# CaStL: Constraints as Specifications through LLM Translation for Long-Horizon Task and Motion Planning

arXiv: https://arxiv.org/abs/2410.22225 · HTML: https://mlsanity.com/paper/2410.22225/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2024.

## Built on by (most cited first, 10 of 10)

- [Open-World Task and Motion Planning via Vision-Language Model Generated Constraints](https://mlsanity.com/paper/2411.08253/) (2024)
- [Uncertainty-Aware Trajectory Prediction via Rule-Regularized Heteroscedastic Deep Classification](https://mlsanity.com/paper/2504.13111/) (2025)
- [Hierarchical LLM-Based Multi-Agent Framework with Prompt Optimization for Multi-Robot Task Planning](https://mlsanity.com/paper/2602.21670/) (2026)
- [Large-Language-Model-Guided State Estimation for Partially Observable Task and Motion Planning](https://mlsanity.com/paper/2603.03704/) (2026)
- ["Don't Do That!": Guiding Embodied Systems through Large Language Model-based Constraint Generation](https://mlsanity.com/paper/2506.04500/) (2025)
- [Grounded Vision-Language Interpreter for Long-Horizon Bimanual Task and Motion Planning](https://mlsanity.com/paper/2506.03270/) (2025)
- [CAPER: Constrained and Procedural Reasoning for Robotic Scientific Experiments](https://mlsanity.com/paper/2602.09367/) (2026)
- [Robust Asynchronous Planning via Auto-Formalization](https://mlsanity.com/paper/2606.00981/) (2026)
- [Evidence-Gated Task and Motion Planning with Vision-Language Models](https://mlsanity.com/paper/2608.20084/) (2026)
- [Leveraging Inter-object Affordances for Efficient Planning in Contact-rich Tasks](https://mlsanity.com/paper/2608.25641/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated remarkable ability in long-horizon Task and Motion Planning (TAMP) by translating clear and straightforward natural language problems into formal specifications such as the Planning Domain Definition Language (PDDL). However, real-world problems are often ambiguous and involve many complex constraints. In this paper, we introduce Constraints as Specifications through LLMs (CaStL), a framework that identifies constraints such as goal conditions, action ordering, and action blocking from natural language in multiple stages. CaStL translates these constraints into PDDL and Python scripts, which are solved using an custom PDDL solver. Tested across three PDDL domains, CaStL significantly improves constraint handling and planning success rates from natural language specification in complex scenarios.