**3. Control allocation**

The role of the control law is to generate a generalised force to apply to the vehicle such that a desired state is approached. This force, *τ*, for underwater vehicles consists of six components, one for each DoF, as seen in (23). The control allocation system is responsible for distributing this desired force amongst all available actuators onboard the vehicle such that this generalised 6 DoF force is realised. This means that the control allocation module must have apriori knowledge of the types, specifications, and locations, of all actuators on the vehicle.

Fully Coupled 6 Degree-of-Freedom Control of an Over-Actuated Autonomous Underwater Vehicle 159

for control surfaces on an AUV is to have four independently controlled fins arranged in two pairs orientated horizontally and vertically at the stern of the vehicle. The structure of *ti*

[ ] 010 0 *<sup>T</sup>*

These structures of *ti* show that horizontal surfaces produce a heave force as well as roll and pitch moments, while vertical surfaces produce a sway force as well as roll and yaw moments. What must be considered here is that the force being produced by control surfaces relies on the vehicle moving relative to the water around it. If the vehicle is stationary compared to the surrounding water, control surfaces are ineffective. However, if the vehicle is moving relative to the surrounding water, these actuators are capable of

The previously mentioned limitation of control surfaces can be overcome by the use of tunnel thrusters. These thrusters are usually implemented by being placed in tunnels transverse to the longitudinal axis of the vehicle. Similar to control surfaces, the typical arrangement is to position two horizontal tunnel thrusters equidistant fore and aft of the centre of gravity, and two vertical tunnel thrusters also equidistant fore and aft of the centre

[ ] 010 0 *<sup>T</sup>*

What can be observed here is that horizontal thrusters provide a sway force as well as a roll and yaw moment, while vertical thrusters provide a heave force as well as roll and pitch moment. In general, horizontal tunnel thrusters are located such that *lz* is zero, and vertical thrusters are located such that *ly* is zero. The result of this choice is that no roll moment is

The advantage of tunnel thrusters is that forces and moments can be produced even if the vehicle is stationary with respect to the surrounding water. This greatly increases the manoeuvrability of the vehicle, as control of the vehicle when moving at low speeds is possible. However, there are limitations associated with the use of these actuators. Firstly, these actuators consume more power when activated compared to control surfaces. This is due to force being produced by the thrusters only when the thruster itself is activated. In contrast, control surfaces consume power when the deflection angle is altered, but require very little power to hold the surface in place once the desired angle has been achieved.

applying forces and moments to the vehicle while consuming very little power.

*T <sup>i</sup> y x t ll* <sup>=</sup> <sup>⎡</sup> <sup>−</sup> <sup>⎤</sup> <sup>⎣</sup> <sup>⎦</sup> (36)

*<sup>i</sup> z x t ll* = − (37)

*<sup>i</sup> z x t ll* = − (38)

*T <sup>i</sup> y x t ll* <sup>=</sup> <sup>⎡</sup> <sup>−</sup> <sup>⎤</sup> <sup>⎣</sup> <sup>⎦</sup> (39)

for the horizontal fins is given in (36),

and for vertical fins given in (37).

**3.2.3 Tunnel thrusters** 

produced by these actuators.

of gravity.

001 0

The structure of *ti* for horizontal thrusters is given in (38),

while the structure for vertical thrusters is given in (39).

001 0

## **3.1 Role**

The role of the control allocation module is to generate the appropriate signals to the actuators in order for the generalised force from the control law to be applied to the vehicle. Since the vehicle under consideration is over-actuated, which means multiple actuators can apply forces to a particular DoF, the control allocation is responsible for utilising all available actuators in the most efficient way to apply the desired force to the vehicle. Power consumption is of particular importance for all autonomous vehicles, as it is a key factor in determining the total mission duration. The control allocation is therefore responsible for applying the desired forces to the vehicle, while minimising the power consumed.
