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A distributed improved robust integral line-of-sight (RILOS) guidance-based sliding mode controller is designed for multiple underactuated autonomous surface vessels (ASVs) to perform cooperative maritime search operations. First, a parallel circle search pattern is designed based on the detection range of ASVs, which can provide the reference formation shape. Second, an improved RILOS method is presented by introducing an integral term into the improved robust LOS method, which can counteract the disadvantageous effect of the unknown sideslip angle and kinematic discrepancy simultaneously. Third, distributed improved RILOS guidance is presented by integrating the extended second-order consensus algorithm into the improved RILOS method; then, the desired heading angle and desired velocity are generated for the control system simultaneously. Finally, the fuzzy logic system is integrated into the sliding mode control (SMC) method to approximate the unknown nonlinear function; then, a distributed improved RILOS guidance-based SMC controller is presented for multiple ASVs. The closed-loop signals are proved to be stable by the Lyapunov theory. The effectiveness of the presented method is verified by multiple simulations.

Freeness occupies an important position in the study of hyperplane arrangements. In this paper, we conclude the freeness of three special classes of signed graphic arrangements based on the addition–deletion theorem and Abe’s free path theory.

In this paper, an improved robust line-of-sight (RLOS) guidance-based fuzzy sliding mode controller is presented to control underactuated ships to conduct the cooperative maritime search operation under the presented improved creeping line search method. First, considering that the ship cannot perform turning with corners, an improved creeping line search method is presented by integrating the Bezier method into the traditional creeping line search method to smooth the transition points with corners and employing the cubic spline interpolation method to generate continuous reference paths. Second, an improved RLOS guidance method is presented for the first time by exploring the idea of robust adaptive control to mitigate the chattering effect of the RLOS guidance. Third, the fuzzy logic system with approximate ability is integrated into the design of sliding mode controller to handle unknown nonlinear model dynamics and environmental disturbances. Finally, an improved RLOS guidance-based fuzzy sliding mode controller is presented. The closed-loop stability is guaranteed by the Lyapunov theorem. Comparative simulations are conducted to illustrate the advantages and verify the effectiveness of the presented method.