[Paper Review] A simple controller for the transition maneuver of a tail-sitter drone

A. Flores, Andrés Montes de+1 more|arXiv (Cornell University)|Oct 26, 2018

Adaptive Control of Nonlinear Systems1 references4 citations

TL;DR

This paper proposes a smooth, non-switching controller for the transition maneuver of a tail-sitter VTOL drone using time-scale separation between attitude and position dynamics. Based on Lyapunov stability theory and linear saturation functions, the controller ensures local asymptotic stability and effectively handles actuator limits, as validated by simulations in both hover-to-cruise and cruise-to-hover transitions with bounded, continuous control inputs.

ABSTRACT

This paper presents a controller for the transition maneuver of a tail-sitter drone. The tail-sitter model considers aerodynamic terms whereas the proposed controller considers the time-scale separation between drone attitude and position dynamics. The controller design is based on Lyapunov approach and linear saturation functions. Simulations experiments demonstrate the effectiveness of the derived theoretical results.

Motivation & Objective

• To design a stable, continuous controller for the complex transition maneuver of a tail-sitter UAV, avoiding control switching between flight modes.
• To incorporate realistic constraints such as actuator saturation and aerodynamic forces into the control design.
• To leverage time-scale separation between fast attitude dynamics and slower position dynamics for simplified control synthesis.
• To ensure theoretical stability using Lyapunov methods while maintaining practical implementability.
• To demonstrate effectiveness through simulations of both hover-to-cruise and cruise-to-hover transitions.

Proposed method

• The controller uses time-scale separation, treating attitude dynamics as fast and position dynamics as slow, enabling hierarchical control design.
• A virtual control input θd is derived from a Lyapunov-based design to stabilize the position subsystem (u, w) via feedback of velocity errors.
• The torque τ is designed using a saturated linear feedback: τ = -kθ(θ - θd) - kq(q - qd) + q̇d, ensuring bounded control effort.
• Thrust T is computed via a saturated feedback law: T = -σ3(u - ud) + g√(1 - ε²) - f1(u, w, q) + u̇d, with σ3 as a saturation function.
• The system is modeled in 2D (x, z) plane with full aerodynamic terms (drag D, lift L, angle of attack α), and the control inputs are thrust T and torque τ.
• Stability is proven using a Lyapunov function V = ½x₁² + ½x₂², showing asymptotic stability of the closed-loop system under the proposed control laws.

Experimental results

Research questions

• RQ1 Can a smooth, non-switching controller achieve stable transition between hover and cruise flight modes in a tail-sitter UAV?
• RQ2 How can time-scale separation between attitude and position dynamics be exploited to simplify controller design?
• RQ3 What control structure ensures stability and actuator saturation compliance while including aerodynamic effects?
• RQ4 Can Lyapunov-based design with saturation functions guarantee local asymptotic stability in the presence of nonlinear aerodynamics?
• RQ5 How do the control inputs behave during transition, and do they remain bounded and continuous?

Key findings

• The controller successfully achieved stable transition from hover to cruise mode, with u increasing significantly (from ~0.18 to ~1.0) and w remaining small, resulting in low angle of attack (α) and reduced thrust requirement.
• During cruise-to-hover transition, velocities u and w decreased toward zero, causing α to approach zero, which required increased thrust to maintain altitude, as shown in the control input profile.
• The control inputs τ and T remained bounded and smooth throughout both transitions, with no abrupt switching or chattering, confirming the effectiveness of the saturation function design.
• The Lyapunov-based stability proof confirmed local asymptotic stability of the closed-loop system under the proposed control laws.
• Simulations demonstrated that the controller maintains desired trajectory tracking and handles nonlinear aerodynamic forces (D, L) effectively.
• The controller design is practical for real-world implementation due to its bounded, continuous control signals and reliance on standard sensor states (u, w, θ, q).