Distributed Harmonic-Covariance Feedback for Hole Closure in Planar Robot Swarms

What happened

The closed loop has a unique global trajectory from every safe initial state. This polynomial is evaluated through local operator applications.

The model data and initial state are supplied with procedures for approximation to any requested accuracy with explicit error bounds. Under these conditions, offline finite calculations produce rational lower bounds for the cumulative hole area on the time horizon without querying trajectory data.

These bounds converge to that cumulative area, whether finite or infinite. If it is finite, holes close in the time-averaged sense: the average normalized hole area over every fixed-length time window tends to zero as time tends to infinity.