Virtual uncrewed system sampling in the hurricane environment. Part 1: rigid-wing surface vehicle simulator

Uncrewed vehicles (UxS) are the frontier of atmospheric and oceanic measurements in extreme regimes and remote areas. The combination of Uncrewed Surface Vehicles (USVs), Uncrewed Underwater Vehicles (UUVs) and Uncrewed Aerial Vehicles (UAVs) has the potential to transform air-sea coupling observations through co-located sampling of the lower atmosphere, upper ocean and air-sea interface. Although individual platforms have reached a relatively mature operational stage, designing coordinated missions remains challenging. UxS navigation is strongly affected by environmental conditions their and deployment can be logistically complex and poorly repeatable. We take a first step towards co-locating UxS under environmental influences by developing a novel physics-based, dynamical simulator for a rigid-wing, wind-powered USV that: a) reproduces the observed USV navigation during the NOAA Atlantic Hurricane missions, b) can be virtually navigated in numerical simulations. Starting from force-balance principles, the simulator reproduces the USV surge, sway and yaw, given wind, ocean current information, and control wing and rudder angle inputs. Model parameters are calibrated and validated using observations from the NOAA Atlantic Hurricane missions. A virtual controller is also developed to enable waypoint-based navigation within numerical environmental simulations to support repeatable experiments assessing the feasibility and design of coordinated USV–UUV sampling strategies.

Exchanges of heat, momentum, and gases, such as carbon dioxide, between the atmosphere and ocean are critical to a wide range of weather and climate variability and their predictions. These air-sea fluxes occur within the Air-Sea Transition Zone (ASTZ), which is composed of the atmospheric boundary layer, the air-sea interface and the ocean mixed layer, and drive the coupling between the atmosphere and ocean. Accurately monitoring them therefore requires collecting high-quality measurements across the Air-Sea Transition Zone (ASTZ) and, in particular, near the air-sea interface. Traditionally, such in-situ observations have been available only from research vessels and aircraft or moored buoys, with significant limitations in terms of cost, logistics, spatial resolution and most importantly coverage. Direct ASTZ measurements inside tropical cyclones (TCs), for instance, are particularly scarce even though they have fundamental implications for improving TC predictions to reduce their societal impacts. While remote-sensing observations have been substantially advanced, satellites still cannot provide many accurate measurements near the sea surface (e.g., humidity) and cannot sample subsurface ocean conditions.

The ongoing development of uncrewed observing systems (UxS) has opened new doors to observing extreme and remote environments beyond the traditional means (e.g Cione et al., 2020; Miles et al., 2021; Ricciardulli et al., 2022; Mordy et al., 2017; Chiodi et al., 2021, 2024; Zhang et al., 2022a, 2023a, b). Uncrewed underwater vehicles (UUV) (e.g., ocean gliders) measure upper ocean profiles (e.g. Ruiz et al., 2012; Hemsley et al., 2015; Thompson et al., 2016; Laurent and Merrifield, 2017; Merrifield et al., 2019; Rudnick, 2016; Miles et al., 2021), and uncrewed surface vehicles (USV) measure near-surface variables needed for estimates of air-sea fluxes (e.g. Zhang et al., 2019, 2022a; Chiodi et al., 2024; Sivam et al., 2024; Eyre et al., 2023; Foltz et al., 2026). Uncrewed aerial vehicles (UAV), when deployed from a ship, airplane, or coastal land, can measure the atmospheric boundary layer (Cione et al., 2020; Witte et al., 2017; Wetz et al., 2021; Bonin et al., 2013). When all three types of UxS are coordinated to move in concert, they can take simultaneous and collocated measurements of the entire ASTZ.

Recent deployments of uncrewed underwater vehicles (UUV) (e.g., ocean gliders) and uncrewed surface vehicles (USV), such as the NOAA Atlantic Hurricane missions, not only demonstrated the potential to achieve co-located measurements of the upper ocean and air-sea interface in extreme conditions but also highlighted the challenges of co-locating UxS (e.g. Merrifield et al., 2019; Saksvik et al., 2022). Each UxS has its own navigation capabilities, which are often strongly influenced by winds, currents and sea states, especially in extreme conditions, such as the hurricane environment. To make Coordinated UxS (CUxS) measurements a reality, and improve the success of future deployments, it is paramount to assess their navigational capabilities and devise process-specific sampling strategies.

