Article Request Page ASABE Journal Article ## Towards Autonomous, Optimal Water Sampling with Aerial and Surface Vehicles for Rapid Water Quality Assessment

Anh Nguyen^{1}, John-Paul Ore^{2}, Celso Castro-Bolinaga^{3}, Steven G. Hall^{3}, Sierra Young^{4,*}## Published in

Journal of the ASABE67(1): 91-98 (doi: 10.13031/ja.15796). Copyright 2024 American Society of Agricultural and Biological Engineers.

^{1}Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina, USA.

^{2}Computer Science, North Carolina State University, Raleigh, North Carolina, USA.

^{3}Biological and Agricultural Engineering, North Carolina State University, Raleigh, North Carolina, USA.

^{4}Civil and Environmental Engineering, Utah State University, Logan, Utah, USA.

^{*}Correspondence: sierra.young@usu.eduThe authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/

Submitted for review on 29 August 2023 as manuscript number NRES 15796; approved for publication as a Research Brief and as part of the “Digital Water: Computing Tools, Technologies, and Trends” Collection by Associate Editor Dr. Sushant Mehan and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 13 November 2023.

Highlights

A practical workflow for optimizing sampling tours for a team of surface and aerial vehicles was developed.Proposed workflow considers unique sensing capabilities of surface vehicles when assigning sampling locations.Likely optimal tours can be found in less than 30 s for practical water quality sampling requirements.

Abstract.Most current marine aquaculture operations are located in coastal estuarine areas within one mile of the shoreline, and water quality in these production areas can quickly become unfavorable due to hydrodynamic processes and excessive runoff. The deployment of autonomous, robotic systems can improve the speed and spatiotemporal resolution of water sampling and sensing in mariculture production areas to assess water quality in the context of food safety. Specifically, teams of both aerial and surface vehicles can be deployed simultaneously to capitalize on the benefits of each system; however, a method to optimally design a feasible sampling tour for each robot is needed to maximize sample capacity and ensure efficient water sampling missions. This research brief presents the problem formulation and a solution method to determine optimal tours for a team of aquatic surface and aerial vehicles while considering different vehicle sampling capacities and endurance constraints. This method was implemented to design sampling missions of 15, 20, and 30 samples in both a 0.25 km2 and 3.9 km2 site, using sampling capacity and endurance constraints corresponding to real-world robots used for water sampling in mariculture environments. Results indicate that this optimization problem can be solved in near-real time in the field and yields feasible sampling tours for surface and aerial vehicles under different constraints. This work is a practical step towards developing teams of collaborative robots to persistently monitor adverse mariculture growing conditions so producers can implement data-driven, timely management strategies.

Mariculture, Robotics, Traveling salesperson problem, Vehicle routing. Keywords.Aquaculture is the fastest-growing protein sector globally (FAO, 2018), and an existing ˜$17 billion seafood deficit in the US is driving efforts to develop new, larger nearshore marine aquaculture systems to meet national demand (National Marine Fisheries Service, 2020). Most current mariculture operations are located along the coast within one mile of the shoreline, and water conditions in these nearshore production sites can quickly become unfavorable due to hydrodynamic near-shore processes and limited control over system boundaries. Poor water quality presents serious concerns for food safety and health, as over 80% of seafood produced in the US consists of bivalve mollusks, such as oysters and clams (National Marine Fisheries Service, 2020). Of particular concern is the presence of fecal pathogens, or disease-causing organisms, which may be present in mariculture systems and are harmful when ingested. When these pathogens are present—or when fecal coliform bacteria, a proxy for fecal pathogens, are present in high enough concentrations—water may be closed to shellfish harvesting. These closures present a significant hardship and economic loss to coastal communities, with estimated losses of up to 25% of total revenue (Evans et al., 2016). Therefore, frequent water quality monitoring in marine aquaculture systems is necessary to prevent unnecessary closures and ensure food safety.

