Multi-time-scale 3-D coordinated formation control for multi-underactuated AUV with uncertainties: Design and stability analysis using singular perturbation methods

This paper is concerned with a multi-underactuated AUV three-dimensional (3-D) formation control method with a multi-time-scale structure in the presence of uncertain nonlinearities and environmental disturbances. First, a double-layer independent position-velocity fixed topology is adopted to overcome the drawback of narrow bandwidth of underwater communication. Then, an extended high-gain observer (EHGO) is utilized to provide compensation to uncertain nonlinearities and environmental disturbances. Moreover, the consensus theory is incorporated with an integral sliding mode controller to guarantee that the multi-underactuated AUV system can track the desired trajectory while maintaining the predefined formation. In addition, based on the analysis for the whole formation control system, the extended high-gain observer is on the ultra-fast time scale, the integral sliding mode controller is on the fast time scale, and the system state converges to the desired state on the slow time scale. Such multi-time scale structure allows independent analysis of the dynamics in each time scale, and the singular perturbation method is effectively utilized to establish the exponential stability of the equilibrium. Finally, simulation results are presented to illustrate the control performance.