A Koopman Operator-based NMPC Framework for Mobile Robot Navigation under Uncertainty

2025-04-29

AI Summary

To address the insufficient navigation robustness of mobile robots under system uncertainties—such as abrupt ground friction changes and sensor noise—this paper proposes a lifted bilinear predictive framework integrating Koopman operator learning with nonlinear model predictive control (NMPC). Methodologically, it innovatively decouples Koopman-space constraints from state-space optimization, preserving prediction accuracy while substantially reducing NMPC’s real-time computational burden. The framework enables end-to-end closed-loop navigation without requiring a priori dynamical models. It encompasses data-driven modeling, stochastic system representation, and Gazebo-based digital twin simulation. Comprehensive validation includes numerical simulations, high-fidelity simulations, and physical robot experiments. Results demonstrate stable obstacle-avoidance navigation under diverse disturbances, including strong robustness against additive stochastic velocity perturbations.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Natural Language Processing: Safety and Robustness

Application Category

• 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
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited when considering such variations, making them fragile to varying types of uncertainty. One way to address this is by leveraging learned prediction models by means of the Koopman operator into nonlinear model predictive control (NMPC). This paper describes the formulation of, and provides the solution to, an NMPC problem using a lifted bilinear model that can accurately predict affine input systems with stochastic perturbations. System constraints are defined in the Koopman space, while the optimization problem is solved in the state space to reduce computational complexity. Training data to estimate the Koopman operator for the system are given via randomized control inputs. The output of the developed method enables closed-loop navigation control over environments populated with obstacles. The effectiveness of the proposed method has been tested through numerical simulations using a wheeled robot with additive stochastic velocity perturbations, Gazebo simulations with a realistic digital twin robot, and physical hardware experiments without knowledge of the true dynamics.

Problem

• Addressing mobile robot navigation under system uncertainty
• Integrating Koopman operator into NMPC for robust control
• Handling stochastic perturbations and constraints in dynamic environments

Innovation

• Koopman operator-based NMPC for uncertainty
• Lifted bilinear model predicts stochastic perturbations
• Training data via randomized control inputs