In areas subject to potential contamination from fecal pathogens, water samples must be collected and analyzed off-site for fecal coliform bacteria concentrations. Manual sampling is the most common method for monitoring water quality in aquaculture operations, and while it is a reliable approach, manual sampling is limited in spatiotemporal coverage and may miss events of concern. Robotic systems, including both aerial and surface vehicles, have been explored for autonomous water sample collection (Dunbabin and Marques, 2012; Koparan et al., 2020; Manjanna et al., 2018; Ore et al., 2015; Schwarzbach et al., 2014). These platforms enable the rapid and smart collection of water samples and can improve the spatiotemporal throughput of water quality monitoring. However, selecting the optimal vehicle for water sampling missions is challenging, as they each have different merits and challenges (see table 1). While surface vehicles tend to have higher capacities and longer endurance, they generally operate at low speeds and have physical limitations to deployment, such as minimum water depths and flow velocities. Aerial vehicles can overcome some limitations by flying over shallow or fast-moving water to reach sampling locations at higher speeds; however, their payload capacities are often much lower than those of surface vehicles. An emerging solution that takes advantage of the benefits of both aerial and surface vehicles is deploying a heterogeneous, multi-robot team.

Table 1. Summary of the merits and challenges of deploying UAVs and USVs for water quality monitoring. USVs UAVs + Longer endurance + Faster travel speeds + Higher payload capacity + Greater accessibility + Potential to collect in situdata- Shorter endurance - Slower Speeds - Smaller payload capacity - Limited accessibility - Potentially greater regulation Multi-robot teams offer significant advantages for exploration and monitoring missions in challenging aquatic environments. Heterogeneous multi-robot teams may consist of multiple systems representing one type of vehicle (e.g., aerial or aquatic) with different capabilities or a team of different types of vehicles (e.g., ground-air, aquatic-air). A heterogeneous team of surface vehicles, including one water quality sensing vehicle and one water sampling vehicle, was deployed for sensor-informed water sampling, where one vehicle acts as the explorer and the other as the sampler (Manjanna et al., 2018). A team of aerial, surface, and underwater vehicles was used to achieve multi-domain coral reef monitoring, where areas of interest were identified by the aerial vehicle and subsequently investigated by the aquatic systems (Shkurti et al., 2012). A similar approach was taken by Manderson et al. (2019), where aerial vehicles identified a region of interest and planned a path for surface vehicles. These multi-vehicle systems rely on one vehicle for exploring or scouting and others for sample collection. However, for applications where sample coverage is the primary concern, multi-robot systems that utilize all vehicles for sampling can result in more samples obtained during each mission. In this scenario, however, the efficiency of the vehicle path to visit each sample determines how many samples can be collected within vehicle endurance constraints.

The problem of finding the shortest path to collect a specific number of water samples at given locations can be formulated as a Traveling Salesperson Problem (TSP) (Flood, 1956). Specifically, for a given list of locations (or cities) and the distances between each pair of locations, the TSP seeks to find the shortest possible route that goes through each location exactly once and returns to the original location, or depot. The TSP is one of the most widely studied combinatorial optimization problems (Laporte, 1992; Osaba et al., 2020) and has been used to solve optimal paths for single water sampling vehicles (Zhang et al., 2023). A coverage orienteering problem, which is a generalized case of the TSP, has also been used to solve the water sampling problem for surface vehicles (Zhang et al., 2020). However, when multiple vehicles are considered, a generalized case of the TSP—the multiple traveling salesperson problem (MTSP)—must be used where more than one salesperson is allowed (Cheikhrouhou and Khoufi, 2021). Given a set of locations and a cost metric (e.g., distance, time) for each pair of locations, the objective of the MTSP is to determine a set of routes for

nsalespeople to minimize the total cost of thenroutes. For a heterogeneous team of robots, a solution is required that considers each vehicle's different endurance constraints.Many studies have evaluated the MTSP, including several variations on the problem’s constraints (Cheikhrouhou and Khoufi, 2021). MTSP variants are imposed to formulate the problem for a specific domain; for robotic water sampling, endurance or capacity constraints must be imposed, and closed paths (i.e., each robot must start and end at the same location) are often required. Here, we describe a practical problem formulation for the MSTP specifically for water quality sensing and sampling with one unoccupied surface vehicle (USV) and multiple unoccupied aerial vehicles (UAVs). We proposed a two-step solution that first determines a surface vehicle tour for a random set of samples spread across the site, then solves the MTSP for multiple aerial vehicles to collect the remaining samples. This enables the USV to collect

