Comparison between Optimal Control Allocation with Mixed Quadratic & Linear Programming Techniques

The paper provides a comparison between different control allocation techniques in over-actuated Autonomous Underwater Vehicles. The pseudoinverse, Linear Programming (LP), Quadratic Programming (QP), Mixed Integer Linear Programming (MILP) and Mixed Integer Quadratic Programming (MIQP) are evaluated in simulation on the V-Fides vehicle model. The MILP and MIQP techniques allow to include in their implementations a more detailed characterization of the non-linear static behaviour of the actuators. This customizability can be also exploited to improve the practical stability of the system. The metrics used for comparison include the maximum attainable forces and torques, the integral of the error allocation and the required thrusters effort. Our simulation results show that, in particular with respect to thrusters effort, MILP and MIQP are the preferred allocation methods. The computational complexity associated to both methods is not such to compromise their implementation in operating vehicles; in particular, the MILP version is currently implemented in the V-Fides vehicle.