geometry. Our system enables realistic simulations of decoupling motions, collisions, and fractures driven by user-specified impulses, supporting complex interactions within and across multiple scenes. We validate DecoupledGaussian through a comprehensive user study and quantitative benchmarks. This system enhances digital interaction with objects and scenes in real-world environments, benefiting industries such as VR, robotics, and autonomous driving. Our project page is at: https://wangmiaowei.github.io/DecoupledGaussian.github.io/.

Chunked vision-language-action (VLA) policies predict multi-step robot controls, conditioning each update on the current visual observation alone. Yet robot actions cause contact, occlusion, and object motion, and the geometry that later decisions depend on can change before the next visual update arrives. Spatial VLAs improve current-frame geometry. Temporal VLAs aggregate past frames. Neither maintains an action-updated scene prior across chunks. We argue for a persistent action-updated scene state across control calls, and introduce EvoScene-VLA. Its recurrent scene prefix carries a geometry-aware scene state across chunks. At each vision-language model (VLM) call, the VLM combines scene information from the current observation with the action-updated prior from the previous chunk; the action decoder outputs both the next action chunk and a compact scene update. This update becomes the next prior, which the VLM corrects against the new observation when the next call arrives. Each control call therefore starts from a scene prior that reflects both recent actions and fresh visual evidence. During training, Scene Predictor supplies future scene-token targets, and Geometric Anchor aligns scene slots with frozen depth and 3D teachers. We discard both modules at deployment. On 31 RoboTwin tasks, EvoScene-VLA raises average success from 87.2% to 89.1% in fixed evaluation and from 86.1% to 88.5% in randomized evaluation. On the Galaxea R1-Lite real robot, EvoScene-VLA outperforms all baselines.

Capturing and maintaining geometric interactions among different body parts is crucial for successful motion retargeting in skinned characters. Existing approaches often overlook body geometries or add a geometry correction stage after skeletal motion retargeting. This results in conflicts between skeleton interaction and geometry correction, leading to issues such as jittery, interpenetration, and contact mismatches. To address these challenges, we introduce a new retargeting framework, MeshRet, which directly models the dense geometric interactions in motion retargeting. Initially, we establish dense mesh correspondences between characters using semantically consistent sensors (SCS), effective across diverse mesh topologies. Subsequently, we develop a novel spatio-temporal representation called the dense mesh interaction (DMI) field. This field, a collection of interacting SCS feature vectors, skillfully captures both contact and non-contact interactions between body geometries. By aligning the DMI field during retargeting, MeshRet not only preserves motion semantics but also prevents self-interpenetration and ensures contact preservation. Extensive experiments on the public Mixamo dataset and our newly-collected ScanRet dataset demonstrate that MeshRet achieves state-of-the-art performance. Code available at https://github.com/abcyzj/MeshRet.

Tactile sensing provides robots with direct observations of contact physics, local geometry, and interaction dynamics, making it a vital source of feedback for contact-rich manipulation. However, existing tactile manipulation studies are often developed and evaluated within specific task settings, making it difficult to systematically compare how tactile information contributes under different interaction conditions. In this work, we develop a benchmark in simulation comprising 128 tasks organized around three complementary evaluation regimes: Precise, Recognition, and Dynamic. The benchmark further includes controlled static and dynamic task variants and 12 perturbation settings for evaluating robustness under changes in visual and physical conditions. These settings motivate studying tactile information as a temporally evolving interaction representation rather than only as an instantaneous observation. We therefore propose an action-conditioned latent predictive world model that integrates tactile history and learns a tactile state through prediction of future tactile latents. Building on this representation, we design a model that conditions action generation on the learned tactile state and uses predicted future tactile information to refine candidate actions through predictive tactile reflection. Experiments on the proposed benchmark show consistent gains from incorporating tactile information across the evaluated regimes. Project Page: https://tacmind-bench.github.io/

Tactile sensing is one of the modalities humans rely on heavily to perceive the world. Working with vision, this modality refines local geometry structure, measures deformation at the contact area, and indicates the hand-object contact state. With the availability of open-source tactile sensors such as DIGIT, research on visual-tactile learning is becoming more accessible and reproducible. Leveraging this tactile sensor, we propose a novel visual-tactile in-hand object reconstruction framework VTacO, and extend it to VTacOH for hand-object reconstruction. Since our method can support both rigid and deformable object reconstruction, no existing benchmarks are proper for the goal. We propose a simulation environment, VT-Sim, which supports generating hand-object interaction for both rigid and deformable objects. With VT-Sim, we generate a large-scale training dataset and evaluate our method on it. Extensive experiments demonstrate that our proposed method can outperform the previous baseline methods qualitatively and quantitatively. Finally, we directly apply our model trained in simulation to various real-world test cases, which display qualitative results. Codes, models, simulation environment, and datasets are available at https://sites.google.com/view/vtaco/.

Resistive pressure arrays are the cheapest and most widely shipped tactile sensors, yet tactile representation learning has concentrated on optical sensors that image a deforming gel. We present Tactus, an open model that answers text queries from pressure data alone: on the STAG benchmark (27 objects, held-out recordings), it reaches 0.771 +/- 0.062 top-1 over four runs (top-3 0.935), matching, and at best exceeding, the dataset's supervised closed-set CNN at 0.76, with no trained classifier head. The recipe is small-data: 187 training recordings, masked-autoencoder pretraining on 144k unlabeled same-sensor frames, and the sensor's own calibration affine, which recovered more accuracy than every architecture change combined. The released model's errors concentrate in a few contact-ambiguous classes, are uncorrelated with text-target geometry (Spearman rho <= 0.05 over 702 class pairs), and survive paraphrased and even bare-name queries within one point; two diverse frames recover 89% of eight-frame accuracy. Failures are reported with equal precision: cross-sensor pretraining pooling gave no gain, vision co-training degraded touch, and a mis-normalized input pipeline silently discarded 97% of the sensor's dynamic range while producing plausible intermediate results. Weights, code, and the memory layer the model plugs into are released openly.

Generalist robot policies benefit from large-scale visual pretraining but often struggle with contact-rich dexterous manipulation, where force, compliance, and incipient slip are hard to observe from images. We present Spark-0, a spatially aligned vision-tactile-language-action (VTLA) model that uses touch in two complementary ways. During pretraining, image-space contact maps derived from tactile gloves, together with features from a frozen 3D geometry teacher, supervise the visual tokens; these objectives are removed at inference. In parallel, a tactile pathway encodes regional force histories and 3D taxel states to condition the action expert. A single checkpoint therefore supports both vision-only and tactile-conditioned deployment. To scale this supervision, we build HumanTouch, a 1,000-hour dataset of full-hand tactile human manipulation, and pretrain Spark-0 on it together with egocentric video, robot data, and simulation. We also release SparkArena, which pairs vision-only simulated tasks with tactile-conditioned real-robot tasks on one dexterous embodiment. Spark-0 achieves the highest mean success rate on both SparkArena tracks and ranks first on all eight aggregate metrics of the Ego Humanoid Manipulation Benchmark. Compared with vision-only pretraining on the same data and compute with touch discarded, retaining the touch of 1,000 hours of HumanTouch raises vision-only success on Ego Humanoid from 52.5% to 71.7%, and success on SparkArena-Real, where touch is also used at deployment, from 44.0% to 52.0%, indicating that touch serves not only as a policy input but also as scalable supervision for dexterous visuomotor pretraining. The Website is available at: https://xsparkai.com/Spark-0.

Learned simulators for deformable linear objects (DLOs) such as cables have to predict the motion of cables they were not trained on and stay stable over long rollouts. Most of their error occurs where the cable touches itself or the floor. Attention over all pairs of cable segments can represent contact between parts of the cable that are far apart along its length, but attention has no notion of geometry. A cable has two pairwise distances, which agree only while it is straight: the arc-length distance along the cable, which governs elastic forces, and the Euclidean distance in space, which governs contact. We add a physical attention bias, an additive term on the attention logits with a learned rate, and ask which distance it should use. We compare no bias, each distance alone, and both distances on disjoint sets of heads, keeping the rest of the model and the training protocol fixed. A physical bias improves prediction on unseen cables. The gain is largest when attention is the only mechanism that connects distant segments: there, the arc-length bias reduces prediction error by 15% and more than halves the drift in segment length. The Euclidean bias alone stays close to unbiased attention, while assigning both distances across heads is best or near-best on every metric we report. Code and per-run records: https://github.com/avihaig/dlogps.

