**7. Conclusion**

30 Will-be-set-by-IN-TECH

A cruise is started in a formation. However, very soon the formation encounters the first obstacle. As the leading formation-members are momentarily slowed down before they circumnavigate to either side of the obstacle, the trailing members "pile up" in front of this artificial potential barrier (especially the AUV closest to the origin). This is evident in the dips and temporary confusion before the first, circular obstacle. However, the operational safety approach that is implicitly encapsulated by the *cross-layer design* is preserved. The vehicles break formation, so that one of the vehicle circumnavigates the first obstacle on the left, and the others on the right. Since this produces a significantly different trajectory from the rest of

The other 3 vehicles (2, 3 and 4), before being able to restore a formation encounter the first of the two large rectangular obstacles. Note that vehicles 2 and 3 remain in the leader-follower arrangement as evidenced by their closely matching trajectories in this phase of the cruise. The "outrigger" vehicle 4, trying to keep in formation with 2 and 3, encounters the large rectangular obstacle at a bearing much closer to head-on. Therefore, it executes a significant course change manoeuvre, during which it cannot satisfactorily compromise between safe avoidance of the obstacle and staying in formation with 2 and 3. As vehicles 2 and 3 navigate in formation through the strait in between the circular and the first large rectangular obstacle, the leader vehicle 3 starts to manoeuvre to starboard towards the way-point. This manoeuvre causes the formation cell vertex trailing behind vehicle 3 that represents the dominant navigation goal for vehicle 2 to start accumulating speed in excess of what 2 is able to match. This is due to the fact that as 3 swings to starboard, the formation cell vertex "sweeps" through water with a velocity that consists of the sum of linear velocity of vehicle 3 and the tangential velocity contributed by the "arm" of the formation cell *f* . Therefore, the

However, the breaking of formation between 2 and 3 occurs at such a time that 1 catches up with 2 before 2 gets much farther afield, presenting its trailing cell vertex as a local navigation goal to 2. That is why 2 exhibits a hard break to starboard, trying to form itself up as a follower of vehicle 1. However, just as 2 is completing its formation, vehicle 1, manoeuvres around the final obstacle – the small diagonally presented rectangle. As the trailing cell vertex of 1 is, from 2's viewpoint, shadowed by the obstacle's repulsion, it reorients towards what until then is a secondary navigation goal in its vicinity – the cell vertex of the "latecomer" of Phase 2, vehicle 4. This reorientation is what contributes to 2's "decision" to circumnavigate the diagonal rectangle to starboard, rather than to port, as would be optimal if no formation influences were present. Phase 3 finishes as vehicle 2 is trying to pursue vehicle 4, and vehicle 4 corners

Phase 4 is entered into without formations. This phase is characterized by converging on the way-point, which all the vehicles reach independently, followed by re-establishing the formation. However, an ideal formation is impossible due to operational safety, as no vehicle is "willing" to approach the second large rectangle (towards the top of the figure). This is

the group, vehicle 1 isn't able to rejoin the formation until much later.

**6.2.1 Cruise phase 1**

**6.2.2 Cruise phase 2**

**6.2.3 Cruise phase 3**

**6.2.4 Cruise phase 4**

formation is temporarily completely broken.

the diagonal rectangle, getting away from vehicle 2.

The chapter has presented a virtual potentials-based decentralized formation guidance framework that operates in 2D. The framework guarantees the stability of trajectories, convergence to the way-point which is the global navigation goal, and avoidance of salient, hazardous obstacles. Additionally, the framework offers a *cross-layer* approach to subsuming two competing behaviours that AUVs in a formation guidance framework need to combine – a priority of formation maintenance, opposed by operational safety in avoiding obstacles while cruising amidst clutter.

Additionally to the theoretical contribution, a well-rounded functional hardware-in-the-loop system (HILS) for realistic simulative analysis was presented. Multiple layers of realistic dynamic behaviour are featured in the system:

