Fast control allocation algorithm for tilt-rotor VTOL aircraft

TL;DR

This work tackles nonlinear propeller–wing coupling in tilt-rotor VTOLs by developing a control-allocation framework that inverts a trigonometric forward map from actuator inputs ($T$, $\delta$) to body-forces ($F_x$, $F_z$) using Groebner-basis methods. The approach employs lifting variables to polynomialize the relations and computes actuator commands via eigenvalues of multiplication matrices, enabling real-time implementation with computation times under $10$ ms. Relative allocation accuracy remains below $8\%$ across extensive Monte Carlo tests, and the method supports hover-to-cruise regimes with transition handling between coupled and decoupled dynamics. By enabling direct virtual control of forces and moments, the framework facilitates the use of simple $LTI$ controllers for attitude and airspeed control, with potential for CFD-parametrized modeling and hardware validation.

Abstract

Control algorithms initially developed for tilt-wing vertical take-off and landing (VTOL) aircraft are adapted to the tilt-rotor design. The main difference between the two types of planes is the more complicated interaction between propellers and wings in the tilt-rotor design. Unlike tilt-wing design, the tilt-rotor case varies the angle between the propeller disk and wing cord line, thus introducing a non-linear dependency of lift on thrust and tilt angle. In this paper we develop a precise control allocation method, utilizing Groebner basis algorithms to mask the non-linearity of the control action and allow the use of linear time-invariant control laws for attitude and velocity control architectures. The performance of our approach is discussed and quantified w.r.t. the accuracy of the developed propeller-wing interaction model.

Figures (8)

• Figure 1: Joby aviation tilt-rotor pre-production aircraft, shown in hover (left) and cruise (right) configuration. Reproduced from www.jobyaviation.com
• Figure 2: Schematic description of control architecture.
• Figure 3: Geometry of the propeller wing configuration, with propeller and wing components (green), propeller-related vectors (blue), overall forces (red), and wind-related vectors (black).
• Figure 4: Geometry of the interaction between propeller-induced airflow and wing location.
• Figure 5: Two examples of modeled relation between model inputs (thrust $T$ and tilt angle $\delta$ and model outputs ($F_x$ and $F_z$) with varying parameter values ($v_\infty$ and $\alpha_\infty$)