Coordinate control of multi-UUVs formation under double independent topologies with time-vary delays

This paper provides a new method which uses consensus algorithm to solve the coordinate control problems of multi-UUVs in the case of leaderless formation. As band width is constraint in the water, a new topology method is proposed which divides the communication topologies into two independent parts, position communication topology and velocity communication topology. And in the novel communication topologies there are different time-varying delays. In additions, the math model of UUV is nonlinear and coupled. With the help of state feedback linearization method, the nonlinear math model of UUV can be transferred into a double-integrator dynamic model. Based on the result of linearized model, the UUVs formation coordinate control can be regarded as a consensus problem with time-varying communication delays. As a result, sufficient conditions for the stability of system are proposed and they are proven by using the Laypunov-Razumikhin theorem. In the end, the simulation results are presented to confirm and illustrate the theoretical results.