Generating 3D humans that functionally interact with 3D scenes remains an open problem with applications in embodied AI, robotics, and interactive content creation. The key challenge involves reasoning about both the semantics of functional elements in 3D scenes and the 3D human poses required to achieve functionality-aware interaction. Unfortunately, existing methods typically lack explicit reasoning over object functionality and the corresponding human-scene contact, resulting in implausible or functionally incorrect interactions. In this work, we propose FunHSI, a training-free, functionality-driven framework that enables functionally correct human-scene interactions from open-vocabulary task prompts. Given a task prompt, FunHSI performs functionality-aware contact reasoning to identify functional scene elements, reconstruct their 3D geometry, and model high-level interactions via a contact graph. We then leverage vision-language models to synthesize a human performing the task in the image and estimate proposed 3D body and hand poses. Finally, the proposed 3D body configuration is refined via stage-wise optimization to ensure physical plausibility and functional correctness. In contrast to existing methods, FunHSI not only synthesizes more plausible general 3D interactions, such as "sitting on a sofa'', while supporting fine-grained functional human-scene interactions, e.g., "increasing the room temperature''. Extensive experiments demonstrate that FunHSI consistently generates functionally correct and physically plausible human-scene interactions across diverse indoor and outdoor scenes.

Simulation is widely used in robotics for system verification and large-scale data collection. However, simulating sensors, including tactile sensors, has been a long-standing challenge. In this paper, we propose Taxim, a realistic and high-speed simulation model for a vision-based tactile sensor, GelSight. A GelSight sensor uses a piece of soft elastomer as the medium of contact and embeds optical structures to capture the deformation of the elastomer, which infers the geometry and forces applied at the contact surface. We propose an example-based method for simulating GelSight: we simulate the optical response to the deformation with a polynomial look-up table. This table maps the deformed geometries to pixel intensity sampled by the embedded camera. In order to simulate the surface markers' motion that is caused by the surface stretch of the elastomer, we apply the linear elastic deformation theory and the superposition principle. The simulation model is calibrated with less than 100 data points from a real sensor. The example-based approach enables the model to easily migrate to other GelSight sensors or its variations. To the best of our knowledge, our simulation framework is the first to incorporate marker motion field simulation that derives from elastomer deformation together with the optical simulation, creating a comprehensive and computationally efficient tactile simulation framework. Experiments reveal that our optical simulation has the lowest pixel-wise intensity errors compared to prior work and can run online with CPU computing. Our code and supplementary materials are open-sourced at https://github.com/CMURoboTouch/Taxim.

Automatic fall recovery is a crucial prerequisite before humanoid robots can be reliably deployed. Hand-designing controllers for getting up is difficult because of the varied configurations a humanoid can end up in after a fall and the challenging terrains humanoid robots are expected to operate on. This paper develops a learning framework to produce controllers that enable humanoid robots to get up from varying configurations on varying terrains. Unlike previous successful applications of humanoid locomotion learning, the getting-up task involves complex contact patterns, which necessitates accurately modeling the collision geometry and sparser rewards. We address these challenges through a two-phase approach that follows a curriculum. The first stage focuses on discovering a good getting-up trajectory under minimal constraints on smoothness or speed / torque limits. The second stage then refines the discovered motions into deployable (i.e. smooth and slow) motions that are robust to variations in initial configuration and terrains. We find these innovations enable a real-world G1 humanoid robot to get up from two main situations that we considered: a) lying face up and b) lying face down, both tested on flat, deformable, slippery surfaces and slopes (e.g., sloppy grass and snowfield). To the best of our knowledge, this is the first successful demonstration of learned getting-up policies for human-sized humanoid robots in the real world. Project page: https://humanoid-getup.github.io/

Text- and image-conditioned video generation models have achieved strong visual fidelity and temporal coherence, but they often fail to generate motion governed by kinematic and geometric constraints. In these settings, object parts must remain rigid, maintain contact or coupling with neighboring components, and transfer motion consistently across connected parts. These requirements are especially explicit in articulated mechanical assemblies, where motion is constrained by rigid-link geometry, contact/coupling relations, and transmission through kinematic chains. A generated video may therefore appear plausible while violating the intended mechanism, such as rotating a part that should translate, deforming a rigid component, breaking coupling between parts, or failing to move downstream components. To evaluate this gap, We introduce MechVerse, a benchmark for mechanically consistent image-to-video generation. MechVerse contains 21,156 synthetic clips from 1,357 mechanical assemblies across 141 categories, organized into three tiers of increasing kinematic complexity: independent articulation, pairwise coupling, and densely coupled multi-part mechanisms. Each clip is paired with a structured prompt describing part identities, stationary supports, moving components, motion primitives, direction, speed/extent, and inter-part dependencies. We evaluate proprietary, open-source, and fine-tuned image-to-video models using standard video metrics, instruction-following scores, and human judgments of motion correctness and kinematic coupling. Results show that current models can preserve appearance and smoothness while failing to generate mechanically admissible motion, with errors increasing as coupling complexity grows. MechVerse provides a benchmark for measuring and improving mechanism-aware video generation from image and language inputs.

Hand-object interaction (HOI) modeling remains challenging because it requires joint reasoning about hand articulation, object geometry, contact, semantics, and dynamics under severe visual uncertainty. Foundation models introduce transferable prior knowledge learned from large-scale cross-domain data, offering new ways to address these challenges beyond task-specific data and models. However, the rapidly growing literature remains fragmented, and existing studies typically describe these methods simply as ``using large models'' without systematically characterizing what knowledge is introduced, where it enters the HOI pipeline, or which HOI uncertainty it helps reduce. This survey presents the first systematic review of foundation-model priors for HOI. We organize the literature into six HOI tasks spanning reconstruction and generation. More importantly, we establish a taxonomy of eight foundation-model sub-priors grouped into geometric, semantic, and visual families. Geometric priors encompass shape retrieval, shape reconstruction, and spatial reconstruction; semantic priors include semantic grounding and language reasoning; and visual priors cover visual representation, image generation, and video generation. Based on this taxonomy, we systematically analyze how different priors are represented, injected, and adapted across HOI pipelines and tasks. Beyond how foundation models empower HOI, we further examine how HOI-derived knowledge is used in robot learning, including human-data pretraining, human-to-robot skill transfer, and HOI-to-robot data generation. Finally, we summarize datasets and evaluation protocols, and discuss limitations and future directions toward more generalizable HOI systems. To support long-term progress, we curate a live repository that continuously aggregates emerging methods and benchmarks.

Egocentric video has become a primary source of supervision for embodied models, and its value rests on recovering hand motion in world coordinates, which camera motion and hand occlusion make difficult. Existing reconstruction pipelines typically separate hand and scene estimation, leave interaction attributes to separate task-specific models, and invoke several models per video, so no prior reconstruction model estimates these attributes and throughput becomes a practical constraint on large-scale annotation. We therefore introduce EgoFound3R, a unified end-to-end model that estimates world-space hand geometry in a metric scale shared with the scene, and predicts point-wise interaction attributes, including visibility, contact, and distance. The model integrates three designs: (i) structured hand prompts that transfer pretrained geometric priors to world-space hand reconstruction; (ii) an explicit hand representation that decodes hand geometry and interaction attributes; and (iii) a shared-parameter multi-rate design that lowers inference cost. Together, these designs predict hand geometry and point-wise attributes in one pass. On OakInk-v2, TACO, and HOI4D, EgoFound3R reduces the mean per-joint position error (MPJPE) by 43.2%, 22.4%, and 11.6% over previous methods and predicts point-wise contact and distance alongside the geometry in the same pass, while attaining approximately 6x higher throughput.

