Consensus-based source-seeking with a circular formation of agents

This paper deals with the source-seeking problem in which a group of autonomous vehicles must locate and follow the source of some signal based on measurements of the signal strength at different positions. As recently suggested, the gradient of the signal strength can be approximated by a circular formation of agents via a simple weighted average of the signal measured by the agents. Using this result, we propose a distributed source-seeking algorithm based on a consensus method which is guaranteed to steer the circular formation towards the source location using the estimated gradient direction. The proposed algorithm is provided with two tunable parameters that allow for a tradeoff between speed of convergence, noise filtering and formation stability. The benefit of using consensus-based algorithms resides in a more realist discrete time control of the agents and in asynchronous communication resilient to delays which is particularly relevant for underwater applications. The analytic results are finally complemented with numerical simulations.