Robust 3-D autonomous navigation of submersible ship using averaged sub-gradient version of integral sliding mode

This study presents the design of a state feedback controller for an Unmanned Underwater Mobile Vehicle (UUMV) considering the implementation of an Averaged Sub-Gradient (ASG) version of the Integral Sliding Modes (ISM) method. The control problem is formulated here as an extreme seeking problem for the UUMV dynamics, which must track attainable reference trajectories in three-dimensional space. The dynamic nature of the UUMV induces the application of the extended version of ISM, where the integral term represents an ASG of the tracking error norm. The realized trajectory tracking is compared with the trajectories enforced by a traditional state feedback controller with gravity effect compensation. The proposed controller exhibits better tracking and similar control magnitude than the considered classical state feedback realization. These two results confirm the benefits of introducing the mixed extended strategy, including ISM and ASG as an extreme seeking controller for the considered UUMV.