# Probabilistic Trajectory Prediction with Structural Constraints

arXiv: https://arxiv.org/abs/2107.04193 · HTML: https://mlsanity.com/paper/2107.04193/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 9 Jul 2021.

## Builds on (most cited first, 8 of 8)

- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANs](https://mlsanity.com/paper/1904.09507/) (2019)
- [TH"OR: Human-Robot Navigation Data Collection and Accurate Motion Trajectories Dataset](https://mlsanity.com/paper/1909.04403/) (2019)
- [Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1601.03648/) (2016)
- [Kernel Trajectory Maps for Multi-Modal Probabilistic Motion Prediction](https://mlsanity.com/paper/1907.05127/) (2019)
- [OCTNet: Trajectory Generation in New Environments from Past Experiences](https://mlsanity.com/paper/1909.11337/) (2019)

## Built on by (most cited first, 4 of 4)

- [Instructing Robots by Sketching: Learning from Demonstration via Probabilistic Diagrammatic Teaching](https://mlsanity.com/paper/2309.03835/) (2023)
- [Stochastic Trajectory Prediction under Unstructured Constraints](https://mlsanity.com/paper/2503.14203/) (2025)
- [3D Foundation Models Enable Simultaneous Geometry and Pose Estimation of Grasped Objects](https://mlsanity.com/paper/2407.10331/) (2024)
- [Joint Flow Trajectory Optimization For Feasible Robot Motion Generation from Video Demonstrations](https://mlsanity.com/paper/2509.20703/) (2025)

## Abstract (arXiv)

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.