**4. Overall control system**

Overall, the control system of any autonomous underwater vehicle consists of a control law module and a control allocation module. The former is responsible for generating the generalised force in 6 DoF based on current and desired states, while the latter is responsible for distributing this generalised force amongst the actuators of the vehicle. Due to the modularity of such a control system, each of these subsystems can be designed and implemented independently, yet both must work cooperatively in order to accurately control the vehicle.

As discussed, the inputs to the control system are the desired state from the guidance system, and the current state from the navigation system. These are also the inputs to the control law. The outputs from the control system are the control signals that are sent to the individual actuators on the vehicle, which are the outputs generated by the control allocation. The intermediate signals connecting the control law to the control allocation are the 6 DoF generalised forces which are the outputs from the control law and therefore the inputs to the control allocation. Figure 3 shows the overall control system. As can be seen, the modularity of the system allows for control laws and control allocation schemes to be easily replaced, provided the inputs and outputs are of the same dimensions.

Fig. 3. Overall Control System Block Diagram.

For comparison purposes, both the uncoupled SMC law and the coupled SMC law are simulated here. Both simulations consist of identical control allocation modules that contain the previously described 2-stage scheme. The vehicle model used for these simulations is based on that which was proposed by Prestero (2001a, 2001b). This is a mathematical model for the REMUS (Remote Environmental Monitoring Unit) underwater vehicle developed by the Woods Hole Oceanographic Institute's Oceanographic Systems Laboratory. Alterations have been made to this model, based on current technology, which enable the vehicle to become fully actuated. These changes include the placement of four tunnel thrusters, two fore and two aft, such that sway, heave, pitch, and yaw motions are possible without any water flow over the control surfaces. Furthermore, the position of the vertical thrusters along the *y*-axis of the body, and the position of the horizontal thrusters along the *z*-axis of 162 Autonomous Underwater Vehicles

Overall, the control system of any autonomous underwater vehicle consists of a control law module and a control allocation module. The former is responsible for generating the generalised force in 6 DoF based on current and desired states, while the latter is responsible for distributing this generalised force amongst the actuators of the vehicle. Due to the modularity of such a control system, each of these subsystems can be designed and implemented independently, yet both must work cooperatively in order to accurately

As discussed, the inputs to the control system are the desired state from the guidance system, and the current state from the navigation system. These are also the inputs to the control law. The outputs from the control system are the control signals that are sent to the individual actuators on the vehicle, which are the outputs generated by the control allocation. The intermediate signals connecting the control law to the control allocation are the 6 DoF generalised forces which are the outputs from the control law and therefore the inputs to the control allocation. Figure 3 shows the overall control system. As can be seen, the modularity of the system allows for control laws and control allocation schemes to be

For comparison purposes, both the uncoupled SMC law and the coupled SMC law are simulated here. Both simulations consist of identical control allocation modules that contain the previously described 2-stage scheme. The vehicle model used for these simulations is based on that which was proposed by Prestero (2001a, 2001b). This is a mathematical model for the REMUS (Remote Environmental Monitoring Unit) underwater vehicle developed by the Woods Hole Oceanographic Institute's Oceanographic Systems Laboratory. Alterations have been made to this model, based on current technology, which enable the vehicle to become fully actuated. These changes include the placement of four tunnel thrusters, two fore and two aft, such that sway, heave, pitch, and yaw motions are possible without any water flow over the control surfaces. Furthermore, the position of the vertical thrusters along the *y*-axis of the body, and the position of the horizontal thrusters along the *z*-axis of

Control Law Control

τ

Allocation

*u*

easily replaced, provided the inputs and outputs are of the same dimensions.

Fig. 3. Overall Control System Block Diagram.

*x*

**4. Overall control system** 

control the vehicle.

*d x*

the body are set to 0m. Hence, there is no roll moment applied to the vehicle when these thrusters are activated. The thrusters introduced to the model are based on the 70mm IntegratedThrusterTM produced by TSL Technology Ltd. This particular device can provide a maximum thrust of 42N, and due to its compact size, is well suited to this particular application. Also, the propulsion unit has been altered within the model. The simulation model used contains a propulsion unit based on the Tecnadyne Model 540 thruster. This device is able to provide approximately 93.2N of thrust and, with a propeller diameter of 15.2cm, is therefore well suited for this application.

The trajectory that the vehicle is asked to follow here consists of a series of unit step inputs applied to each DoF. The translational DoFs experience a step input of 1 metre whereas the rotational DoFs experience a step input of 1 radian, or approximately 60°. All inputs are applied for a period of 20 seconds, such that both transient and steady state behaviour can be observed. These unit step inputs excite the vehicle in all combinations of DoFs, from a single DoF, through to all DoFs being excited at once. This simulation assumes no water current, and therefore no water flow over the vehicle when it is stationary. Hence, roll cannot be compensated for when stationary and for this reason this simulation does not excite the roll component of the model. All other DoFs are excited, however.

