A submodularity-based approach for multi-agent optimal coverage problems

We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. We first show that the objective function is monotone submodular, a class of functions for which a simple greedy algorithm is known to be within 1-1/e of the optimal solution. We then derive two tighter lower bounds by exploiting the curvature information of the objective function. We further show that the tightness of these lower bounds is complementary with respect to the sensing capabilities of the agents. Simulation results show that this approach leads to significantly better performance relative to previously used algorithms.