Behavior based chemical plume tracing

Fig. 5 displays the behaviors and switching logic used to implement CPT algorithms using BBP. In Fig. 5, S and d are Boolean variables. The symbols S and S indicate that the source location has or has not been declared, respectively. The symbol d indicates that chemical has been detected. The symbol d indicates that the behavior completed without detecting chemical. Prior to source declaration, whenever chemical is detected, the Track-In behavior

Fig. 5. Behavior Switching Diagram. The symbol d denotes a behavior switch that occurs when chemical is detected. The symbol d denotes a behavior switch that occurs when chemical is not detected prior to the end of the behavior. S indicates that the source location has been declared. S indicates that the source location has not been declared.

Fig. 5. Behavior Switching Diagram. The symbol d denotes a behavior switch that occurs when chemical is detected. The symbol d denotes a behavior switch that occurs when chemical is not detected prior to the end of the behavior. S indicates that the source location has been declared. S indicates that the source location has not been declared.

is triggered. Due to the intermittency caused by the turbulent flow, an instantaneous chemical reading below the detection threshold does not necessarily imply that the AUV is "out of the plume." Therefore, the sequence of behaviors Track-Out, Reacquire, Find is instantiated as the time since the last detection increases. The specific aspects of each behavior and the logic for switching between the behaviors are described in later. The planner is implemented on a PC104 computer that will be referred to as the Adaptive Mission Planner (AMP).

5.1 Go-To behavior

The Go-To behavior is used to drive the vehicle to a desired location. This is used for example at the start of a mission to maneuver the vehicle to a desired starting location. The Go-To behavior directly executes the Go-To guidance command.

5.2 Find behavior

Since there is no prior information about the location of the source, the AUV may be required to search the entire OpArea. Since the odor plume will be downflow from the source, the search is designed to start at the most downflow corner of the OpArea. From this starting location, the AUV should proceed across the flow until it either reaches a boundary of the OpArea or detects chemical. Although the largest component of the commanded velocity is across the flow, there must also be a component either up or down the flow so that the AUV will explore new locations in the OpArea. If chemical is detected, then the behavior switches to Track-In. If the AUV meets the boundary without detecting chemical, then the reaction is described below.

When the AUV arrives at a boundary, four candidate directions are computed as: ± 90 ± 20, where is the flow direction in degrees. Of these four candidate directions, the behavior selects the direction that maintains the same sign of the velocity along the boundary and reverses the sign of the velocity perpendicular to the boundary. When none of the four candidates satisfies this condition, then the motion is continued parallel to the boundary until the condition is achieved or another boundary is met. At such a corner, two directions of motion must be changed, and the solution can always be found. When the flow is parallel to a boundary, then this Find strategy results in a billiard ball type of reflection at the OpArea boundary.

5.3 Track-In behavior

Studies described in (Li et al., 2001) show that immediately following a chemical detection, good plume tracking performance is attained by driving at an angle P e [20,70] degree offset relative to upflow. When driving at a nonzero angle P offset relative to upflow and contact with the plume is ultimately lost, the AUV can predict which side of the plume it exited from and perform a counterturn to reacquire the plume. Such counterturning strategies are exhibited in several biological entities. The Track-in behavior implements an engineered version of such a strategy.

Pseudo-code for the Track-In behavior is contained in Table 1. The AMP will stay in TrackIn behavior as long as there has been an above threshold concentration sensed in the last X seconds. While chemical is being detected, AMP adjusts the commanded heading to be offset by LHS*P relative to the upflow direction = + 180. In this expression P is a constant and LHS is a variable that switches based on the relative directions of the AUV and flow. LHS is 1 if we expect the AUV to drive out of the plume from the left side (when looking upflow) of the plume. Otherwise, LHS is -1. Each time chemical is detected, the current AUV position is saved; therefore, when Track-In exits, the last detection point is available and saved in a list named lost_pnts.

Table 1. Pseudo Code for Track-In Behavior

As long as the AUV is detecting chemical at least every X seconds, it will make up flow progress. The actual AUV trajectory will include small angle, counter-turning oscillations relative to the upflow direction. If the AUV fails to detect chemical for X seconds, then AMP saves the last detection point (at most 6 points are saved) and switches to Track-Out.

