Flocking of a team of Lagrangian agents

Flocking of a team of Lagrangian agents is investigated in this paper. The motion equation of agents with Lagrangian dynamics and its properties are reviewed. The centrifugal and coriolis effects and gravitational terms in the dynamics of agents have been neglected in previous works on flocking problem. However the dynamics of many dynamical systems which would be the agents in practical applications can be assumed as Lagrangian with the above mentioned terms. The proposed flocking scheme is based on a gradient algorithm in which the collective potential is systematically constructed to cause the velocity of the agents to reach a consensus. It is explained that the suggested algorithm satisfies three rules of flocking demonstrated by Reynolds: cohesion, separation, and alignment. For this purpose the Hamiltonian of a team of agents with Lagrangian dynamics is considered and is treated as the Lyapunov like for the Multi-Agent system. Then considering the properties of the Lagrangian systems and also using the algebraic graph theory, it is shown that the derivative of the Hamiltonian is in order that the Reynolds´ rules are satisfied and the conditions under which flocking is achieved are derived. The analytical tools provided here are relayed on algebraic graph theory, matrix theory, and control theory. In simulation results, a group of wheeled mobile robots are used to show the effectiveness of the suggested algorithm.