Chemical signal guided search is complicated by the nature of fluid flow and the resulting odor plume characteristics. An initial approach to designing an AUV chemcial plume-tracing strategy might attempt to calculate a concentration gradient. Gradient following based plume navigation algorithms have been proposed for a few biological entities that operate in low Reynolds number environments (Berg, 1990); however, gradient based algorithms are not feasible in environments with medium to high Reynolds numbers (Elkinton et al., 1984; Jones, 1983; Murlis et al, 1992). At low Reynolds numbers, the evolution of the chemical distribution in the flow is dominated by molecular diffusion resulting in a chemical concentration field that is reasonably well-defined by a continuous function with a peak near the source. At medium and high Reynolds numbers, the evolution of the chemical distribution in the flow is turbulence dominated (Shraiman & Siggia, 2000). The flow contains eddying motions of a wide range of sizes that produce a patchy and intermittent distribution of the above threshold chemical (Jones, 1983). For an image of the plume, the gradient is time-varying, steep, and frequently in the wrong direction. Even so, such plume images are not available to the AUV. Due to the rate of spatial and temporal variations in the flow and plume relative to the maneuvering limitations of existing AUV, gradient computation and following is not practical.
If a dense array of sensors were distributed over an area through which a turbulent flow was advecting chemical and the output of each sensor were averaged for a suitably long time (i.e., several minutes), then this average chemical distribution would be Gaussian (Sutton, 1947; Sutton 1953); however, the required dense spatial sampling and long time-averaging makes such an approach inefficient in a turbulence dominated environment (Naeema1 et al., 2007). It is known that the instantaneous chemical distribution will be distinct from the time-averaged plume (Jones, 1983; Murlis et al., 1992). The major differences include: the time-averaged plume is smooth and unimodal while the instantaneous plume is discontinuous and multi-modal; the time-averaged plume is time invariant (assuming ergodicity) while the instantaneous plume is time varying; instantaneous concentrations well-above the time-averaged concentration will be detected much more often than predicted by the Gaussian plume model. Such time-averaged plumes are useful for long-term exposure studies, but are not useful for studies of responses to instantaneously sensed chemical (Murlis et al, 1992). One of the reasons that olfaction is a useful long distance sense is the fact that instantaneous concentrations well above the time-average are available at significant distances from the source (Grasso, 2001). Turbulent diffusion results in filaments of high concentration chemical at significant distances from the source, but also results in high intermittency (Jones, 1983; Murlis et al., 1992; Mylne, 1992). Intermittency increases with down flow distance both due to the meander of the instantaneous plume caused by spatial and temporal variations in the flow and due to the increasing spread with distance of the filaments composing the instantaneous plume. High intermittency and large search areas motivate the need to acquire as much information as is possible from each chemical detection event.
The challenge using chemical signals on AUV is to design effective algorithms to trace the chemical plume and determine the chemical source location even though the chemical source concentration is not know, the advection distance of the detected chemical is unknown, and the flow varies with both location and time.
Various studies have developed biomimetic robotic plume tracing algorithms based on olfactory sensing. The most commonly used olfactory-based navigation algorithms is "chemotaxis" , which was introduced by Berg and Brown (Berg & Brown , 1972; Berg, 1993). This strategy is based on the detection of a concentration difference between two chemical sensors and a steering mechanism toward the direction of higher concentration with a constant moving speed. Chemotaxis-based navigational strategies yield smooth movement trajectories in the environment that the concentration is high enough to ensure its difference measured at two nearby locations is larger than typical fluctuations. Belanger and Willis (Belanger & Willis 1998) presented plume tracing strategies inspired by moth behavior and analyze the performance in a "wind tunnel-type" computer simulation. The main goal of that study was to improve the understanding of moth interaction with an odor stimulus in a wind tunnel. Grasso et al. (Grasso et al. 1996; Grasso, 2001; Grasso, et al., 2000) evaluate biometric strategies and challenge theoretical assumptions of the strategies by implementing biometric strategies on their robot lobster. Li et al. (Li et al., 2001; Li et al., 2006) develop, optimize, and evaluate a counter-turning strategy originally inspired by moth behavior. Vergassola et al. (Vergassola et al., 2007; Martinez 2007) proposed a search algorithm, "infotaxis", based on information and coding theory. For infotaxis, information plays a role similar to concentration in chemotaxis. The infotaxis strategy locally maximizes the expected rate of information gain. Its effciency was demonstrated using a computational model of odor plume propagation and experimental data on mixing flows. Infotactic trajectories feature zigzagging and casting paths similar to those observed in the fight of moths. Spears et al. (Spears et al., 2005; Zarzhitsky et al., 2004) developed a physics-based distributed chemical plume tracing algorithm. The algorithm uses a network of mobile sensing agents that sense the ambient fluid velocity and chemical concentration, and calculate derivatives based on formal principles from the field of fluid mechanics.
The fundamental aspects of these research efforts are sensing the chemical, sensing or estimating the fluid velocity, and generating a sequence of searcher speed and heading commands such that the motion is likely to locate the odor source. Typical maneuvers include: sprinting upflow upon detection, moving crosswind when not detecting, and manipulating the relative orientation of a multiple sensor array either to follow an estimated plume edge or to maintain the maximum mean reading near the central sensor. In each of these articles, the algorithms for generating speed and heading commands use only instantaneous (or filtered) sensor readings.
This chapter extends plume tracing research by presenting a complete strategy for finding a plume, tracing the plume to its source, and maneuvering to accurately declare the source location; and, by presenting results from successful, large-scale, in-water tests of this strategy. The assumptions made herein relative to the chemical and flow are that the chemical is a neutrally buoyant and passive scalar being advected by a turbulent flow. The AUV is capable of sensing position, concentration, and flow velocity. The concentration sensor is used as a binary detector (above or below threshold). We solve the plume-tracing problem in two dimensions. A main motivation for implementing the algorithms in two dimensions is the computational simplification achieved; however, neutral buoyancy of the chemical or stratification of the flow (Stacey, 2000) will often result in a plume of limited vertical extent, which may be approximated as two-dimensional.
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