Dynamic memory periodic event-triggered distributed practical fixed-time 3D formation control for underactuated AUVs

Abstract This article develops a dynamic memory periodic event-triggered (DMPET) distributed practical fixed-time control scheme for the 3D formation of underactuated autonomous underwater vehicles (AUVs) subject to uncertain dynamics and unknown external disturbances. These vehicles serve as mobile sensing and measurement platforms for ocean observation, seabed surveying, and environmental monitoring, in which the accuracy, availability, and timely transmission of relative-position measurement information, together with the reconstruction of unmeasurable quantities, fundamentally determine formation performance. Using a piecewise constant function, we create a novel sufficient condition of practical fixed-time stability (PFTS) which contains only a single fractional power term. Based on this novel PFTS sufficient condition, a practical fixed-time disturbance observer (PFTDO) is designed to estimate the compound disturbances, which are integrated by uncertain dynamics and unknown external disturbances. A DMPET communication mechanism between AUVs is designed as a resource-constrained sampling and transmission scheduling scheme to reduce communication resource consumption. A distributed practical fixed-time 3D formation control law is developed for each follower AUV by incorporating the PFTDO and DMPET communication mechanism into the dynamic surface design framework. Therein, a modified conditional disturbance negation term containing the compound disturbance estimation provided by the PFTDO can accelerate the convergence of tracking errors by compensating only for the disturbances that hinder it. The stability analysis reveals that the developed formation control scheme enables AUVs to achieve the desired formation within a fixed settling time. Simulation and comparative studies demonstrate the efficacy and advantages of the developed control scheme.