Recent advances in musculoskeletal modeling and reinforcement learning have enabled muscle-actuated agents to reproduce increasingly complex human motions. Yet these capabilities remain largely confined to flat ground, in part because motion datasets rarely include aligned terrain geometry and because retargeting terrain interactions to complex musculoskeletal bodies is challenging. We present TERRA, an end-to-end pipeline for terrain-aware retargeting and control of musculoskeletal locomotion. From kinematic trajectories alone, TERRA combines terrain priors, estimated contacts, and negative free-space evidence to recover task-relevant support geometry. TERRA further considers anatomical, tendon-continuity, and contact constraints during retargeting. Using the resulting motion-terrain pairs from five datasets, we successfully train a single muscle-actuated control policy on 9.4 hours of diverse locomotion. Across reconstruction, retargeting, and held-out tracking benchmarks, TERRA improves terrain accuracy, sharply reduces anatomical and interaction violations, and achieves the highest observed completion rate over supported terrain families. Overall, TERRA provides a practical route from scene-less motion data to muscle-actuated locomotion over diverse non-flat terrain. Project website: https://cnai.epfl.ch/terra/

Bimanual manipulation policies require large and diverse training datasets, yet collecting demonstrations on physical robots is expensive and difficult to scale. Simulation can generate data efficiently, but existing pipelines typically operate within closed asset libraries and predefined scenes: adding a newly observed object or environment still requires substantial effort to reconstruct geometry, specify physical and semantic properties, annotate interactions, and integrate the result into executable tasks. We present RoboCousin, an extensible simulation-based data-generation platform that turns user-provided observations into reusable assets, scenes, and expert trajectories for bimanual manipulation. Built on RoboTwin~2.0, RoboCousin converts object images into simulation-ready assets with visual and collision geometry, semantic and physical metadata, and automatically generated grasp-contact candidates. It further constructs digital cousins that vary compatible objects, backgrounds, layouts, and language instructions while preserving task-relevant affordances and spatial relations. The same asset system supports tabletop and room-level scene construction, with collision-aware base control for interaction beyond a fixed workspace. We release RoboCousin-OBD, containing more than 3,000 annotated object instances and 50 background environments, and use RoboCousin to generate over one million expert trajectories across 50 tasks. Simulation and real-robot experiments show that the automatically generated interaction annotations are comparable to curated annotations, generated assets provide effective sim-to-real supervision, and tabletop cousins can improve transfer beyond training on a single reconstructed scene. RoboCousin therefore provides a practical path for expanding both the scale and coverage of synthetic bimanual manipulation data.

Modeling 3D human-object interaction (HOI) is a problem of great interest for computer vision and a key enabler for virtual and mixed-reality applications. Existing methods work in a one-way direction: some recover plausible human interactions conditioned on a 3D object; others recover the object pose conditioned on a human pose. Instead, we provide the first unified model - TriDi which works in any direction. Concretely, we generate Human, Object, and Interaction modalities simultaneously with a new three-way diffusion process, allowing to model seven distributions with one network. We implement TriDi as a transformer attending to the various modalities' tokens, thereby discovering conditional relations between them. The user can control the interaction either as a text description of HOI or a contact map. We embed these two representations into a shared latent space, combining the practicality of text descriptions with the expressiveness of contact maps. Using a single network, TriDi unifies all the special cases of prior work and extends to new ones, modeling a family of seven distributions. Remarkably, despite using a single model, TriDi generated samples surpass one-way specialized baselines on GRAB and BEHAVE in terms of both qualitative and quantitative metrics, and demonstrating better diversity. We show the applicability of TriDi to scene population, generating objects for human-contact datasets, and generalization to unseen object geometry. The project page is available at: https://virtualhumans.mpi-inf.mpg.de/tridi.

Synthesizing semantic-aware, long-horizon, human-object interaction is critical to simulate realistic human behaviors. In this work, we address the challenging problem of generating synchronized object motion and human motion guided by language descriptions in 3D scenes. We propose Controllable Human-Object Interaction Synthesis (CHOIS), an approach that generates object motion and human motion simultaneously using a conditional diffusion model given a language description, initial object and human states, and sparse object waypoints. While language descriptions inform style and intent, waypoints ground the motion in the scene and can be effectively extracted using high-level planning methods. Naively applying a diffusion model fails to predict object motion aligned with the input waypoints and cannot ensure the realism of interactions that require precise hand-object contact and appropriate contact grounded by the floor. To overcome these problems, we introduce an object geometry loss as additional supervision to improve the matching between generated object motion and input object waypoints. In addition, we design guidance terms to enforce contact constraints during the sampling process of the trained diffusion model.

World models have become indispensable tools for embodied intelligence, serving as powerful simulators capable of generating realistic robotic videos while addressing critical data scarcity challenges. However, current embodied world models exhibit limited physical awareness, particularly in modeling 3D geometry and motion dynamics, resulting in unrealistic video generation for contact-rich robotic scenarios. In this paper, we present RoboScape, a unified physics-informed world model that jointly learns RGB video generation and physics knowledge within an integrated framework. We introduce two key physics-informed joint training tasks: temporal depth prediction that enhances 3D geometric consistency in video rendering, and keypoint dynamics learning that implicitly encodes physical properties (e.g., object shape and material characteristics) while improving complex motion modeling. Extensive experiments demonstrate that RoboScape generates videos with superior visual fidelity and physical plausibility across diverse robotic scenarios. We further validate its practical utility through downstream applications including robotic policy training with generated data and policy evaluation. Our work provides new insights for building efficient physics-informed world models to advance embodied intelligence research. The code is available at: https://github.com/tsinghua-fib-lab/RoboScape.

Understanding the physical structure is essential for real-world applications such as embodied agents, interactive design, and long-horizon manipulation. Yet, prevailing Vision-Language Model (VLM) evaluations still center on structure-agnostic, single-turn setups (e.g., VQA), which fail to assess agents' ability to reason about how geometry, contact, and support relations jointly constrain what actions are possible in a dynamic environment. To address this gap, we introduce the Causal Hierarchy of Actions and Interactions (CHAIN) benchmark, an interactive 3D, physics-driven testbed designed to evaluate whether models can understand, plan, and execute structured action sequences grounded in physical constraints. CHAIN shifts evaluation from passive perception to active problem solving, spanning tasks such as interlocking mechanical puzzles and 3D stacking and packing. We conduct a comprehensive study of state-of-the-art VLMs and diffusion-based models under unified interactive settings. Our results show that top-performing models still struggle to internalize physical structure and causal constraints, often failing to produce reliable long-horizon plans and cannot robustly translate perceived structure into effective actions. The project is available at https://social-ai-studio.github.io/CHAIN/.

Reliable insertion of industrial connectors remains a central challenge in robotics, requiring sub-millimeter precision under uncertainty and often without full visual access. Vision-based approaches struggle with occlusion and limited generalization, while learning-based policies frequently fail to transfer to unseen geometries. To address these limitations, we leverage tactile sensing, which captures local surface geometry at the point of contact and thus provides reliable information even under occlusion and across novel connector shapes. Building on this capability, we present Touch2Insert, a tactile-based framework for arbitrary peg insertion. Our method reconstructs cross-sectional geometry from high-resolution tactile images and estimates the relative pose of the hole with respect to the peg in a zero-shot manner. By aligning reconstructed shapes through registration, the framework enables insertion from a single contact without task-specific training. To evaluate its performance, we conducted experiments with three diverse connectors in both simulation and real-robot settings. The results indicate that Touch2Insert achieved sub-millimeter pose estimation accuracy for all connectors in simulation, and attained an average success rate of 86.7\% on the real robot, thereby confirming the robustness and generalizability of tactile sensing for real-world robotic connector insertion.

Generalist robot policies must follow user instructions while reasoning about how objects, cameras, and robot actions interact in the 3D physical world. Recent vision-language-action models (VLAs) and video world-action models (WAMs) inherit strong semantic or temporal priors from large-scale foundation models, but they still operate primarily on 2D image frames or 2D-derived latent spaces, leaving implicit the 3D geometry required for contact-rich manipulation. We propose the Geometric Action Model (GAM), a language-conditioned manipulation policy that directly repurposes a pretrained geometric foundation model (GFM) as a shared substrate for perception, temporal prediction, and action decoding. GAM splits the GFM at an intermediate layer: the shallow layers serve as an observation encoder, and a causal future predictor inserted at the split layer forecasts future latent tokens conditioned on language, proprioception, and action history. The predicted future tokens are then routed through the remaining GFM blocks for feature propagation and decoding, allowing a single backbone to produce both future geometry and actions. This design equips the GFM with language-conditioned temporal world modeling through minimal architectural modification while preserving its rich geometric priors. Across a broad suite of simulation and real-robot manipulation benchmarks, GAM is more accurate, more robust, faster, and lighter than current foundation-model-scale baselines.

Egocentric RGB-D videos offer a natural source of human dexterous manipulation demonstrations, but existing data is difficult to use for robot learning because object pose, geometry, and contact information are often missing or require pre-scanned object assets. We present EgoAERO, the first framework that learns dexterous manipulation from a single egocentric RGB-D human demonstration without object assets. EgoAERO reconstructs contact-consistent hand-object trajectories through asset-free object tracking and reconstruction, ego motion compensation, and adaptive contact optimization, then converts them into robot policies using two-stage residual learning. We further introduce an online quality assessment mechanism and construct EgoDex-R, a large-scale egocentric dataset with 4.3M RGB-D frames for dexterous policy learning. Simulation and real-world experiments show that EgoAERO enables single-demonstration dexterous manipulation and achieves downstream performance close to CAD-based reconstructions on HOI4D.