The operational maturity of USVs and UUVs allows us to focus on how they should be navigated and coordinated to meet specific scientific objectives. Operations in extreme environments can be costly, logistically demanding, and often require intensive human supervision. Consequently, observations from field missions alone provide a limited basis for systematically comparing mission designs or quantifying sensitivity to environmental conditions and mission uncertainty. A data-constrained simulator provides this capability by reproducing observed vehicle behavior while enabling repeatable counterfactual experiments across many environmental, control, and sampling scenarios. Such experiments can be used to characterize navigation envelopes, identify potential failure modes and quantify mission uncertainty, ultimately leading to real-time mission manager support.

Simulation is used in marine robotics for developing and evaluating navigation, guidance, and control algorithms before field deployment. Different frameworks exist that provide valuable tools for testing uncrewed system behaviors, typically focusing on generic or motor-propelled USVs, sensor emulation, and autonomy-software development rather than on the navigation of wind-powered observing platforms under spatially and temporally varying geophysical forcing (e.g. Bingham et al., 2019; Paravisi et al., 2019). Similarly, physics-based models have been used to represent aerodynamic and hydrodynamic forces, and vessel motion for controller design and synthetic-data generation of autonomous sailboats (e.g. Melin, 2015; Melin et al., 2016; Bühler et al., 2018; Setiawan et al., 2020), while hardware-in-the-loop simulators have been used to diagnose autonomous-pilot behavior under wind, current, and wave forcing (Akiyama et al., 2023). Other have combined simplified sailboat dynamics with data-driven controllers or have incorporated wind and current effects and energy-efficient path planning (e.g. Dong et al., 2021; Gu et al., 2022; Zhang et al., 2022b). While these studies demonstrate the value of simulation for controller development and route optimization, many use idealized environmental scenarios, coefficients adopted from generic vessels, or simulation-only validation. In the context of hurricane monitoring, Zhang et al. (2023a) estimated potential Saildrone tracks from modeled winds and currents using a simplified empirical wind-efficiency relationship.

A remaining need is therefore a computationally efficient simulator that is physically tailored to rigid-wing, wind-powered USVs, constrained by observations, and capable of reproducing both vehicle translation and heading response under realistic environmental forcing. The objective of this study is to develop and validate an efficient navigation simulator for rigid-wing, wind-powered USVs that can support such virtual mission-design experiments. The simulator is formulated around four requirements: it should (i) be based on physically interpretable force balances, (ii) represent the principal surge, sway, and yaw responses to environmental forcing and control inputs, (iii) reproduce observed USV navigation across independent deployments, and (iv) be sufficiently efficient for repeated application within numerical environmental simulations. We formulate the model using wind and ocean-current forcing together with commanded wing and rudder angles, calibrate its parameters using observations from one Saildrone deployment, and evaluate its transferability using two additional Saildrone vehicles from the NOAA Atlantic Hurricane missions. We also develop a virtual controller that permits waypoint-based navigation without continuous manual input. The resulting framework provides a validated virtual USV for controller testing, mission planning, sensitivity and uncertainty analysis, and evaluation of sampling feasibility. Coordinated USV–UUV sampling within coupled atmosphere–wave–ocean simulations is a key application of this framework and is examined separately in the companion study (Mazza et al., 2026).

Saildrone environmental and navigation data

Over the 2021, 2022, 2023 and 2024 Atlantic hurricane seasons, NOAA and Saildrone have collaborated to deploy 36 Explorer Saildrone uncrewed surface vehicles across active hurricane regions in the North Atlantic and the Caribbean Basin (Figure 1).

