Optimal Thrust Allocation Methods for Dynamic Positioning of Ships

The first Dynamic Positioning (DP) systems emerged in the 1960’s from the need for deep water drilling by the offshore oil and gas industry, as conventional mooring systems, like a jack-up barge or an anchored rig, can only be used in shallow waters. GustoMSC has been developing DP drill ships since the early 1970’s and it is still one of their core businesses. DP systems automatically control the position and heading of a ship subjected to environmental and external forces, using its own actuators. The thrust allocator of a DP system is responsible for the thrust distribution over the actuators of the ship. Apart from minimizing the power consumption an ideal thrust allocator can also take other aspects into account, such as forbidden/spoil zones and thruster relations. Because the Lagrange multiplier method, used inhouse by GustoMSC for thrust allocation, cannot accurately describe fullscale DP systems with rudders and forbidden/spoil zones, new methods need to be explored. Various optimal thrust allocation methods for dynamic positioning of ships are considered and their practical use is tested with DP capability calculations and time domain simulations with online optimization routines. The shortcomings of Lagrange multiplier methods are illustrated and quadratic programming methods combined with disjunctive programming techniques are used to present a more elaborate solution to optimal thrust allocation problems. Using disjunctive programming each actuator is modeled by a finite union of convex polygons representing the attainable thrust region. This approach allows combinations of non-rotatable thrusters, rotatable azimuth thrusters with forbidden/spoil zones and main propeller/rudder pairs to be used. As a consequence the allocation problem decomposes into a finite number of subproblems that all need to be solved separately in order to find the optimal solution of the main problem. For time domain simulations the dynamic limitations of the thrusters are taken into account by adding more convex thrust regions to the problem. Briefly, the potential use of linear matrix inequalities for optimal thrust allocation problems is treated. The obtained results are discussed and conclusions are given.