**7.1 Underwater recovery**

The goal of underwater recovery (Yakimenko et al., 2008) is to be able to compute a rendezvous trajectory from any point on the UUV holding pattern to any point on the MURS holding pattern as shown in Fig.19 (note hereinafter that depth values are shown as negative numbers).

While the stochastic simulation shown in Fig.19 employs circular race tracks, in practice the MURS would establish a race track that allowed it to travel back and forth along two long track legs (see Fig.20). These legs are needed to allow sufficient time to contact the UUV (which is assumed to be in its holding pattern somewhere within communication range) and allow it to transit from its holding pattern to the rendezvous point. The proposed sequence of events is to have the MURS (at position 1 in Fig.20) signal the UUV (at position 2) and command it to proceed to a rendezvous point by a certain time. The UUV computes the trajectory required to comply with the command. If the commanded rendezvous is feasible, the UUV sends an acknowledgement message. Otherwise (i.e. the request violated some constraint) the UUV sends a denial message (stage A in Fig.20) and requests that the MURS command a different rendezvous point or time. The final point of the trajectory is located in the approximate location of the MURS docking station at a given time. Knowing the 88 Autonomous Underwater Vehicles

Fig. 18. Simulation results for vertical OA using UUV altitude control mode

The proposed path-planning method can be tailored to a specific vehicle or operational domain by modifying the performance index *J* to incorporate vehicle or actuator dynamics (feasibility constraints) and mission objectives such as OA or underwater rendezvous. This section presents simulated and in-water experimental results for four different applications which use the proposed trajectory optimization framework for UMV guidance: i) underwater docking of a UUV with a mobile underwater recovery system (MURS); ii) optimal exploitation of a terrain-relative feature map to improve UUV self-localization accuracy; iii) 2D or 3D OA in cluttered environments; and iv) specific USV implementations

The goal of underwater recovery (Yakimenko et al., 2008) is to be able to compute a rendezvous trajectory from any point on the UUV holding pattern to any point on the MURS holding pattern as shown in Fig.19 (note hereinafter that depth values are shown as

While the stochastic simulation shown in Fig.19 employs circular race tracks, in practice the MURS would establish a race track that allowed it to travel back and forth along two long track legs (see Fig.20). These legs are needed to allow sufficient time to contact the UUV (which is assumed to be in its holding pattern somewhere within communication range) and allow it to transit from its holding pattern to the rendezvous point. The proposed sequence of events is to have the MURS (at position 1 in Fig.20) signal the UUV (at position 2) and command it to proceed to a rendezvous point by a certain time. The UUV computes the trajectory required to comply with the command. If the commanded rendezvous is feasible, the UUV sends an acknowledgement message. Otherwise (i.e. the request violated some constraint) the UUV sends a denial message (stage A in Fig.20) and requests that the MURS command a different rendezvous point or time. The final point of the trajectory is located in the approximate location of the MURS docking station at a given time. Knowing the

**7. Computer simulations and sea trials** 

for sonar-based OA in riverine operations.

**7.1 Underwater recovery** 

negative numbers).

geometry of the MURS allows the planner to construct a "keep out" zone corresponding to the MURS propeller and aft control surfaces. The UUV rendezvous trajectory must avoid this area. Once the rendezvous plan has been agreed upon and acknowledged, both the UUV and the MURS proceed to position 3 for rendezvous (stage B). Finally, at position 4 the recovery operation (stage C) is completed.

Fig. 19. Manifold of initial and final conditions

Fig. 20. Proposed rendezvous scenario

The simulated rendezvous scenario assumes three stages: communication (A), execution (B), and recovery (C), respectively. From the trajectory generation standpoint we are primarily concerned with optimizing the path that would bring the UUV from its current position (point 2) to a certain rendezvous state (point 3) in the preset time *Tr* proposed by the MURS, while obeying all possible real-life constraints and avoiding the MURS keep out zone.

Figures 21 and 22 present a computer simulation in which a MURS is moving due east at 1*m*/*s* (1.94*kn*) with the docking station at a depth of 15m. A UUV is located 800 meters away. The MURS wishes to conduct a rendezvous operation *Tr* minutes later and sends the corresponding information to the UUV. This information includes the proposed final position *<sup>f</sup> x* , *<sup>f</sup> y* , *<sup>f</sup> z* rendezvous course, speed, and time. Figure 21 shows several generated trajectories, which meet the desired objectives for this scenario and also avoid an obstacle located along the desired path to MURS. These trajectories differ by the arrival time *Tr* .

During handshaking communications with the MURS, the UUV determines whether the suggested *Tr* is feasible. Of the four trajectories shown, the trajectory generated for