To design the USV simulator, we employ 5-minute frequency data from the 2024 SD-1030 deployment, linearly interpolated to 1-minute intervals. The data include environmental variables, namely wind speed and direction and ocean current speed and direction, as well as navigational variables, specifically position, speed-over-ground, heading, and wing and rudder angles. For the development and testing of the USV simulator, we focused on a 12-hour window of navigation following SD-1030 deployment SW of Puerto Rico. The window was selected because it provided a long-stretch of navigation under varying wind and current conditions, as well as different sailing regimes, from almost pure running (directly downwind) to almost close reach (approximately 50-60° to the wind). Additionally, during this window the navigation exclusively aimed at sailing as efficiently as possible to bring the USV to the north of Puerto Rico, thus it does not involve any complex maneuvers.

Validation of the USV simulator is performed on three independent 160-hour windows of of navigation for SD-1030 near Puerto Rico, SD-1045 offshore South Carolina and SD-1057 in the eastern Gulf (Figure 1).

Uncrewed surface vehicle simulator

The core of the work is the development of a USV simulator that can be virtually navigated within numerical model output to reproduce the motion and sampling of USVs. We take inspiration from the mini-12 sailboat model of (Melin, 2015; Melin et al., 2016). They employed force-balance principles to build a 3-degrees of freedom simulator of the boat surge, sway and yaw. We extend and substantially modify it to be applicable to rigid wing USVs. The model can be used to forecast the USV position (x, y) and heading (θ), given the wind and ocean current vectors as well as two piloting controls, namely the angles of the wing (δs) and rudder (δr) (Equation 1). While the wing angle of the SD Explorer is indirectly controlled by a wing actuator, in our simplified model we approximate it as directly controlled.

As in Melin’s original formulation, our model (Equation 1) contains three expressions for the time derivative of x, y and and two expressions for the linear (v) and angular acceleration (ω) that balance the forces acting on the wing, keel, hull and rudder. The environmental and piloting information is contained in the vector c.

The kinematic expressions for x and y simply include the projection on the x, y plane of the surge vector v along with two terms that describe the windage and ocean drift on the vessel. The yaw rate of change is simply given by the angular velocity. How the surge velocity changes in time is given by a balance of the forces acting on the USV, which consist of the combination of wing-generated lift and drag acting in the x direction (F sx), a rudder breaking force F br and a surge drag force (S d). The propulsion is provided by the combination of lift and drag forces on the rigid wing, counteracted by the breaking effect of the rudder-generated drag and the quadratic damping term. The lift and drag forces vary as a quadratic function of the apparent wind speed, and depend on lift and drag coefficients, respectively. They are also scaled by an effective wing force scale (p 4), which converts the pressure on the wing into lift and drag forces, and includes the influence of air pressure and wing area. Whenever the rudder is deflected, it will also induce a breaking effect that depends on the square of the effective through-water velocity as well as on a breaking coefficient (p 1 1). Additional damping on the surge speed is provided by a quadratic drag induced by the motion of the USV through the water (Equation 2).

Wind-powered USVs typically generate propulsion using a rigid wing. The first major contribution of our USV simulator is to replace the sail physics of Melin (2015); Melin et al. (2016) with representations of the force balance acting on a rigid wing.

The flow on the wing induces lift and drag forces that can propel the vessel forward. First, we compute the apparent wind and in turn the angle of attack (α). We approximate the lift and drag coefficients (C l and C d) behavior in two regimes, for small and large α, respectively. At small angles of attack (| α |<= α max), the wing acts as a thin foil, with linearly increasing lift and quadratic drag (Equation 3.1).

As α grows (i.e. | α | > α max), the behavior smoothly transitions to a flat plate-like regime with strong broadside drag and post-stall lift. We first cap the attached lift (Equation 3.2), then we construct the flat-plat expressions (Equation 3.3). The transition is handled through a blend (logistic) function f (| α |) that approaches zero for small angles of attack and 1 for large ones, for the lift (Equation 3.4) and the drag coefficient (Equation 3.5). After careful testing, the angle of attack that separates between the two regimes is chosen to be α max = 18°, with C d 0 = 0.02,C dk = 0.1,C la = 3.18,C d, 90 = 1.2,C l,max = 1.0.