Due to the way the aforementioned trajectory is supplied to the vehicle model, no guidance system is present. The step inputs will be applied at set times regardless of the state of the vehicle, and therefore observation of the control performance can be observed without influence from unnecessary systems. Therefore total execution time is constant for all simulations. Performance metrics used here in evaluating each control system is the accumulated absolute error between the desired translation/rotation and actual translation/rotation for each DoF. By looking at the following plots, observations can be made regarding such time-domain properties as rise time, settling time and percentage overshoot.

Figures 4-13 show the desired and actual trajectories for each individual DoF when this complex set of manoeuvres is applied to both the uncoupled SMC and the coupled SMC. Figures 4, 6, 8, 10 and 12 show the complete trajectory for each DoF, while Figures 5, 7, 9, 11 and 13 show these same trajectories with the focus being on the last 300 seconds of the mission. This latter section of the mission is when multiple DoFs, particularly the rotational DoFs, are excited simultaneously.

Figure 4 shows the surge motion of the vehicle for the two different control systems. As can be seen, both systems exhibit desired properties for the first 180 seconds. During this period, all manoeuvring is exciting only the translational DoFs which the main propeller and tunnel thrusters can handle independently. After 180 seconds, the other DoFs are also excited, and the effect of this combined motion produces significant overshoots, especially for the uncoupled system, within the surge motion of the vehicle. This is more easily seen in Figure 5 where the larger overshoots can be seen for the uncoupled system compared to the coupled system.

The sway motion of the AUV is shown in Figure 6. Minor overshooting is observed for both systems, especially when rotational DoFs are excited in combination with the translational DoFs. This can be observed in Figure 7. However, when the sway motion is excited, convergence to the desired set point is observed.

Fully Coupled 6 Degree-of-Freedom Control of an Over-Actuated Autonomous Underwater Vehicle 165

Pitch motion is observed in Figure 10. The first observation that can be made from this plot is the relatively large spikes in the motion for both the coupled and uncoupled systems between 800 seconds and 1000 seconds. The second observation is that a steady state error is observed when the uncoupled system attempts a pitch of 1 radian. This is more clearly observed in Figure 11. Due to the vertical offset of the vehicle's centre of buoyancy from its centre of gravity, a restorative moment will always be applied to the vehicle for non-zero pitch angles. This plot indicates that it is difficult for the uncoupled system to compensate for this effect. However, the coupled system is able to not only eliminate this steady state error, it also has significantly smaller overshoot in general, as can be seen in Figure 10.

Fig. 6. Sway trajectory.

Fig. 7. Sway trajectory magnified.

Fig. 4. Surge trajectory.

Fig. 5. Surge trajectory magnified.

Heave motion is shown in Figure 8. Here, the initial position of the vehicle is chosen to be 10 metres below the surface of the water, such that the vehicle is completely submerged for the entire trajectory. When observing the heave motion in Figure 9, it is clear that when heave is excited, convergence to the desired set point is achieved. However, it is also evident that significant coupling exists between this DoF and other DoFs as divergence from the desired set point occurs when the heave motion is not excited.

Fig. 6. Sway trajectory.

164 Autonomous Underwater Vehicles

Heave motion is shown in Figure 8. Here, the initial position of the vehicle is chosen to be 10 metres below the surface of the water, such that the vehicle is completely submerged for the entire trajectory. When observing the heave motion in Figure 9, it is clear that when heave is excited, convergence to the desired set point is achieved. However, it is also evident that significant coupling exists between this DoF and other DoFs as divergence from the desired

Fig. 4. Surge trajectory.

Fig. 5. Surge trajectory magnified.

set point occurs when the heave motion is not excited.

Fig. 7. Sway trajectory magnified.

Pitch motion is observed in Figure 10. The first observation that can be made from this plot is the relatively large spikes in the motion for both the coupled and uncoupled systems between 800 seconds and 1000 seconds. The second observation is that a steady state error is observed when the uncoupled system attempts a pitch of 1 radian. This is more clearly observed in Figure 11. Due to the vertical offset of the vehicle's centre of buoyancy from its centre of gravity, a restorative moment will always be applied to the vehicle for non-zero pitch angles. This plot indicates that it is difficult for the uncoupled system to compensate for this effect. However, the coupled system is able to not only eliminate this steady state error, it also has significantly smaller overshoot in general, as can be seen in Figure 10.

Fully Coupled 6 Degree-of-Freedom Control of an Over-Actuated Autonomous Underwater Vehicle 167

Overall, the simulation trajectory used here is extremely complex as it excites all possible combinations of DoFs without any water current present. This level of complexity allows for the coupling that exists between DoFs within an AUV model to be highlighted. For example, looking at the period of 0 to 660 seconds in Figure 12, the yaw motion is not being excited, yet motion in this DoF is observed. This coupling between multiple DoFs is the reason why

Fig. 10. Pitch trajectory.

