{'fraction_non_alphanumeric': 0.01700404858299595, 'fraction_numerical': 0.0, 'mean_word_length': 5.338461538461538, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Analytical Expressions for Positioning Uncertainty Propagation in Networks of Robots

In this paper we present an analysis of the positioning uncertainty increase rate for a group of mobile robots. The simplified version for a group of N robots moving along one dimension is considered. The one dimension restriction permits us to extract an exact expression for the accumulation of positioning uncertainty in a group of robots equipped with proprioceptive (odometric in this case) and exteroceptive (relative distance between robots) sensors. The solution obtained provides insight in the structure of the multirobot localization problem. In addition, it serves both as an approximation and a starting point for examining the more realistic case ofN robots moving on a plane. Our derivation is based on a Kalman filter estimator that combines all measurements from all robots in the group. Furthermore, we analyze the effect of initial uncertainty, number of robots (N ) and sensor noise on the rate of positioning uncertainty increase. The analytical results derived in this paper and the impact of the different parameters are validated in simulation. Keywords— Multirobot Localization, Cooperative Localization, Networks of Robots.