In this paper, we first consider a simple Bayesian fusion problem in a matrix Lie group, and propose to tackle it using the unscented transform. The method is then leveraged to derive two simple alternative unscented Kalman filters on Lie groups, for both cases of noisy partial measurements of the state, and full state noisy measurements of the state on the group. The general method is applied to a robot localization problem, and results based on experimental data combined with extensive Monte-Carlo simulations at various noise levels illustrate the superiority of the approach over the standard UKF.

Micro air vehicles with transitioning flight capabilities, or simply hybrid micro air vehicles, combine the beneficial features of fixed-wing configurations, in terms of endurance, with vertical takeoff and landing capabilities of rotorcrafts to perform five different flight phases during typical missions, such as vertical takeoff, transitioning flight, forward flight, hovering and vertical landing. This promising micro air vehicle class has a wider flight envelope than conventional micro air vehicles, which implies new challenges for both control community and aerodynamic designers. One of the major challenges of hybrid micro air vehicles is the fast variation of aerodynamic forces and moments during the transition flight phase which is difficult to model accurately. To overcome this problem, we propose a flight control architecture that estimates and counteracts in real-time these fast dynamics with an intelligent feedback controller. The proposed flight controller is designed to stabilize the hybrid micro air vehicle attitude as well as its velocity and position during all flight phases. By using model-free control algorithms, the proposed flight control architecture bypasses the need for a precise hybrid micro air vehicle model that is costly and time consuming to obtain. A comprehensive set of flight simulations covering the entire flight envelope of tailsitter micro air vehicles is presented. Finally, real-world flight tests were conducted to compare the model-free control performance to that of the Incremental Nonlinear Dynamic Inversion controller, which has been applied to a variety of aircraft providing effective flight performances.

In this paper, we proposed a novel approach for nonlinear state estimation, named π-IUKF (Invariant Unscented Kalman Filter), which is based on both invariant filter estimation and UKF theoretical principles. Several research works on nonlinear invariant observers have been led and provide a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical properties and systems symmetries. The general invariant observer guarantees a straightforward form of the nonlinear estimation error dynamics whose properties are remarkable. The developed π-IUKF estimator suggests a systematic approach to determine all the symmetry-preserving correction terms, associated with a nonlinear state-space representation used for prediction, without requiring any linearization of the differential equations. The exploitation of the UKF principles within the invariant framework has required the definition of a compatibility condition on the observation equations. As a first result, the estimated covariance matrices of the π-IUKF converge to constant values due to the symmetry-preserving property provided by the nonlinear invariant estimation theory. The designed π-IUKF method has been successfully applied to some relevant practical problems such as the estimation of Attitude and Heading for aerial vehicles using low-cost AH reference systems (i.e., inertial/magnetic sensors characterized by low performances).

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