Global Singularity-Free Aerodynamic Model for Algorithmic Flight Control of Tail Sitters

Abstract

This paper addresses fundamental issues in tail-sitting and transition flight aerodynamics modeling in view of sumof- squares (SOS) algorithmic guidance and control design. A novel approach, called ϕ theory, for modeling aerodynamic forces and moments is introduced herein. It yields polynomial-like differential equations of motion that are well suited to SOS solvers for real-time algorithmic guidance and control law synthesis. The proposed ϕ theory allows for first principles model parameter identification and captures dominant dynamical features over the entire flight envelope. Furthermore, ϕ theory yields numerically stable and consistent models for 360 deg angles of attack and sideslip. Additionally, an algorithm is provided for analytically computing all feasible longitudinal flight operating points. Finally, to establish ϕ-theory validity, predicted trim points and wind-tunnel experiments are compared.