Multi-robot teams find applications in emergency response, search and rescue operations, convoy support and many more. Teams of autonomous aerial vehicles can also be used to protect a cargo of airplanes by surrounding them in some geometric shape. This research develops a control algorithm to attract UAVs to one or a set of bounded geometric shapes while avoiding collisions, re-configuring in the event of departure or addition of UAVs and maneuvering in mission space while retaining the configuration. Using potential field theory, weighted vector fields are described to attract UAVs to a desired formation. In order to achieve this, three vector fields are defined: one attracts UAVs located outside the formation towards bounded geometric shape; one pushes them away from the center towards the desired region and the third controls collision avoidance and dispersion of UAVs within the formation. The result is a control algorithm that is theoretically justified and verified using MATLAB which generates velocity vectors to attract UAVs to a loose formation and maneuver in the mission space while remaining in formation. This approach efficiently scales to different team sizes
