## Info

1 Cz /\

' * ) l C3 1

\ C* J

Fig. 4. Depiction of the Go to Point With Heading mode.

Fig. 4 shows an example of Go to Point with Heading mode. The AUV starts from position p1 with orientation angle d1 and should go to position p2 with orientation angle d2. Here we use two unit vectors V1 and V2 to represent the start and destination positions and orientation angles. First, we generate four circles C1, C2, C3, C4, whose radii are the minimal allowed turning radius Rm. The first two circles C1, C2 are tangent to V1 at p1: C3, C4, are tangent to V2 at p2. Note that arcs C1, C4 are counterclockwise and C2, C3 are clockwise. Second, we generate four line segments Lij, where i=1,2 and j=3,4 (only showing two lines in Fig. 4). Line Lij connects Ci to Cj in a continuous fashion. Now, we have four possible candidate paths, namely, C1L13C3; C1L14C4; C2L23C3; C2L24C4. Third, we calculate the length for each of the four candidate paths and select the shortest path as the trajectory for the AUV.

### 4.4 Cage

The Cage mode has two responsibilities related to the safety of the AUV. First, it should prevent the AUV from leaving the operating area or return the AUV to the operating area if it has left the operating area. Second, if the AUV is more than 30 m outside the operating envelope, then the Cage mode must abort the mission. Aborting the mission in the latter case is straightforward.

When the AUV is outside the OpArea or is near (within 5 m) an edge, we find the outward unit normal N=[Ne,Nn] and the distance 8 to the nearest edge. If the AUV is inside the OpArea (i.e., 0<8<5), then the commanded heading that results from the guidance system is modified to remove a portion of its outward component:

where "atan2" is the four quadrant arc tangent function. Therefore, when inside the OpArea, the AUV should not drive itself out of the OpArea; however, a navigation fix could instantaneously change the computed AUV position to be outside of the OpArea. If the AUV is outside the OpArea, then the heading command is = atan2(-Ne,-Nn).

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