# Learning to Nudge: A Scalable Barrier Function Framework for Safe Robot Interaction in Dense Clutter

arXiv: https://arxiv.org/abs/2601.02686 · HTML: https://mlsanity.com/paper/2601.02686/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2026.

## Built on by (most cited first, 2 of 2)

- [Safe Embodied AI for Long-horizon Tasks: A Cross-layer Analysis of Robotic Manipulation](https://mlsanity.com/paper/2606.05660/) (2026)
- [ManiDreams: An Open-Source Library for Robust Object Manipulation via Uncertainty-aware Task-specific Intuitive Physics](https://mlsanity.com/paper/2603.18336/) (2026)

## Abstract (arXiv)

Robots operating in everyday environments must navigate and manipulate within densely cluttered spaces, where physical contact with surrounding objects is unavoidable. Traditional safety frameworks treat contact as unsafe, restricting robots to collision avoidance and limiting their ability to function in dense, everyday settings. As the number of objects grows, model-based approaches for safe manipulation become computationally intractable; meanwhile, learned methods typically tie safety to the task at hand, making them hard to transfer to new tasks without retraining. In this work we introduce Dense Contact Barrier Functions(DCBF). Our approach bypasses the computational complexity of explicitly modeling multi-object dynamics by instead learning a composable, object-centric function that implicitly captures the safety constraints arising from physical interactions. Trained offline on interactions with a few objects, the learned DCBFcomposes across arbitrary object sets at runtime, producing a single global safety filter that scales linearly and transfers across tasks without retraining. We validate our approach through simulated experiments in dense clutter, demonstrating its ability to enable collision-free navigation and safe, contact-rich interaction in suitable settings.