# Real-Time Learning of Predictive Dynamic Obstacle Models for Robotic Motion Planning

arXiv: https://arxiv.org/abs/2511.00814 · HTML: https://mlsanity.com/paper/2511.00814/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 2 Nov 2025.

## Builds on (most cited first, 13 of 13)

- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Deep Learning in Robotics: A Review of Recent Research](https://mlsanity.com/paper/1707.07217/) (2017)
- [TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis](https://mlsanity.com/paper/2402.16412/) (2024)
- [Autonomous Drone Racing: A Survey](https://mlsanity.com/paper/2301.01755/) (2023)
- [Online dynamic mode decomposition for time-varying systems](https://mlsanity.com/paper/1707.02876/) (2017)
- [Pedestrian Models for Autonomous Driving Part II: High-Level Models of Human Behavior](https://mlsanity.com/paper/2003.11959/) (2020)
- [A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing](https://mlsanity.com/paper/1801.02302/) (2018)
- [What Matters in Learning from Large-Scale Datasets for Robot Manipulation](https://mlsanity.com/paper/2506.13536/) (2025)
- [Koopman Operators in Robot Learning](https://mlsanity.com/paper/2408.04200/) (2024)
- [Episodic Koopman Learning of Nonlinear Robot Dynamics with Application to Fast Multirotor Landing](https://mlsanity.com/paper/2004.01708/) (2020)
- [On Low-Rank Hankel Matrix Denoising](https://mlsanity.com/paper/2012.07433/) (2020)
- [Safe Payload Transfer with Ship-Mounted Cranes: A Robust Model Predictive Control Approach](https://mlsanity.com/paper/2510.16953/) (2025)

## Abstract (arXiv)

Autonomous systems often must predict the motions of nearby agents from partial and noisy data. This paper asks and answers the question: "can we learn, in real-time, a nonlinear predictive model of another agent's motions?" Our online framework denoises and forecasts such dynamics using a modified sliding-window Hankel Dynamic Mode Decomposition (Hankel-DMD). Partial noisy measurements are embedded into a Hankel matrix, while an associated Page matrix enables singular-value hard thresholding (SVHT) to estimate the effective rank. A Cadzow projection enforces structured low-rank consistency, yielding a denoised trajectory and local noise variance estimates. From this representation, a time-varying Hankel-DMD lifted linear predictor is constructed for multi-step forecasts. The residual analysis provides variance-tracking signals that can support downstream estimators and risk-aware planning. We validate the approach in simulation under Gaussian and heavy-tailed noise, and experimentally on a dynamic crane testbed. Results show that the method achieves stable variance-aware denoising and short-horizon prediction suitable for integration into real-time control frameworks.