Probabilistic Trajectory Prediction with Structural Constraints

TL;DR

This paper introduces a probabilistic framework that combines machine learning with constrained optimization to predict and enforce realistic, collision-aware trajectories of moving objects in complex environments.

Contribution

It presents a novel approach integrating probabilistic learning with chance-constrained optimization to produce realistic, constraint-compliant motion trajectories.

Findings

Effective in real-world and simulated datasets

Produces more robust and higher quality trajectories

Enforces environment-based constraints during prediction

Abstract

This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from observed trajectories, with no mechanism to directly incorporate known rules. We propose a novel framework, which combines probabilistic learning and constrained trajectory optimisation. The learning component of our framework provides a distribution over future motion trajectories conditioned on observed past coordinates. This distribution is then used as a prior to a constrained optimisation problem which enforces chance constraints on the trajectory distribution. This results in constraint-compliant trajectory distributions which closely resemble the prior. In particular, we focus our investigation on collision constraints, such that extrapolated future trajectory distributions conform to the environment structure. We empirically demonstrate on real-world and simulated datasets the ability of our framework to learn complex probabilistic motion trajectories for motion data, while directly enforcing constraints to improve generalisability, producing more robust and higher quality trajectory distributions.