Predefined-time robust three-dimensional formation control of underactuated autonomous underwater vehicles under input saturations.

In this paper, a predefined-time (PT) robust three-dimensional (3-D) formation control scheme is proposed for underactuated autonomous underwater vehicles (AUVs) subject to input saturations, uncertain dynamics and unknown time-varying ocean environment disturbances. Based on the idea of PT control, a new predefined-time stability criterion (PTSC) is created, whose Lyapunov inequality involves only one fractional power term by means of a piecewise constant function. Using the created PTSC, a novel predefined-time integral sliding mode disturbance observer (PTISMDO) is designed to estimate the compound disturbances lumped by the uncertain dynamics and the unknown environment disturbances, whose estimation errors are ensured to converge to zero within a predefined settling time (ST). A prescribed performance function that reaches its terminal value at a specified time is then introduced to constrain the formation errors, and an error mapping transforms the constrained errors into equivalent unconstrained variables. An auxiliary dynamic system (ADS) is constructed to address the input saturations. Incorporating the PTISMDO and the ADS into the dynamic inversion control method, a PT robust 3-D formation control law is proposed for each follower AUV to maintain a desired relative position with the leader, while ensuring that the formation errors reach and stay inside the prescribed tolerance error bands within a predefined ST such that all AUVs can move in a desired 3-D formation pattern. Simulation results and comparisons validate the effectiveness and superiority of the proposed formation control scheme.