Distance-constrained formation tracking control

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 introducing a proportional control gain term to a gradient controller that stabilizes infinitesimally rigid formations, we are able to prove stability of the formation error dynamics with velocity input while ensuring that the steady state formation error is bounded. Upper bounds on the steady-state error are also given in terms of properties of the specified formation. Numerical simulations are shown to illustrate the theoretical results.