A sub-modular receding horizon approach to persistent monitoring for a group of mobile agents over an urban area

Abstract

We consider the problem of persistent monitoring of a finite number of interconnected geographical nodes for event detection via a group of heterogeneous mobile agents. We assume that the probability of the events occurring at the geographical points of interest follow known Poisson processes. We tie a utility function to the probability of detecting an event in each point of interest and use it to incentivize the agents to visit the geographical nodes with higher probability of event occurrence. We show that the design of an optimal monitoring policy that specifies the sequence of the geographical nodes and time of visit of those nodes for each mobile agent so that the utility of event detection over a mission horizon is maximized is an NP-hard problem. To reduce the time complexity of constructing the feasible set of the optimal approach and also to induce robustness to changes in event occurrence and other operational factors, we consider a receding horizon approach. We note that, with the number of agents growing, the cost of finding the optimal path grows exponentially even with shortened horizon. To overcome this issue, we introduce a sub-modular optimization approach that has a polynomial time complexity and also comes with a known sub-optimality lower bound. We demonstrate our results through simulations.