A case study of formation constrained optimal multi-agent coordination

The centralized optimal multi-agent coordination problem is studied for a particular formation constraint. The problem is formulated as an optimal control problem, and the first-order necessary condition is derived analytically in a suitably chosen coordinate system. A candidate solution satisfying the necessary condition is proposed. The Jacobi equation characterizing the conjugate points along the candidate solution is derived and solved analytically by using the theory of matrix differential equations. The optimal centralized coordinated motions derived in this paper will yield a performance lower bound for those generated by decentralized algorithms.