Despite significant interest in tailless flapping-wing micro aerial vehicle designs, tailed configurations are often favoured, as they offer many benefits, such as static stability and a simpler control strategy, separating wing and tail control. However, the tail aerodynamics are highly complex due to the interaction between the unsteady wing wake and tail, which is generally not modelled explicitly. We propose an approach to model the flapping-wing wake and hence the tail aerodynamics of a tailed flapping-wing robot. First, the wake is modelled as a periodic function depending on wing flap phase and position with respect to the wings. The wake model is constructed out of six low-order sub-models representing the mean, amplitude and phase of the tangential and vertical velocity components. The parameters in each sub-model are estimated from stereo-particle image velocimetry measurements using an identification method based on multivariate simplex splines. The computed model represents the measured wake with high accuracy, is computationally manageable and is applicable to a range of different tail geometries. The wake model is then used within a quasi-steady aerodynamic model, and combined with the effect of free-stream velocity, to estimate the forces produced by the tail. The results provide a basis for further modelling, simulation and design work, and yield insight into the role of the tail and its interaction with the wing wake in flapping-wing vehicles. It was found that due to the effect of the wing wake, the velocity seen by the tail is of a similar magnitude as the free stream and that the tail is most effective at 50-70% of its span.

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High-speed flight in GPS-denied environments is currently an important frontier in the research on autonomous flight of micro air vehicles. Autonomous drone races stimulate the advances in this area by representing a very challenging case with tight turns, texture-less floors, and dynamic spectators around the track. These properties hamper the use of standard visual odometry approaches and imply that the micro air vehicles will have to bridge considerable time intervals without position feedback. To this end, we propose an approach to trajectory estimation for drone racing that is computationally efficient and yet able to accurately estimate a micro air vehicle's state (including biases) and parameters based on sparse, noisy observations of racing gates. The key concept of the approach is to optimize unknown and difficult-to-observe state variables so that the observations of the racing gates best fit with the known control inputs, estimated attitudes, and the quadrotor dynamics and aerodynamics during a time window. It is shown that a gradient-descent implementation of the proposed approach converges $4 times quicker to (approximately) correct bias values than a state-of-the-art 15-state extended Kalman filter. Moreover, it reaches a higher accuracy, as the predicted end-point of an open-loop turn is on average only $20 cm away from the actual end-point, while the extended Kalman filter and the gradient descent method with kinematic model only reach an accuracy of $50 cm. Although the approach is applied here to drone racing, it generalizes to other settings in which a micro air vehicle may only have sparse access to velocity and/or position measurements.

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