Fully distributed and resilient source seeking for robot swarms

We propose a self-contained, resilient and fully distributed solution for locating the maximum of an unknown scalar field using a swarm of robots that travel at a constant speed. Unlike conventional reactive methods relying on gradient information, our methodology enables the swarm to determine an ascending direction so that it approaches the source with an arbitrary precision. Our source-seeking solution consists of three distributed algorithms running simultaneously in a slow-fast closed-loop system. The fastest algorithm provides the centroid-relative coordinates of the robots and the next slower one provides the ascending direction to be tracked. The tracking of the ascending direction by single integrators is instantaneous; howeverin this paper we will also focus on 2D unicycle-like robots with a constant speed. The third algorithm, the slowest one since the speed of the robots can be chosen arbitrarily slow, is the individual control law for the unicycle to track the estimated ascending direction.We will show that the three distributed algorithms converge exponentially fast to their objectives, allowing for a feasible slow-fast closed-loop system. The robots are not constrained to any particular geometric formation, and we study both discrete and continuous distributions of robots.The swarm shape analysis reveals the resiliency of our approach as expected in robot swarms, i.e., by amassing robots we ensure the source-seeking functionality in the event of missing or misplaced individuals or even if the robot network splits in two or more disconnected subnetworks.We exploit such an analysis so that the swarm can adapt to unknown environments by morphing its shape and maneuvering while still following an ascending direction. We analyze our solution with robots as kinematic points in n-dimensional Euclidean spaces and extend the analysis to 2D unicycle-like robots with constant speeds.