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In this study, Lyapunov-based technique and graph theory are combined to address the problem of coordinated path following where multiple mobile robots are required to follow some prescribed paths while maintaining a desired inter-robot formation pattern. The authors address this problem by developing decentralised feedback law that drives each robot to its desired path while adjusting its speed to the nominal velocity profile based on the exchange of information with its neighbours. The decentralised feedback law builds upon a non-linear control strategy with integral actions, that decouples the path following from the coordination control problem, the obtained subsystems are shown to be in a cascade connection of each other and therefore the stability of the entire closed-loop system is guaranteed by the small-gain theorem. The authors explicitly address the situation where the exchange of information among mobile robots takes place according to a quantised communication network and provide conditions under which the complete coordinated path-following closed-loop system is stable. Finally, the theoretical results are validated by simulations on a platform of three mobile robots. [ABSTRACT FROM AUTHOR]

In this study, the authors solve the problem of uniform global asymptotic stabilisation and global exponential tracking for an underactuated ship with only two propellers. A unified backstepping design methodology is proposed to tackle both the stabilisation and tracking problems. The obvious advantage of this framework is that the controller design procedure is systematic and analytically simple. The study also addresses the tracking problem with constant bias of environmental disturbances. Simulation results are provided to validate our theoretical results. [ABSTRACT FROM AUTHOR]