  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.
