# Avoiding Dense and Dynamic Obstacles in Enclosed Spaces: Application to Moving in Crowds

arXiv: https://arxiv.org/abs/2105.11743 · HTML: https://mlsanity.com/paper/2105.11743/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2021.

## Built on by (most cited first, 9 of 9)

- [Multi-Agent Dynamic Relational Reasoning for Social Robot Navigation](https://mlsanity.com/paper/2401.12275/) (2024)
- [Neural Contractive Dynamical Systems](https://mlsanity.com/paper/2401.09352/) (2024)
- [HEIGHT: Heterogeneous Interaction Graph Transformer for Robot Navigation in Crowded and Constrained Environments](https://mlsanity.com/paper/2411.12150/) (2024)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [HeR-DRL:Heterogeneous Relational Deep Reinforcement Learning for Decentralized Multi-Robot Crowd Navigation](https://mlsanity.com/paper/2403.10083/) (2024)
- [Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regions](https://mlsanity.com/paper/2411.11405/) (2024)
- [Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations](https://mlsanity.com/paper/2504.18860/) (2025)
- [Future-Oriented Navigation: Dynamic Obstacle Avoidance with One-Shot Energy-Based Multimodal Motion Prediction](https://mlsanity.com/paper/2505.00237/) (2025)
- [Learning-Based Motion Planning for Dynamic Environments: From Foundational Algorithms to Emerging Paradigms](https://mlsanity.com/paper/2608.00625/) (2026)

## Abstract (arXiv)

This paper presents a closed-form approach to constrain a flow within a given volume and around objects. The flow is guaranteed to converge and to stop at a single fixed point. We show that the obstacle avoidance problem can be inverted to enforce that the flow remains enclosed within a volume defined by a polygonal surface. We formally guarantee that such a flow will never contact the boundaries of the enclosing volume and obstacles, and will asymptotically converge towards an attractor. We further create smooth motion fields around obstacles with edges (e.g. tables). Both obstacles and enclosures may be time-varying, i.e. moving, expanding and shrinking. The technique enables a robot to navigate within an enclosed corridor while avoiding static and moving obstacles. It was applied on an autonomous robot (QOLO) in a static complex indoor environment, and also tested in simulations with dense crowds. The final proof of concept was performed in an outdoor environment in Lausanne. The QOLO-robot successfully traversed a marketplace in the center of town in presence of a diverse crowd with a non-uniform motion pattern.