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

Stella Kombo, Masih Haseli, Skylar Wei, Joel W. Burdick

TL;DR

The paper addresses real-time learning of nonlinear predictive models for unknown, dynamic obstacles from partial noisy observations in robotics. It introduces an online, adaptive framework that denoises delay-embedded measurements using a Page-Hankel SVHT rank transfer and Cadzow projection, then learns a lifted linear predictor via Hankel-DMD to produce multi-step forecasts. The method yields variance estimates for uncertainty-aware planning and is validated under Gaussian and heavy-tailed noise in both simulations and hardware (a moving-base crane testbed), showing robust short-horizon prediction and stable denoising. It demonstrates potential for real-time control integration, with time-varying models and stability suitable for MPC-style planning.

Abstract

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.

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

TL;DR

The paper addresses real-time learning of nonlinear predictive models for unknown, dynamic obstacles from partial noisy observations in robotics. It introduces an online, adaptive framework that denoises delay-embedded measurements using a Page-Hankel SVHT rank transfer and Cadzow projection, then learns a lifted linear predictor via Hankel-DMD to produce multi-step forecasts. The method yields variance estimates for uncertainty-aware planning and is validated under Gaussian and heavy-tailed noise in both simulations and hardware (a moving-base crane testbed), showing robust short-horizon prediction and stable denoising. It demonstrates potential for real-time control integration, with time-varying models and stability suitable for MPC-style planning.

Abstract

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.

Paper Structure

This paper contains 17 sections, 1 theorem, 27 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Definition
  3. Preliminaries
  4. Hankel and Page Matrices
  5. Hankel-DMD
  6. Cadzow Algorithm for Denoising
  7. Singular Value Hard Thresholding (SVHT)
  8. Adaptive Hankel-DMD for Noisy Data
  9. Denoising Hankel Matrices
  10. Step I: Page-Hankel Rank Transfer
  11. Rank Estimation using SVHT
  12. Cadzow Algorithm
  13. Online Identification and Multi-Step Prediction
  14. Simulations and Experiments
  15. Simulation: Noisy Unicycle
  16. ...and 2 more sections

Key Result

Lemma 1

Consider a locally valid linear output model with $z_k\in\mathbb{R}^{n_z}$, $A\in\mathbb{R}^{n_z\times n_z}$, and $C\in\mathbb{R}^{n_x\times n_z}$. Let $\{x_{0} \dots,x_{N-1}\}\subset\mathbb{R}^{n_x}$ be the noise-free measurements generated by the system above from the initial condition $z_0$. Let $L \geq n_z$ be the embedding window and let

Figures (5)

  • Figure 1: Gaussian noise: Top: noisy (gray), denoised (red) and ground truth (black dashed); call-outs show SNR improvement and average noise reduction. Bottom: zoomed segment and log-scale error.
  • Figure 2: AR(1)-Laplace noise: The denoising algorithm remains effective under heavy-tailed, correlated disturbances: call-outs: SNR $+6.9$ dB and $54.4\%$ noise reduction.
  • Figure 3: Stewart‐platform testbed. Left: Moving‐base crane with target, obstacle, payload, and arm/tip cameras. Right: Base-mounted VectorNav VN-100 IMU supplying orientation and angular rates to the sliding window Hankel-DMD predictor.
  • Figure 4: Top: context buffer ($N=250$, gray) and 31-step forecasts (red) overlaid with ground truth (black dashed). Bottom: absolute prediction error $|e_t|$ (blue) compared to threshold $\varepsilon$ (red dashed).
  • Figure 5: Evolution of eigenvalue across sliding windows: full spectra with iteration-colored progression.

Theorems & Definitions (2)

  • Lemma 1: Page–Hankel Rank Equivalence
  • proof : Proof of Lemma \ref{['lem:rank-equivalence']}