[Paper Review] Modeling for Control of Symmetric Aerial Vehicles Subjected to Aerodynamic Forces

Daniele Pucci, Tarek Hamel+2 more|arXiv (Cornell University)|Dec 7, 2012

Control and Dynamics of Mobile Robots12 references3 citations

TL;DR

This paper presents a unified nonlinear control framework for symmetric aerial vehicles subjected to lift and drag forces by identifying a class of aerodynamic models that allow transformation into an equivalent spherical vehicle model with only orientation-independent drag. The key contribution is a condition on aerodynamic characteristics that enables application of existing stable control laws, extending prior 2D results to 3D and broadening the applicable model family, ensuring asymptotic stability with a large domain of attraction.

ABSTRACT

This paper participates in the development of a unified approach to the control of aerial vehicles with extended flight envelopes. More precisely, modeling for control purposes of a class of thrust-propelled aerial vehicles subjected to lift and drag aerodynamic forces is addressed assuming a rotational symmetry of the vehicle's shape about the thrust force axis. A condition upon aerodynamic characteristics that allows one to recast the control problem into the simpler case of a spherical vehicle is pointed out. Beside showing how to adapt nonlinear controllers developed for this latter case, the paper extends a previous work by the authors in two directions. First, the 3D case is addressed whereas only motions in a single vertical plane was considered. Secondly, the family of models of aerodynamic forces for which the aforementioned transformation holds is enlarged.

Motivation & Objective

• To develop a unified control approach for aerial vehicles operating across diverse flight regimes, including both VTOL and fixed-wing flight modes.
• To address the limitation of prior 2D control methods by extending the analysis to full 3D motion dynamics.
• To identify a class of aerodynamic force models for symmetric vehicles that allow reduction of the complex control problem to the simpler case of a spherical body with only orientation-independent drag.
• To enable the application of existing nonlinear control schemes—originally designed for spherical bodies—on realistic, symmetric aerial vehicles with significant lift and drag forces.
• To provide a foundation for robust control of convertible aerial vehicles during transitions between hovering and high-speed cruising, where aerodynamic forces vary significantly.

Proposed method

• Derives the full 3D dynamic equations of motion for a symmetric aerial vehicle, accounting for thrust, gravity, and aerodynamic forces (lift and drag) acting along the body-fixed axis.
• Introduces a transformation condition on the aerodynamic force model that allows the system to be recast as equivalent dynamics of a spherical vehicle subject only to orientation-independent drag.
• Identifies a family of lift and drag models satisfying this condition, using experimental data from elliptic-shaped and missile-like bodies to validate and tune the model parameters.
• Adapts a velocity control law from prior work on spherical bodies, incorporating integral action to handle unmodeled constant disturbances and improve robustness.
• Uses a skew-symmetric matrix representation for angular velocity and applies a nonlinear feedback control law based on velocity error and integral correction to ensure asymptotic stability.
• Establishes theoretical stability results, proving that the equilibrium point (zero velocity and zero pitch angle) is asymptotically stable with a domain of attraction covering all of ℝ³ × (−π, π).

Experimental results

Research questions

• RQ1 Under what conditions on the aerodynamic force model can the control problem for a symmetric aerial vehicle be reduced to that of a spherical vehicle with only orientation-independent drag?
• RQ2 How can existing nonlinear control laws designed for spherical bodies be adapted to control realistic symmetric aerial vehicles with significant lift and drag forces?
• RQ3 What is the extent of the domain of attraction for the resulting control system in 3D space, and how does it compare to previous 2D results?
• RQ4 How can integral action be incorporated into the control law to ensure robustness against constant unmodeled disturbances?
• RQ5 What are the implications of this transformation for the control of convertible aerial vehicles during transitions between hovering and high-speed flight?

Key findings

• The paper identifies a specific family of aerodynamic force models for symmetric vehicles that allow the control problem to be transformed into the simpler case of a spherical body with only orientation-independent drag.
• The transformed system allows direct application of existing nonlinear control schemes, ensuring asymptotic stability of the equilibrium point (zero velocity and zero pitch angle).
• The domain of attraction for the controlled system is proven to be ℝ³ × (−π, π), indicating strong global stability properties in practice.
• The inclusion of integral correction terms in the control law ensures robustness against almost constant unmodeled additive perturbations, enhancing practical applicability.
• The method successfully extends prior 2D control results to 3D, broadening the scope of applicability to full 3D flight dynamics.
• The approach is validated using experimental data from real-world bodies (elliptic-shaped and missile-like), demonstrating its feasibility for real-world vehicle modeling and control.