Dexterous interaction with articulated objects is important for household, assistive, and humanoid manipulation, where multi-finger hands can provide compliant contact patterns beyond parallel-jaw grasping. However, articulated-object manipulation differs from static-object manipulation: the target part cannot be directly actuated, and its motion must emerge through sustained physical hand--handle contact. This makes the transition from object-centric articulated generation to hand-driven dexterous hand--object interaction non-trivial, since geometric trajectory replay or open-loop execution does not model the contact dynamics required to move the articulated part. Moreover, policies trained only for task completion under fixed dynamics can overfit nominal contact loads, especially without tactile or force feedback, and may degrade when the contact load changes. To address these challenges, we present DragMesh-2, a contact-driven framework for dexterous interaction with articulated objects that extends articulated interaction from object-centric generation to hand-driven dexterous hand--object interaction, where articulated motion must arise through physical contact. We further propose PICA, a physically informed contact-aware training mechanism that injects physical signals into policy learning without tactile or force feedback, improving robustness and task success under changing contact loads. Finally, we conduct systematic evaluation across multiple damping conditions and articulated-object categories to study robustness under contact-load variation, and provide a pure-geometry dexterous interaction resource to support future loco-manipulation and humanoid hand--object interaction research. Across seven GAPartNet objects, DragMesh-2 achieves stronger robustness under contact-load variation than the compared methods while maintaining high task success across damping conditions.

Reconstructing articulated objects with multiple movable parts is essential for understanding object structure and enabling physical interaction. However, this reconstruction task poses significant challenges due to the entanglement of geometry, appearance, and motion parameters during optimization. Existing methods rely primarily on photometric supervision, which commonly fails to disentangle these interdependent components, resulting in poor part decomposition with blurred boundaries and geometric artifacts. To address this limitation, we introduce StructureGS, a reconstruction framework for articulated objects that integrates structure-aware guidance into 3D Gaussian Splatting. Our approach leverages oriented bounding boxes of object parts to enforce two key structural properties: spatial coherence, which constrains each part's geometry to remain compact and spatially coherent within its designated region, and structural connectivity, which enforces physically plausible contact relationships between adjacent parts. These properties are realized through structure-aware losses that inject explicit structural constraints into the optimization process. Extensive experiments demonstrate that our method achieves state-of-the-art performance in articulated object reconstruction, producing high-quality results with well-defined part geometries.

Multifingered grasping is a crucial robotic skill, but current deep-learning grasp planners often struggle to generalize to new objects because they are trained on limited, object-specific datasets. We introduce a fundamentally different approach, grounded in the observation that the gripper and the object share identical surface geometry at their mutual contact points. We propose GOAG: Generative and Object-Agnostic Grasp Planner for Dexterous Robotic Manipulation, a novel deep generative model that learns a compact latent representation of a specific gripper's contact surface distribution, enabling the efficient sampling of valid grasp configurations without relying on object-specific training data. We show that by introducing object features only at inference time, our model can effectively retrieve admissible contact areas that are compatible with the gripper's capabilities. We validate our approach through extensive experiments on established grasp protocols in both simulated and real-world scenarios, demonstrating its effectiveness with different grippers from the literature. Our method delivers state-of-the-art results on the objects from the MultiDex dataset, achieving an average success rate of 86.93%. It offers significantly faster processing when generating numerous grasps, while matching the performance of leading approaches specifically trained on this dataset. Unlike these methods, our approach does not rely on object-specific training data, highlighting the advantages of object-agnostic learning. It effectively addresses the generalization challenges faced by traditional data-driven grasp planners. Code and videos are available on our project website https://cea-list.github.io/goagweb/ .

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.

Developing world models that understand complex physical interactions is essential for advancing robotic planning and simulation.However, existing methods often struggle to accurately model the environment under conditions of data scarcity and complex contact-rich dynamic motion.To address these challenges, we propose ContactGaussian-WM, a differentiable physics-grounded rigid-body world model capable of learning intricate physical laws directly from sparse and contact-rich video sequences.Our framework consists of two core components: (1) a unified Gaussian representation for both visual appearance and collision geometry, and (2) an end-to-end differentiable learning framework that differentiates through a closed-form physics engine to infer physical properties from sparse visual observations.Extensive simulations and real-world evaluations demonstrate that ContactGaussian-WM outperforms state-of-the-art methods in learning complex scenarios, exhibiting robust generalization capabilities.Furthermore, we showcase the practical utility of our framework in downstream applications, including data synthesis and real-time MPC.

Part-aware 3D asset generation enables applications such as editing, articulation, simulation, and fabrication, yet existing methods can generate visually complete individual parts without ensuring that they form a valid physical assembly. Consequently, generated neighboring parts may interpenetrate, lack valid connections, or collapse under gravity. We propose a physics-guided framework for improving single-image part-aware 3D generation with physically compatible geometry and stable connections. Our method resolves inter-part penetration, recovers a contact graph between neighboring parts, and introduces parameterized connectors at their contact surfaces. Using feedback from physical simulation, we refine connector placement, orientation, and dimensions to improve assembly stability while preserving the generated geometry. We further introduce a physics-based evaluation protocol that complements conventional geometric metrics by directly testing assembly validity and stability under gravity. Experiments comparing against multiple part-aware 3D generators show substantial improvements in physical realizability and stability while maintaining geometric quality. We additionally validate the resulting parts through 3D printing and real-world assembly.

We show that classical cylindrical contact homology over Z, equipped with its decomposition by free homotopy classes, is not invariant under changes of hypertight contact form. Specifically, we construct two nondegenerate hypertight perturbations of the standard Seifert contact form on Σ(2,4,5) whose cylindrical contact homologies in the regular-fiber class are respectively torsion-free and contain Z/5-torsion.

This paper presents a novel object-centric contact representation ContactGen for hand-object interaction. The ContactGen comprises three components: a contact map indicates the contact location, a part map represents the contact hand part, and a direction map tells the contact direction within each part. Given an input object, we propose a conditional generative model to predict ContactGen and adopt model-based optimization to predict diverse and geometrically feasible grasps. Experimental results demonstrate our method can generate high-fidelity and diverse human grasps for various objects. Project page: https://stevenlsw.github.io/contactgen/

In this paper we study pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudoholomorphic curve with brake symmetry and the corresponding moduli space. Then we get the virtual dimension of the moduli space.

Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and proving, especially in geometry for its combination of numerical and spatial elements. We introduce TongGeometry, a Euclidean geometry system supporting tree-search-based guided problem proposing and solving. The efficient geometry system establishes the most extensive repository of geometry theorems to date: within the same computational budget as the existing state-of-the-art, TongGeometry discovers 6.7 billion geometry theorems requiring auxiliary constructions, including 4.1 billion exhibiting geometric symmetry. Among them, 10 theorems were proposed to regional mathematical olympiads with 3 of TongGeometry's proposals selected in real competitions, earning spots in a national team qualifying exam or a top civil olympiad in China and the US. Guided by fine-tuned large language models, TongGeometry solved all International Mathematical Olympiad geometry in IMO-AG-30, outperforming gold medalists for the first time. It also surpasses the existing state-of-the-art across a broader spectrum of olympiad-level problems. The full capabilities of the system can be utilized on a consumer-grade machine, making the model more accessible and fostering widespread democratization of its use. By analogy, unlike existing systems that merely solve problems like students, TongGeometry acts like a geometry coach, discovering, presenting, and proving theorems.

