FinsSim

Demo Video

T1 / Station keeping

Each setpoint compares simulation and pool-trial replays for the Calibrated Fossen policies with and without domain randomization.

Setpoint

Calibrated Fossen + DR

Calibrated Fossen + NoDR

Point 01

Simulation

Pool trial

Simulation

Pool trial

Point 02

Simulation

Pool trial

Simulation

Pool trial

T2 · Trajectory-tracking video comparisons

Hardware replays are organized by trajectory. Each comparison places the simulation, recorded top-view trail, and side-view motion for the Calibrated Fossen + DR policy side by side.

Straight line

Simulation

Top-view trail

Side view

Broken line

Simulation

Top-view trail

Side view

Ellipse

Simulation

Top-view trail

Side view

Lemniscate

Simulation

Top-view trail

Side view

Abstract

Underwater robot learning relies on simulators that integrate high-fidelity hydrodynamics, convenient learning interfaces, and a credible transition to real scenarios. In this work, we present FinsSim, a reality-aligned integrated simulation platform for Sim‑to‑Real underwater robot learning. FinsSim first constructs high-fidelity simulation with selectable backends to adapt to diverse requirements. To facilitate underwater robot research, it further offers standard control baselines, alongside with unified robot learning workflows. For reliable Sim-to-Real transfer, FinsSim adopts a multi-sensor fusion scheme to provide low-cost yet precise localization. Moreover, it implements calibrated thruster-hydrodynamics models and constrained wrench allocation algorithm. Bridging these modules by ROS~2, FinsSim establishes a complete Sim-to-Real transfer pipeline. Through matched simulations and experiments, it is demonstrated that reliable Sim-to-Real transfer of underwater robot control policies can be achieved with the FinsSim framework. Separate ablation studies also validate that the modules of FinsSim can address the pivotal issues of underwater Sim-to-Real from different aspects. Overall, this work aims to bridge the gap between theoretical research and practical applications, ultimately driving advancements in the field of underwater robotics.

Specifically Designed for Underwater Robot Learning

Table I summarizes the platform scope reported by the cited primary publications, including multi-agent support, simulation backend, hydrodynamics, ROS, learning interfaces, training parallelism, and Sim-to-Real evidence.

Platform scope reported by the cited primary publications.
Platform	MA	Backend	Hydrodynamics	ROS	Learning interface	Parallel training	Sim-to-Real evidence
UUV Simulator ^[1]	No	Gazebo Classic	Fossen-form dynamics	ROS 1	None reported	No	Not reported
DAVE ^[2]	No	Gazebo Classic	Fossen-form dynamics	ROS 1	None reported	No	Not reported
HoloOcean ^[3]	Yes	Unreal Engine	Fossen-form dynamics	ROS 2	Python	No	Not reported
Stonefish ^[4]	No	Bullet / OpenGL	Mesh-based hydrodynamics	ROS 1 / 2	None reported	No	Not reported
MARUS ^[5]	Yes	Unity	Simplified mesh-based hydrodynamics	ROS 1 / 2	None reported	No	Not reported
MarineGym ^[6]	Yes	Isaac Lab	Simplified Fossen-form dynamics	None reported	TorchRL / TensorDict	Yes	Not reported
UNav-Sim ^[7]	No	UE5 / AirSim	Fossen-form dynamics	ROS 1 / 2	AirSim Gym / SB3	No	Not reported
Orca ^[8]	No	Gazebo Harmonic / ArduSub SITL	Simplified Fossen-form dynamics	ROS 2	None reported	No	Not reported
FinsSim	Yes	Unity / Isaac Lab	Simplified Fossen, calibrated Fossen, physics mesh	ROS 2	Python / Gym-like, TorchRL / TensorDict, SB3, IL, MARL	Yes	Yes

Architecture

Simulation layer

Unity supplies scene-rich and sensor-oriented simulation, while Isaac Lab provides a GPU-native path for high-throughput state-based training. The vehicle can switch among calibrated Fossen, physics-mesh, and simplified Fossen dynamics.