in situwater quality data across the site when traveling between sampling locations while ensuring optimal tours for collecting the remaining samples using UAVs. Preliminary results are presented for two test locations representing nearshore oyster leases in North Carolina. While further experiments are needed to validate this method in the field, the proposed method can identify tours for robotic sampling by a heterogenous team of robots, each with unique capabilities and constraints, that researchers and practitioners can use to monitor water quality using autonomous systems.

Materials and Methods

Problem DescriptionThis brief presents an MSTP formulation that describes water quality monitoring and sampling for nearshore aquaculture operations using a team of one USV and multiple UAVs. The proposed system consists of one USV equipped with a water quality sonde capable of measuring various water quality parameters

in situand a water sampling payload for collecting physical samples, andnUAVs that are only capable of collecting water samples (i.e., no water quality sensing capabilities). In the proposed scenario, it is desirable to have the USV path spread across the site as much as possible to collect water quality data in between water sample locations to maximize the spatial information gained from the sonde. This requirement is considered in a preliminary step to determine the optimal USV tour separate from the UAV tours. Solving the USV tour separately is a reasonable approach, given that USVs typically have larger payload capacities, can carry additional sensors than UAVs, and thus have different mission requirements. In the proposed problem formulation, the UAV payload capacities are designated entirely for water sampling to maximize payload efficiency.This problem considers several constraints and assumptions. First, it assumes that all the vehicle paths are closed, and all aerial and surface vehicle tours must start and end at the starting node (depot), regardless of their tour. It also assumes that the surface vehicle is deployed exactly once with a fixed number of eight samples, and that UAVs can collect the remaining samples via multiple flights. This requirement can be met with multiple UAVs or simply additional batteries, given that the UAV returns to the depot after each tour and can receive a new battery after each flight to collect additional samples. This is reasonable in practice given that USVs typically have longer endurances (i.e., 1-2 hours) and travel at slower speeds to each location, while UAVs can cover more ground in shorter amounts of time and have flight durations of approximately15-30 minutes when payloads are near capacity. This problem does not include time window requirements for collecting samples, as it assumes operators can deploy UAV and USV systems simultaneously, and the samples collected would represent conditions within the sampling window. Finally, we assume that line-of-sight FAA requirements can be relaxed and are not considered in the tour length of the UAVs. Finally, the proposed MTSP seeks to minimize the total length of the tours for the USV and UAVs.

Sampling Points InitializationTo ensure the USV tour is spatially distributed throughout the site, a USV sampling point initialization procedure was developed to determine the surface vehicle sampling tour. Given the rectangle boundary of the site, this process determines: (1) a set of quasi-random sampling points such that they are spread out over the entire area of interest; and (2) selects a subset of points for the surface vehicle to visit. First, the set of quasi-random points is created using the Sobol sampling method. This method uses a Sobol sequence (Sobol, 1967) to sample a space of probabilities more evenly than pseudorandom sampling. The Sobol algorithm delivers random points in powers of two; in reality, the required number of samples may not be an exact power of two. Therefore, if

k(k> 0) water samples are desired in the area of interest, the Sobol method is used to generateNpoints, whereNis a power of two andN=k. IfN>k,kpoints are selected using random sampling with a uniform probability. It is noted that this may leave some spatial gaps where samples have been eliminated, and other procedures can easily be used in place of the Sobol method for determining the initial set of samples, such as basic grid sampling.Next, a set of

qpoints is selected for the surface vehicle tour from thekpoints, whereqis the sampling capacity of the USV. First, the area of interest is divided intoqequal subregions, and the centroid of each subregion is determined. Then, the sampling point in each subregion closest to the centroid is selected. The result isqpoints that are spread across the subregions within the area of interest for sampling by the USV. The remainingk–qpoints are assigned to the UAV(s), and the UAV tours are solved using the MTSP formulation described below.

