Estimation of Unmodeled Dynamics: Nonlinear MPC and Adaptive Control Law With Momentum Observer Dynamic

Abstract

This article proposes an enhancement to estimate unmodeled dynamics within the simplified dynamic model of a quadcopter by integrating three key methodologies: Nonlinear Model Predictive Control (NMPC), a Momentum Observer Dynamics (MOD), and an adaptive control law. Termed as Adaptive NMPC with MOD, this integrated approach leverages NMPC, implemented using the CasADi framework, for real-time decision-making, while the momentum observer facilitates system state estimation and uncertainty mitigation. Simultaneously, the adaptive control law adjusts parameters to estimate errors in unmodeled dynamics. Through digital twin and Model in Loop (MiL) simulations, the effectiveness of this framework is demonstrated. Specifically, the study focuses on the simplified quadcopter model, acknowledging often overlooked inherent dynamics resulting from the simplification by not considering the nonlinearities induced by the drone’s attitude angles. Addressing these unmodeled dynamics is critical, and the Adaptive NMPC with MOD method emerges as a robust solution, showcasing its potential across various scenarios.

Keywords

• NMPC
• adaptive control
• disturbance estimation
• UAV dynamics
• momentum observer
• CasADi