## For Underwater Vehicles

Thor I. Fossen12, Tor Arne Johansen1 and Tristan Perez3 1Dept. of Eng. Cybernetics, Norwegian Univ. of Science and Techn. 2Centre for Ships and Ocean Structures, Norwegian Univ. of Science and Techn. 3Centre of Excellence for Complex Dyn. Syst. and Control, Univ. of Newcastle,

12Norway 3Australia

### 1. Introduction

A control allocation system implements a function that maps the desired control forces generated by the vehicle motion controller into the commands of the different actuators. In order to achieve high reliability with respect to sensor failure, most underwater vehicles have more force-producing actuators than the necessary number required for nominal operations. Therefore, it is common to consider the motion control problem in terms of generalised forces â€”independent forces affecting the different degrees of freedomâ€”, and use a control allocation system. Then, for example, in case of an actuator failure the remaining ones can be reconfigured by the control allocation system without having to change the motion controller structure and tuning.

The control allocation function hardly ever has a close form solution; instead the values of the actuator commands are obtained by solving a constrained optimization problem at each sampling period of the digital motion control implementation loop. The optimization problem aims at producing the demanded generalized forces while at the same time minimizing the use of control effort (power).

Control allocation problems for underwater vehicles can be formulated as optimization problems, where the objective typically is to produce the specified generalized forces while minimizing the use of control effort (or power) subject to actuator rate and position constraints, power constraints as well as other operational constraints. In addition, singularity avoidance for vessels with rotatable thrusters represents a challenging problem since a non-convex nonlinear program must be solved. This is useful to avoid temporarily loss of controllability. In this article, a survey of control allocation methods for over-actuated underwater vehicles is presented. The methods are applicable for both surface vessels and underwater vehicles.

Over-actuated control allocation problems are naturally formulated as optimization problems as one usually wants to take advantage of all available degrees of freedom (DOF) in order to minimize power consumption, drag, tear/wear and other costs related to the use of control, subject to constraints such as actuator position limitations, e.g. Enns (1998), Bodson (2002) and Durham (1993). In general, this leads to a constrained optimization problem that is hard to solve using state-of-the-art iterative numerical optimization software at a high sampling rate in a safety-critical real-time system with limiting processing capacity and high demands for software reliability. Still, real-time iterative optimization solutions can be used; see Lindfors (1993), Webster and Sousa (1999), Bodson (2002), Harkegard (2002) and Johansen, Fossen, Berge (2004). Explicit solutions can also be found and implemented efficiently by combining simple matrix computations, logic and filtering; see S0rdalen (1997), Berge and Fossen (1997) and Lindegaard and Fossen (2003).

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