The second major departure from Melin (2015); Melin et al. (2016) is the inclusion of the keel/hull restoring moment in the rotational dynamics. The yaw dynamics of the USV are, in fact, controlled by the balance between the wing torque (T s), the rudder torque (T r), the yaw restoring moment (N k) induced by the keel/hull, a surge-speed-dependent hydrodynamic damping (N d) and speed-independent viscous damping (R d) shown in Equation 1 and Equation 4. The wing torque (T s) results from the force F acting on the wing (whose components in x, y directions are F sx and F sy) at a point x ce, y ce (i.e. center of effort) away from the USV center of mass. The torque induced by any rudder deflection depends on the rudder force Fry (Equation 5) acting at a distance (p 8) away from the USV center of mass. The rotation induced by the wing and rudder torques is primarily compensated by the yaw moment N k, induced by the restoring force (Y k, Equation 5) generated by the keel and hull in response to leeway (β) acting at a distance x cl from the USV center of mass. Along with the sideways restoring force there is a hydrodynamic damping (N d), which depends on through-water velocity (U b,eff) and angular speed (ω), and a viscous damping term (R d) proportional to the angular speed. Note that in the hydrodynamic damping and the keel restoring force, a simple speed gain G u is applied so that these forces are smoothly approaching 0 when the flow around the USV is small.

The USV simulator is integrated forward in time using a fixed-step fourth order Runge-Kutta method with a timestep of 0.2 s, while the model state is sampled and the control vector is updated at 1-minute intervals.

USV simulator parameter estimation

The USV simulator includes several constant parameters that depend on the geometry of the vehicle, including wing area and rudder arm length. These parameters can be fixed a priori based on the knowledge of the USV design or can be estimated from the observed navigation. In its current form, the USV simulator features 16 parameters (Table 1), 3 of them have been fixed a priori, and 13 have been estimated from the navigation of saildrone SD-1030 during the 2024 NOAA-Saildrone Atlantic hurricane mission. For the parameter estimation we selected a 12-hour window of navigation, following SD-1030 deployment out of St. Thomas, USVI (Figure 2). Computational limitations are the primary constraint on the length of the training windows. Both the results presented in the subsequent sections and in the companion manuscript (Mazza et al., 2026), however, indicate that the training windows selected are sufficient to identify a suitable model fit that reproduces the observed behavior over a wide range of navigation conditions. The window features several important characteristics that made it suitable: the navigation had a transit purpose, with rather steady velocity and limited maneuvers that involved complex controller inputs. However it featured a variety of wind and current conditions, as well as different points of sail, from downwind run to beam reach. As such, the model fit should be able to capture realistic dynamics of the USV navigation under multiple regimes.

The USV simulator parameters (Table 1) represent the model parameter vector p v, whose estimation can be achieved in multiple ways. For this application, we employed a Markov Chain Monte Carlo (MCMC) approach (Hastings, 1970; Gelman et al., 2013; Goodman and Weare, 2010) to estimate the posterior probability P r (p v | obs). Instead of solving for the posterior distribution directly, MCMC explores many possible parameter combinations. For each proposed set p v, the model is run, its agreement with the observations is evaluated, and the proposal is either accepted or rejected. Given the large number of parameters in p v and the possibility of strong correlations between them, we employ an ensemble sampler instead of a single walker (Goodman and Weare, 2010; Foreman-Mackey et al., 2013). For the MCMC estimation, we partitioned the 12-hour window in six 2-hour sections and followed the sequence below:

•For a given parameter set, we integrate the USV model over each window using the observed control vector time series and compare the simulated evolution of the state vector against the observations.

•The likelihood function estimates the mismatch between the simulations and the observations and includes 5 residual (i.e. error) terms: along/across-track position, heading, surge speed (water relative) and yaw rate. The total log-likelihood is given by the sum over all windows.

•For each parameter in p v, we provide a prior estimate based on geometry and knowledge of the USV and a bounded range of values within which the MCMC sampler can move. For the positive-definite parameters we use log-normal priors and weak Gaussian priors for selected parameters.

