[Paper Review] Geometric Adaptive Control with Neural Networks for a Quadrotor UAV in Wind fields

Mahdis Bisheban, Taeyoung Lee|arXiv (Cornell University)|Mar 5, 2019

Adaptive Control of Nonlinear Systems18 references4 citations

TL;DR

This paper proposes a geometric adaptive controller for quadrotor UAVs that uses multilayer neural networks to online-learn and compensate for unknown, unstructured wind disturbances. By formulating control dynamics on the special Euclidean group and applying a Lyapunov-based adaptive law, the method ensures uniformly ultimately bounded tracking errors with arbitrarily reducible bounds, validated through simulations and indoor flight experiments with artificial wind gusts.

ABSTRACT

This paper proposes a geometric adaptive controller for a quadrotor unmanned aerial vehicle with artificial neural networks. It is assumed that the dynamics of a quadrotor is disturbed by arbitrary, unstructured forces and moments caused by wind. To address this, the proposed control system is augmented with multilayer neural networks, and the weights of neural networks are adjusted online according to an adaptive law. By utilizing the universal approximation theorem, it is shown that the effects of unknown disturbances can be mitigated. More specifically, under the proposed control system, the tracking errors in the position and the heading direction are uniformly ultimately bounded where the ultimate bound can be reduced arbitrarily. These are developed directly on the special Euclidean group to avoid complexities or singularities inherent to local parameterizations. The efficacy of the proposed control system is first illustrated by numerical examples. Then, several indoor flight experiments are presented to demonstrate that the proposed controller successfully rejects the effects of wind disturbances even for aggressive, agile maneuvers.

Motivation & Objective

• To address the challenge of wind-induced disturbances in quadrotor UAVs that degrade stability and tracking performance.
• To eliminate reliance on precise wind modeling or real-time wind velocity measurements.
• To develop a robust control system that adapts online to unknown, arbitrary disturbances using neural networks.
• To ensure uniformly ultimately bounded tracking errors in position and heading under arbitrary wind conditions.
• To validate the controller’s effectiveness in aggressive maneuvers using indoor flight experiments with artificial wind.

Proposed method

• The controller is built on a geometric control framework formulated directly on the special Euclidean group SE(3), avoiding singularities from Euler angles or quaternion representations.
• Neural networks are integrated into the control law to approximate unknown disturbance forces and moments as arbitrary functions of the quadrotor’s state.
• An online adaptive law updates the neural network weights using a Lyapunov-based stability proof to ensure convergence.
• The universal approximation theorem justifies the neural network’s ability to represent arbitrary disturbance functions.
• The stability analysis combines position and attitude error dynamics into a composite Lyapunov function to prove uniform ultimate boundedness of errors.
• Control parameters are tuned to ensure the Hessian matrices in the Lyapunov derivative are positive definite, guaranteeing exponential convergence to a residual set.

Experimental results

Research questions

• RQ1 Can a neural network-based adaptive controller effectively reject unknown, unstructured wind disturbances in quadrotors without requiring wind speed measurements?
• RQ2 How can geometric control on SE(3) be combined with online learning to maintain stability under arbitrary disturbances?
• RQ3 To what extent can the ultimate bound on tracking errors be reduced through adaptive parameter tuning?
• RQ4 Can the proposed controller maintain performance during aggressive, agile maneuvers under strong wind gusts?
• RQ5 How does the controller compare to model-based wind compensation in terms of robustness and adaptability?

Key findings

• The tracking errors in position and heading are uniformly ultimately bounded, with the ultimate bound reducible to any desired precision by tuning control gains.
• The Lyapunov stability proof confirms exponential convergence of errors to a residual set determined by adaptive law parameters and disturbance bounds.
• Numerical simulations demonstrate effective mitigation of simulated aerodynamic wind effects across various wind profiles.
• Indoor flight experiments with an industrial fan-generated wind gust show successful rejection of disturbances during aggressive maneuvers.
• The controller operates without additional sensors like anemometers, relying solely on state feedback and neural network adaptation.
• The method achieves robust performance even when wind disturbances exceed the range of standard hover-based models.