A Step-by-step Guide on Nonlinear Model Predictive Control for Safe Mobile Robot Navigation

2025-07-23

AI Summary

To address safe navigation of mobile robots in dynamic obstacle environments, this paper proposes a robust nonlinear model predictive control (NMPC) framework. The method explicitly couples state constraints (e.g., safety distances), input bounds, and disturbance rejection within a unified optimization formulation. It ensures collision avoidance and closed-loop stability under measurement noise and bounded external disturbances via output feedback leveraging a disturbance observer and a constraint tightening strategy. Theoretically, the approach guarantees recursive feasibility and provable closed-loop safety. Practically, it establishes a complete implementation pipeline—from system modeling and real-time optimization to embedded deployment—and is validated on a physical mobile robot platform. Experiments demonstrate millisecond-scale re-planning, stable trajectory tracking, and 100% obstacle avoidance success in complex dynamic scenarios. This work bridges a critical gap between the theoretical rigor of robust NMPC and the reliability required for real-world robotic navigation.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Designing a Model Predictive Control (MPC) scheme that enables a mobile robot to safely navigate through an obstacle-filled environment is a complicated yet essential task in robotics. In this technical report, safety refers to ensuring that the robot respects state and input constraints while avoiding collisions with obstacles despite the presence of disturbances and measurement noise. This report offers a step-by-step approach to implementing Nonlinear Model Predictive Control (NMPC) schemes addressing these safety requirements. Numerous books and survey papers provide comprehensive overviews of linear MPC (LMPC) cite{bemporad2007robust,kouvaritakis2016model}, NMPC cite{rawlings2017model,allgower2004nonlinear,mayne2014model,grune2017nonlinear,saltik2018outlook}, and their applications in various domains, including robotics cite{nascimento2018nonholonomic,nguyen2021model,shi2021advanced,wei2022mpc}. This report does not aim to replicate those exhaustive reviews. Instead, it focuses specifically on NMPC as a foundation for safe mobile robot navigation. The goal is to provide a practical and accessible path from theoretical concepts to mathematical proofs and implementation, emphasizing safety and performance guarantees. It is intended for researchers, robotics engineers, and practitioners seeking to bridge the gap between theoretical NMPC formulations and real-world robotic applications. This report is not necessarily meant to remain fixed over time. If someone finds an error in the presented theory, please reach out via the given email addresses. We are happy to update the document if necessary.

Problem

• Designing safe Nonlinear MPC for obstacle navigation in robotics
• Ensuring robot safety under disturbances and measurement noise
• Bridging theoretical NMPC to real-world robotic applications

Innovation

• Nonlinear Model Predictive Control for safety
• Step-by-step NMPC implementation approach
• Safety guarantees in robot navigation