•To initialize the sampler in a plausible region of parameter space, we first performed a short L-BFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) optimization. We then started 128 walkers (parallel chains) near that solution by adding small Gaussian perturbations. The sampler was run for 500 burn-in iterations to reduce the influence of the initial conditions, followed by a 5000-iteration production run used to estimate the posterior distribution.

USV virtual navigation

To apply the USV simulator in a virtual environment, we need to implement a controller that commands the input wing and rudder angle to the system and determines its forward progress based on the simulated environmental conditions. Several controllers exist with different levels of complexity and objectives, including Proportional-Integral-Derivative (PID), Linear Quadratic Regulator (LQR) and Nonlinear Model Predictive Control (NMPC) controllers. Recent examples of USV controls include Dong et al. (2021); Córdova et al. (2023). Our application required a controller that is robust in the context of non-linear dynamics and limited controls but also simple enough to be easily interpretable. Therefore, we construct a simple receding-horizon controller that selects the controls from a finite set of candidates obtained by iterating over a range of wing and rudder angles based on the minimization of a rather simple, but physically-motivated, cost function J that accounts for the ground-relative displacement, water-relative velocity and USV heading (Equation 6). At each time t, the controller generates n candidates by forward simulating the dynamics over a short horizon (60 s). The wing angle is allowed to vary over [-180°, 180°], and the rudder angle is limited between [-90°, 90°], at 1° intervals. The cost function J is defined as the weighted sum of these three terms, each normalized by a corresponding scale so that the weights are comparable despite these quantities having different units and ranges.

An example of the controller application is shown in Figure 3, in which out of a finite set of possible candidates, the controller selects the one that minimizes the cost function J.

To identify the best set of model parameters for simulating actual USV performance in the virtual environment, we rely on the MCMC estimation, which aims to minimize the residuals between the simulated and observed USV navigation. The model dynamics include several gains that control the surge and yaw evolution. To assess the ability of the data and the MCMC sampler to constrain the USV dynamics we focus on 7 of them: a forward-drive gain (p 4 /p 9), a surge-drag gain (p 2 /p 9), a sail turning gain (p 4 p 6 /p 10), a rudder turning gain (p 5 p 8 /p 10), a linear restoring gain (p 15 p 13 /p 10), yaw damping gain (p 16 U b,ref /p 10) and current drift gain (p 12). Figure 4 shows the joint posterior distributions for the selected gains as a result of the ensemble MCMC estimation. Most posteriors in the corner plot appear to be uni-modal and well-constrained within the parameter ranges, suggesting the data can constrain the core dynamics of the simulated navigation and that the resulting parameter vector (Table 1) can reproduce a realistic representation of a rigid-wing wind-powered USV motion.

The estimated integrated autocorrelation times ranged from 137 to 182 iterations, corresponding to approximate effective sample sizes of 3,439–4,563 for the seven reported effective parameters (Table 1). Moreover, monte Carlo standard errors were small relative to the corresponding posterior uncertainties. This is below the conservative 50 τ threshold used for a highly reliable estimate of the autocorrelation time, nevertheless, the stable traces, very close split-half posterior summaries, small Monte Carlo standard errors, and substantial approximate effective sample sizes indicate that the posterior are numerically stable and suggest the effective parameters are practically identifiable for the purposes of this study.

The median walker acceptance fraction was 0.08, with a 5th–95th percentile range of 0.068–0.089. While the proposal acceptance was low, it was relatively uniform across the ensemble. We interpret this as a sign of inefficient sampling, likely associated with the strongly correlated posterior geometry, rather than evidence of systematic temporal drift.

The effective driving and drag coefficients were in fact strongly correlated (0.88), reflecting their compensating roles in the translational force balance. The yaw-related coefficients exhibited stronger correlations, ranging from approximately 0.91 to 0.998. These coefficients share common physical scaling factors and jointly influence the modeled heading response. In contrast, the current-drift parameter was largely independent of the translational and yaw-related coefficients. The SD USV observations therefore seem to constrain their combined dynamical effect more strongly than each individual term independently.

