Bio-inspired Source Seeking with no Explicit Gradient Estimation*

Inspired by behaviors of fish groups seeking darker (shaded) regions in environments with complex lighting variations, we develop distributed source-seeking algorithms for a group of sensing agents with no explicit gradient estimation. We choose a baseline for agent groups and decompose the velocity of each agent into two parts. The first part, which is perpendicular to the baseline, is chosen to be proportional to the measurements, agreeing with observations from fish groups. The second part, which is parallel to the baseline, can be designed to control the relative distances among the agents. This decomposition is leveraged to implement formation-maintaining strategies and source seeking behaviors for the entire group. We prove that the moving direction of a group will converge towards the gradient direction while the formation is maintained.