Virtual strategies in the kinematic and dynamical models applied to fault-tolerant strategy of underwater vehicles by using state-dependent Riccati equations

A new kind of kinematic underwater vehicle modelling, which uses the screw theory and the Davis method, is proposed. This latter one makes possible to treat the direct and inverse kinematic in the same way, using virtual kinematic chains. By a specific way, the kinematic model allows simplifying the Jacobian matrix, since it is not restricted to the base frame. A transformation from Euler angles to Octonions avoids possible singularities. In addition, a new linear quadratic regulator control that uses the design of variables gains based on low-pass filter and l∞ norm. Global stability of the State-Dependent Riccati Equation is performed by using Lyapunov analysis with La'Salle's Principle. The allocation of faults in this strategy by using virtual fuzzy thrusters is addressed, which minimises the fault impact expressed as an abrupt discontinuity in the thruster system, as observed in the simulation results.