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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 close to the optimal positions after the agents execute in parallel a number of sensing/movement/computation rounds that is essentially 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 close to the optimal positions after the agents execute in parallel a number of sensing/communication/computation/movement rounds that is essentially linear in the number of agents. Crucially, both algorithms are fully distributed and robust to unpredictable loss and addition of agents.

Nonuniform coverage control on the line