where xr denotes the longitudinal position of the rudders relative to the adopted body-fixed reference system, Vpr0p is the flow velocity in the wake of the propeller, Nc is the yaw moment demanded by the vehicle motion controller. Step 3: Thruster Allocation

In nominal operational conditions, we can use the same demand for the two thrusters. This demand is computed to implement the desired thrust demanded by the controller and to compensate the drag induced by the fins and rudders

where Xc is the surge force demanded by the vehicle motion controller, and Xcs is the added resistance due to the deflection of all the control surfaces

Xcs = kD (8p2b + 88b) + kD (88 +881) + kD 8 +82 ), (1.57)

with the following drag related coefficients for the bow fins, stern fins, and rudders respectively

In this section, we have considered a case study and formulated the control allocation problem for a particular AUV with two thrusters and six control surfaces. We have made some simplifying assumptions and considered the nominal operational conditions. Similar modelling procedures to that followed in this case study can be applied to other AUV with different actuators.

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