Real-Time Model Predictive Control for the Swing-Up Problem of an Underactuated Double Pendulum

TL;DR

The paper tackles real-time stabilization and swing-up of an underactuated double pendulum (Acrobot and Pendubot) by framing a nonlinear MPC problem solved online with the acados framework. It employs a multiple-shooting discretization over a horizon with $N$ steps and step size $\delta t$, and enhances real-time feasibility through SQP-RTI, asynchronous preparation, angle embedding via $(\cos\theta,\sin\theta)$, friction compensation, and a non-uniform shooting grid. The approach demonstrates robust performance on both pendulum configurations, with Pendubot showing greater resilience to parameter variations and Acrobot presenting more challenges due to friction and actuator noise; the results indicate the method’s viability for real-time hardware implementations with manageable delays ($\approx 0.025$ s). Overall, the work presents a competitive, optimization-based alternative to learning-based swing-up strategies for underactuated robotic systems.

Abstract

The 3rd AI Olympics with RealAIGym competition poses the challenge of developing a global policy that can swing up and stabilize an underactuated 2-link system Acrobot and/or Pendubot from any configuration in the state space. This paper presents an optimal control-based approach using a real-time Nonlinear Model Predictive Control (MPC). The results show that the controller achieves good performance and robustness and can reliably handle disturbances.

Figures (3)

• Figure 1: Robustness metrics in both Setups
• Figure 2: Simulation of the disturbed Pendubot system, controlled by the MPC
• Figure 3: Simulation of the disturbed Acrobot system, controlled by the MPC