MANGO-Grasp: Mahalanobis Fields over Geometry-Oriented 3D Gaussians for Cross-Embodiment Dexterous Grasping

Grasp synthesis aims to generate stable and physically plausible hand--object interactions, and has become a fundamental problem in both human hand modeling and robotic manipulation. However, a unified representation across human and robotic hands is still lacking, mainly due to differences in hand morphology and surface modeling. Prior methods typically rely on either contact maps or dense implicit descriptors to represent interaction, but these representations are often incomplete or computationally expensive and redundant. We propose InterMASH, a unified geometric representation that establishes cross-embodiment correspondence using sphere-fixed anchors. At each anchor, low-degree spherical harmonics compactly encode local hand geometry, object geometry, and contact, forming an explicit and interpretable token sequence. Building on this natively tokenized structure, we introduce a conditional Diffusion Transformer that operates directly in the proposed InterMASH representation space and jointly generates hand geometry and contact, improving consistency and physical plausibility. Our method achieves competitive performance with state-of-the-art methods on key physical feasibility metrics in a large-scale ShadowHand benchmark, supports joint training across multiple hands, and shows that cross-embodiment fine-tuning with human grasp data can improve robotic grasp success and diversity. Project page is available at https://inter-mash.github.io/.

Achieving reliable robotic manipulation, such as dexterous grasping, requires a synergy between physically stable interactions and semantic task guidance, yet these objectives are often treated as separate, disjoint goals. In this paper, we investigate how to integrate dexterous grasping techniques, i.e., physically stable grasps for object lifting and language-guided grasp generation, to achieve both physical stability and semantic understanding. To this end, we propose SECOND-Grasp (SEmantic CONtact-guided Dexterous Grasping), a unified framework that enables robotic hands to dynamically adjust grasping strategies based on semantic reasoning while ensuring physical feasibility. We begin by obtaining coarse contact proposals through vision-language reasoning to infer where contacts should occur based on object properties, followed by segmentation to localize these regions across views. To further ensure consistency across multiple viewpoints, we introduce Semantic-Geometric Consistency Refinement (SGCR), which refines initial contact predictions by enforcing semantic consistency across views and removing geometrically invalid regions, yielding reliable 3D contact maps. Then, we derive a feasible hand pose for each contact map via inverse kinematics, generating a supervision signal for policy learning. Our approach, trained on DexGraspNet, consistently outperforms baselines in lifting success rate on both seen and unseen categories, achieving 98.2% and 97.7%, respectively, while also improving intent-aware grasping by 12.8% and 26.2%. We further show promising results on additional datasets and robotic hands, including Shadow Hand and Allegro Hand.

This work addresses sequentially grasping multiple objects with a single dexterous hand without releasing those already held. Most dexterous grasping methods commit all of the hand's degrees of freedom to a single object, underutilizing its dexterity and leaving no redundancy for subsequent grasps. The proposed solution, MoDex, is a diffusion policy that predicts the next gripper pose directly from observations, conditioned on an opposition space and point cloud. The opposition space condition specifies which fingers participate in the current grasp, enabling the gripper to use only a subset of its available degrees of freedom while reserving the remaining degrees of freedom for subsequent grasps. To facilitate sim-to-real transfer, MoDex is trained in two stages: first through imitation learning on expert demonstrations, and subsequently through reinforcement learning fine-tuning, which consistently improves success rates over the pre-trained policy. We evaluate MoDex in simulation on a MuJoCo-based Franka Emika Panda robot equipped with an Allegro Hand and on the corresponding real-world hardware platform. Across both simulation and real-world experiments, MoDex achieves higher success rates than the evaluated learning-based baselines, improving performance by 2.92-17.92% and 6.67-17.78%, respectively. Project page: https://modex2026.github.io/.