Optimal time-invariant formation tracking for a second-order multi-agent system

Given a multi-agent linear system, we formalizeand solve a trajectory optimization problem that encapsulatestrajectory tracking, distance-based formation control and inputenergy minimization. To this end, a numerical projectionoperator Newton’s method is developed to find a solution bythe minimization of a cost functional able to capture all thesedifferent tasks. To stabilize the formation, a particular poten-tial function has been designed, allowing to obtain specifiedgeometrical configurations while the barycenter position andvelocity of the system follows a desired trajectory.