A Distributed Control Law for Optimum Sensor Placement for Source Localization

We formulate a nonlinear distributed control law that guides the motion a group of sensors to achieve a configuration that permits them to optimally localize a hazardous source they must keep a prescribed distance from. Earlier work shows that such a configuration involves the sensors being placed in an equispaced manner on a prescribed circle. The nonlinear control law we propose assumes that each sensor resides and moves on the prescribed circle, by accessing only the states of its two immediate clockwise and counterclockwise neighbors. We theoretically prove and verify through simulations, that the law allows the sensors to achieve the desired configuration while avoiding collisions.