Real-Time Optimal Guidance and Obstacle Avoidance for UMVs 91

In the last decade, several different UUVs have been developed to perform a variety of underwater missions. Survey-class vehicles carry highly accurate navigational and sonar payloads for mapping the ocean floor, but these payloads make such vehicles very expensive. Vehicles which lack these payloads can perform many useful missions at a fraction of the cost, but their performance will degrade over time from inaccurate selflocalization unless external navigation aids are available. Therefore, it is interesting to consider collaborative operations via a team of vehicles for maximum utility at reasonable cost. The NPS CAVR has been investigating one such concept of operations called featurebased navigation. This technique allows vehicles equipped only with a GPS receiver and low cost imaging sonar to exploit an accurate sonar map generated by a survey vehicle. This map is comprised of terrain or bottom object features that have utility as future navigational references. This sonar map is downloaded to the low-cost follow-on vehicles before launch. Starting from an initial GPS position fix obtained at the surface, these vehicles then navigate underwater by correlating current sonar imagery with the sonar features from the survey vehicle's map. The localization accuracy of vehicles performing feature-based navigation can be improved by maximizing the number of times navigational references are detected with the imaging sonar. The following simulation demonstrates how the IDVD trajectory generation framework can be tailored to this application. By incorporating a simple geometric model of an FLS having a range of 60m, 30-degree horizontal FOV and operating at a nominal ping rate of 1Hz, a new performance index was designed to favour candidate trajectories, which point the sonar toward navigational references in the *a priori* feature map. For this example, we sought trajectories that could obtain at least three sonar images of each feature in the map. Figure 23 shows results of a computer simulation in which the number of times each target was imaged by the sonar has been annotated. The resulting trajectory is feasible (i.e. satisfies turn rate constraints) and yields three or more sonar images of all but

Fig. 23. Simulation results for a feature-based navigation application

**7.2 Feature-based navigation** 

two targets.

450 *T s <sup>r</sup>* = happens to be infeasible (the constraints on controls are violated). The solution of the minimum-time problem for this scenario yielded 488 seconds as the soonest possible rendezvous time.

The other three trajectories shown in Fig.21 are feasible. That means that the boundary conditions are met (by construction) and all constraints including OA are satisfied (via optimization). As an example, Fig.22 shows the time histories for the yaw rate ψ *<sup>c</sup>* and flight path angle *<sup>c</sup>* γ vehicle control parameters as well as the UUV's speed as it followed the trajectory for 600 *T s <sup>r</sup>* = .

Fig. 21. Examples of rendezvous trajectories

Fig. 22. Constrained vehicle parameters for 600 *T s <sup>r</sup>* =

Stochastic simulations of the manifolds shown in Fig.21 illustrate that a successful rendezvous can take place in all cases as long as *Tr* is greater than a certain value. Furthermore, they show that minimization of the performance index using the IDVD method ensures that a smooth, realizable trajectory is calculated in just a few seconds, regardless of the initial guess. Converting code to an executable file in lieu of using an interpretative programming language reduces execution time down to a fraction of a second.

#### **7.2 Feature-based navigation**

90 Autonomous Underwater Vehicles

450 *T s <sup>r</sup>* = happens to be infeasible (the constraints on controls are violated). The solution of the minimum-time problem for this scenario yielded 488 seconds as the soonest possible

The other three trajectories shown in Fig.21 are feasible. That means that the boundary conditions are met (by construction) and all constraints including OA are satisfied (via

Stochastic simulations of the manifolds shown in Fig.21 illustrate that a successful rendezvous can take place in all cases as long as *Tr* is greater than a certain value. Furthermore, they show that minimization of the performance index using the IDVD method ensures that a smooth, realizable trajectory is calculated in just a few seconds, regardless of the initial guess. Converting code to an executable file in lieu of using an interpretative programming language

vehicle control parameters as well as the UUV's speed as it followed the

ψ

*<sup>c</sup>* and flight

optimization). As an example, Fig.22 shows the time histories for the yaw rate

rendezvous time.

path angle *<sup>c</sup>*

γ

Fig. 21. Examples of rendezvous trajectories

Fig. 22. Constrained vehicle parameters for 600 *T s <sup>r</sup>* =

reduces execution time down to a fraction of a second.

trajectory for 600 *T s <sup>r</sup>* = .

In the last decade, several different UUVs have been developed to perform a variety of underwater missions. Survey-class vehicles carry highly accurate navigational and sonar payloads for mapping the ocean floor, but these payloads make such vehicles very expensive. Vehicles which lack these payloads can perform many useful missions at a fraction of the cost, but their performance will degrade over time from inaccurate selflocalization unless external navigation aids are available. Therefore, it is interesting to consider collaborative operations via a team of vehicles for maximum utility at reasonable cost. The NPS CAVR has been investigating one such concept of operations called featurebased navigation. This technique allows vehicles equipped only with a GPS receiver and low cost imaging sonar to exploit an accurate sonar map generated by a survey vehicle. This map is comprised of terrain or bottom object features that have utility as future navigational references. This sonar map is downloaded to the low-cost follow-on vehicles before launch. Starting from an initial GPS position fix obtained at the surface, these vehicles then navigate underwater by correlating current sonar imagery with the sonar features from the survey vehicle's map. The localization accuracy of vehicles performing feature-based navigation can be improved by maximizing the number of times navigational references are detected with the imaging sonar. The following simulation demonstrates how the IDVD trajectory generation framework can be tailored to this application. By incorporating a simple geometric model of an FLS having a range of 60m, 30-degree horizontal FOV and operating at a nominal ping rate of 1Hz, a new performance index was designed to favour candidate trajectories, which point the sonar toward navigational references in the *a priori* feature map. For this example, we sought trajectories that could obtain at least three sonar images of each feature in the map. Figure 23 shows results of a computer simulation in which the number of times each target was imaged by the sonar has been annotated. The resulting trajectory is feasible (i.e. satisfies turn rate constraints) and yields three or more sonar images of all but two targets.

Fig. 23. Simulation results for a feature-based navigation application

Real-Time Optimal Guidance and Obstacle Avoidance for UMVs 93

a)

b)

Fig. 24. Simulated 2D (a) and 3D (b) near-optimal OA trajectories

Fig. 25. REMUS sea trial results demonstrating periodic planning and path following