Learning and control layer

PID, RL, IL, and MARL workflows share sensor, state, action, and evaluation contracts. Policies can operate through a six-channel body wrench or an eight-thruster interface.

Hardware layer

A fixed overhead camera, onboard AprilTags, pressure, and IMU measurements feed a fused state estimate. It’s the perception of the physical world. A hardware bridge and MCU turn bounded force commands into calibrated thruster execution.

FinsSim consists of a simulation platform and a hardware-connected physical platform, linked through ROS 2. The simulation platform supports Unity ML-Agents ^[10] and Isaac Lab ^[11] as simulation backends. It provides calibrated Fossen-form, simplified Fossen-form, and mesh-based hydrodynamic models, together with learning and control interfaces for policy training and evaluation. The physical platform combines a low-cost global localization system based on refractive AprilTags, pressure and IMU sensing, multi-sensor state estimation, and a ROS 2 hardware bridge that relays bounded control commands to the onboard MCU for calibrated eight-thruster actuation on FinsROV.

Features

Fidelity-Scalable Simulation

FinsSim provides three interchangeable hydrodynamic models to accommodate diverse simulation and learning requirements.

Hydrodynamic backends exposed by FinsSim.
Backend	Hydrodynamic model	Characteristics and use
Calibrated Fossen	$\boldsymbol{\tau}_{\mathrm{h}}^{\mathrm{F}} = \boldsymbol{\tau}_{\mathrm{H}} + \boldsymbol{\tau}_{\mathrm{D}}(\boldsymbol{\nu}_{\mathrm{r}}) - \mathbf{M}_{\mathrm{A}}\dot{\boldsymbol{\nu}}_{\mathrm{r}} - \mathbf{C}_{\mathrm{A}}(\boldsymbol{\nu}_{\mathrm{r}})\boldsymbol{\nu}_{\mathrm{r}}$ ^[9] $\boldsymbol{\tau}_{\mathrm{D}} = -[\mathbf{D}_1 + \mathbf{D}_2\operatorname{diag}(\|\boldsymbol{\nu}_{\mathrm{r}}\|) + \mathbf{D}_u\|u_{\mathrm{r}}\|]\boldsymbol{\nu}_{\mathrm{r}}$	Recommended when vehicle calibration data are available. Single-axis pool trials identify effective inertia, linear and quadratic damping, and bias terms. It gives the closest reported four-axis replay to pool measurements and the strongest reported transfer results.
Physics mesh	$\mathbf{v}_i = \mathbf{v}_{\mathrm{w}}(\mathbf{c}_i) - \mathbf{v}_{\mathrm{body}}(\mathbf{c}_i)$ , $\mathbf{v}_{t,i} = (\mathbf{I} - \mathbf{n}_i\mathbf{n}_i^{\mathsf{T}})\mathbf{v}_i$ $\mathbf{F}_i = \mathbf{F}_i^{\mathrm{form}} + \mathbf{F}_i^{\mathrm{skin}}$	Requires a closed physics mesh. The backend clips the mesh at the water surface and accumulates form and skin drag over submerged faces, making it convenient when mesh geometry is the available starting point for a new vehicle. It can capture geometry-dependent effects, while the reported overall hydrodynamic replay remains less accurate than the calibrated Fossen model.
Simplified Fossen	$\boldsymbol{\tau}_{\mathrm{h}}^{\mathrm{S}} = \boldsymbol{\tau}_{\mathrm{H}} + \boldsymbol{\tau}_{\mathrm{D}}(\boldsymbol{\nu})$	Retains hydrostatics and damping while omitting relative-acceleration estimation and added-mass Coriolis evaluation. It avoids a vehicle-specific calibration procedure; with domain randomization, it supports large-batch RL and parallel training. Its reported replay and transfer fidelity remain below the calibrated Fossen configuration.

Recorded single-axis pool excitations are replayed in Unity with the three hydrodynamic backends across surge, sway, heave, and yaw. Calibrated Fossen yields the lowest equal-weight four-axis NRMSE and the closest match to the measured physical responses, consistent with the T1 station-keeping transfer results.

