Formation control of discrete-time nonlinear multi-glider systems for both leader–follower and no-leader scenarios under switching topology: Cases for a fleet consisting of a wave glider and multiple underwater gliders

Abstract

The formation control of multiple underwater gliders has been incredibly helpful in ocean research and inspection. However, it can be substantially challenging due to its underactuation, nonlinear dynamics, weak mobility, vulnerability to the ocean current, and long communication interval. Based on a fleet with a wave glider and multiple underwater gliders, this study introduces a formation control strategy suitable for leader–follower and no-leader scenarios under switching communication topology. The underwater gliders in the fleet are linearized by feedback linearization and the mathematical model is described in discrete time. The formation control protocol is established by combining the consensus of speed control in the forward direction with the path following control in the lateral direction and applying partial state information of the leader and followers under the randomly switching topology. By performing state transformation and analyzing matrix properties, sufficient conditions are obtained for the discrete-time glider systems under randomly switching topology to achieve the desired formation. Also, convergence results are derived whether the formation feasibility conditions are satisfied or not. Two cases for a fleet consisting of a wave glider and multiple underwater gliders are given in the numerical simulation and sea trials, including the leader–follower scenario for formation control during cruising, and the no-leader scenario for the coordination of underwater gliders in depth direction. The results of simulation and sea trials show that the theoretical results can be used to deal with the formation control problem for multi-glider systems.