# GELATO: Multi-Instruction Trajectory Reshaping via Geometry-Aware Multiagent-based Orchestration

arXiv: https://arxiv.org/abs/2509.06031 · HTML: https://mlsanity.com/paper/2509.06031/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [SAIL: Test-Time Scaling for In-Context Imitation Learning with VLM](https://mlsanity.com/paper/2603.08269/) (2026)

## Abstract (arXiv)

We present GELATO -- the first language-driven trajectory reshaping framework to embed geometric environment awareness and multi-agent feedback orchestration to support multi-instruction in human-robot interaction scenarios. Unlike prior learning-based methods, our approach automatically registers scene objects as 6D geometric primitives via a VLM-assisted multi-view pipeline, and an LLM translates free-form multiple instructions into explicit, verifiable geometric constraints. These are integrated into a geometric-aware vector field optimization to adapt initial trajectories while preserving smoothness, feasibility, and clearance. We further introduce a multi-agent orchestration with observer-based refinement to handle multi-instruction inputs and interactions among objectives -- increasing success rate without retraining. Simulation and real-world experiments demonstrate our method achieves smoother, safer, and more interpretable trajectory modifications compared to state-of-the-art baselines.