MTSP Mathematical FormulationGiven that the TSP is a specific case of the MTSP when the number of salespeople

m= 1, we present the formulation for the MTSP below (Bektas, 2006). Consider a graphG= (V, E), whereVis the set ofN(N= 4) sampling nodes andEis the set of edges between these nodes. There arem(m> 1) robots that all must start and end their tour at the depot. This problem seeks to minimize:(1)

where

cis the cost (distance) of edge_{ij}Additionally, the following constraints are imposed:

(2)

(3)

(4)

(5)

(6)

where

uand_{i}uare the positions of nodes_{j}iandjin a tour, andpis the maximum number of nodes an agent can visit. Constraint (2) ensures that all agents start at a depot (i.e., exactlymagents start at the depot, usually denoted as node 1), while constraint (3) ensures all agents finish at the depot. Constraint (4) ensures that each node is visited exactly once, while constraint (5) ensures that the total distance traveled for each agent does not exceed the agent’s distance capacity. Finally, constraint (6) eliminates subtours, or solutions that do not visit all points. Note that the number of required UAVs is determined manually as a constraint and depends on the required number of samples. For example, if 15 samples are required, it would take one USV tour to collect eight samples, and two additional UAV tours to collect the remaining seven samples.

Solution ImplementationThe computational complexity of solving the TSP increases exponentially as the number of locations increases (Hosseinabadi et al., 2014). Given the computational complexity of finding exact solutions to the MTSP, a heuristic algorithm was implemented that approximates a feasible solution but does not guarantee absolute optimality. Specifically, the proposed solution method uses guided local search to solve the TSP for the USV tour and the MTSP for the UAV tours. Guided local search is often used to solve vehicle routing problems (Arnold and Sörensen, 2019; Voudouris et al., 2010) and uses penalties to help escape from local minima and plateaus. The guided local search solver was provided through Google OR-Tools, an open-source software suite for optimization (Perron and Furnon, 2022). Note that most metaheuristics lack termination conditions that are based on the quality of the solution provided by the algorithm (Corominas, 2023) and are typically terminated by other criteria, such as the number of iterations. Therefore, a solution time limit is provided for the solver as a termination condition. Given the relatively low number of nodes typically required for water sampling (i.e., tens of samples rather than thousands of samples), a default of 30 seconds is used in the implementation. Distances between points were calculated as latitude-longitude distances, assuming the Earth’s radius is 6,371 km. The problem was modeled using Python (v3.10.8), and all code can be found at the following GitHub repository: https://github.com/anguyen216/mTSP-work/.

Results and DiscussionThe methods described above were implemented for a USV with a capacity of eight samples, a UAV with a capacity of five samples, and a total sampling requirement of 15, 20, and 30 locations. Two regions of interest were evaluated that represent nearshore shellfish lease areas in North Carolina near the city of Otway (see fig. 1). Site 1 is approximately 0.25 km

^{2,}and Site 2 is approximately 3.9 km^{2}. The vehicle distance capacities were determined experimentally and were approximately 5.5 km for the USV and 4.5 km for the UAV, assuming average speeds of 1.5 m/s and 5.0 m/s, respectively. The solver implementation was run on a 2022 Mac Studio with 64 GB of memory.

Figure 1. Location of test sites 1 and 2 located near Otway, NC. The coordinates of Site 1 for the lower left and upper right corners are (34.774226, -76.574711) and (34.7769266, -76.5679482), and for Site 2 are (34.749973, -76.613341) and (34.769743, -76.594136), respectively.