The resulting USV track, speed-through-water and heading for each of the 6 calibration windows are shown in Figure 5. Each window represents a 2-hour simulation using the best-fit parameter vector from the MCMC calibration (Table 1). Across the 12 hours, the observed USV sailed in a N/NW direction under varying wind conditions: in windows 1 to 4 the USV ran downwind or sailed at broad reach. Window 5 features a transition between broad reach and beam reach, while window 6 is steadily in a beam reach configuration. Overall, the simulated USV navigation successfully reproduces the observed navigation. Both the STW and heading track the observed time series well, with very small biases and a root mean square error of 0.23 ms −1 and 0.15 radians respectively. Window 5 appears to be the least successful one.

There could be several explanations for this, including insufficient control representation. For example, in window 5 winds strongly shifted from southeasterly to northeasterly, causing a change from broad reach to beam reach sailing. In this case, our use of 5-minute input control frequency, might not sufficiently describe the complex control strategy needed to maintain the USV on its intended heading given the wind shift. Nevertheless, the results indicate that despite its simplified physics and relatively coarse-frequency control inputs, our USV simulator is able to realistically reproduce the navigation of a rigid-wing, wind-powered surface uncrewed system.

Virtual navigation

To find the best combination of cost function J weights, we explore the parameter space by repeating the simulations and looking for the best combination of α x, α v, α θ (Equation 6) that results in the lowest RMSE (Figure 6). The resulting 3-D parameter space shows a local minimum for α x = 0.9, α v = 0.1 and α θ = 4.0.

To validate the controller strategy, we compare a set of 2-hour forecasts (n=240) for selected navigation windows of SD-1030 (Figure 7A), SD-1045 (Figure 7B) and SD-1057 (Figure 7C) from the 2024 deployment. Each forecast is initialized with a known state vector from the observations, while the environmental conditions (observed wind and current) in the control vector are updated every minute. As shown in Figures 7A, B, C, the virtual navigation closely tracks the observations across most forecasts. The magnitude of the forecast error (Figure 7D), computed as the terminal position error relative to the segment length, is typically lower than 10% (median 8.7%). Similarly, the yaw dynamics appear to be well captured, as the average heading error is smaller than 1 ° (Figure 7E). For all three USVs, the terminal position error appears to be generally insensitive to the environmental conditions. It slightly increases with decreasing wind speed, without an explicit dependence on the sailing geometry (i.e. angle to the wind, Figure 7E). Similarly, the error does not depend on the wave state: it does not vary as a function of the significant wave height or dominant wave period (Figure 7F).

To examine in more detail the ability of the virtual controller to mimic complex sailing patterns, we focus on two distinct sections that involve non-trivial changes of direction: one leveraging the trade winds to sail westward, and another tacking upwind into the trade winds to sail eastward. As shown in Figure 8, our USV simulator is well-suited for reproducing downwind navigation even in strong winds (25 kts or 12.9 ms −1), with a final position error of 134 m over a distance sailed of 5054 m. In particular, the heading evolution is captured extremely well throughout the 2-hour window, while the water-relative speed is slightly underestimated. As a result, the position error relative to the distance sailed remains fairly constant at around 2.5% for the entire simulation.

The USV simulator is also capable of reproducing more complex sailing geometries. Figure 9 shows the simulation of an observed section of navigation of SD-1030 just north-west of Puerto Rico. Given the northeasterly trade winds, and its intended direction, SD-1030 performed a series of upwind tacks, switching on either side of the wind vector. Despite the complex navigation, our USV simulator is able to reproduce the observed speed and heading evolution sufficiently well, with its position error relative to the segment length stabilizing at about 10%.

Uncrewed systems have shown the potential to revolutionize how we measure the natural environment in remote areas and/or under extreme conditions. The combination of USVs, UUVs and UAVs can provide unprecedented observations of atmosphere-ocean interactions in the upper ocean, the air-sea interface and the atmospheric boundary layer, known as the so-called Air-Sea Transition Zone (ASTZ), allowing us to measure critical exchanges of energy and mass between the lower atmosphere and the upper ocean that have wide-reaching implications for weather and climate variability, including extreme events.

