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

TL;DR

This paper introduces a real-time control framework for flow-driven systems using POD-based reduced-order models combined with Model Predictive Control, enabling efficient trajectory planning in complex Navier-Stokes flows.

Contribution

It develops a novel integration of POD-ROM with MPC for optimal path planning in high-dimensional fluid environments, facilitating real-time control.

Findings

Accurate flow-field reconstruction demonstrated.

Efficient trajectory generation in wind environments.

Real-time control enabled by reduced-order modeling.

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.