Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Model Predictive Path Planning in Navier-Stokes Flow with POD-Based Reduced-Order Models

Adam Waterman, Martin Guay

TL;DR

The paper addresses real-time path planning in Navier–Stokes–driven flows by coupling a POD-based reduced-order model with Model Predictive Control. It develops a Galerkin ROM of incompressible flow, integrates an Extended Kalman Filter observer that fuses fixed and mobile sensor data, and uses receding-horizon optimization to generate flow-aware trajectories for a vertically controllable agent. Simulations based on ERA5 wind data demonstrate accurate flow reconstruction and efficient trajectory planning across different prediction horizons, highlighting the method's real-time feasibility and adaptability to evolving flow fields. The work advances flow-aware navigation by providing a physics-informed, data-driven framework that can serve as a high-level guidance module for various aerial and marine platforms operating in complex wind or current fields.

Abstract

We present a framework for optimal trajectory generation in flow-driven systems governed by the Navier-Stokes equations, combining a Proper Orthogonal Decomposition (POD) reduced0order model (ROM) with Model Predictive Control (MPC). The approach (i) approximates the velocity field from data via snapshot POD and orthogonal projection, (ii) derives a Galerkin-projected dynamical model in reduced coordinates, and (iii) employs MPC to plan control inputs that steer an agent through the predicted flow while satisfying state and actuation constraints. By leveraging reduced-order modeling, the method enables real-time control in high-dimensional flow environments. Simulations demonstrate accurate flow-field reconstruction and efficient trajectory generation within realistic wind environments.

Model Predictive Path Planning in Navier-Stokes Flow with POD-Based Reduced-Order Models

TL;DR

The paper addresses real-time path planning in Navier–Stokes–driven flows by coupling a POD-based reduced-order model with Model Predictive Control. It develops a Galerkin ROM of incompressible flow, integrates an Extended Kalman Filter observer that fuses fixed and mobile sensor data, and uses receding-horizon optimization to generate flow-aware trajectories for a vertically controllable agent. Simulations based on ERA5 wind data demonstrate accurate flow reconstruction and efficient trajectory planning across different prediction horizons, highlighting the method's real-time feasibility and adaptability to evolving flow fields. The work advances flow-aware navigation by providing a physics-informed, data-driven framework that can serve as a high-level guidance module for various aerial and marine platforms operating in complex wind or current fields.

Abstract

We present a framework for optimal trajectory generation in flow-driven systems governed by the Navier-Stokes equations, combining a Proper Orthogonal Decomposition (POD) reduced0order model (ROM) with Model Predictive Control (MPC). The approach (i) approximates the velocity field from data via snapshot POD and orthogonal projection, (ii) derives a Galerkin-projected dynamical model in reduced coordinates, and (iii) employs MPC to plan control inputs that steer an agent through the predicted flow while satisfying state and actuation constraints. By leveraging reduced-order modeling, the method enables real-time control in high-dimensional flow environments. Simulations demonstrate accurate flow-field reconstruction and efficient trajectory generation within realistic wind environments.

Paper Structure

This paper contains 17 sections, 31 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. POD-Based Model Reduction
  4. Computation of POD Modes
  5. Observer Design
  6. Model Predictive Path Planning Using a ROM-Predicted Flow Field
  7. Predicted Flow Environment
  8. Path Generation via Model Predictive Optimization
  9. Planning Horizon and Feasibility
  10. Simulation Framework and Results
  11. Overview
  12. Reduced‐Order Flow Model
  13. Path‐Planning Configuration
  14. Performance Metrics
  15. Representative Results
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Simulation results showing slices of the predicted mean-squared velocity field.
  • Figure 3: Total root mean squared velocity error between the estimated and actual velocity fields.
  • Figure 4: Path generated by the predictive planner with a 3-hour prediction horizon. The grey box indicates the spatial boundary, the blue cylinder is the 50 km radius, and the red dashed marker denotes the target location.
  • Figure 6: Performance characteristics corresponding to Fig. \ref{['fig:traj3hr']}. Altitude adjustments allow the agent to exploit favorable wind strata.