# Executable Analytic Concepts as the Missing Link Between VLM Insight and Precise Manipulation

arXiv: https://arxiv.org/abs/2510.07975 · HTML: https://mlsanity.com/paper/2510.07975/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 46 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 30 of 43)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [PaLM-E: An Embodied Multimodal Language Model](https://mlsanity.com/paper/2303.03378/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [Grounded SAM: Assembling Open-World Models for Diverse Visual Tasks](https://mlsanity.com/paper/2401.14159/) (2024)
- [Vision-Language Models for Vision Tasks: A Survey](https://mlsanity.com/paper/2304.00685/) (2023)
- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [Evaluating Real-World Robot Manipulation Policies in Simulation](https://mlsanity.com/paper/2405.05941/) (2024)
- [FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects](https://mlsanity.com/paper/2312.08344/) (2023)
- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [A Survey on Vision-Language-Action Models for Embodied AI](https://mlsanity.com/paper/2405.14093/) (2024)
- [Hi Robot: Open-Ended Instruction Following with Hierarchical Vision-Language-Action Models](https://mlsanity.com/paper/2502.19417/) (2025)
- [Where are we in the search for an Artificial Visual Cortex for Embodied Intelligence?](https://mlsanity.com/paper/2303.18240/) (2023)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Where2Act: From Pixels to Actions for Articulated 3D Objects](https://mlsanity.com/paper/2101.02692/) (2021)
- [ManipLLM: Embodied Multimodal Large Language Model for Object-Centric Robotic Manipulation](https://mlsanity.com/paper/2312.16217/) (2023)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [AHA: A Vision-Language-Model for Detecting and Reasoning Over Failures in Robotic Manipulation](https://mlsanity.com/paper/2410.00371/) (2024)
- [GraspVLA: a Grasping Foundation Model Pre-trained on Billion-scale Synthetic Action Data](https://mlsanity.com/paper/2505.03233/) (2025)
- [CoPa: General Robotic Manipulation through Spatial Constraints of Parts with Foundation Models](https://mlsanity.com/paper/2403.08248/) (2024)
- [What Matters in Building Vision-Language-Action Models for Generalist Robots](https://mlsanity.com/paper/2412.14058/) (2024)
- [Manipulate-Anything: Automating Real-World Robots using Vision-Language Models](https://mlsanity.com/paper/2406.18915/) (2024)

## Built on by (most cited first, 3 of 3)

- [RoboRSI: Stable, efficient, and reusable robot self-evolution in complex real-world environments](https://mlsanity.com/paper/2610.12424/) (2026)
- [DualManip: Agentic Dynamic Manipulation via Dual-Path Semantic Reasoning and Geometric Adaptation](https://mlsanity.com/paper/2609.31112/) (2026)
- [Explicit Kinematic Guidance from Analytic Concepts for Vision-Language-Action Models](https://mlsanity.com/paper/2607.26513/) (2026)

## Abstract (arXiv)

Enabling robots to perform precise and generalized manipulation in unstructured environments remains a fundamental challenge in embodied AI. While Vision-Language Models (VLMs) have demonstrated remarkable capabilities in semantic reasoning and task planning, a significant gap persists between their high-level understanding and the precise physical execution required for real-world manipulation. To bridge this "semantic-to-physical" gap, we introduce GRACE, a novel framework that grounds VLM-based reasoning through executable analytic concepts (EAC)-mathematically defined blueprints that encode object affordances, geometric constraints, and semantics of manipulation. Our approach integrates a structured policy scaffolding pipeline that turn natural language instructions and visual information into an instantiated EAC, from which we derive grasp poses, force directions and plan physically feasible motion trajectory for robot execution. GRACE thus provides a unified and interpretable interface between high-level instruction understanding and low-level robot control, effectively enabling precise and generalizable manipulation through semantic-physical grounding. Extensive experiments demonstrate that GRACE achieves strong zero-shot generalization across a variety of articulated objects in both simulated and real-world environments, without requiring task-specific training.