Four-axis pool-to-Unity replay error.
Backend	NRMSE	Bootstrap 95% CI
Calibrated Fossen	0.315	[0.255, 0.338]
Physics mesh	1.104	[0.923, 1.282]
Simplified Fossen	1.374	[1.201, 1.447]

Pool and simulation hydrodynamic response envelopes across surge, sway, heave, and yaw — Dynamics replay. Across the measured four-axis protocol, Calibrated Fossen gives the closest response envelope to the recorded pool measurements.

Low-cost Global Positioning

A fixed overhead camera observes two vehicle-mounted AprilTags ^[12] through a calibrated air-water interface. The camera ray is intersected with the interface, then refracted using Snell’s law before reconstruction at the pressure- and IMU-constrained tag-corner height. This provides horizontal position and yaw, while pressure supplies depth and the IMU constrains roll and pitch.

\mathbf r_{p,i}^{\mathrm{w}} = \eta\mathbf r_{p,i}^{\mathrm{a}} + \left(\eta c_i - \sqrt{1 - \eta^2(1-c_i^2)}\right)\mathbf n_{\Pi,i}

Constrained refractive AprilTag measurement through a calibrated air-water interface — Constrained refractive AprilTag measurement. Pressure determines corner height, IMU constrains roll and pitch, and the refracted multi-tag geometry estimates horizontal position and yaw.

The resulting AprilTag measurement is fused by a position-velocity EKF and a separate yaw filter. Across 720 archived images at 170 surveyed pool locations, the refraction-aware measurement reaches 0.73 cm horizontal RMSE and 1.45 cm P95, compared with 5.74 cm and 11.41 cm for pinhole PnP.

Cost comparison of localization infrastructure.
Method	Infrastructure	Cost
FinsSim	Overhead camera, 2×AprilTag, IMU, pressure sensor	$101
SBL acoustic positioning	GPS/acoustic base station, antenna, acoustic locator, ROV-integrated component	$8,990
Underwater optical motion capture	Underwater motion-capture cameras, synchronization network, marker rig, calibration tools, software	$118k–226k

Reality-aligned

FinsSim separates vehicle-specific calibration from task specification. The calibrated vehicle stack includes hydrodynamic coefficients, directional thrust curves, allocation geometry, and safety bounds; the same ROS 2 interface then connects simulation, controllers, and the FinsROV hardware bridge.

Hydrodynamic calibration

Single-axis trials identify effective mass or inertia, linear damping, quadratic damping, and constant bias for surge, sway, heave, and yaw. Roll and pitch use the corresponding restoring-moment model, and the resulting vehicle profile is transferred into the calibrated Fossen backend.

\tau_i = m_i^{\mathrm{eff}}\dot{\nu}_i + d_{1,i}\nu_i + d_{2,i}|\nu_i|\nu_i + b_i

Thrust-curve calibration

Each thruster uses separately identified forward and reverse steady-state quadratic curves. The bridge maps requested force to target RPM, and the onboard MCU closes a feedforward-plus-PID speed loop using measured RPM feedback.

T_i = c_i^{\pm}\omega_i|\omega_i|

Forward and reverse steady-force sweep for the FinsROV horizontal-left-front thruster — Representative H_LF horizontal-thruster steady-force sweep. Points are measured steady means and curves are separate forward and reverse fits.

Bounded hardware execution

For body-wrench commands, a constrained allocator respects calibrated directional force limits and regularizes unnecessary thrust effort before sending the shared eight-channel command to Unity or the hardware bridge.

Learning Task Contracts

FinsSim specifies task-specific observations, normalized actions, reward functions, safety conditions, and evaluation metrics for underwater control. The reported policies use Proximal Policy Optimization ^[13] through Stable-Baselines3 ^[14]. PPO-Wrench6 and PPO-Thruster8 share task-specific observations and calibrated force limits while providing distinct action interfaces.

