Millisecond NMPC for Swing-Up and Stabilization of the Furuta Pendulum in Real World

The Furuta pendulum’s swing-up and stabilization control is currently used by many researchers to benchmark nonlinear control algorithms. In this brief, we give a systematic overview of important contributions to the control of the Furuta pendulum presented in the last 15 years. Furthermore, we use nonlinear model predictive control (NMPC) to design a real-time capable holistic controller. An optimal control problem (OCP) including a detailed nonlinear system dynamics model is defined, transcribed into a nonlinear optimization problem via direct multiple shooting, and solved in real time on an embedded system using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {acados}$</tex-math> </inline-formula>. A breakthrough concerning the control performance was achieved by the usage of efficient discretization via a nonuniform grid, solving the tradeoff between a long prediction horizon and a fast sample time. The control strategy shows excellent performance in simulation and real-world experiments using a custom-made pendulum prototype. Videos of the experiments are available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://www.youtube.com/shorts/oJYyD5beMqM/</uri>