A Speeding-Up and Slowing-Down Strategy for Distributed Source Seeking With Robustness Analysis

Inspired by behaviors of schools of fish seeking darker (shaded) regions in environments, this paper proposes a distributed source seeking strategy for a mobile sensor network. The strategy allows each sensing agent to take instantaneous measurements of the field and collectively move against the direction of spatial gradient, without explicitly estimating the gradient. For each agent, one portion of its velocity is designed to be proportional to its measurement of the field, and another portion of its velocity is devoted to keep a formation with other agents. This strategy generates a speeding-up and slowing-down (SUSD) behavior that is very similar to what has been observed in schools of fish. Convergence analysis of this SUSD strategy shows that the moving direction of the agent formation will be aligned with the opposite gradient direction so that the formation moves toward a local minimum of the field, which is referred to as the source of the field. The SUSD strategy is also robust to deterministic disturbances and stochastic noise, which is rigorously justified by proving that the resulting closed-loop system is input-to-state stable and noise-to-state stable. Both simulation and experimental results are presented to demonstrate the SUSD strategy.