Topological Trajectory Prediction with Homotopy Classes

TL;DR

This paper introduces a novel approach to trajectory prediction in cluttered environments by classifying trajectories into homotopy classes, enabling high-level predictions that improve low-level trajectory accuracy.

Contribution

The paper presents a lightweight learning framework that uses homotopy classes and Markov processes to enhance trajectory prediction in robotics.

Findings

Homotopy class-based prediction improves trajectory accuracy.

The framework outperforms naive GMM in real dataset tests.

High-level classification simplifies complex trajectory spaces.

Abstract

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.