# Winding Through: Crowd Navigation via Topological Invariance

arXiv: https://arxiv.org/abs/2109.05084 · HTML: https://mlsanity.com/paper/2109.05084/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2021.

## Built on by (most cited first, 11 of 11)

- [Interactive Joint Planning for Autonomous Vehicles](https://mlsanity.com/paper/2310.18301/) (2023)
- [InteRACT: Transformer Models for Human Intent Prediction Conditioned on Robot Actions](https://mlsanity.com/paper/2311.12943/) (2023)
- [Categorical Traffic Transformer: Interpretable and Diverse Behavior Prediction with Tokenized Latent](https://mlsanity.com/paper/2311.18307/) (2023)
- [HEIGHT: Heterogeneous Interaction Graph Transformer for Robot Navigation in Crowded and Constrained Environments](https://mlsanity.com/paper/2411.12150/) (2024)
- [SELFI: Autonomous Self-Improvement with Reinforcement Learning for Social Navigation](https://mlsanity.com/paper/2403.00991/) (2024)
- [ManiCast: Collaborative Manipulation with Cost-Aware Human Forecasting](https://mlsanity.com/paper/2310.13258/) (2023)
- [From Obstacles to Etiquette: Robot Social Navigation with VLM-Informed Path Selection](https://mlsanity.com/paper/2602.09002/) (2026)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [Visual Forecasting as a Mid-level Representation for Avoidance](https://mlsanity.com/paper/2310.07724/) (2023)
- [RUMOR: Reinforcement learning for Understanding a Model of the Real World for Navigation in Dynamic Environments](https://mlsanity.com/paper/2404.16672/) (2024)
- [Structured Graph Network for Constrained Robot Crowd Navigation with Low Fidelity Simulation](https://mlsanity.com/paper/2405.16830/) (2024)

## Abstract (arXiv)

We focus on robot navigation in crowded environments. The challenge of predicting the motion of a crowd around a robot makes it hard to ensure human safety and comfort. Recent approaches often employ end-to-end techniques for robot control or deep architectures for high-fidelity human motion prediction. While these methods achieve important performance benchmarks in simulated domains, dataset limitations and high sample complexity tend to prevent them from transferring to real-world environments. Our key insight is that a low-dimensional representation that captures critical features of crowd-robot dynamics could be sufficient to enable a robot to wind through a crowd smoothly. To this end, we mathematically formalize the act of passing between two agents as a rotation, using a notion of topological invariance. Based on this formalism, we design a cost functional that favors robot trajectories contributing higher passing progress and penalizes switching between different sides of a human. We incorporate this functional into a model predictive controller that employs a simple constant-velocity model of human motion prediction. This results in robot motion that accomplishes statistically significantly higher clearances from the crowd compared to state-of-the-art baselines while maintaining competitive levels of efficiency, across extensive simulations and challenging real-world experiments on a self-balancing robot.