# A sub-modular receding horizon solution for mobile multi-agent persistent monitoring

## TL;DR

This paper presents a submodular receding horizon approach for optimizing persistent monitoring by heterogeneous mobile agents, balancing computational efficiency and robustness in complex, NP-hard scenarios.

## Contribution

It introduces a novel suboptimal dispatch policy leveraging submodularity and receding horizon techniques for multi-agent persistent monitoring.

## Key findings

- The proposed method achieves near-optimal rewards in simulations.
- Receding horizon approach reduces computational complexity.
- Incorporating nodal importance improves monitoring effectiveness.

## Abstract

We study the problem of persistent monitoring of a finite number of inter-connected geographical nodes by a group of heterogeneous mobile agents. We assign to each geographical node a concave and increasing reward function that resets to zero after an agent's visit. Then, we design the optimal dispatch policy of which nodes to visit at what time and by what agent by finding a policy set that maximizes a utility that is defined as the total reward collected at visit times. We show that this optimization problem is NP-hard and its computational complexity increases exponentially with the number of the agents and the length of the mission horizon. By showing that the utility function is a monotone increasing and submodular set function of agents' policy, we proceed to propose a suboptimal dispatch policy design with a known optimality gap. To reduce the time complexity of constructing the feasible search set and also to induce robustness to changes in the operational factors, we perform our suboptimal policy design in a receding horizon fashion. Then, to compensate for the shortsightedness of the receding horizon approach for reward distribution beyond the feasible policies of the agents over the receding horizon, we add a new term to our utility, which provides a measure of nodal importance beyond the receding horizon's sight. This term gives the policy design an intuition to steer the agents towards the nodes with higher rewards on the patrolling graph. Finally, we discuss how our proposed algorithm can be implemented in a decentralized manner. A simulation study demonstrates our results.