In extreme wave conditions, single or multiple thrusters in the dynamic positioning system (DPS) are in saturated state. The conventional thrust allocation algorithm with the minimum power consumption as the optimization objective cannot fully exert capabilities of the propulsion system, thereby affecting the ship's positioning performance. In order to improve the adaptability of the thrust allocation algorithm of DP ships in extreme operating conditions, this paper proposes a novel saturation protocol to refine the thrust allocation algorithm, which can improve response speed to drastic changes in control force, and can give a more reasonable thrust allocation result. The effectiveness of the optimized algorithm is verified by time-domain simulation of a semi-submersible offshore platform operating in extreme wave conditions.


A dynamic positioning system (DPS) aims at regulating the horizontal position and heading of the vessel exclusively by means of its own propulsion system (Sørensen, 2011). With the ocean exploration and exploitation moving into deep and distant sea, the DPS has been increasingly used in offshore operations, such as offshore oil and gas drilling, underwater cable and pipe laying, diving support (Hassani et al., 2013). Further details on the DPS, including the early history, can be found in Morgan (1978) and Fay (1990).

Thrust allocation algorithm is a specific implementation method of the control action for a DP vessel. Its responsibility is to generate appropriate forces and moments to resist environmental loads and guarantee that the ship reaches the target equilibrium position (position and heading). The achieved force could be much smaller than the required force if the propulsion system cannot work normally due to its own limitations or failures, which can directly weaken the positioning capability of the vessel. In order to minimize this effect, DP vessels are usually equipped, with more than three thrusters, forming an over-actuated propulsion system to ensure their long-term work safety and reliability (Johansen, et al., 2004). The over-actuated system helps the vessel to obtain higher maneuverability and reliability. However, the increase in the number of thrusters also brought many challenges to the thrust allocation. For a given control force, there are multiple combinations of different thrusts and angles for the over-actuated system, but only one combination is actually needed. Therefore, thrust allocation is a constrained optimization problem whose objective is to minimize power consumption. And the constraints are usually to guarantee that the achieved thrusts equal to the commanded ones. Moreover, some other factors should also be taken into accounts such as singular configurations, hydrodynamic interaction, rate constraints on the azimuth angles, propeller speeds, see Durham (1993), Enns (1998), Bodson (2002), and Cozijn and Hallmann (2013). For the thrust allocation strategy of DPs, the solving of the constrained optimization problem in real time has been addressed by Harkegard (2002). Xu et al. (2016) proposed a dynamic forbidden sector skipping strategy, which can provide a more feasible zone for the azimuth thruster. Fossen and Johansen (2006) and Fossen (2011) have carefully classified and analyzed the existing thrust allocation algorithms. Ruth (2008) also summarized the existing literature on DP thrust allocation problem in detail.

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