Mathematics – Optimization and Control
Scientific paper
2011-04-04
Mathematics
Optimization and Control
Scientific paper
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 in a number of sensing/movement 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 an order of magnitude faster, namely in a number of sensing/communication/movement rounds that is essentially linear in the number of agents; this scaling is nearly optimal since any control law requires at least linearly many rounds of communication to drive agents close to their optimal positions. Crucially, both algorithms are fully distributed and robust to unpredictable loss and addition of agents.
Leonard Naomi Ehrich
Olshevsky Alex
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