# Geometry Matching for Multi-Embodiment Grasping

arXiv: https://arxiv.org/abs/2312.03864 · HTML: https://mlsanity.com/paper/2312.03864/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2023.

## Built on by (most cited first, 12 of 12)

- [CEDex: Cross-Embodiment Dexterous Grasp Generation at Scale from Human-like Contact Representations](https://mlsanity.com/paper/2509.24661/) (2025)
- [House of Dextra: Cross-embodied Co-design for Dexterous Hands](https://mlsanity.com/paper/2512.03743/) (2025)
- [Invariance Co-training for Robot Visual Generalization](https://mlsanity.com/paper/2512.05230/) (2025)
- [RobotFingerPrint: Unified Gripper Coordinate Space for Multi-Gripper Grasp Synthesis and Transfer](https://mlsanity.com/paper/2409.14519/) (2024)
- [MachaGrasp: Morphology-Aware Cross-Embodiment Dexterous Hand Articulation Generation for Grasping](https://mlsanity.com/paper/2510.06068/) (2025)
- [UniMorphGrasp: Diffusion Model with Morphology-Awareness for Cross-Embodiment Dexterous Grasp Generation](https://mlsanity.com/paper/2602.00915/) (2026)
- [KITE: Decoupling Kinematics and Interaction for Zero-Shot Cross-Embodiment Manipulation](https://mlsanity.com/paper/2606.22113/) (2026)
- [FunGrasp: Functional Grasping for Diverse Dexterous Hands](https://mlsanity.com/paper/2411.16755/) (2024)
- [MANGO-Grasp: Mahalanobis Fields over Geometry-Oriented 3D Gaussians for Cross-Embodiment Dexterous Grasping](https://mlsanity.com/paper/2608.02014/) (2026)
- [GOAG: Generative and Object-Agnostic Grasp Planner for Dexterous Robotic Manipulation](https://mlsanity.com/paper/2608.19759/) (2026)
- [CoToGrasp: Contact-Topology-Conditioned Dexterous Grasp Synthesis via Canonical Workspace Learning](https://mlsanity.com/paper/2608.19776/) (2026)
- [Gripper-aware Vision Language Action Models](https://mlsanity.com/paper/2608.24603/) (2026)

## Abstract (arXiv)

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.