  We investigate the distributed planning of robot trajectories for optimal
execution of cooperative tasks with time windows. In this setting, each task
has a value and is completed if sufficiently many robots are simultaneously
present at the necessary location within the specified time window. Tasks keep
arriving periodically over cycles. The task specifications (required number of
robots, location, time window, and value) are unknown a priori and the robots
try to maximize the value of completed tasks by planning their own trajectories
for the upcoming cycle based on their past observations in a distributed
manner. Considering the recharging and maintenance needs, robots are required
to start and end each cycle at their assigned stations located in the
environment. We map this problem to a game theoretic formulation and maximize
the collective performance through distributed learning. Some simulation
results are also provided to demonstrate the performance of the proposed
approach.
