Global finite-time guidance algorithm and constrained formation control using novel nonlinear mapping function for underactuated multiple unmanned surface vehicles

Abstract

The formation control issue of multiple underactuated unmanned surface vehicles (USVs) with state constraints is discussed in this work. First, the leader–followers system is used to present a global finite-time guidance algorithm for followers with velocity constraints. This algorithm can handle the case where the starting formation is not the intended formation. Second, the state constraints of the USV control subsystem is then handled by a novel nonlinear mapping function (NMF), which has the following benefits: (1) The designed NMF can respond to changing conditions with flexibility since it can handle symmetric constraints. (2) The situation where constraint bounds trend to infinity can be handled by it. (3) The designed NMF has a speed factor that enables it to be modified to track speed. Third, finite-time constrained controllers are proposed to provide formation control for multiple USVs by utilizing the unconstrained system. Next, while guaranteeing that the states are contained within the bounds, the theoretical analysis verifies that the system tracking error stabilizes in finite time and establishes the boundedness of all tracking error signals. To confirm the accuracy and superiority of the theoretical results, two case studies are created.