T1 / Station keeping

Hold a registered 4-DOF pose

Observation: 16 dimensions: body-frame target displacement, continuous relative attitude, linear and angular velocity, and scalar distance-to-goal.
Action: Wrench6 emits a normalized six-axis body wrench in [-1, 1]. Thruster8 emits normalized commands for the eight canonical thrusters. Reported hardware results use Wrench6.
Reward: Position tracking and a sustained-hold bonus, attitude and angular-rate preference, low-energy smooth commands, and a penalty on task failure.
Evaluation: Eight fixed setpoints, 60 s per trial. Position and yaw RMSE are measured in the 40-60 s late-hold window; roll and pitch are safety guards.

T2 / Trajectory tracking

Follow a time-indexed 3D reference

Observation: 30 dimensions: four future body-relative reference points, reference velocity and tangent, vehicle linear and angular velocity, control state, and trajectory encoding.
Action: The same Wrench6 and Thruster8 policy contracts are available. Hardware comparisons report Wrench6, which maps a normalized wrench to bounded thruster forces.
Reward: Path-tracking quality, uprightness and low yaw-rate preferences conditioned on tracking, low-energy actuation, and failure termination penalties.
Evaluation: Straight-line, broken-line, elliptical, and lemniscate references. The task tracks translation, with yaw, roll, and pitch maintained as stabilized axes.

Experimental Results

The experiments evaluate refractive localization accuracy, simulation dynamics reliability, and Sim-to-Real policy transfer through matched simulation and pool trials.

T1 hardware component ablation and PID baseline.
Configuration	3D position RMSE [m]	Yaw RMSE [deg]	Success
Calibrated Fossen + NoDR	0.077	6.54	7 / 8
Calibrated Fossen + DR	0.092	5.42	7 / 8
Physics mesh	0.746	12.19	0 / 8
Physics mesh + DR	0.197	8.62	0 / 8
Simplified Fossen	0.598	23.37	0 / 8
Traditional PID	0.176	44.08	0 / 8

T2 hardware tracking errors.
Configuration	Trajectory	Horizontal RMSE [m]	Vertical RMSE [m]	3D P95 [m]
Calibrated Fossen + DR	Straight line	0.068	0.129	0.409
	Broken line	0.086	0.084	0.265
	Ellipse	0.091	0.080	0.366
	Lemniscate	0.051	0.073	0.134
Calibrated Fossen + NoDR	Straight line	0.135	0.139	0.406
	Broken line	0.136	0.133	0.310
	Ellipse	0.166	0.102	0.338
	Lemniscate	0.163	0.103	0.305
Traditional PID	Straight line	0.182	0.146	0.405
	Broken line	0.196	0.152	0.426
	Ellipse	0.174	0.134	0.433
	Lemniscate	0.207	0.170	0.514

Station-keeping position and yaw error responses across simulation backends and PID — T1 station keeping. The Calibrated Fossen reference policy sustains 7 of 8 setpoints; the figure shows the associated position and yaw error responses.

Four representative hardware trajectory tracking results for the Calibrated Fossen plus domain randomization configuration — T2 trajectory tracking. Calibrated Fossen with domain randomization follows straight, broken-line, elliptical, and lemniscate references in pool trials.

Citation

@article{zhang2026finssim,
  title={FinsSim: A Reality-Aligned Integrated Simulation Platform for Underwater Robot Learning},
  author={Zhang, Yu and Song, Yuanmingqing and Rao, Xiangyun and Fong, Pangkit and Zhang, Kunhao and Fang, Chongrong and He, Jianping},
  journal={arXiv preprint arXiv:2609.23943},
  year={2026},
  doi={10.48550/arXiv.2609.23943},
  url={https://arxiv.org/abs/2609.23943}
}

Demo Video

T1 / Station keeping

T2 · Trajectory-tracking video comparisons

Abstract

Specifically Designed for Underwater Robot Learning

Architecture

Simulation layer

Learning and control layer

Hardware layer

Features

Fidelity-Scalable Simulation

Low-cost Global Positioning

Reality-aligned

Hydrodynamic calibration

Thrust-curve calibration

Bounded hardware execution

Learning Task Contracts

Hold a registered 4-DOF pose

Follow a time-indexed 3D reference

Experimental Results

Citation

References