' uB '

fM _

, u =

UM _

Then we have the following equation with respect to the input of the vehicle:

MmVo + mbm< + NbbV + mBM< + /B — UB . And the time derivative of Equation (8) is s — Cv0 + D< + Cv0 + D<. Comparing with Equations (21) and (22), C — Mbb , D — Mbm , C — Nbb , D — Nbm and s — Ub - /b are obtained. Moreover,

œ1 x kn where bi =(a>i x ki )x (pe - pi ) + ki (pe - pi ). Therefore, all elements of W and W in Equation (16) can be calculated.

3.2 Disturbance compensation of vehicle

From the viewpoint of underwater robot control, parameters and coefficients of hydrodynamic models are generally used as constant values that depend on the shape of robots (Fossen, 1995). The RAC law (17) can reduce the influence of the modelling errors of hydrodynamics by position and velocity feedbacks. Here, to obtain higher control performance, the influence of hydrodynamic modelling error with respect to the vehicle is treated as a disturbance and a disturbance compensation method is introduced. First, the basic disturbance compensation is described. For MBB in Equation (21) the nominal model using constant values of added mass, added moment of inertia and drag coefficient is defined as MBB . Moreover, the basic disturbance is defined as mBB m BM

mmb mmm nmb n mm

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