Fig. 11. Pitch trajectory magnified.

controlling AUVs is a complex and challenging task.

Fig. 8. Heave trajectory.

Fig. 9. Heave trajectory magnified.

Figure 12 shows the desired yaw motion of the vehicle. Here we can see significant overshooting from both systems, especially during the time period before the yaw motion is excited. By observing Figure 13, it can be seen that the coupled system achieves faster dynamics in terms of rise time, but the cost of this is overshoot. The uncoupled system has significantly less overshoot, and this is due to it taking slightly longer to react to trajectory changes.

Fig. 10. Pitch trajectory.

166 Autonomous Underwater Vehicles

Figure 12 shows the desired yaw motion of the vehicle. Here we can see significant overshooting from both systems, especially during the time period before the yaw motion is excited. By observing Figure 13, it can be seen that the coupled system achieves faster dynamics in terms of rise time, but the cost of this is overshoot. The uncoupled system has significantly less overshoot, and this is due to it taking slightly longer to react to trajectory

Fig. 8. Heave trajectory.

Fig. 9. Heave trajectory magnified.

changes.

Fig. 11. Pitch trajectory magnified.

Overall, the simulation trajectory used here is extremely complex as it excites all possible combinations of DoFs without any water current present. This level of complexity allows for the coupling that exists between DoFs within an AUV model to be highlighted. For example, looking at the period of 0 to 660 seconds in Figure 12, the yaw motion is not being excited, yet motion in this DoF is observed. This coupling between multiple DoFs is the reason why controlling AUVs is a complex and challenging task.

Fully Coupled 6 Degree-of-Freedom Control of an Over-Actuated Autonomous Underwater Vehicle 169

Due to the increased adoption of AUVs for civilian and defence operations, accuracy and reliability are two key factors that enable an AUV to successfully complete its mission. The control system is just one of the various components within the autonomy architecture of an AUV that helps in achieving this goal. Within the control system, the control law should be robust to both external disturbances and model parameter uncertainties, while the control allocation should utilise the various actuators of the vehicle to apply the desired forces to

PID control has been successfully implemented on a variety of systems to effectively provide compensation. However, since PID control is better suited to linear models, the level of performance provided by PID control is not to the same standard as other, particularly nonlinear, control schemes when applied to complex nonlinear systems. Sliding mode control has proven to be a control law that is robust to parameter uncertainties, and therefore is a prime candidate for implementation within this context due to the highly complex coupled nonlinear underwater vehicle model. Active utilisation of the coupled structure of this model is what coupled SMC attempts to achieve, such that induced motion in one DoF due to motion in another DoF is adequately compensated for. This is where coupled SMC has a distinct advantage over uncoupled SMC for trajectory tracking

Various schemes exist for control allocation with the ultimate goal being to apply the desired generalised forces while minimising power consumption, both due to the actuator usage and computational demands. Non-optimal schemes exist where a generalised inverse of the force produced by all actuators is used as the allocation scheme, with the limitation being that there is no functionality to bias actuators under certain operating conditions, such as utilising control surfaces over thrusters during relatively high speed manoeuvring. Quadratic programming incorporates a weighting matrix that can bias control surface usage over tunnel thrusters, and has been implemented both online and offline, with each having advantages and disadvantages. Online optimisation allows for changes to the actuator configuration, such as failures or varied saturation limits, but is computationally demanding. Offline optimisation is less computationally demanding during mission execution, but cannot allow for altered actuator dynamics. A compromise between these schemes is the proposed 2-stage scheme where control surfaces are utilised to their full

Overall, the goal of the control system is to provide adequate compensation to the vehicle, even in the presence of unknown and unmodelled uncertainties while also minimising power consumption and therefore extending mission duration. Choosing wisely both the control law and the control allocation scheme within the overall control system is

Uncoupled System 1.3173x104 (metres) 8.3713x103 (radians) Coupled System 1.2003x104 (metres) 6.7580x103 (radians)

Accumulated Absolute Rotational Error

Control System Accumulated Absolute

the vehicle while minimising the power expended.

applications when multiple DoFs are excited at once.

extent, and the tunnel thrusters used only when needed.

fundamental to achieving both of these goals.

**5. Conclusions** 

Translational Error

Table 1. Accumulated Absolute Translational and Rotational Errors.

Fig. 12. Yaw trajectory.

Fig. 13. Yaw trajectory magnified.

Furthermore, if the absolute error between actual and desired position is accumulated over the entire mission for each DoF, a measure of the accuracy of the control system can be obtained. A comparison can be made using Table 1. Here, we can see that by summing together the values obtained from the three translational DoFs, the coupled system improves upon the uncoupled system by 9.75%, while by summing together the values obtained from the three rotational DoFs, the coupled improves upon the uncoupled system by 23.87%. This indicates that the coupled system is superior to the uncoupled system for both translational and rotational motion, when looking at the accumulated absolute error.


Table 1. Accumulated Absolute Translational and Rotational Errors.
