Pattern Formation in Swarming Spacecrafts using Tersoff-Brenner Potential Field

We present a distributed control strategy that lets a swarm of spacecrafts autonomously form a lattice in orbit around a planet. The system, based on the artificial potential field approach, proposes a novel way to divide the artificial field into two main terms: a global artificial potential field mainly based on the famous C-W equations that gathers the spacecrafts around a predefined meeting point, and a local term exploited the well-known Tersoff-Brenner potential that allows a spacecraft to place itself in the correct position relative to its closest neighbors. Moreover, in order to obtain convergence from all initial distributions of the spacecrafts, a dissipation term depended on the velocity of agent is introduced. The new methodology is demonstrated in the problem of forming a hexagon lattice, the structure unit of graphite. It is shown that a pattern formation can operate around a planet. By slightly changing the scenario our method can be easily applied to shape other configurations, such as a regular tetrahedron (with central point), the structure unit, etc.