In the first panel, the black contours shown are reachability front forecasts, at 6 hour intervals (with increasing line thickness for later times). The reachability front is the boundary of the largest set (the reachable set) that the glider can reach within that duration. It is computed by numerically solving our exact governing PDE for this time-optimal reachability front. The time-optimal path from the starting postion to the desired recovery position is shown by the purple curve.
In the second panel we show a zoom of the optimal path along with the reachability fronts and heading/velocity data along the optimal path. The red vectors are the optimal vehicle headings; the blue vectors, the current; and the green vectors, the resultant (sum of the current vector and propulsion vector in the heading direction).
In the third panel, the optimal heading angle (degrees, measured clockwise from true north) vs. time is shown. Note that time is plotted on the y-axis (so the starting time is on the bottom).
The fourth panel also shows the optimal heading angle with time, as a polar plot with time on the r-axis.
| Speed (cm/s) | Level Sets and Time-Optimal Path | Time-Optimal Path with Headings and Current | Optimal Headings vs. Time | |
|---|---|---|---|---|
| Rectangular | Polar | |||
| 50 |
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| 40 |
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| 30 |
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| 20 |
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