Reliable odometry for legged robots without cameras or LiDAR remains challenging due to IMU drift and noisy joint velocity sensing. This paper presents a purely proprioceptive state estimator that uses only IMU and motor measurements to jointly estimate body pose and velocity, with a unified formulation applicable to biped, quadruped, and wheel-legged robots. The key idea is to treat each contacting leg as a kinematic anchor: joint-torque--based foot wrench estimation selects reliable contacts, and the corresponding footfall positions provide intermittent world-frame constraints that suppress long-term drift. To prevent elevation drift during extended traversal, we introduce a lightweight height clustering and time-decay correction that snaps newly recorded footfall heights to previously observed support planes. To improve foot velocity observations under encoder quantization, we apply an inverse-kinematics cubature Kalman filter that directly filters foot-end velocities from joint angles and velocities. The implementation further mitigates yaw drift through multi-contact geometric consistency and degrades gracefully to a kinematics-derived heading reference when IMU yaw constraints are unavailable or unreliable. We evaluate the method on four quadruped platforms (three Astrall robots and a Unitree Go2 EDU) using closed-loop trajectories. On Astrall point-foot robot~A, a sim200\,m horizontal loop and a sim15\,m vertical loop return with 0.1638\,m and 0.219\,m error, respectively; on wheel-legged robot~B, the corresponding errors are 0.2264\,m and 0.199\,m. On wheel-legged robot~C, a sim700\,m horizontal loop yields 7.68\,m error and a sim20\,m vertical loop yields 0.540\,m error. Unitree Go2 EDU closes a sim120\,m horizontal loop with 2.2138\,m error and a sim8\,m vertical loop with less than 0.1\,m vertical error. github.com/ShineMinxing/Ros2Go2Estimator.git

Contact-rich policies often fail because distinct physical states look alike yet require different actions. Cameras may not reveal whether a connector is aligned or fully seated, while many normal-only tactile sensors can miss the tangential interactions perpendicular to the grasping direction that distinguish these states. We ask whether a learning policy needs calibrated shear measurements, or only a repeatable observation that separates shear-dependent contact states. We introduce TacGooseBumps (TacGB), a passive domed film that mechanically encodes tangential loading as pattern changes in an existing sensor's pressure map. Tangential loading tilts each dome and redistributes pressure across its footprint; an end-to-end policy consumes the resulting maps without added electronics, force reconstruction, or taxel-level dome alignment. Across four imitation-learning tasks and two data-collection pipelines, TacGB improves goal attainment, efficiency, and contact quality: insertion success increases by up to 36 percentage points, and successful insertions are completed faster, while fragile-object placement becomes gentler and drawing becomes more continuous and straight. Signal, stage-wise, failure-mode, and trajectory analyses link these gains to contact regimes in which task-relevant tangential interactions are poorly resolved by vision and normal pressure alone. Together, these results show that shear need not be measured metrically to benefit robot learning; it can instead be mechanically encoded without changing the underlying tactile sensor or the policy's pressure-map input format.

Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.

Daily activities require humans to coordinate whole-body motion with the motion of surrounding objects. Despite recent progress in human-object interaction (HOI) generation, most existing methods assume interactions with a single rigid object and do not extend well to scenarios involving a variable number of objects or articulated objects with diverse joint mechanisms. We propose surface keypoint trajectories as an object motion representation: for each rigid component, whether a standalone object or one part of an articulated assembly, we track a small set of non-collinear surface points over time. This representation handles multi-object coordination and diverse articulation mechanisms directly from point dynamics without requiring explicit joint-type specification. To model when and where each body region contacts each object, we introduce a spatio-temporal contact distance field that extends distance-based contact modeling to whole-body, multi-object, and articulated settings. We factorize HOI generation into three stages: generating object motions from text or waypoints, predicting the contact distance field, and synthesizing whole-body motion with contact-guided optimization. Experiments on ParaHome, HIMO, ARCTIC, and OMOMO demonstrate better or comparable performance to existing methods across single-object, multi-object, and articulated interaction settings.

Physics simulation for contact-rich robotics is often bottlenecked by contact resolution: mainstream engines enforce non-penetration and Coulomb friction via complementarity constraints or constrained optimization, requiring per-step iterative solves whose cost grows superlinearly with contact density. We present ComFree-Sim, a GPU-parallelized analytical contact physics engine built on complementarity-free contact modeling. ComFree-Sim computes contact impulses in closed form via an impedance-style prediction--correction update in the dual cone of Coulomb friction. Contact computation decouples across contact pairs and becomes separable across cone facets, mapping naturally to GPU kernels and yielding near-linear runtime scaling with the number of contacts. We further extend the formulation to a unified 6D contact model capturing tangential, torsional, and rolling friction, and introduce a practical dual-cone impedance heuristic. ComFree-Sim is implemented in Warp and exposed through a MuJoCo-compatible interface as a drop-in backend alternative to MuJoCo Warp (MJWarp). Experiments benchmark penetration, friction behaviors, stability, and simulation runtime scaling against MJWarp, demonstrating near-linear scaling and 2--3 times higher throughput in dense contact scenes with comparable physical fidelity. We deploy ComFree-Sim in real-time MPC for in-hand dexterous manipulation on a real-world multi-fingered LEAP hand and in dynamics-aware motion retargeting, demonstrating that low-latency simulation yields higher closed-loop success rates and enables practical high-frequency control in contact-rich tasks.

Parametric computer-aided design (CAD) is the dominant paradigm in mechanical engineering for physical design. Distinguished by relational geometry, parametric CAD models begin as two-dimensional sketches consisting of geometric primitives (e.g., line segments, arcs) and explicit constraints between them (e.g., coincidence, perpendicularity) that form the basis for three-dimensional construction operations. Training machine learning models to reason about and synthesize parametric CAD designs has the potential to reduce design time and enable new design workflows. Additionally, parametric CAD designs can be viewed as instances of constraint programming and they offer a well-scoped test bed for exploring ideas in program synthesis and induction. To facilitate this research, we introduce SketchGraphs, a collection of 15 million sketches extracted from real-world CAD models coupled with an open-source data processing pipeline. Each sketch is represented as a geometric constraint graph where edges denote designer-imposed geometric relationships between primitives, the nodes of the graph. We demonstrate and establish benchmarks for two use cases of the dataset: generative modeling of sketches and conditional generation of likely constraints given unconstrained geometry.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

The relationship between balance laws and the Principle of Virtual Work as well as the structure of contact interactions in continua remain foundational issues in Mechanics. In this work, we revisit these issues within the distributional framework emphasized by Paul Germain. We show that while the Principle of Virtual Work implies balance of forces and moments for nth-gradient continua, balance laws alone do not suffice to characterize equilibrium for n geq 2. We then reexamine Noll's classical theorem asserting that surface contact forces depend solely on the unit normal to the surface and identify the precise role of his additional assumptions, namely the absence of edge and wedge contact interactions and the boundedness of the surface contact density on the space of oriented surfaces. We demonstrate that these hypotheses fail for general higher-gradient continua. Consequently, the presence of curvature-dependent surface contact forces in such materials does not conflict with Noll's theorem and refutes his claim of their nonexistence.

Generating realistic 3D Human-Object Interactions (HOI) is a fundamental task for applications ranging from embodied AI to virtual content creation, which requires harmonizing high-level semantic intent with strict low-level physical constraints. Existing methods excel at semantic alignment, however, they struggle to maintain precise object contact. We reveal a key finding termed Geometric Forgetting: as diffusion model depth increases, semantic feature tend to overshadow object geometry feature, causing the model to lose its perception to object geometry. To address this, we propose MaMi-HOI, a hierarchical framework reconciling Macro-level kinematic fluidity with Micro-level spatial precision. First, to counteract geometric forgetting, we introduce the Geometry-Aware Proximity Adapter (GAPA), which explicitly re-injects dense object details to perform residual snapping corrections for precise contact. Nevertheless, such aggressive local enforcement can disrupt global dynamics, leading to robotic stiffness. In response, we introduce the Kinematic Harmony Adapter (KHA), which proactively aligns whole-body posture with spatial objectives, ensuring the skeleton actively accommodates constraints without compromising naturalness. Extensive experiments validate that MaMi-HOI simultaneously achieves natural motion and precise contact. Crucially, it extends generation capabilities to long-term tasks with complex trajectories, effectively bridging the gap between global navigation and high-fidelity manipulation in 3D scenes. Code is available at https://github.com/DON738110198/MaMi-HOI.git

Modeling the hand-object (HO) interaction not only requires estimation of the HO pose, but also pays attention to the contact due to their interaction. Significant progress has been made in estimating hand and object separately with deep learning methods, simultaneous HO pose estimation and contact modeling has not yet been fully explored. In this paper, we present an explicit contact representation namely Contact Potential Field (CPF), and a learning-fitting hybrid framework namely MIHO to Modeling the Interaction of Hand and Object. In CPF, we treat each contacting HO vertex pair as a spring-mass system. Hence the whole system forms a potential field with minimal elastic energy at the grasp position. Extensive experiments on the two commonly used benchmarks have demonstrated that our method can achieve state-of-the-art in several reconstruction metrics, and allow us to produce more physically plausible HO pose even when the ground-truth exhibits severe interpenetration or disjointedness. Our code is available at https://github.com/lixiny/CPF.

