Distributed Source Seeking Without Global Position Information

We present a distributed control law to steer a group of autonomous communicating sensors toward the source of a diffusion process. The graph describing the communication links between sensors has a time-invariant topology, and each sensor is able to measure (in addition to the quantity of interest) only the relative bearing angle with respect to its neighbor, but has no absolute position information and does not know any relative distance. Using multiple sensors is useful in wide environments (e.g., under the sea), or when the function describing the diffusion process is slowly changing in space, so that a single sensor may have to travel long distances before having a good gradient estimation. Our approach is based on a two-fold control law, which is able to bring and keep the set of sensors on a circular equispaced formation, and to steer the circular formation toward the source via a gradient-ascent technique. The effectiveness of the proposed algorithm is theoretically proven and supported by simulation results.