Complex Analysis for Reconstruction from Controlled Motion

We address the problem of control-based recovery of robot pose and the environmental lay-out. Panoramic sensors provide us with a 1D projection of characteristic features of a 2D operation map. Trajectories of these projections contain information about the position of a priori unknown landmarks in the environment. We introduce here the notion of spatiotemporal signatures of projection trajectories. These signatures are global measures, characterized by considerably higher robustness with respect to noise and outliers than the commonly applied point correspondence. By modeling the 2D motion plane as the complex plane we show that by means of complex analysis the reconstruction problem is reduced to a system of two quadratic - or even linear in some cases - equations in two variables. The algorithm is tested in simulations and real experiments.