Parameter Search

To maximize PF on the selected plume data, the next-hit procedure was used to ex-

amine a range of parameter values across all algorithm types. In all, 7 Straight,

49 Step, 94 Zig-Zag, and 48 Spiral algorithms were evaluated. The parameter

stantial region of the parameter space but do not represent an exhaustive search. To reduce simulation requirements and simplify evaluation procedures, the maximum agent speedVwas limited to twice the average flow speed in the plume, and the search time-out valueU was fixed to 50 seconds for all algorithms.

Table 6.3: Parameter Evaluation Ranges. Parameter definitions can be found in Table 6.2 Behavior V [cm/s] U [s] D [cm] b [rad] G [cm]

Straight 0.1-10 50 - - -

Step 0.1-10 50 1-30 - -

Zig-Zag 1-10 50 2-30 π/2.1 - π/5 -

Spiral 2-10 50 5-20 - 2-20

To illustrate the evaluative process, data is presented from the best algorithm of each type at σ = 0. These algorithms are referred to as Straight, Step, Zig-Zag, and

Spiral respectively, and their parameters are shown in Table 6.4. Table 6.4: Optimal Parameter Values at σ= 0 Algorithm V [cm/s] U [s] D [cm] b [rad] G [cm]

Straight 2 50 - - -

Step 10 50 20 - -

Zig-Zag 5 50 10 π/2.5 -

Spiral 10 50 20 - 5

For the subsequent graphs, the plume data set was split into 10 sections of 250 frames. The metrics (PH, T, X, Y, PF) were calculated at every 10th frame, pooled

within each section, and then compared across sections so standard error information could be generated. In sample tests this procedure was shown to produce results that were not significantly different from data generated from 25 sections of 100 frames each in which all frames were evaluated, and reducing the number of evaluated frames offers a substantial savings in evaluation time. An evaluation of a single algorithm using the reduced data sampling takes 190 minutes on a 1 GHz Pentium III.

Figure 6.4a shows the probability of receiving the next odor hit PH versus wind

ing another plume hit decreases across all of the algorithms, although by different amounts. Step has the lowest off-axis performance because it moves quickly out of the plume. Straight takes the same trajectory but a lower velocity allows more time within the plume envelope to receive an odor hit. Zig-Zag and Spiral are more ef- fective at maintaining contact with the plume. Performance is not symmetric with respect to the wind error because the algorithms are not symmetric with respect to the plume axis. However, alternating the orientation of the behaviors after each hit will average out the differences, so the absolute value of the wind error is the critical value. −1.5 −1 −0.5 0 0.5 1 1.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Wind Direction Error [rad]

Probability of Receiving Next Plume Hit

Straight Step Zig−Zag Spiral −1.50 −1 −0.5 0 0.5 1 1.5 2 4 6 8 10 12 14 16 18

Wind Direction Error [rad]

Expected Time of Next Plume Hit [s]

Straight Step Zig−Zag Spiral

(a) (b)

Figure 6.4: (a) Odor hit probability for each of the different plume tracing algorithms. (b) Expected time to next odor hit for each of the different plume tracing algorithms. Note that if the odor hit probability is low then the expected time of the next odor hit is of little importance. All error bars represent standard error of the mean.

Figure 6.4b shows the expected time T of receiving the next odor hit versus wind error. Note that since lower times are better,Straight can be said to be performing the best of all the behaviors, although this is largely correlated with its low hit probability and therefore is not a useful feature. The large times shown for Spiral suggest that for some wind error values it is able to regain plume contact after initially exiting the plume envelope.

hit for all of the behaviors versus wind error. Larger metric values are better because they indicate that fewer hits are necessary to traverse the plume, so Spiral is the performance leader in this category. Straight suffers due to its low velocity, because even though it has a higher probability of getting a hit than Step, it also requires more consecutive hits to reach the plume source.

−1.5 −1 −0.5 0 0.5 1 1.5 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Wind Direction Error [rad]

Expected X Location of Next Plume Hit [m]

Straight Step Zig−Zag Spiral −1.5 −1 −0.5 0 0.5 1 1.5 −0.03 −0.02 −0.01 0 0.01 0.02 0.03

Wind Direction Error [rad]

Expected Y Location of Next Plume Hit [m]

Straight Step Zig−Zag Spiral

(a) (b)

Figure 6.5: (a) Expected downstream traversal before next odor hit for each of the different plume tracing algorithms. Error bars represent standard error of the mean. (b) Expected cross-stream traversal before next odor hit for each of the different plume tracing algorithms. Error bars represent standard error of the mean.

Figure 6.5b shows the expected cross-stream locationY of receiving the next odor hit for all of the behaviors versus wind error. The cross-stream movement of Spiral

and ZigZag renders their curves asymmetric, although the behaviors can be mirrored after each hit so the net cross-plume travel tends toward 0.

Figure 6.6a shows that for this plume with 0 wind noiseZig-Zag performs the best of this group of algorithms, and its near-perfect performance is not surprising given the rather simple structure of the plume being tracked. Spiral does almost as well, but the simpler algorithms do significantly worse. A tougher test of an algorithm’s capability comes when wind information is not perfect. The algorithms shown are not the best found for larger wind direction errors, but they demonstrate the relevant trends. As the wind information degrades, performance falls as well, suggesting that investing in the development of a good wind sensor is critical. Also, more complex

plumes in which large-scale meander separates the plume axis from the wind axis may be difficult to track effectively.

−1.50 −1 −0.5 0 0.5 1 1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Wind Direction Error [rad]

Probability of Successful Plume Traversal

Straight Step Zig−Zag Spiral 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SD of Wind Direction [rad]

Probability of Successful Plume Traversal

Straight Step Zig−Zag Spiral

(a) (b)

Figure 6.6: (a) Expected probability of successful source locationPF for each behavior. (b) Expected probability of successful source locationPF for each behavior. Note that the algorithms shown are optimized forσ= 0, so better performance may be achievable at higher wind variances.

Combining the above data according to the expected heading error frequency for a given wind sensor error standard deviation σ leads to the data seen in Figure 6.6b. This graph directly relates sensor error to algorithm performance, although the relationships between the individual algorithms as the wind error grows are not par- ticularly relevant because these are only the optimal algorithms for σ = 0. However, as one might expect, the trend of decreasing performance with increasing wind error holds across all algorithms.