Decentralized progressive shape formation with robot swarms

We address the problem of progressively deploying a set of robots to a formation defined as a point cloud, in a decentralized manner. To achieve this, we present an algorithm that transforms a given point cloud into an acyclic directed graph. This graph is used by the control law to allow a swarm of robots to progressively form the target shape based only on local decisions. This means that free robots (i.e., not yet part of the formation) find their location based on the perceived location of the robots already in the formation. We prove that for a 2D shape it is sufficient for a free robot to compute its distance from two robots in the formation to achieve this objective. We validate our method using physics-based simulations and robotic experiments, showing consistent convergence and minimal formation placement error.