Guaranteed Encapsulation of Targets with Unknown Motion by a Minimalist Robotic Swarm

We present a decentralized control algorithm for a robotic swarm given the task of encapsulating static and moving targets in a bounded unknown environment. We consider minimalist robots without memory, explicit communication, or localization information. The state-of-the-art approaches generally assume that the robots in the swarm are able to detect the relative position of neighboring robots and targets in order to provide convergence guarantees. In this work, we propose a novel control law for the guaranteed encapsulation of static and moving targets while avoiding all collisions, when the robots do not know the exact relative location of any robot or target in the environment. We make use of the Lyapunov stability theory to prove the convergence of our control algorithm and provide bounds on the ratio between the target and robot speeds. Furthermore, our proposed approach is able to provide stochastic guarantees under the bounds that we determine on task parameters for scenarios where a target moves faster than a robot. Finally, we present an analysis of how the emergent behavior changes with different parameters of the task and noisy sensor readings.