Stable emergent agent distributions under sensing and travel delays

In order for a team of cooperating agents to achieve a group goal (such as searching for targets, monitoring an environment, etc.) those agents must be able to share information and achieve some level of coordination. Since realistic methods of communication between agents have limited range and speed, the agents' decision-making strategies must operate with incomplete and outdated information. Moreover, in many situations the agents must travel to particular locations in order to perform various tasks, and so there will also be a delay between any particular decision and its effect. In this paper we develop an asynchronous framework that models the behavior of a group of agents that is spatially distributed across a predefined area of interest. We derive general conditions under which the group is guaranteed to converge to a specific distribution within the environment without any form of central control and despite unknown but bounded delays in sensing and travel. The achieved distribution is optimal in the sense that the proportion of agents allocated over each area matches the relative importance of that area. Finally, based on the derived conditions, we design a cooperative control scheme for a multi-agent surveillance problem. Via Monte Carlo simulations we show how sensing and travel delays and the degree of cooperation between agents affect the rate at which they achieve the desired coverage of the region under surveillance.