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 3D scalar field using a swarm of robots that travel at constant speeds. 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 arbitrary precision. Our source-seeking solution consists of three algorithms. The first two algorithms run sequentially and distributively at a high frequency providing barycentric coordinates and the ascending direction respectively to the individual robots. The third algorithm is the individual control law for a robot to track the estimated ascending direction. We show that the two algorithms with higher frequency have an exponential convergence to their eventual values since they are based on the standard consensus protocol for first-order dynamical systems; their high frequency depends on how fast the robots travel through the scalar field. The robots are not constrained to any particular geometric formation, and we study both discrete and continuous distributions of robots within swarm shapes. The 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 into two or more disconnected subnetworks. In addition, we also enhance the robustness of the algorithm by presenting conditions for \emph{optimal} swarm shapes, in the sense that the ascending directions can be closely parallel to the field's gradient. 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.

Behavioral-based circular formation control for robot swarms

This paper focuses on coordinating a robot swarm orbiting a convex path without collisions among the individuals. The individual robots lack braking capabilities and can only adjust their courses while maintaining their constant but different speeds. Instead of controlling the spatial relations between the robots, our formation control algorithm aims to deploy a dense robot swarm that mimics the behavior of tornado schooling fish. To achieve this objective safely, we employ a combination of a scalable overtaking rule, a guiding vector field, and a control barrier function with an adaptive radius to facilitate smooth overtakes. The decision-making process of the robots is distributed, relying only on local information. Practical applications include defensive structures or escorting missions with the added resiliency of a swarm without a centralized command. We provide a rigorous analysis of the proposed strategy and validate its effectiveness through numerical simulations involving a high density of unicycles.