5.4 Track-Out behavior

Pseudo-code for the Track-Out behavior is contained in Table 2. When the AMP switches to Track-Out, it has detected chemical slightly more than X seconds previously; in addition, there will be at least one point on the list of last detection points. Normally, the most recent detection point will be the last one on the list; however, since other behaviors manipulate the list, this is not guaranteed. Also, the variable LHS indicates on which side of the plume the AUV was located when contact with the plume was lost.

The Track-Out behavior attempts both to make progress towards the source (upflow) and to quickly reacquire contact with the plume. To accomplish these two objectives, AMP commands the AUV to go to a point that is Lu meters upflow and Lc meters across the flow from the most upflow point on the list of last detection points. The crossflow direction is selected so that, if chemical is not detected, the AUV is expected to end up on the opposite side of the plume, since crossing the plume increases the likelihood of detecting chemical. Track-Out ends either when chemical is detected or the AUV arrives at the commanded location. In either case the BBP checks whether it can declare a source location prior to determining the next maneuver. If the source is declared, then post-declaration maneuvering begins. If chemical is detected and the source location cannot be declared, then the behavior switches to Track-In. In this case, the AUV is at a location further up the plume than the previous most upflow detection point. If the AUV arrives at the commanded point without detecting and the source location cannot be declared, then the behavior switches to Reacquire.

Table 2. Pseudo Code for Track-Out Behavior. F is a unit vector in the direction of the flow. Fp is rotated positively by 90 degree relative to F in the horizontal plane. R, Lu, and Lc are positive constants.

Table 3. Pseudo Code for Reacquire Behavior 5.5 Reacquire behavior

Pseudo-code for the Reacquire behavior is contained in Table 3. When the AMP switches to Reacquire, it has not detected chemical for several seconds; however, there will be at least one point on the list of last detection points. Also, the variable LHS indicates the side of the plume on which the AUV was when it lost contact with the plume. To switch to the Reacquire behavior, the Track out behavior must have completed without detecting chemical. Therefore, several scenarios could have occurred:

• The AUV could be upflow from the source.

• The AUV could have crossed the (intermittent) plume without detecting chemical.

• If the LHS variable was incorrect, then the AUV would have moved further across the flow in the direction away from the plume.

In any of these cases, the AUV should next maneuver relative to the most upflow detection point. This Reacquire maneuver must be achievable by the AUV and useful in any of the three circumstances.

The maneuver that we designed, referred to as a Bowtie, is depicted in Fig. 6. The Bowtie maneuver first tracks a line that starts on the side of the plume on which we estimate that the AUV is located. This line is angled -15 degrees relative to upflow. The upflow 15 degree angle is small enough so that the transition to Track-In is smooth, if chemical is detected. If that line completes without a detection, then the AUV transitions to the start of a second line that passes through the same center point, but has an angle of 15 degrees relative to upflow. In Fig. 6, the narrow lines indicate distances while the wide lines show the nominal AUV trajectory. If the Bowtie completes without a detection, then the last line would be followed by a clockwise turn toward downflow, which would have a radius of at least 5.0 m.

Therefore, this maneuver explores at least 13 m on each side of its center in the direction perpendicular to the flow.

Fig. 6. Illustration of the BOWTIE maneuver used during the Reacquire maneuver. The image is not to scale.

The Reacquire behavior will perform at most N_re (>1) repetitions of the Bowtie in the vicinity of a single point on the lost point list. The first Bowtie is centered 10 m upflow from the most upflow point on the list of last detection points. The last Bowtie is centered on the most upflow point on the list of last detection points. The remaining (N_re-2) Bowtie centers are equally spaces between the first and last centers.

If this sequence of N_re Bowties completes without chemical detection, then the behavior removes the most upflow point from the list of last detection points. It then repeats the behavior at the most upflow point on the remaining list. This process repeats until a detection occurs or the list becomes empty. A detection at any time switches the behavior to Track-In. If the list becomes empty, then the AUV reverts to the Find behavior. If the AUV started the Reacquire behavior upflow from the source, the shape of the Bowtie repetitions, as the center point moves downflow towards the last detection point, provides useful information for accurately declaring the source location. If the AUV starts the Reacquire behavior after crossing the plume without detecting, the repetitions of the Bowtie give the AUV several more chances to detect odor. If the AUV starts the Reacquire behavior across the flow from the plume, the repetitions of the Bowtie, at and upflow from the most upflow last detection point, will bring the AUV back towards the location where the plume is likely to be. The Bowtie is sufficiently wide so that it is able to recontact the plume as long as the plume has meandered across the flow less than 13 m away from the most upflow last detection point.

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