Geometric Nonlinear PID Control of a Quadrotor UAV on SE(3) (1304.6765v1)

Abstract: Nonlinear PID control systems for a quadrotor UAV are proposed to follow an attitude tracking command and a position tracking command. The control systems are developed directly on the special Euclidean group to avoid singularities of minimal attitude representations or ambiguity of quaternions. A new form of integral control terms is proposed to guarantee almost global asymptotic stability when there exist uncertainties in the quadrotor dynamics. A rigorous mathematical proof is given. Numerical example illustrating a complex maneuver, and a preliminary experimental result are provided.

Geometric Nonlinear PID Control of a Quadrotor UAV

The paper presents a sophisticated approach to controlling the dynamics of a quadrotor unmanned aerial vehicle (UAV) using geometric nonlinear PID controllers. The control systems are designed to achieve attitude and position tracking under conditions of uncertainty in the UAV's dynamics, directly utilizing the special Euclidean group to overcome the singularity issues associated with traditional minimal attitude representations such as Euler angles and quaternion ambiguities.

Main Contribution

The primary contribution is the development of novel nonlinear PID controllers that ensure almost global asymptotic stability for both attitude and position tracking. This is accomplished through:

1. Development on Special Euclidean Group: The controllers operate on the special Euclidean group $\mathrm{SE}(3)$ to eradicate complexities related to conventional attitude representation methods.
2. Inclusion of Integral Control Terms: Unique integral control terms were introduced, explicitly enhancing stability in the presence of dynamic uncertainties.
3. Propositional and Lemma Framework: Rigorous mathematical proofs underpinning the control system are provided, ensuring the robustness of the proposed methods.

Methodology

The research delineates two flight modes:

• Attitude Controlled Flight Mode: Focuses on tracking a desired attitude command, where the moment vector $M$ caters to the nuanced dynamics using proportional, derivative, and integral terms. This mode is particularly potent for completing intricate rotational maneuvers.
• Position Controlled Flight Mode: Engages in tracking a position trajectory by adjusting both thrust and attitude, thereby addressing the coupled translational and rotational dynamics. This mode is crucial for aligning the UAV's inertia with spatial directives.

Results

Simulations demonstrate exceptional tracking of complex maneuvers, with the proposed controller effectively managing aggressive flips and changes in heading direction. Preliminary experimental results affirm the controller's capability, showcasing reliable attitude tracking performance in a lab-setting.

Strong Numerical Results

Quantitative analysis in the simulations illustrates successful tracking performance, with steady-state errors effectively mitigated when employing integral control terms—highlighting the system's robustness under uncertainties. Stability is confirmed through numerical validations of the controller parameters, with simulations proving the efficacy of theoretical predictions.

Implications and Future Work

Practically, this research sets a framework for developing robust UAV control systems capable of tackling uncertain environments without the need for excessive sensor data or computational overhead. Theoretically, it extends the domain of geometric control theory and contributes to the foundational understanding of nonlinear PID controller implementations on $\mathrm{SE}(3)$. Looking forward, potential advancements could focus on refining controller adaptability to real-time environmental changes and exploring the integration of advanced machine learning techniques to predict and adjust to dynamic alterations preemptively.

In conclusion, the paper furnishes a comprehensive exploration into nonlinear PID control for quadrotors that substantially contributes to both academic discourse and practical application in UAV technologies.