Efficient Optimal Path Planning in Dynamic Environments Using Koopman MPC

2025-10-02

AI Summary

This work addresses the challenge of real-time optimal path planning for mobile robots operating in dynamic environments under nonlinear dynamics and collision-avoidance constraints. We propose a data-driven Model Predictive Control (MPC) framework grounded in the Koopman operator theory. Our key innovation is a bilinear Koopman realization that globally linearizes both state-input-coupled dynamics and quadratic obstacle-avoidance constraints—achieved for the first time in this unified manner. The bilinear model is identified from trajectory data via Extended Dynamic Mode Decomposition (EDMD), and an efficiently solvable quadratic programming (QP) MPC formulation is constructed in the lifted feature space. Experimental results demonstrate that, while preserving safety and optimality guarantees, the proposed method achieves a 320× speedup in computation time over conventional nonlinear MPC, significantly enhancing real-time planning capability in dynamic scenarios.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization of system dynamics only, our work focuses on finding a global linear representation for the optimal path planning problem that includes both the nonlinear robot dynamics and collision-avoidance constraints. We deploy extended dynamic mode decomposition to identify linear and bilinear Koopman realizations from input-state data. Our open-loop analysis demonstrates that only the bilinear Koopman model can accurately capture nonlinear state-input couplings and quadratic terms essential for collision avoidance, whereas linear realizations fail to do so. We formulate a quadratic program for the robot path planning in the presence of moving obstacles in the lifted space and determine the optimal robot action in an MPC framework. Our approach is capable of finding the safe optimal action 320 times faster than a nonlinear MPC counterpart that solves the path planning problem in the original state space. Our work highlights the potential of bilinear Koopman realizations for linearization of highly nonlinear optimal control problems subject to nonlinear state and input constraints to achieve computational efficiency similar to linear problems.

Problem

• Develops bilinear Koopman model for robot dynamics and collision avoidance
• Solves optimal path planning with moving obstacles in lifted space
• Achieves 320x faster computation than nonlinear MPC for safety

Innovation

• Bilinear Koopman model captures nonlinear dynamics
• Lifted space quadratic program enables fast planning
• Koopman MPC achieves 320x speed over nonlinear MPC