| Abstract | This work proposes a game theoretic approach 
to tackle the problem of multi-robot coordination 
in critical scenarios where communication is 
limited and the robots must accomplish different tasks 
simultaneously. An important application falls in underwater 
robotic framework where robots are used to 
protect a ship against asymmetric threats guaranteeing 
simultaneously the coverage of the area around the ship 
and the tracking of a possible intruder. The problem is 
modelled as a potential game for which novel learning 
protocols are introduced. Indeed, a general extension 
of pay-off based algorithms is herein proposed where 
the main difference with state-of-the-art protocols is 
that the trajectory optimization is considered instead 
of single action optimization. Moreover, the proposed 
T-algorithms, steer the robots toward Nash equilibria 
that will be shown to correspond to the accomplishment 
of different, possibly antagonistic, goals. Finally, performances 
of the algorithms, under different scenarios, 
have been evaluated in simulations. 
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