Abstract
In this paper we study the time evolution of the position estimates’ covariance in Cooperative Simultaneous Localization and Mapping (C-SLAM), and obtain analytical upper bounds for the positioning uncertainty. The derived bounds provide descriptions of the asymptotic positioning performance of a team of robots in a mapping task, as a function of the characteristics of the proprioceptive and exteroceptive sensors of the robots, and of the graph of relative position measurements recorded by the robots. A study of the properties of the Riccati recursion, which describes the propagation of uncertainty through time, yields (i) the guaranteed accuracy for a robot team in a given C-SLAM application, as well as (ii) the maximum expected steady-state uncertainty of the robots and landmarks, when the spatial distribution of features in the environment can be modeled by a known distribution. The theoretical results are validated both in simulation and experimentally.
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