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

•A class of ISM controllers is proposed to realize the autonomous navigation of UUMV.•The Lagrange equation of the model of the UUMVs is considered to design the online optimization controller based on ISM with ASG of the tracking error norm.•The suggested robust control solves the tracking of reference trajectories in the (x-y-z)-coordinates for the UUMV.•The realized ISM controller with ASG integral term is studied analytically, including the convergence and the rate convergence analysis.•The controller is robust with respect to a wide class of model uncertainties such as the tensor of inertia and non-potential forces (friction, hysteresis, Coriolis, damping, centripetal effects). 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.