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

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.

💡 Research Summary

This paper presents a novel online framework for real-time learning of predictive models for dynamic obstacles, a critical capability for autonomous robots operating in uncertain environments. The core challenge addressed is learning a nonlinear model of another agent’s motion from streaming, partial, and noisy observations, suitable for short-horizon prediction in control and planning loops.

The proposed solution centers on an adaptive, sliding-window variant of Hankel Dynamic Mode Decomposition (Hankel-DMD). Standard Hankel-DMD, which uses time-delay embeddings to approximate Koopman operators for nonlinear systems, is sensitive to measurement noise and typically requires long, stationary data sequences. To overcome these limitations, the authors integrate a principled denoising step directly into the online learning pipeline.

The algorithm operates on a fixed-length buffer of recent measurements. At each time step, it performs several key operations:

1. Structured Embedding: The data is embedded into both a Hankel matrix (with overlapping columns) and a Page matrix (with non-overlapping blocks).
2. Data-Driven Rank Estimation: The Page matrix, which avoids the entry-wise correlations of noise present in the Hankel structure, is subjected to Singular Value Hard Thresholding (SVHT). This method, based on the asymptotically optimal threshold of Gavish and Donoho, estimates the effective rank of the underlying signal without requiring prior noise knowledge or arbitrary thresholds.
3. Cadzow Denoising: The estimated rank is then used to denoise the original Hankel matrix via the Cadzow algorithm. This algorithm iteratively projects the matrix onto the set of low-rank matrices and then back onto the set of Hankel matrices, effectively smoothing the data while preserving its dynamical structure.
4. Model Learning and Prediction: From the pair of denoised, time-shifted Hankel matrices, a local linear predictor (the DMD matrix) is computed via least squares. This model is used to generate multi-step forecasts.
5. Uncertainty Quantification: The residual between the original and denoised Hankel matrix provides an estimate of the local noise variance, offering a valuable uncertainty signal for downstream risk-aware planners.

The authors provide a theoretical justification, proving that under mild conditions, the finite-sample rank of the Page and Hankel matrices from the same data are equal, validating the transfer of the SVHT rank estimate.

The framework is extensively validated. Simulations demonstrate its robustness under both Gaussian and correlated heavy-tailed noise distributions, showing significant improvement over using raw noisy data for Hankel-DMD. A hardware experiment on a dynamic crane testbed, where a robotic arm must predict the motion of a swinging payload, confirms the method’s practical efficacy in a real-world, real-time control scenario.

In summary, this work makes a significant contribution by bridging the gap between theoretically-grounded Koopman-based modeling and the demands of real-time robotics. It delivers a computationally feasible, adaptive, and noise-resilient pipeline for online dynamics learning and short-horizon prediction, moving beyond the idealized assumptions of geometric planners and the offline, data-hungry nature of many modern learning-based approaches.