Fast embedded tube-based MPC with scaled-symmetric ADMM for high-order systems: Application to load transportation tasks with UAVs.

Abstract

One of the most significant advantages of Model Predictive Control (MPC) is its ability to explicitly incorporate system constraints and actuator specifications. However, a major drawback is the computational cost associated with calculating the optimal control sequence at each sampling time, posing a substantial challenge for real-time implementation in high-order systems with fast dynamics. Additionally, uncertainties are inherently present in dynamic systems, requiring a robust formulation that accounts for these uncertainties. Additionally, uncertainties are inherently present in dynamic systems, requiring a robust formulation that accounts for these uncertainties. The tube-based MPC is one of the robustification formulations that can tackle these challenges. We propose a comprehensive methodology for designing a tube-based MPC framework specifically tailored for high-order Linear Parameter-Varying (LPV) systems with fast dynamics, along with its real-time implementation in embedded systems. Our innovations include the use of zonotopes for the offline computation of reachable sets, significantly reducing computational costs, and the development of new Linear Matrix Inequality (LMI) conditions that ensure the existence of nominal control and state sets. Additionally, we introduce a novel scaled-symmetric ADMM-based optimization algorithm, which diverges from conventional quadratic programming structures and integrates acceleration strategies and normalization techniques for enhanced numerical robustness and rapid convergence. The methodology is validated on a tiltrotor UAV with a suspended load, demonstrating its effectiveness in a trajectory tracking problem. Experimental results using a controller-in-the-loop (CIL) framework with a high-fidelity 3D simulator confirm its suitability for real-time control in practical scenarios.