Optimal constrained control allocation in marine surface vessels with rudders

Abstract

A propeller with a rudder can produce a thrust vector within a range of directions and magnitudes in the horizontal plane for low-speed maneuvering and dynamic positioning. The set of attainable thrust vectors is non-convex because significant lift can be produced by the rudder only with forward thrust. We suggest to decompose the attainable thrust region into a finite union of convex polyhedral sets and derive a mixed-integer-like convex quadratic programming formulation of the optimal control allocation problem for marine vessels with any number of rudders as well as thrusters and other propulsion devices. Actuator rate and position constraints are explicitly taken into account. Using multi-parametric quadratic programming software, an explicit piecewise linear representation of the least-squares optimal control allocation law is pre-computed. It can be implemented with low computational complexity and high software reliability without the use of real-time optimization. The method is illustrated using a scale model ship in a basin.