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

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.