Characterization of Partial Agent Collapses and Collision Avoidance

Characterize partial collapses of subsets of agents under entropy-regularized semi-discrete optimal-transport coverage control and develop conditions or mechanisms that enforce collision-free trajectories.

Background

The paper proves that when the entropy-regularization parameter exceeds the largest eigenvalue of the target-density covariance matrix, the fully collapsed configuration at the global barycenter is a strict local minimum. However, the authors note that this threshold addresses only full collapse: subsets of agents may cluster even below the threshold. Because coincident positions are admissible in the regularized formulation, the controller also does not guarantee collision-free trajectories. The unresolved problem is therefore to characterize partial clustering phenomena and to incorporate collision constraints or otherwise guarantee collision avoidance.