# Embodied CAD: Solver-Grounded LLM Agents for Parametric B-Rep Assembly Modeling

arXiv: https://arxiv.org/abs/2606.31252 · HTML: https://mlsanity.com/paper/2606.31252/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal and embodied agents, one of 16 directions in LLM agents and tool use.
- Builds on 17 of its 22 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Placed in

- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)

## Builds on (most cited first, 17 of 17)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021)
- [SolidGen: An Autoregressive Model for Direct B-rep Synthesis](https://mlsanity.com/paper/2203.13944/) (2022)
- [JoinABLe: Learning Bottom-up Assembly of Parametric CAD Joints](https://mlsanity.com/paper/2111.12772/) (2021)
- [CAD-Coder: Text-to-CAD Generation with Chain-of-Thought and Geometric Reward](https://mlsanity.com/paper/2505.19713/) (2025)
- [CAD-Coder: An Open-Source Vision-Language Model for Computer-Aided Design Code Generation](https://mlsanity.com/paper/2505.14646/) (2025)
- [CAD-Assistant: Tool-Augmented VLLMs as Generic CAD Task Solvers](https://mlsanity.com/paper/2412.13810/) (2024)
- [TOOLCAD: Exploring Tool-Using Large Language Models in Text-to-CAD Generation with Reinforcement Learning](https://mlsanity.com/paper/2604.07960/) (2026)

## Built on by (most cited first, 4 of 4)

- [TraceCAD: Trace-Guided Repair for Agentic CAD Generation](https://mlsanity.com/paper/2608.03062/) (2026)
- [Test-Time Scaling for CAD Generation via Verifier-Free Consensus Selection](https://mlsanity.com/paper/2608.09706/) (2026)
- [Encoded but Not Actionable: Auditing the Decode-Generate-Steer Gap in Frozen LLMs for Geometric Constraints](https://mlsanity.com/paper/2608.17843/) (2026)
- [AgenticCADedit: A Stateful, Tool-Mediated Agentic Approach to Multimodal 3D CAD Editing](https://mlsanity.com/paper/2609.29621/) (2026)

## Abstract (arXiv)

Large language models can write plausible CAD scripts, but reliable industrial CAD modeling requires more than syntactically valid code: every feature, placement, and assembly relation must be accepted by an exact geometric kernel while remaining editable as parametric boundary representation geometry. We present Embodied CAD, solver-grounded LLM agents for parametric B-Rep assembly modeling. Instead of generating a complete script in one pass, the agent iteratively selects actions from a stratified L0-L4 CAD skill library, resolves them into typed geometric operations, executes them in a CAD backend, and uses solver feedback to plan, repair, and learn. The framework combines action grammar constraints, deterministic parameter resolution, and solver-derived rewards for supervised warm-up and GRPO-style refinement. We evaluate Embodied CAD on multi-step mechanical, industrial equipment, and mold-oriented assembly tasks using solver-aligned metrics: executable rate, skill accuracy, operation-family accuracy, exact policy accuracy, and task completion success. The results show that solver-grounded planning executes all strong-planner workflows in the current benchmark, while learned controllers reach high executable rates and expose the remaining gap between valid tool calls and exact long-horizon policy prediction.