Sliding mode formation control of leaderless unmanned surface vehicles with environmental disturbances

This paper, in light of the sliding mode control (SMC) approach, concerns the formation regulation for a network of unmanned surface vehicles (USVs) with environmental disturbances. The formation pattern is configured within the consensus-based leaderless framework. Undirected connected graphs are exploited to portray the network communication in a switching manner. To begin with, thanks to the definition on relative formation error, one mathematically formulates the concerned formation control problem into the leaderless consensus design for resultant formation error systems. Then an integral-type sliding surface is constructed by a collection of neighboring USVs’ position and velocity information. Based on a characterized orthogonal transformation, the regulation of the formation performance upon the sliding surface is cast into the asymptotic stability analysis of the reduce-order sliding mode system. By partitioning the state space into agreement and disagreement subspaces, a formation reference function (FRF) with determined initial condition is derived as a disturbance-free autonomous system, whose dynamical behavior explicitly symbolizes the global movement of the leaderless USV formation system. Finally, to ensure the finite-time reachability of the sliding surface, a distributed sliding mode controller is designed by utilizing the tool from finite-time stabilization technique. As a byproduct, the theoretical analysis is extended to the case of fixed topology. The derived results are validated by some numerical examples. •The consensus-based leaderless framework is exploited to regulate the formation.•The partition-based technique is proposed to determine the agreement dynamic.•The global movement of the formation system is symbolized by a FRF.•A novel sliding surface is constructed to promisingly control the state trajectory.•A novel SMC controller is designed by finite-time stabilization technique.