USVs and UUVs, in particular, have demonstrated the ability to withstand the extreme winds, currents and waves typically observed in tropical cyclones, providing critically important measurements (e.g. Ricciardulli et al., 2022; Zhang et al., 2023a; Chiodi et al., 2024; Foltz et al., 2026; Miles et al., 2021). However, fully understanding the complex interactions between the ocean and the atmosphere in extreme environments requires the coordination of multiple uncrewed systems to achieve simultaneous and colocated sampling of the ASTZ. This study, along with its companion manuscript (Mazza et al., 2026), takes a first step to address the issue of coordinating UxS under environmental influences using a combination of numerical simulations of the environment and USV simulators.

In this work we develop and test a novel, fully-dynamical simulator that reproduces the navigation of a rigid-wing, wind-powered USV that can be seamlessly integrated in numerical simulations of the ASTZ to devise optimal process-based sampling strategies. Starting from force-balance principles, we construct a 3 degrees-of-freedom system that reproduces the surge, sway and yaw evolution of a rigid-wing USV under the influence of winds and currents. The simulator builds upon the mini-12 sailboat model of Melin (2015); Melin et al. (2016) to include the restoring forces induced by the hull/keel and adapts it to be applicable to rigid-wing USVs. The system is entirely controlled through a wing angle and a rudder angle. The surge is controlled by the balance between the lift and drag forces generated by the air flow around the wing, the breaking induced by the rudder, and the damping caused by the motion of the USV through water. Conversely, the yaw dynamics reflect the influence of the torque acting on the sail and the rudder, combined with a leeway restoring force from the keel and rotational damping.

The USV simulator parameters are estimated with a Markov Chain Monte Carlo approach (MCMC) using data from the observed navigation of the SD-1030 Explorer saildrone during the 2024 NOAA Atlantic hurricane mission. Leveraging an ensemble sampler, the MCMC explores the parameter space to find the combination of parameters that best matches the observed USV behavior in terms of along-track and across-track displacement, heading, surge speed (water relative) and yaw rate. To integrate the USV simulator within numerical simulations of the hurricane environment, a controller is required to select the input controls (wing and rudder angle). To do so, we construct a simple receding-horizon controller that selects the controls from a finite set of candidates by forward simulating the USV trajectory over a short horizon (60 s), iterating over a range of possible wing and rudder angles. The best candidate is chosen by minimizing a cost function that accounts for the ground-relative and water-relative velocity.

The USV simulator is tested against the observed navigation of SD-1030, SD-1045 and SD-1057 over 6-day periods that included various sailing geometries as well as different wind, waves and current conditions. Using 3 sets of 80 2-hour forecasts, we estimate that the simulator has a median position error of approximately 9%, with very limited variation across the different USVs. Terminal position errors weakly vary with wind speed: larger errors are more commonly observed in weak wind conditions. At wind speed > 5 ms −1, the error is typically much lower than 10%. We also tested whether the simulated navigation is influenced by the sea-state conditions. However, terminal position errors do not appear to vary as a function of the significant wave height nor of the dominant wave period. Even more robust is the simulation of the yaw dynamics, with a median heading error of less than 1°.

We demonstrated that the USV simulator is capable of reproducing complex navigation patterns, such as downwind change of directions as well as upwind tacking. Our simulator was developed from first principles and can be tuned using a relatively short training period. As such, pending a re-estimation of the vehicle-specific model parameters, it can be generally applicable to a wider range of similarly designed USVs that rely on the propulsion generated by a rigid wing to navigate.

The development and testing of a fully-dynamical USV simulator is the first step towards a better understanding of the UxS coordination in extreme environments. In its companion manuscript (Mazza et al., 2026), we integrate the simulator in high-resolution, fully-coupled atmosphere-wave-ocean simulations of Hurricane Fiona, to test different sampling strategies that leverage the co-location of USVs and UUVs.