This paper addresses the problem of obtaining an Earth-fixed trajectory and map (ETM), with the associated uncertainty, using the sensor-based map provided by a globally asymptotically/exponentially stable (GES) SLAM filter. The algorithm builds on an optimization problem with a closed-form solution, and its uncertainty description is derived resorting to perturbation theory. The combination of the algorithm proposed in this paper with sensor-based SLAM filtering results in a complete SLAM methodology, which is directly applied to the three main different formulations: range-and-bearing, range-only, and bearing-only. Simulation and experimental results for all these formulations are included in this work to illustrate the performance of the proposed algorithm under realistic conditions. The ETM algorithm proposed in this paper is truly sensor-agnostic, as it only requires a sensor-based map and imposes no constraints on how this map is acquired nor how egomotion is captured. However, in the experiments presented herein, all the sensor-based filters use a sensor to measure the angular velocity and, for the range-only and bearing-only formulations, a sensor to measure the linear velocity.
- Perturbation theory
- Procrustes problem