Improving the Region of Attraction of a Multi-rotor UAV by Estimating Unknown Disturbances

TL;DR

This work addresses robust ROA estimation for a planar quadrotor under unknown disturbances by integrating a neural network–predicted disturbance model into the LQR framework. The learned disturbances are incorporated to update the linearized A and B matrices, enabling a graphical ROA computation that yields a significantly larger region of attraction than the nominal model and far larger than Lyapunov-based estimates. Specifically, the ROA grows from $81{,}763.019$ $m^2$ (nominal) to $88{,}426.015$ $m^2$ (with learned disturbances), while the Lyapunov-based ROA remains highly conservative at $12.715$ $m^2$. These results demonstrate that machine-learning–assisted dynamic modeling can substantially enhance safety and robustness of UAV control, with planned extension to 3D quadrotor systems for broader applicability.

Abstract

This study presents a machine learning-aided approach to accurately estimate the region of attraction (ROA) of a multi-rotor unmanned aerial vehicle (UAV) controlled using a linear quadratic regulator (LQR) controller. Conventional ROA estimation approaches rely on a nominal dynamic model for ROA calculation, leading to inaccurate estimation due to unknown dynamics and disturbances associated with the physical system. To address this issue, our study utilizes a neural network to predict these unknown disturbances of a planar quadrotor. The nominal model integrated with the learned disturbances is then employed to calculate the ROA of the planer quadrotor using a graphical technique. The estimated ROA is then compared with the ROA calculated using Lyapunov analysis and the graphical approach without incorporating the learned disturbances. The results illustrated that the proposed method provides a more accurate estimation of the ROA, while the conventional Lyapunov-based estimation tends to be more conservative.

Figures (4)

• Figure 1: Planar quadrotor system
• Figure 2: Comparison of the ROA of the planar quadrotor with and without disturbance estimation - ROA of the convex hull is outlined in red. Each color denotes the trajectory of each initial point towards $(0,0)$; arrows define velocities at each trajectory point.
• Figure 3: Training and validation loss
• Figure 4: ROA of planar quadrotor from Lyapunov Analysis

Theorems & Definitions (1)

• Definition 1