H-SPAR: Hydrodynamic-aware Simulation for Particle Transport and Autonomous Robots

H-SPAR is an open-source, hydrodynamic-aware simulation framework designed to evaluate autonomous marine sampling missions by jointly modeling spatio-temporally varying flow fields, Lagrangian particle transport, and closed-loop Uncrewed Surface Vehicle (USV) autonomy. This integrated approach addresses the limitations of existing simulators by enabling the evaluation of mission cost and sampling performance under consistent hydrodynamic conditions across planning, execution, and sampling levels.

The gist: H-SPAR integrates spatially and temporally varying velocity fields, Lagrangian particle transport, probabilistic sampling, and ROS 2/Gazebo-based uncrewed surface vehicle (USV) autonomy to evaluate particle-sampling missions under marine flow conditions.

Unified System Architecture

H-SPAR integrates a hydrodynamic-aware backend implemented in ROS 2 with a physics-aware frontend implemented in Gazebo, as shown in Fig. 2. This architecture separates the environmental modeling from the vehicle dynamics, allowing for modularity and independent incorporation of disturbances. The system utilizes a shared fine-grained velocity field representation generated using Firedrake [16] and provided as input to H-SPAR.

The framework operates through a pipeline where the ROS 2 backend hosts current-aware path and motion planning, hydrodynamic flow modeling, and Lagrangian particle transport. Gazebo provides the simulated aquatic environment, including USV models with rigid-body dynamics, virtual sensors, obstacles, and plugins for buoyancy and hydrodynamic effects. Sensor measurements are transmitted from Gazebo to ROS 2 via the ROS 2–Gazebo bridge.

Environmental Velocity Field

H-SPAR represents the hydrodynamic environment using fine-grained velocity fields that describe the local water motion. These fields can be obtained from various sources, including physics-based hydrodynamic solvers [18], analytical flow models [2], and data-driven predictors [19]. The computational domain is discretized using an unstructured triangular mesh generated with Gmsh [20].

To balance fidelity and scalability, the velocity fields used in this study are generated using the depth-averaged Shallow Water Equations (SWE) [23]. This formulation captures large-scale horizontal flow structures while remaining computationally tractable for mission-level robotic simulation, making it appropriate for scenarios where particle advection and USV motion are primarily influenced by large-scale horizontal currents.

Current-Aware Path Planning

Water currents significantly affect the hydrodynamic difficulty of missions, necessitating planning that accounts for this influence. H-SPAR implements and evaluates geometry-based RRT∗ planner and two current-aware variants, VF-RRT∗ [1] and SVF-RRT∗ [2]. These planners additionally query the environmental velocity field along candidate path segments, allowing them to favor trajectories that are more aligned with the local flow and avoid regions with strong opposing currents.

The hydrodynamic difficulty is quantified using an upstream-cost metric adapted from Eq. (1) of SVF-RRT∗ [2], which depends on the motion of the USV relative to the local current field, evaluated along the generated path using the local velocity field at planning level.

Current-Aware USV Dynamics

H-SPAR estimates current-induced drag based on the spatial and temporal state of each USV. This is achieved by querying the corresponding local current velocity and computes the resulting drag force and moment at each simulation time step. The hydrodynamic drag is modeled using a quadratic damping formulation to represent surge, sway, and yaw effects [9].

The relative flow velocity for each hull i is calculated as:

urel,i = ui/vi + −ωiry,i / ωirx,i - uw, (1)

where uw is the current velocity vector expressed in the hull body frame. The drag force in surge and sway directions is modeled by Eq. (2), and the yaw torque is defined by Eq. (3). The resulting hydrodynamic wrench is then applied to the USV model through the bridge.

Lagrangian Particle Transport

The fine-grained Eulerian velocity fields are interpolated at each particle location to update the motion of Lagrangian particles in the water. Particle transport accounts for both advection by the local flow velocity and diffusion [28], modeled by:

dx/dt = u(x, t) + R(t), (7)

where x(t) denotes particle position, u(x, t) the interpolated velocity field, and R(t) an optional stochastic term for subgrid-scale turbulent diffusion.

Probabilistic Particle Sampling Model

To evaluate monitoring missions, H-SPAR includes a mission-level probabilistic sampling model that estimates whether particles encountered by the USV are sampled based on their relative motion with respect to the robot. A particle is considered inside the sampling region if its position in the robot frame satisfies∥ rxp∥ ≤ rs.

Here are the specific improvements that could be made to AI systems based on the H-SPAR framework, along with what those improved systems could accomplish:

The core contribution of H-SPAR is enabling closed-loop simulation where environmental flow, vehicle dynamics, particle transport (Lagrangian), and sampling probability are evaluated simultaneously. This capability moves AI from optimizing single stages (planning OR execution) to optimizing the entire mission lifecycle under realistic physical coupling.

Here are specific improvements and capabilities:

2. Unified Closed-Loop Mission Optimization:

This system integrates a planning module (like VF-RRT/SVF-RRT) with an execution module (DWA/ROS 2 control) that is directly informed by the Lagrangian particle transport model and current-induced drag forces.

Improvement: Instead of treating planning and execution as separate optimization steps, the AI optimizes a single objective function that minimizes a combined cost:

Cost = (Planning-level Upstream Cost) + (Execution-level Trajectory Deviation) + (Sampling Efficiency Metric).

Capabilities: The resulting USV can generate paths that are not only geometrically efficient but also robust against unmodeled current variations and optimized specifically for maximizing particle capture probability, leading to significantly lower mission costs and higher sampling rates than traditional planners.

3. Hydrodynamic-Aware Path Planning with Temporal Robustness:

Improvement: Implement path planning algorithms (RRT variants) that can explicitly handle the discrepancy between the flow field used during planning (time-averaged) and the actual time-varying flow field encountered during execution, as demonstrated by Experiment 1. This involves developing a mechanism to quantify flow uncertainty or temporal mismatch.

Capabilities: AI systems will be able to generate paths that maintain high performance even when environmental conditions change rapidly over the mission duration, reducing trajectory deviation and ensuring consistent upstream cost across dynamic environments.

4. Coverage Strategy Optimization based on Particle Dynamics:

Improvement: Develop a coverage planning module that evaluates different sweep orientations (e.g., 0°, 45°, 90°) not just based on geometric line-of-sight, but by simulating the resulting particle encounter probability derived from the Lagrangian transport and relative velocity models.

Capabilities: AI systems will intelligently select optimal survey patterns (e.g., sweep direction) that maximize the actual number of successfully sampled particles, rather than just maximizing mission duration or geometric coverage area.

6. Physics-Informed Sampling Decision Making:

Improvement: Integrate a probabilistic sampling module directly into the AI's decision loop for particle collection, using the capture probability function derived from relative velocity and pump design (Eq. 10).

Capabilities: The robot can make real-time decisions on whether to target a specific particle based on its calculated likelihood of capture, allowing for smart sampling strategies that prioritize particles most likely to be successfully collected, leading to higher data quality per unit of energy expenditure.

7. Open-Source Simulation and Benchmarking Infrastructure:

Improvement: Leverage the open-source ROS 2/Gazebo framework and the standardized metrics (Path Deviation, Executed Upstream Cost) to create a standardized benchmark suite for evaluating autonomous marine sampling AI algorithms across various hydrodynamic conditions.

Capabilities: Researchers can rapidly iterate on new planning or control algorithms by testing them against a high-fidelity, coupled simulation environment that accurately reflects real-world hydrodynamic challenges without needing expensive, full CFD runs for every test case.