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we study the Discretizable Molecular Distance Geometry Problem whose feasible solutions provide a discretization scheme for the DGP. We propose the first constraint programming formulations as well as a set of checks for proving infeasibility, domain reduction techniques, symmetry breaking constraints and valid inequalities. Our computational results indicate that our formulations outperform the state-of-the-art integer programming formulations, both for feasible and infeasible instances.

In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric properties of these developable surfaces, we study the geometry of gluing two surfaces.

Most learned dexterous grasp generators relegate contact forces to a downstream verification step, so a kinematically-plausible pose can still violate the conditions for a stable physical grasp. We address this with EquiDexFlow, an SE(3)-equivariant flow-matching model that jointly predicts wrist pose, joint angles, fingertip contacts, surface normals, and contact forces from an object point cloud. Our architecture projects contacts onto the object surface and forces into the Coulomb friction cone by construction, so placement and friction compliance hold without loss penalties. We prove end-to-end SE(3) equivariance and verify it empirically over 200 rotations, with wrist residuals below 0.04^circ and exactly zero joint deviation. Trained on 8,100 force-closure grasps across 81 objects for the 16-DoF Allegro Hand, our model achieves zero friction violations, the best composite score, and the lowest wrench residual among all ablation variants. We retarget decoded fingertip contacts to a 16-DoF LEAP Hand via per-finger inverse kinematics, and our hardware-feasible refinement places every joint at least 5% inside its actuator envelope while preserving wrench balance. On the physical robot, retargeted EquiDexFlow-decoded grasps complete open-loop pick-and-hold trials on all six test objects, with every asymmetric object succeeding at both the canonical pose and a 120^circ co-rotation. Videos, code, and checkpoints are available at https://equidexflow.github.io.

Touch and vision go hand in hand, mutually enhancing our ability to understand the world. From a research perspective, the problem of mixing touch and vision is underexplored and presents interesting challenges. To this end, we propose Tactile-Informed 3DGS, a novel approach that incorporates touch data (local depth maps) with multi-view vision data to achieve surface reconstruction and novel view synthesis. Our method optimises 3D Gaussian primitives to accurately model the object's geometry at points of contact. By creating a framework that decreases the transmittance at touch locations, we achieve a refined surface reconstruction, ensuring a uniformly smooth depth map. Touch is particularly useful when considering non-Lambertian objects (e.g. shiny or reflective surfaces) since contemporary methods tend to fail to reconstruct with fidelity specular highlights. By combining vision and tactile sensing, we achieve more accurate geometry reconstructions with fewer images than prior methods. We conduct evaluation on objects with glossy and reflective surfaces and demonstrate the effectiveness of our approach, offering significant improvements in reconstruction quality.

Reinforcement learning explores effectively in domains such as Atari games, navigation, and locomotion, where novelty over states or dynamics is a sufficient signal. In contrast, dexterous manipulation requires rich physical hand--object interactions, but existing methods often suffer from unstable contact-based novelty signals, inefficient distance novelty signals, or reliance on task-specific priors. We propose ContactExplorer, a general exploration method for dexterous manipulation tasks. ContactExplorer represents contact as the intersection between object surface points and hand keypoints, encouraging dexterous hands to discover diverse and novel contact patterns, namely which fingers contact which object regions. It maintains a contact counter conditioned on discretized object states obtained via learned hash codes. This counter is leveraged in two complementary ways: (1) a count-based contact coverage reward that promotes exploration of novel contact patterns, and (2) an energy-based reaching reward that guides the agent toward under-explored contact regions. We evaluate ContactExplorer on seven contact-rich manipulation tasks and five dexterous hand embodiments. Experimental results show that ContactExplorer substantially improves sample efficiency and success rates over existing exploration methods, that it reduces the need for task-specific priors, and that it remains effective across hand embodiments and transfers to the real world. Project page is https://contact-explorer.github.io.

3D fragment reassembly aims to recover the rigid poses of unordered fragment point clouds or meshes in a common object coordinate system to reconstruct the complete shape. The problem becomes particularly challenging as the number of fragments grows, since the target shape is unknown and fragments provide weak semantic cues. Existing end-to-end approaches are prone to cascading failures due to unreliable contact reasoning, most notably inaccurate fragment adjacencies. To address this, we propose Structure-Aware Reassembly (SARe), a generative framework with SARe-Gen for Euclidean-space assembly generation and SARe-Refine for inference-time refinement, with explicit contact modeling. SARe-Gen jointly predicts fracture-surface token probabilities and an inter-fragment contact graph to localize contact regions and infer candidate adjacencies. It adopts a query-point-based conditioning scheme and extracts aligned local geometric tokens at query locations from a frozen geometry encoder, yielding queryable structural representations without additional structural pretraining. We further introduce an inference-time refinement stage, SARe-Refine. By verifying candidate contact edges with geometric-consistency checks, it selects reliable substructures and resamples the remaining uncertain regions while keeping verified parts fixed, leading to more stable and consistent assemblies in the many-fragment regime. We evaluate SARe across three settings, including synthetic fractures, simulated fractures from scanned real objects, and real physically fractured scans. The results demonstrate state-of-the-art performance, with more graceful degradation and higher success rates as the fragment count increases in challenging large-scale reassembly.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Contact often occurs without macroscopic surface deformation, such as during interaction with liquids, semi-liquids, or ultra-soft materials. However, most existing tactile sensors rely on deformation to infer contact, making such light-contact interactions difficult to perceive robustly. To address this, we present LightTact, a visual-tactile fingertip sensor that makes contact directly visible via a deformation-independent principle. LightTact features an ambient-blocking optical configuration that suppresses both external light and internal illumination at non-contact regions, while transmitting only the scattered light generated at true contacts. As a result, LightTact produces high-contrast raw images in which non-contact pixels remain near-black (mean gray value < 3) and contact pixels preserve the natural appearance of the contacting surface. Built on this, LightTact achieves accurate pixel-level contact segmentation that is robust to material properties, contact force, surface appearance, and environmental lighting. We further demonstrate that LightTact unlocks new robotic manipulation behaviors that require detection of extremely light contact, including water spreading, facial-cream dipping, and soft thin-film interaction. In addition, we show that LightTact's spatially aligned visual-tactile images can be directly interpreted by vision-language models.

We give a complete characterization of the holonomies of strictly convex cusps and of round cusps in convex projective geometry. We build families of generalized cusps of non-maximal rank associated to each strictly convex or round cusp. We also extend Ballas-Cooper-Leitner's definition of generalized cusp to allow for virtually solvable fundamental group, and we produce the first such example with non-virtually nilpotent fundamental group. Along with a companion paper, this allows to build strictly convex cusps and generalized cusps whose fundamental group is any finitely generated virtually nilpotent group. This also has interesting consequences for the theory of relatively Anosov representations.

Humans constantly contact objects to move and perform tasks. Thus, detecting human-object contact is important for building human-centered artificial intelligence. However, there exists no robust method to detect contact between the body and the scene from an image, and there exists no dataset to learn such a detector. We fill this gap with HOT ("Human-Object conTact"), a new dataset of human-object contacts for images. To build HOT, we use two data sources: (1) We use the PROX dataset of 3D human meshes moving in 3D scenes, and automatically annotate 2D image areas for contact via 3D mesh proximity and projection. (2) We use the V-COCO, HAKE and Watch-n-Patch datasets, and ask trained annotators to draw polygons for the 2D image areas where contact takes place. We also annotate the involved body part of the human body. We use our HOT dataset to train a new contact detector, which takes a single color image as input, and outputs 2D contact heatmaps as well as the body-part labels that are in contact. This is a new and challenging task that extends current foot-ground or hand-object contact detectors to the full generality of the whole body. The detector uses a part-attention branch to guide contact estimation through the context of the surrounding body parts and scene. We evaluate our detector extensively, and quantitative results show that our model outperforms baselines, and that all components contribute to better performance. Results on images from an online repository show reasonable detections and generalizability.

