A1496
Title: Polynomial regression on SE(3) with an arbitrary connection
Authors: Johan Aubray - ENAC (France) [presenting]
Florence Nicol - ENAC (France)
Abstract: The problem of estimating the position of a mobile, such as a drone, from noisy position measurements is addressed. The framework of differential geometry is used. More precisely, the trajectory of the mobile is modelled as a Lie group-valued curve, the group in question being the special Euclidean group SE(n), with $n=2$ or 3. Based on this approach, the goal is to implement this technique in the Lie group SE(3) context. Last year, the idea limited to the Levi-Civita connection was presented. It is now extended to an arbitrary connection. A more general mathematical formulation is established by using differential forms. Applications to simulated data are proposed to illustrate the approach with measurements of the $R^2$ score. The limitations of such a method and future perspectives are discussed.
