Recursive nullspace-based control allocation with strict prioritization for marine craft

In control allocation it is often important to prioritize among the directions to produce control effort, especially in cases of limited capacity. Motivated by a requirement for strict prioritization among the control directions, a recursive nullspace-based allocation design based on direct use of the generalized pseudoinverses and nullspace matrices is proposed. The allocation design divides the overall problem into r subproblems according to a prioritization sequence, and a recursive method is proposed to solve the allocation subproblem in each step. By hiding the allocated controls from subsequent steps in the nullspace corresponding to the present step, the influence of lower priority control actions onto higher priority directions are nullified to achieve the specified prioritization. The method is verified by analyzing the thruster capacity of an Arctic intervention vessel based on experimental ice towing data.