[Paper Review] High-Gain Disturbance Observer for Robust Trajectory Tracking of Quadrotors

Mohammadreza Izadi, Reza Faieghi|arXiv (Cornell University)|May 30, 2023

Adaptive Control of Nonlinear Systems4 citations

TL;DR

This paper proposes a high-gain disturbance observer (HGDO) for quadrotor trajectory tracking that estimates external disturbances in real time and feeds them into a sliding mode control (SMC) law to enhance robustness. The HGDO ensures fast convergence of disturbance estimates and guarantees bounded tracking errors via Lyapunov stability analysis, significantly improving trajectory accuracy and precision under wind, ground effect, and unmodeled dynamics in both simulation and hardware experiments.

ABSTRACT

This paper presents a simple method to boost the robustness of quadrotors in trajectory tracking. The presented method features a high-gain disturbance observer (HGDO) that provides disturbance estimates in real-time. The estimates are then used in a trajectory control law to compensate for disturbance effects. We present theoretical convergence results showing that the proposed HGDO can quickly converge to an adjustable neighborhood of actual disturbance values. We will then integrate the disturbance estimates with a typical robust trajectory controller, namely sliding mode control (SMC), and present Lyapunov stability analysis to establish the boundedness of trajectory tracking errors. However, our stability analysis can be easily extended to other Lyapunov-based controllers to develop different HGDO-based controllers with formal stability guarantees. We evaluate the proposed HGDO-based control method using both simulation and laboratory experiments in various scenarios and in the presence of external disturbances. Our results indicate that the addition of HGDO to a quadrotor trajectory controller can significantly improve the accuracy and precision of trajectory tracking in the presence of external disturbances.

Motivation & Objective

• Address the challenge of external disturbances—such as wind gusts, airflow distortion, and ground effect—that degrade quadrotor trajectory tracking performance.
• Overcome limitations of existing disturbance observers, including high complexity, computational burden, and tuning difficulty in sliding mode and adaptive observers.
• Develop a simple, computationally efficient, and easily tunable disturbance observer using high-gain observer principles to estimate disturbances in real time.
• Integrate the HGDO with a standard robust controller (sliding mode control) to improve disturbance rejection without requiring a more complex model.
• Demonstrate the effectiveness of the HGDO-based control framework in both simulation and real-world experiments under diverse disturbance conditions.

Proposed method

• Design a high-gain disturbance observer (HGDO) based on auxiliary variable techniques to mitigate measurement noise amplification, ensuring robustness in noisy environments.
• Formulate the HGDO in a second-order controllability canonical form for the quadrotor’s full six-degree-of-freedom dynamics, enabling direct estimation of disturbances affecting position and attitude.
• Use a single scalar gain parameter for tuning the observer, simplifying implementation and reducing design complexity compared to adaptive or sliding mode observers.
• Integrate the HGDO estimates into a sliding mode control (SMC) law to actively compensate for disturbances, improving trajectory tracking performance.
• Perform Lyapunov stability analysis to prove semi-global uniform ultimate boundedness of both disturbance estimation error and trajectory tracking error.
• Implement the full control architecture with an extended Kalman filter for state estimation and the HGDO as an additional layer on top of SMC, enabling real-time disturbance compensation.

Experimental results

Research questions

• RQ1 Can a high-gain disturbance observer (HGDO) achieve fast and accurate disturbance estimation for quadrotor trajectory tracking under external disturbances?
• RQ2 Does integrating HGDO with a sliding mode controller improve trajectory tracking accuracy and robustness compared to standard SMC without disturbance estimation?
• RQ3 How does the HGDO perform in the presence of measurement noise and unmodeled dynamics, particularly in challenging scenarios like ground effect or aggressive maneuvers?
• RQ4 Can the HGDO-based control system maintain bounded tracking and estimation errors under realistic disturbances such as wind and ground effect?
• RQ5 Is the HGDO framework generalizable to other Lyapunov-based controllers beyond sliding mode control?

Key findings

• The HGDO achieves fast convergence of disturbance estimation error to an adjustable neighborhood of the true disturbance, with short transient response time.
• In position hold experiments, the SMC+HGDO method achieved higher tracking accuracy than SMC alone, even outperforming SMC in the no-disturbance case due to compensation of unmodeled dynamics.
• In circular path tracking, the HGDO-based controller reduced position tracking error significantly compared to SMC, demonstrating effectiveness against unmodeled dynamics.
• During landing, the HGDO successfully estimated the larger disturbances caused by ground effect, particularly along the z-axis, leading to more consistent and accurate touchdown positioning.
• The disturbance estimation plots confirmed that the HGDO captured ground effect disturbances, which were not fully accounted for in the nominal model, validating its ability to estimate complex, time-varying disturbances.
• The experimental results confirmed theoretical stability guarantees, showing bounded tracking and estimation errors across all scenarios, including wind disturbances and ground effect.