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Distributed Koopman Operator Learning for Perception and Safe Navigation

Ali Azarbahram, Shenyu Liu, Gian Paolo Incremona

TL;DR

The paper tackles safe, predictive navigation in dynamic transportation environments using distributed perception. It introduces a consensus-based distributed Koopman operator learning framework that lifts high-dimensional perceptual data to forecast obstacle density maps and translates these forecasts into linear, polytopic constraints for MPC. The authors establish convergence guarantees for the distributed learning and demonstrate, via simulations, reliable, safe, and scalable obstacle avoidance in complex scenes. The work advances cooperative perception and distributed control for intelligent transportation systems and multi-agent sensing networks.

Abstract

This paper presents a unified and scalable framework for predictive and safe autonomous navigation in dynamic transportation environments by integrating model predictive control (MPC) with distributed Koopman operator learning. High-dimensional sensory data are employed to model and forecast the motion of surrounding dynamic obstacles. A consensus-based distributed Koopman learning algorithm enables multiple computational agents or sensing units to collaboratively estimate the Koopman operator without centralized data aggregation, thereby supporting large-scale and communication-efficient learning across a networked system. The learned operator predicts future spatial densities of obstacles, which are subsequently represented through Gaussian mixture models. Their confidence ellipses are approximated by convex polytopes and embedded as linear constraints in the MPC formulation to guarantee safe and collision-free navigation. The proposed approach not only ensures obstacle avoidance but also scales efficiently with the number of sensing or computational nodes, aligning with cooperative perception principles in intelligent transportation system (ITS) applications. Theoretical convergence guarantees and predictive constraint formulations are established, and extensive simulations demonstrate reliable, safe, and computationally efficient navigation performance in complex environments.

Distributed Koopman Operator Learning for Perception and Safe Navigation

TL;DR

The paper tackles safe, predictive navigation in dynamic transportation environments using distributed perception. It introduces a consensus-based distributed Koopman operator learning framework that lifts high-dimensional perceptual data to forecast obstacle density maps and translates these forecasts into linear, polytopic constraints for MPC. The authors establish convergence guarantees for the distributed learning and demonstrate, via simulations, reliable, safe, and scalable obstacle avoidance in complex scenes. The work advances cooperative perception and distributed control for intelligent transportation systems and multi-agent sensing networks.

Abstract

This paper presents a unified and scalable framework for predictive and safe autonomous navigation in dynamic transportation environments by integrating model predictive control (MPC) with distributed Koopman operator learning. High-dimensional sensory data are employed to model and forecast the motion of surrounding dynamic obstacles. A consensus-based distributed Koopman learning algorithm enables multiple computational agents or sensing units to collaboratively estimate the Koopman operator without centralized data aggregation, thereby supporting large-scale and communication-efficient learning across a networked system. The learned operator predicts future spatial densities of obstacles, which are subsequently represented through Gaussian mixture models. Their confidence ellipses are approximated by convex polytopes and embedded as linear constraints in the MPC formulation to guarantee safe and collision-free navigation. The proposed approach not only ensures obstacle avoidance but also scales efficiently with the number of sensing or computational nodes, aligning with cooperative perception principles in intelligent transportation system (ITS) applications. Theoretical convergence guarantees and predictive constraint formulations are established, and extensive simulations demonstrate reliable, safe, and computationally efficient navigation performance in complex environments.

Paper Structure

This paper contains 14 sections, 2 theorems, 54 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Unicycle robot model and feedback linearization
  4. Problem statement
  5. Main Results
  6. Distributed Koopman modeling of dynamic obstacles
  7. Obstacle prediction and constraint formulation for MPC
  8. Simulation Case-Study
  9. Evaluation of distributed Koopman operator learning
  10. Comparison with other distributed Koopman methods
  11. MPC with Koopman-based dynamic obstacle avoidance
  12. Linking Koopman predictions to MPC constraints via intensity–polytope architecture
  13. Conclusion
  14. Acknowledgment

Key Result

Lemma 1

$K^*\in \mathbb{R}^{n\times n}$ is an optimal solution to the problem eq:frobenius_minimization if and only if there exists $W^*\in\mathbb{R}^{n\times Np}$ such that $(K^*, W^*)$ is an optimal solution to the constrained problem where $\bm Y,\bm X$ are defined in def:bA, def:bB.

Figures (9)

  • Figure 1: Prediction discrepancy $O(t)$ between distributed and centralized Koopman operators over iterations.
  • Figure 2: Elementwise absolute difference between the distributed Koopman operator $K_\mathrm{d}$ and the centralized Koopman operator $K^*$.
  • Figure 3: Spectral comparison between the distributed Koopman operator $K_\mathrm{d}$ and the centralized Koopman operator $K^*$.
  • Figure 4: Distributed error heatmap showing the absolute prediction error of the distributed Koopman operator $K_\mathrm{d}$ against the true system snapshots over the prediction horizon.
  • Figure 5: The final robot trajectory with Koopman-predicted dynamic obstacle avoidance.
  • ...and 4 more figures

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4