Compliant Sphere Lattice Contact: Distributed Contact Modeling for Sphere-Based Robot Representations

Contact-rich manipulation requires world models to capture complex interaction dynamics from heterogeneous visual and tactile observations, yet the representation properties that enable reliable predictive planning remain poorly understood. We present ContactWorld, a systematic study of vision-tactile representations across 12 contact-rich manipulation tasks. Through controlled evaluation within a unified world-model and planning framework, we find that representations preserving spatial structure and temporal continuity consistently support more accurate prediction and stronger planning performance. Point-cloud observations increase average success from 20.7% and 22.0% with wrist- and front-view RGB, respectively, to 32.1%. Tactile sensing provides further gains only when its representation is compatible with the visual modality, with point clouds and tactile force fields achieving the highest overall success rate of 36.1%. These advantages become more pronounced at increasing goal offsets, where prediction errors and contact uncertainty accumulate. Controlled representation studies and real-world experiments across four manipulation tasks further support these trends. Together, our results establish spatial structure, temporal continuity, and cross-modal compatibility as key principles for designing vision-tactile world models for contact-rich robotic manipulation.

We propose an optimization-based framework for robust contact-rich manipulation. Recent contact-implicit methods enable online hybrid planning across contact modes, allowing closed-loop manipulation for a given target state and contact location sequence of the robot and object. However, most existing approaches lack the ability to autonomously reason and generate diverse contact location sequences and manipulation trajectories, i.e., active contact location selection, which limits their applicability to relatively simple tasks. Active contact location selection is challenging due to complementarity in contact dynamics and the sparse gradients, making the design of a unified framework for contact selection and planning difficult. To address these challenges, we introduce Simultaneous Contact Selection and Planning (SCSP), a cascaded optimization framework comprising Contact Selection Optimization (CSO) and Contact Planning Optimization (CPO). CSO leverages a surrogate contact model and discrete-continuous optimization to efficiently resolve the nonsmoothness and coupling in contact selection, enabling online global searching of optimal contact locations. CPO performs prior-guided contact planning by evaluating the reference contact locations produced by CSO and generating corresponding manipulation trajectories in real time for redundant manipulators. Extensive simulations and real-world experiments demonstrate that SCSP produces diverse manipulation behaviors and robust control under inaccurate dynamics and perceptual noise. We further validate the generalization of the framework on challenging manipulation tasks. Project website: \href{https://sites.google.com/view/scsp-robot}{https://sites.google.com/view/scsp-robot}.

Real-world robotic assembly at sub-millimeter tolerances demands spatial precision, compliant interaction, and robustness to contact failures. We present Facet-0, a robotic foundation model that predicts and values the contact consequences of its actions. Facet-0 unifies multimodal representation learning and reinforcement learning (RL) post-training around a joint action-wrench proposal: a causal wrench history is aligned with vision-language semantics and kinematic state, and flow matching generates each action chunk together with the future wrist-wrench profile it is expected to induce. Deployment rollouts train a distributional Action-Wrench Critic to distinguish motions with similar task progress but different contact outcomes, while phase-aware rewards and contact-selective credit concentrate policy improvement on decisive interactions. To accommodate part-specific dynamics, a lightweight bounded actor reuses the frozen representation for on-robot adaptation; RL remains defined over executable Cartesian actions, while an auxiliary wrench head preserves predictive, non-commanded action-contact coupling. Trained on ManuFacet-1K, a 1,000-hour force-synchronized corpus spanning three embodiments and multiple manufacturing cells, the bounded task-adapted system reaches 82% mean success on five sub-millimeter computer-assembly tasks, compared with 15% for the strongest baseline, with 0.5 mm placement accuracy and 50 ms command latency.