# Topological Trajectory Prediction with Homotopy Classes

arXiv: https://arxiv.org/abs/2301.09821 · HTML: https://mlsanity.com/paper/2301.09821/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2023.

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

- [Real-Time Sampling-based Online Planning for Drone Interception](https://mlsanity.com/paper/2502.14231/) (2025)

## Abstract (arXiv)

Trajectory prediction in a cluttered environment is key to many important robotics tasks such as autonomous navigation. However, there are an infinite number of possible trajectories to consider. To simplify the space of trajectories under consideration, we utilise homotopy classes to partition the space into countably many mathematically equivalent classes. All members within a class demonstrate identical high-level motion with respect to the environment, i.e., travelling above or below an obstacle. This allows high-level prediction of a trajectory in terms of a sparse label identifying its homotopy class. We therefore present a light-weight learning framework based on variable-order Markov processes to learn and predict homotopy classes and thus high-level agent motion. By informing a Gaussian Mixture Model (GMM) with our homotopy class predictions, we see great improvements in low-level trajectory prediction compared to a naive GMM on a real dataset.