Rigid formation control systems modelled by double integrators: System dynamics and convergence analysis

In this paper we study rigid formation control systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely, the formation stabilization system and the flocking control system. Certain novel observations on the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results. We also establish some links between single-integrator formation systems and double-integrator formation systems via a parameterized Hamiltonian system, which further provide stability criteria for different equilibria in double-integrator formation systems by using available results in single-integrator formation systems.