Nonuniform coverage control on the line

This paper investigates control laws allowing mobile, autonomous agents to optimally position themselves on the line for distributed sensing in a nonuniform field. We show that a simple static control law, based only on local measurements of the field by each agent, drives the agents to the optimal positions in time that is quadratic in the number of agents. Further, we exhibit a dynamic control law which, under slightly stronger assumptions on the capabilities and knowledge of each agent, drives the agents to the optimal positions an order of magnitude faster, namely in time that is linear in the number of agents. Both algorithms are fully distributed and robust to unpredictable loss and addition of agents.