Every robot already carries high-resolution contact sensors: its own joints. Legged robots and humanoids exploit them to walk, run, and track whole-body motions without vision, but there the contacts are large and forceful. Is joint sensing also enough for precise, contact-rich assembly, where the robot must find a millimeter-scale opening, mesh gear teeth, or catch a thread through light contact? We study this question by training blind assembly policies that observe only a short history of joint positions, velocities, and their own actions, without visual, force, torque, or tactile sensing. The poses of both the fixture and the part are unknown to the policy, and the grasp is randomized substantially. The policy must therefore assemble the parts through contact, sensed exclusively through its own proprioception. Trained with reinforcement learning entirely in simulation over randomized parts, grasps, and contacts, such policies learn peg insertion, gear meshing, and nut threading. The peg insertion policy transfers zero-shot to the real world and inserts pegs of different shapes and sizes in 73% of trials. Controlled comparisons with matched visual policies in simulation show that blind policies generalize far better to unseen part shapes and sizes, though they can be slower. Training such policies needs thousands of different assemblies, each simulated with its clearance intact, so we also release an open-source generator that builds them procedurally from exact convex pieces for MuJoCo; it is more accurate and faster than convex decomposition or MuJoCo's signed-distance collision. Videos and interactive simulations are at https://younghyopark.me/blind-proprioceptive-assembly/.

This is the second paper devoted to the numerical version of Signature-inverse Theorem in terms of the underlying joint invariants. Signature Theorem and its Inverse guarantee any application of differential invariant signature curves to the invariant recognition of visual objects. We first show the invalidity of Curvature-inverse and Signature inverse theorems, meaning non-congruent meshes may have the same joint invariant numerical curvature or signature. Then by classifying three and five point ordinary meshes respectively in the Euclidean and affine cases, we look for conditions in terms of the associated joint invariant signatures which make these theorems correct. Additionally, we bring forward The Host Theorem to provide a simpler version of Signature-inverse Theorem for closed ordinary meshes.

We analyse the boundary behaviour of the gradient of the torsion function w_Om in convex domains OmsubsetR^d. We prove that its L^infty-norm is attained at a boundary point and establish the stability of this norm under general (convex) perturbations. For problems of the form $sup{|nabla w_{Om}|_infty: Om subset R^d,open, bounded and convex, G(Om)=m}, where G is either volume or perimeter, we show the existence of maximisers which are C^1-smooth, rotationally symmetric about an axis and contain a (d-1)$- dimensional ball (of estimated size) in their boundary. Other constraints, whether geometric (such as diameter or circumradius) or variational (such as torsion or first Dirichlet eigenvalue), are also briefly discussed, and some of their characteristic behaviours are highlighted.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Modeling the physical contacts between the hand and object is standard for refining inaccurate hand poses and generating novel human grasp in 3D hand-object reconstruction. However, existing methods rely on geometric constraints that cannot be specified or controlled. This paper introduces a novel task of controllable 3D hand-object contact modeling with natural language descriptions. Challenges include i) the complexity of cross-modal modeling from language to contact, and ii) a lack of descriptive text for contact patterns. To address these issues, we propose NL2Contact, a model that generates controllable contacts by leveraging staged diffusion models. Given a language description of the hand and contact, NL2Contact generates realistic and faithful 3D hand-object contacts. To train the model, we build ContactDescribe, the first dataset with hand-centered contact descriptions. It contains multi-level and diverse descriptions generated by large language models based on carefully designed prompts (e.g., grasp action, grasp type, contact location, free finger status). We show applications of our model to grasp pose optimization and novel human grasp generation, both based on a textual contact description.

Understanding how humans use physical contact to interact with the world is key to enabling human-centric artificial intelligence. While inferring 3D contact is crucial for modeling realistic and physically-plausible human-object interactions, existing methods either focus on 2D, consider body joints rather than the surface, use coarse 3D body regions, or do not generalize to in-the-wild images. In contrast, we focus on inferring dense, 3D contact between the full body surface and objects in arbitrary images. To achieve this, we first collect DAMON, a new dataset containing dense vertex-level contact annotations paired with RGB images containing complex human-object and human-scene contact. Second, we train DECO, a novel 3D contact detector that uses both body-part-driven and scene-context-driven attention to estimate vertex-level contact on the SMPL body. DECO builds on the insight that human observers recognize contact by reasoning about the contacting body parts, their proximity to scene objects, and the surrounding scene context. We perform extensive evaluations of our detector on DAMON as well as on the RICH and BEHAVE datasets. We significantly outperform existing SOTA methods across all benchmarks. We also show qualitatively that DECO generalizes well to diverse and challenging real-world human interactions in natural images. The code, data, and models are available at https://deco.is.tue.mpg.de.

We characterise sets of points of exceptional Lie incidence geometries, that is, the natural geometries arising from spherical buildings of exceptional types F_4, E_6, E_7, E_8 and G_2, that form a line using the opposition relation. With that, we obtain a classification of so-called ``geometric lines'' in many of these geometries. Furthermore, our results lead to a characterisation of geometric lines in finite exceptional Lie incidence geometries as minimal blocking sets, that is, point sets of the size of a line admitting no object opposite to all of their members, in most cases, and we classify all exceptions. As a further consequence, we obtain a characterisation of automorphisms of exceptional spherical buildings as certain opposition preserving maps.

Monocular geometry estimation has recently achieved impressive performance across diverse scenes. However, state-of-the-art models still face notable distortion in local 3D structure, especially in fine details, like thin structures and small objects. We attribute this limitation to an architectural mismatch: most current models decode 3D geometry within a 2D parameterization, where feature interactions are governed by image-plane proximity rather than true 3D spatial relationships. This inadvertently mixes features from geometrically distant surfaces, resulting in over-smoothed geometry particularly around thin or elongated structure. In this paper, we propose MoGe-3, a fine-detail monocular geometry estimation model with Self-Guided Sparse 3D Refinement (SSR) that lifts monocular geometry modeling from 2D image space to 3D space for high-fidelity metric-scale point maps. MoGe-3 lifts the coarse point map from a foundation base model onto a sparse voxel shell and refines it via SSR. The SSR employs sparse convolutions that aggregate features based on 3D spatial locality, avoiding feature mixing across depth discontinuities. Extensive experiments on diverse datasets demonstrate that MoGe-3 significantly outperforms existing approaches in recovering fine detailed 3D geometry across both quantitative metrics and qualitative visualizations. Project page: https://qft-333.github.io/moge3page/

This paper introduces the first text-guided work for generating the sequence of hand-object interaction in 3D. The main challenge arises from the lack of labeled data where existing ground-truth datasets are nowhere near generalizable in interaction type and object category, which inhibits the modeling of diverse 3D hand-object interaction with the correct physical implication (e.g., contacts and semantics) from text prompts. To address this challenge, we propose to decompose the interaction generation task into two subtasks: hand-object contact generation; and hand-object motion generation. For contact generation, a VAE-based network takes as input a text and an object mesh, and generates the probability of contacts between the surfaces of hands and the object during the interaction. The network learns a variety of local geometry structure of diverse objects that is independent of the objects' category, and thus, it is applicable to general objects. For motion generation, a Transformer-based diffusion model utilizes this 3D contact map as a strong prior for generating physically plausible hand-object motion as a function of text prompts by learning from the augmented labeled dataset; where we annotate text labels from many existing 3D hand and object motion data. Finally, we further introduce a hand refiner module that minimizes the distance between the object surface and hand joints to improve the temporal stability of the object-hand contacts and to suppress the penetration artifacts. In the experiments, we demonstrate that our method can generate more realistic and diverse interactions compared to other baseline methods. We also show that our method is applicable to unseen objects. We will release our model and newly labeled data as a strong foundation for future research. Codes and data are available in: https://github.com/JunukCha/Text2HOI.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

We explicitly construct a pair of immersed tori in three dimensional Euclidean space that are related by a mean curvature preserving isometry. These Bonnet pair tori are the first examples of compact Bonnet pairs. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique smooth compact immersion. Moreover, we prove these isometric tori are real analytic. This resolves a second longstanding open problem on whether real analyticity of the metric already determines a unique compact immersion. Our construction uses the relationship between Bonnet pairs and isothermic surfaces. The Bonnet pair tori arise as conformal transformations of an isothermic torus with one family of planar curvature lines. We classify such isothermic tori in our companion paper (arXiv:2312.14956). The above approach stems from computational investigations of a 5x7 quad decomposition of a torus using a discrete differential geometric analog of isothermic surfaces and Bonnet pairs.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

Given a 3-dimensional (para-)CR structure, its family of chains define a 3-dimensional path geometry. We provide necessary and sufficient conditions that determine whether a path geometry in dimension three arises from chains of a CR or para-CR 3-manifold. We demonstrate how our characterization can be verified computationally for a given 3-dimensional path geometry and discuss a few examples.