USV SubtourFigure 2 shows the example results of the sub-steps involved in finding the eight sampling locations for the USV tour for an example area of interest. Here, 20 samples are identified across the region of interest; then, the points nearest to the centroid of each subregion are selected for the USV to sample. This ensures that the final USV tour is spread across the site, thus forcing the USV to collect water quality data that are more spatially representative of the entire site instead of clustering the USV samples in one area. Note that there are some gaps in coverage for the 20 sampling locations. A simple grid-based approach or manual selection of sampling locations can also be used here instead of the Sobol method, depending on user requirements; however, we opt for selecting a subset of quasi-random samples, assuming no prior knowledge of the site conditions.

UAV ToursFirst, the proposed method was evaluated for the smaller region of interest (Site 1) for 15, 20, and 30 total samples. The MSTP solutions are shown in figure 3. For each case, the USV route always collects eight samples (including collecting one sample at the depot), while the UAV routes collect five samples each flight (not including the depot). Note that here, we assume all vehicles start and end at the same depot for simplicity; however, the UAV depot can easily be modified from the USV depot without affecting the solution implementation, as the USV and UAV tours are solved separately. All tour lengths are within vehicle constraints; the length of the USV tours for the 15, 20, and 30 sample conditions are 1097, 1214, and 998 m, and the longest UAV tour for each condition are 1192, 995, and 931 m, respectively. If all samples were collected by a single platform (i.e., solving the single TSP), the total tour lengths would be 1727, 1842, and 2201 m for 15, 20, and 30 samples. Note that these tour lengths are still within the power capacities of the UAV and USV, as this location represents a relatively small site containing inner coastal shellfish leases; however, these tours would far exceed the sampling capacities of both vehicles.

(a) (b) (c) Figure 2. Example illustration of the processes in identifying USV sampling locations. (a) Twenty samples identified by subsampling the result of the Sobol method; (b) identification of the centroids of each subregion; and (c) location of the nearest sampling point to each centroid. These sample locations are the final set of eight samples for the USV tour. This method was also evaluated for Site 2, which had a larger area, and the results are shown in figure 4. For Site 2, the length of the USV tours for the 15, 20, and 30 sample conditions was 5738, 4757, and 5117 m, and the longest tour for the UAVs for each condition was 3945, 4013, and 3989 m, respectively. If a single platform collected all samples, the total tour lengths would be 5540, 7951, and 10116 m for 15, 20, and 30 samples, all exceeding the power capacity of both the UAV and USV. Note that this site maximizes USV capacity, and occasionally, no viable solution for the USV path is found for the larger sample requirements. In this scenario, the seed for the Sobol sample scrambling can be randomly varied until a solution is found near the vehicle’s endurance capacity.

Solution Method Evaluation

Solution TimeTo evaluate the solution's optimality under the 30 s time constraint, the solver was also allowed to run for a time limit of 120 s and 600 s. Only Site 2 was considered for this analysis, and all three total sample numbers (15, 20, and 30) were evaluated. The same set of samples was analyzed for each time-limit condition. The tour distances are shown in table 2. For the 30, 120, and 600 s time limit, all solutions for the USV and UAV tours are the same for all sample conditions. This indicates that for a relatively low number of nodes, the guided local search solver can reach a likely optimal solution within a short time frame of 30 s. The performance of this solver highlights the potential of this approach to be used in the field for rapidly designing optimal paths for surface and aerial vehicles depending on requirements that can be determined on-site.

Figure 3. Example solutions for the MTSP problem for Site 1. The Nthvehicle tour (orange paths) is always the surface vehicle; the remainingN– 1 tours (blue paths) represent the aerial vehicles.Figure 4. Example solutions for the MTSP problem for Site 2. The Nthvehicle tour (orange paths) is always the surface vehicle; the remainingN –1 tours (blue paths) represent the aerial vehicles.

