Developing distributed control algorithms for multi-agent systems is difficult when each agent is modeled as a nonlinear dynamical system. Moreover, the problem becomes far more complex if the agents do not have sufficient number of actuators to track any arbitrary trajectory. In this paper, we present the first fully decentralized approach to formation control for networks of underactuated surface vessels. The vessels are modeled as three degree of freedom planar rigid bodies with two actuators. Algebraic graph theory is used to model the network as a directed graph and employing a leader-follower model. We take advantage of the cascade structure of the combined nonlinear kinematic and dynamic model of surface vessels and develop a reduced-order error dynamic model using a state transformation definition. The error dynamics and consequently all system states are then stabilized using sliding mode control approach. It is shown that the stabilization of the reduced-order error dynamics guarantees uniform global asymptotic stability of the closed-loop system subject to bounded uncertainties. The proposed control method can be implemented in directed time-invariant communication networks without the availability of global position measurements for any of the vehicles participating in the network. An example of a a network of five surface vessels is simulated to verify the effective performance of the proposed control approach.

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