A proportional-integral controller for distance-based formation tracking

This work considers a multi-agent formation control problem where a designated leader is subjected to an additional velocity reference command. The entire formation should follow the leader while maintaining the inter-agent distance constraints. By augmenting a standard gradient formation controller with a proportional-integral control on the formation error, we are able to prove the stability of the formation error dynamics with velocity input while ensuring zero steady-state formation error. Numerical simulations are shown to illustrate the theoretical results.