Improving the formation-keeping performance of multiple autonomous underwater robotic vehicles

This paper presents the application of the successive Galerkin approximation (SGA) approach to the nonlinear optimal and robust formation control of multiple autonomous underwater robotic vehicles (AURVs). A nonlinear change of coordinates and feedback is made such that the SGA algorithm developed for time-invariant nonlinear systems can be implemented to the formation control system under consideration in this paper. The formation-keeping performance is significantly improved by solving the associated Hamilton-Jacobi-Isaacs (HJI) equation with the SGA algorithm. The synthesized formation-keeping controller also has optimal and robust properties in comparison with the original control law designed for the formation system by using Lyapunov´s direct method. Simulation results are presented to demonstrate the improved formation-keeping performance of a leader-follower formation of AURVs in nonholonomic chained form.