Closed Form Solutions for Reconstruction Via Complex Analysis

We address the problem of control-based recovery of robot pose and environmental lay-out. Panoramic sensors provide 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 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 can be reduced to a quadratic—or even linear in some cases—equation. The algorithm is tested in simulations and in a real experiment.