Maximum reward collection problem: a cooperative receding horizon approach for dynamic clustering

In this paper, the Maximum Reward Collection Problem (MRCP) in uncertain environments is investigated where multiple agents cooperate to maximize the total reward collected from a set of moving targets in the mission space with unknown arrival times, trajectories and dynamics. The reward with respect to each of the targets has a time discounting value and can be collected only if a cluster of agents with proper number of elements visits the targets. Meanwhile, in each cluster, it is assumed that agents are able to extract a larger fraction of reward when their configuration in the cluster is close to specific configuration around the respective target. The inherited uncertainty in the environment and the dynamic clustering factor render the one-shot optimization in MRCP rather impractical. Therefore, a Cooperative Receding Horizon (CRH) controller is utilized toward maximizing the collected reward and based on the prediction of the future positions of targets with the given limited information. Some analytical aspects of problem is discussed and the effectiveness and advantages of the proposed algorithm is demonstrated via numerical simulations.