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Complexity analysis and approximate solutions for two multiple-robot localization problems

We consider the localization problem for a system of mobile robots using inexpensive range sensors. Among many issues for multi-robot systems, two problems are identified and formally defined. The first problem is sensing ranges from all robots as quickly as possible while avoiding sensor cross-talk, and the second problem is to localize a multi-robot system using a minimal number of range sensings. We show that both these problems are NP-complete, and we propose an approximate method for the multi-robot localization problem that takes advantage of the robots pose uncertainty information. Simulation results show the effectiveness of our method for localizing multiple robots.