# Kernel Trajectory Maps for Multi-Modal Probabilistic Motion Prediction

arXiv: https://arxiv.org/abs/1907.05127 · HTML: https://mlsanity.com/paper/1907.05127/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Instructing Robots by Sketching: Learning from Demonstration via Probabilistic Diagrammatic Teaching](https://mlsanity.com/paper/2309.03835/) (2023)
- [SplaTraj: Camera Trajectory Generation with Semantic Gaussian Splatting](https://mlsanity.com/paper/2410.06014/) (2024)
- [PhotoReg: Photometrically Registering 3D Gaussian Splatting Models](https://mlsanity.com/paper/2410.05044/) (2024)
- [Probabilistic Trajectory Prediction with Structural Constraints](https://mlsanity.com/paper/2107.04193/) (2021)
- [3D Foundation Models Enable Simultaneous Geometry and Pose Estimation of Grasped Objects](https://mlsanity.com/paper/2407.10331/) (2024)

## Abstract (arXiv)

Understanding the dynamics of an environment, such as the movement of humans and vehicles, is crucial for agents to achieve long-term autonomy in urban environments. This requires the development of methods to capture the multi-modal and probabilistic nature of motion patterns. We present Kernel Trajectory Maps (KTM) to capture the trajectories of movement in an environment. KTMs leverage the expressiveness of kernels from non-parametric modelling by projecting input trajectories onto a set of representative trajectories, to condition on a sequence of observed waypoint coordinates, and predict a multi-modal distribution over possible future trajectories. The output is a mixture of continuous stochastic processes, where each realisation is a continuous functional trajectory, which can be queried at arbitrarily fine time steps.