Finite time stable path following system with nonlinear parameter varying model for USV

To address the impact of velocity variations and unknown disturbances on the path performance of an unmanned surface vehicle (USV), a novel path following system is developed, featuring a second-order sliding mode vector field guidance law (SOSVFG) and a finite-time stable controller (FTSNPV) for a nonlinear parameter-varying (NPV) model. Firstly, the USV model is reformulated based on kinematic and NPV dynamic models, and an SOSVFG with a non-singular terminal sliding surface is constructed using a vector field with varying surge velocity. Secondly, an FTSNPV controller for heading regulation is designed with H_∞ robust control theory and finite-time stability theory. Furthermore, the stability conditions of the FTSNPV controller are decoupled using the projection theorem and matrix transformation to compute control parameters through sum-of-squares (SOS) programming. Finally, simulation and experimental results demonstrate that the proposed path following system exhibits superior performance in two critical aspects: the SOSVFG generates smoother paths at high speeds, thereby enhancing navigation safety. Moreover, the FTSNPV controller achieves excellent dynamic and steady-state performance in heading regulation.