Abstract
The principle of dynamic positioning with thrusters is described and the problem of thrust allocation discussed. To allocate the demand for surge and sway forces and yaw moment from the DP controller to a greater number of thruster variables requires some extra mathematical conditions to make the problem uniquely solvable. Often the extra conditions are obtained by formulating a criterion for optimal thruster usage, typically an allocation that is power-minimal. Such problems usually cannot be solved without resorting to numerical search methods, which can be unattractive when the available time is scarce, which is the case when DP with allocation is used in model testing or when a large number of long stochastic simulations need to be carried out. For such cases, simple weighted least squares allocation with linear equality constraints is an attractive alternative. This method is very close to being power minimal provided the weights are chosen correctly. To handle cases of thruster saturation a method is proposed, which uses bias thrust and a certain matrix of nullspace vectors. A similar principle is proposed for presetting of favourable angles for azimuth thrusters to reduce the effect of the slow azimuth response.