# GeoManip: Geometric Constraints as General Interfaces for Robot Manipulation

arXiv: https://arxiv.org/abs/2501.09783 · HTML: https://mlsanity.com/paper/2501.09783/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 16 Jan 2025.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Built on by (most cited first, 13 of 13)

- [Pure Vision Language Action (VLA) Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.19012/) (2025)
- [Vision Language Action Models in Robotic Manipulation: A Systematic Review](https://mlsanity.com/paper/2507.10672/) (2025)
- [Affordance Field Intervention: Enabling VLAs to Escape Memory Traps in Robotic Manipulation](https://mlsanity.com/paper/2512.07472/) (2025)
- [COS3D: Collaborative Open-Vocabulary 3D Segmentation](https://mlsanity.com/paper/2510.20238/) (2025)
- [Incentivizing Multimodal Reasoning in Large Models for Direct Robot Manipulation](https://mlsanity.com/paper/2505.12744/) (2025)
- [ManiAgent: An Agentic Framework for General Robotic Manipulation](https://mlsanity.com/paper/2510.11660/) (2025)
- [EPS3D: End-to-End Feed-Forward 3D Panoptic Segmentation](https://mlsanity.com/paper/2606.08980/) (2026)
- [T-Rex: Task-Adaptive Spatial Representation Extraction for Robotic Manipulation with Vision-Language Models](https://mlsanity.com/paper/2506.19498/) (2025)
- [Learning Action Priors for Cross-embodiment Robot Manipulation](https://mlsanity.com/paper/2606.26095/) (2026)
- [ManiSkillFormer: Demonstration-Free Compositional Manipulation via Geometric Contracts and Agentic Skill Graph](https://mlsanity.com/paper/2609.16331/) (2026)
- [DualManip: Agentic Dynamic Manipulation via Dual-Path Semantic Reasoning and Geometric Adaptation](https://mlsanity.com/paper/2609.31112/) (2026)
- [FrankenBot: Brain-Morphic Modular Orchestration for Robotic Manipulation with Vision-Language Models](https://mlsanity.com/paper/2506.21627/) (2025)
- [Rethinking Intermediate Representation for VLM-based Robot Manipulation](https://mlsanity.com/paper/2511.19315/) (2025)

## Abstract (arXiv)

We present GeoManip, a framework to enable generalist robots to leverage essential conditions derived from object and part relationships, as geometric constraints, for robot manipulation. For example, cutting the carrot requires adhering to a geometric constraint: the blade of the knife should be perpendicular to the carrot's direction. By interpreting these constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, enabling greater generalizability across diverse even unseen tasks, objects, and scenarios. Unlike vision-language-action models that require extensive training, operates training-free by utilizing large foundational models: a constraint generation module that predicts stage-specific geometric constraints and a geometry parser that identifies object parts involved in these constraints. A solver then optimizes trajectories to satisfy inferred constraints from task descriptions and the scene. Furthermore, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip's state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.