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.

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Transitioning vehicles experience three different flight phases during typical missions. The hovering and forward flight phases have been researched widely, however the transition phase in between is more challenging and has been the subject of less research. One of the control approaches to handle the transition phase relies on model-based methods which require sophisticated wind-tunnel characterization. Accurate modeling of force and moments of a partially stalled wing and control surfaces is highly challenging and time consuming. In addition, these models usually require several flight measurements (such as angle of attack and low airspeed) that are difficult to obtain. As an alternative, some control approaches manage the transition phase without the need for sophisticated models. One example of such an approach is the Model Free Control (MFC). This paper compares the results obtained from both MFC and Linear Quadratic Regulator (LQR) applied to fixed-wing UAV with transitioning flight capability during hovering, transition and forward flight modes. Both of the controllers are designed for a transitioning vehicle called MAVion. The simulation results demonstrated that MFC increases the stability of the aircraft, especially in disturbed flight conditions.

Advanced large-wing-span aircraft result in more structural flexibility and the potential for instability or poor handling qualities. These shortcomings call for stability augmentation systems that entail active structural control. Consequently, the in-flight estimation of wing shape is beneficial for the control of very flexible aircraft. This paper proposes a new methodology for estimating flexible structural states based on extended Kalman filtering by exploiting ideas employed in aided inertial navigation systems. High-bandwidth-rate gyro angular velocities at different wing stations are integrated to provide a short-term standalone inertial shape estimation solution, and additional low-bandwidth aiding sensors are then employed to bound diverging estimation errors. The proposed filter implementation does not require a flight dynamics model of the aircraft, facilitates the often tedious Kalman filtering tuning process, and allows for accurate estimation under large and nonlinear wing deflections. To illustrate the approach, the technique is verified by means of simulations using sighting devices as aiding sensors, and an observability study is conducted. In contrast to previous work in the literature based on stereo vision, a sensor configuration that provides fully observable state estimation is found using only one camera and multiple rate gyros for Kalman filtering update and prediction phases, respectively. Nomenclature

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