Robotic grasping of thin, flat objects such as coins on hard surfaces remains challenging because conventional methods require reorienting the object, accessing its underside, or adding a dedicated nail mechanism. We previously showed that a rigid nail arrests soft-pad deformation and thereby forms a geometric constraint that improves precision grasping. Here we asked whether an additional constraint-forming boundary, created within the pad by material choice rather than by anatomy, could extend the conditions under which that constraint holds. We fabricated anthropomimetic fingertips with Shore E10 silicone at the center and Shore A60 at the sides, and compared them with uniformly soft E10 fingertips. An automated apparatus performed an oblique rotational tip pinch in which the pad engaged the coin's lateral surface, lifting it from flush contact with no gap beneath it. Over variations in horizontal approach distances, vertical finger displacements, and index-finger rotation, the mixed-stiffness pair maintained high success rates across more tested settings than the uniform pair during both geometric-constraint formation and the transition to a stable grasp. The nail-free pair failed in all 36 conditions of Experiment 1-1. However, the uniform pair performed better when coin position along the finger axis was varied, a condition-dependent trade-off. After tuning for coin size, both fingertip types grasped all six Japanese denominations. These results suggest that the operating range for thin-object grasping depends not only on pad softness but also on where stiffness is placed within a nail-supported pad, making boundary placement a candidate fingertip design variable.

Contact-rich manipulation tasks with stiff frictional elements like connector insertion are difficult to model with rigid-body simulators. In this work, we propose a new approach for modeling these environments by learning a quasi-static contact force model instead of a full simulator. Using a feature vector that contains information about the configuration and control, we find a linear mapping adequately captures the relationship between this feature vector and the sensed contact forces. A novel Linear Model Learning (LML) algorithm is used to solve for the globally optimal mapping in real time without any matrix inversions, resulting in an algorithm that runs in nearly constant time on a GPU as the model size increases. We validate the proposed approach for connector insertion both in simulation and hardware experiments, where the learned model is combined with an optimization-based controller to achieve smooth insertions in the presence of misalignments and uncertainty. Our website featuring videos, code, and more materials is available at https://model-based-plugging.github.io/.

Manipulating a Rubik's Cube with a single dexterous hand is a challenging test of sustained, contact-rich control: the hand must execute successive layer turns while keeping the cube secure. Each turn requires some fingers to support the cube while others push a moving layer, release contact, and reset for the next move. To learn this coordination, we introduce FINGR (Future-supervised Interaction Network with Geometric Representations), a policy that combines finger-relative geometry with future interaction prediction. A shared point encoder expresses the cube relative to each fingertip and aggregates its points without depending on cubie indexing. Learned future tokens share the observation encoder and receive supervision for contact-force changes, layer-turn progress, and finger joint displacement at multiple time scales. The resulting representation conditions a flow policy that directly generates finger actions. On a real dexterous hand, our policy achieves 99.0% success over 300 turn attempts, compared with 79.7% for the base flow policy. Integrated with grasping and table-assisted regrasping, the policy solves all ten scrambled 2times2times2 cubes in a mean complete-system time of approximately 137 seconds. The project website is available at https://www.lyt0112.com/projects/FINGR

The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large. In the field of aerodynamics, traditional polynomial-based parameterization uses as few parameters as possible to describe the geometry of an airfoil. However, because the 3D geometry of a wing is more complicated than the 2D airfoil, polynomial-based parameterizations have difficulty in accurately representing the entire shape of a wing in 3D space. Existing deep learning-based methods can extract massive latent neural representations for the shape of 2D airfoils or 2D slices of wings. Recent studies highlight that directly taking geometric features as inputs to the neural networks can improve the accuracy of predicted aerodynamic coefficients. Motivated by geometry theory, we propose to incorporate Riemannian geometric features for learning Coefficient of Pressure (CP) distributions on wing surfaces. Our method calculates geometric features (Riemannian metric, connection, and curvature) and further inputs the geometric features, coordinates and flight conditions into a deep learning model to predict the CP distribution. Experimental results show that our method, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11 aircraft test set.

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

We introduce multi-task Visuo-Tactile World Models (VT-WM), which capture the physics of contact through touch reasoning. By complementing vision with tactile sensing, VT-WM better understands robot-object interactions in contact-rich tasks, avoiding common failure modes of vision-only models under occlusion or ambiguous contact states, such as objects disappearing, teleporting, or moving in ways that violate basic physics. Trained across a set of contact-rich manipulation tasks, VT-WM improves physical fidelity in imagination, achieving 33% better performance at maintaining object permanence and 29% better compliance with the laws of motion in autoregressive rollouts. Moreover, experiments show that grounding in contact dynamics also translates to planning. In zero-shot real-robot experiments, VT-WM achieves up to 35% higher success rates, with the largest gains in multi-step, contact-rich tasks. Finally, VT-WM demonstrates significant downstream versatility, effectively adapting its learned contact dynamics to a novel task and achieving reliable planning success with only a limited set of demonstrations.

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem is the local analogue of Hilbert's 18th problem, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry, dimensional structure variability, and combinatorial explosion beyond Go limit the scalability and generality of existing methods. Here we model the problem as a two-player matrix completion game and train the reinforcement learning system, PackingStar, to play the games. The matrix entries represent pairwise cosines of sphere center vectors. One player fills entries while another corrects suboptimal ones to improve exploration quality, cooperatively maximizing the matrix size, corresponding to the kissing number. These matrices are decomposed into representative substructures, providing diverse bases and structural constraints that steer subsequent games and make extremely large spaces tractable. PackingStar surpasses records from dimensions 25 to 31 and sets new lower bounds for generalized kissing numbers under various angular constraints. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in other dimensions. Notably, some configurations challenge long-held antipodal paradigms, revealing algebraic correspondences with finite simple groups as well as geometric relationships across dimensions. Inspired by these patterns, humans devised further improved constructions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition via extreme-scale reinforcement learning and open new pathways for the Kissing Number Problem and broader geometry research.

In this paper we study the behavior of geodesics on cones over arbitrary C^3-smooth closed Riemannian manifolds. We show that the geodesic flow on such cones admits first integrals whose values uniquely determine almost all geodesics except for cone generatrices. This investigation is inspired by our results on billiards inside cones over manifolds where similar results hold true.

One goal of dexterous robotic grasping is to allow robots to handle objects with the same level of flexibility and adaptability as humans. However, it remains a challenging task to generate an optimal grasping strategy for dexterous hands, especially when it comes to delicate manipulation and accurate adjustment the desired grasping poses for objects of varying shapes and sizes. In this paper, we propose a novel dexterous grasp generation scheme called GrainGrasp that provides fine-grained contact guidance for each fingertip. In particular, we employ a generative model to predict separate contact maps for each fingertip on the object point cloud, effectively capturing the specifics of finger-object interactions. In addition, we develop a new dexterous grasping optimization algorithm that solely relies on the point cloud as input, eliminating the necessity for complete mesh information of the object. By leveraging the contact maps of different fingertips, the proposed optimization algorithm can generate precise and determinable strategies for human-like object grasping. Experimental results confirm the efficiency of the proposed scheme.

World models offer a promising route toward robot planning by enabling agents to imagine and verify the consequences of actions before execution. However, current video-based world models often struggle to capture the physical constraints that govern manipulation, particularly contact. Further, their action conditioning is often constrained to specific embodiments such as parallel grippers. We propose Contact Flow, an embodiment-agnostic action representation that encodes manipulation through the trajectory of 3D contact points between an actor and a target object. By discarding actor-specific appearance and kinematics, Contact Flow provides a shared conditioning signal for both human demonstrations and robotic execution. Therefore, we can train a large-scale video generative model on both human and robotic object interaction videos conditioned on Contact Flow, yielding a world model that predicts physically plausible manipulation outcomes. We integrate this model into a propose-imagine-verify-act pipeline, where generated rollouts are assessed by a vision-language model before execution. Experiments on the DROID dataset and real-world tabletop manipulation tasks demonstrate that Contact Flow enables transfer between human demonstrations and different robotic embodiments.

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved), hyperbolic space (negatively curved) or hyperspherical space (positively curved) to maintain their specific geometric structures (e.g., chain, hierarchy and ring structures). However, the topological structure of KGs appears to be complicated, since it may contain multiple types of geometric structures simultaneously. Therefore, embedding KGs in a single space, no matter the Euclidean space, hyperbolic space or hyperspheric space, cannot capture the complex structures of KGs accurately. To overcome this challenge, we propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Theoretically, our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities. Experimental results on three well-established knowledge graph completion benchmarks show that our GIE achieves the state-of-the-art performance with fewer parameters.