  A technique that allows a formation-enforcing control (FEC) derived from
graph rigidity theory to interface with a realistic relative localization
system onboard lightweight Unmanned Aerial Vehicles (UAVs) is proposed in this
paper. The proposed methodology enables reliable real-world deployment of UAVs
in tight formation using real relative localization systems burdened by
non-negligible sensory noise, which is typically not fully taken into account
in FEC algorithms. The proposed solution is based on decomposition of the
gradient descent-based FEC command into interpretable elements, and then
modifying these individually based on the estimated distribution of sensory
noise, such that the resulting action limits the probability of overshooting
the desired formation. The behavior of the system has been analyzed and the
practicality of the proposed solution has been compared to pure
gradient-descent in real-world experiments where it presented significantly
better performance in terms of oscillations, deviation from the desired state
and convergence time.