Table 2. Total distance (meters) of the USV tour and combined UAV tours for 15, 20, and 30 samples. Solutions were obtained by running the guided local search solver for 30 s, 120 s, and 600 s time limits. Number

of

Samples30 s limit 120 s limit 600 s limit USV

TourUAV

TourUSV

TourUAV

TourUSV

TourUAV

Tour15 5,378 7,712 5,378 7,712 5,378 7,712 20 4,757 11,810 4,757 11,810 4,757 11,810 30 5,117 18,457 5,117 18,457 5,117 18,457

Vehicle Tours ComparisonIn addition to evaluating the solution time, the USV and UAV tours were compared to assess their spatial coverage of the site. Importantly, the USV is equipped with

in situsensors, and the final USV tour should cover a larger spatial extent, whereas the UAV tours have no objectives other than finding optimal paths for sampling. The extent of all tours was determined by computing the area of the convex hull around the sampling points, which is the tightest convex shape that encloses the sampling points. Convex hull areas were computed using the latitude and longitude coordinates of the sampling points for both sites and all sampling numbers (see table 3). With the exception of one UAV tour for the smaller site when 15 total samples are required, the convex hull area covered by the USV tour is greater than all UAV tours, indicating that the sampling locations are spread over a greater extent across the site. This is beneficial as the USV can take advantage of its ability to collect additionalin situdata when traveling between sampling locations.

ConclusionsThis work demonstrated the formulation and solution metaheuristic of an MTSP for a team of aerial and surface vehicles to collect water samples for water quality monitoring. This problem is unique from previous problem formulations in that it requires the USV sampling tour to be spread across the site to maximize the spatial information gained from

in situwater quality sensors and uses all vehicles within the multi-robot team for sampling. The solution method successfully identified feasible tours for both the USV and multiple UAVs to ensure all required samples are collected. Solutions for sampling requirements consistent with practical field requirements (10-30 samples) reached near optimality after only 30 s, indicating that this approach can easily be deployed in the field prior to sampling. These results are in line with other studies assessing the performance of metaheuristics and exact solution methods for the MTSP. For a relatively small number of samples (<50) and salespeople (<10), solutions can be determined on the order of seconds to several minutes (Hosseinabadi et al., 2014; Husban, 1989; Yousif and Al-Khateeb, 2018), depending on the solution approach and computational hardware.

Table 3. Areas of the convex hulls surrounding the sampling points selected for each tour for each site and total number of samples. Areas were computed using the latitude and longitude coordinates. Number of

SamplesSite 1 Site 2 USV Tour UAV Tours USV Tour UAV Tours 15 0.011 0.013; 0.0084 0.052 0.037; 0.040 20 0.012 0.0096; 0.010; 0.011 0.045 0.038; 0.038; 0.037 30 5,117 0.0092; 0.0059; 0.0067; 0.0097; 0.0094 0.049 0.037; 0.040; 0.038; 0.038; 0.039 While this preliminary work provided a practical solution method and workflow, some limitations exist. First, the region of interest must be rectangular and does not consider large obstacles within the boundary. Solving optimal tours and sampling paths for irregular, potentially non-convex shapes for autonomous systems that contain large obstacles is a non-trivial, complex problem (Deng et al., 2021; Tukan et al., 2022) and is an area of future work. However, it is a reasonable assumption that autonomous vessels are equipped with local object detection and avoidance; thus, the presented method could still be applied for the case of small or mobile obstacles, such as buoys or other marine vehicles. Further, the metaheuristic to solve the MTSP does not guarantee the optimality of the solution; however, it does arrive at a near-optimal solution in a reasonable timeframe, as executing the solver for longer periods of time does not improve the results. The tradeoff between optimality and solution time is always a consideration for vehicle routing applications, and here we prioritize rapid solutions in the context of field deployments over ensuring absolute optimality by using this metaheuristic. Another area of possible future work—given the overlapping paths—is vehicle avoidance within the multivehicle team; this is assumed to be negligible in the present scenario but is a potential concern in real world scenarios. Despite these limitations, this preliminary work demonstrates a viable and practical workflow for designing sampling tours for a team of aerial and surface vehicles that can be implemented for efficient water quality monitoring. Further, this work is timely given the increasing use of robots for water sampling and will enable teams of collaborative robots to persistently monitor and predict adverse growing conditions so mariculture producers can implement data-driven, timely management strategies.

AcknowledgmentsFinancial support for this study was provided by the U.S. Department of Agriculture (USDA) Grant No. 2021-67021-33451.

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