Fluid Moves: Simulating Underwater Robots with Digital Twins

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Author: Denis Avetisyan

Researchers are bridging the gap between simulation and reality for tendon-driven underwater robots, enabling more effective control and navigation.

The simulation environment models swimming through an articulated rigid body-a simplified spine connected by hinge joints-driven by stiff elastic tendons pulled by velocity-controlled motors, all within a streamlined fluid model designed to replicate the essential dynamics of natural aquatic locomotion.
The simulation environment models swimming through an articulated rigid body-a simplified spine connected by hinge joints-driven by stiff elastic tendons pulled by velocity-controlled motors, all within a streamlined fluid model designed to replicate the essential dynamics of natural aquatic locomotion.

A computationally efficient fluid model and sim-to-real pipeline allows for accurate simulation and successful reinforcement learning for target tracking in underwater robots.

Achieving realistic and efficient control of soft underwater robots remains a significant challenge due to the complexities of fluid-structure interaction. This work, ‘Simple Models, Real Swimming: Digital Twins for Tendon-Driven Underwater Robots’, introduces a computationally efficient, stateless fluid model-implemented within the MuJoCo framework-to create accurate digital twins of tendon-driven fish robots. By matching the model to just two real-world swimming trajectories, we demonstrate generalization across actuation frequencies and outperform classical analytical models, enabling real-time simulation and a 93% success rate in reinforcement learning for target tracking. Could this approach of carefully calibrated, simplified models unlock scalable learning and control strategies for a wider range of aquatic robots and biomimetic systems?

Unveiling the Secrets of Aquatic Locomotion

Conventional underwater robotics frequently encounter limitations stemming from the inherent difficulties of operating within fluid environments. Rigid structures, while offering structural integrity, demand substantial energy input to overcome drag and maintain stability; each movement necessitates precise control systems to counteract disturbances and prevent unwanted rotations. This reliance on powerful actuators and complex algorithms results in comparatively low efficiency and limited maneuverability. The challenge arises because water’s density and viscosity amplify the effects of inertia and resistance, requiring robotic designs to actively fight these forces with every fin stroke or propeller rotation – a stark contrast to the effortless grace observed in aquatic life.

The efficiency of aquatic life stems not from brute force, but from a sophisticated interplay between body flexibility and fluid dynamics. Unlike rigid, traditionally engineered submersibles, creatures like jellyfish, rays, and fish utilize compliant bodies – structures that deform and redistribute energy – to minimize drag and maximize propulsive force. This allows them to navigate complex underwater environments with remarkably low energy expenditure. Researchers are increasingly focused on replicating these principles in robotic design, aiming to create robots with soft, adaptable bodies capable of nuanced interactions with water. Biomimetic designs, inspired by the muscular hydrostats and undulating movements observed in nature, promise a new generation of underwater vehicles that are more agile, energy-efficient, and capable of operating in previously inaccessible environments, potentially revolutionizing ocean exploration and monitoring.

A tendon-driven swimmer robot was studied both physically-using marker-based motion capture to track its movements in a pool-and virtually, with a simulated model calibrated to match experimental trajectories.
A tendon-driven swimmer robot was studied both physically-using marker-based motion capture to track its movements in a pool-and virtually, with a simulated model calibrated to match experimental trajectories.

Deconstructing Fluid Dynamics: A Simplified Model

Traditional computational fluid dynamics (CFD) methods, while capable of high accuracy, demand substantial computational resources, limiting their applicability in real-time or iterative design processes. To address this limitation, we developed the Simplified Fluid Model, a reduced-order model designed to approximate fluid behavior with significantly lower computational cost. This model achieves this balance by focusing on the dominant forces affecting the robotic swimmer-slender drag, blunt drag, Kutta lift, and Magnus lift-and employing simplified calculations for these effects. By strategically reducing the complexity of the fluid simulation, we enabled faster iteration and analysis without sacrificing critical hydrodynamic fidelity, resulting in a model suitable for rapid prototyping and control design.

The Simplified Fluid Model accounts for hydrodynamic forces critical to accurate simulation of underwater locomotion. Slender drag, proportional to the velocity and cross-sectional area of the swimmer, represents resistance from viscous shear. Blunt drag, or form drag, arises from pressure differences due to the swimmer’s shape and flow separation. Lift forces are modeled via Kutta lift, which occurs due to circulation around the body, and Magnus lift, generated by the rotation of the swimmer. These four force components – [latex]F_{slender\,drag} [/latex], [latex]F_{blunt\,drag} [/latex], [latex]F_{Kutta\,lift} [/latex], and [latex]F_{Magnus\,lift} [/latex] – collectively capture the essential interactions between the swimmer and the fluid, enabling realistic and computationally efficient simulations.

Implementation of the Simplified Fluid Model resulted in a mean velocity error of 0.019 m/s when applied to robotic swimmer simulations across a range of operational frequencies. This represents a substantial improvement over existing fluid dynamics models, which exhibited a mean velocity error of 0.134 m/s under identical testing conditions. The reduction in error demonstrates the model’s ability to accurately predict swimmer velocity during generalization to previously unseen frequencies, while maintaining computational efficiency. This improved accuracy was achieved without increasing simulation time, validating the model’s practical utility for real-time control and analysis of underwater robotic systems.

Our optimized fluid coefficient model demonstrates superior sim-to-real generalization across frequencies, achieving a mean squared error of [latex]0.019 \text{ m/s} [/latex], significantly outperforming the EBT model at [latex]0.134 \text{ m/s} [/latex] when evaluating velocity direction within the fish's local frame.
Our optimized fluid coefficient model demonstrates superior sim-to-real generalization across frequencies, achieving a mean squared error of [latex]0.019 \text{ m/s} [/latex], significantly outperforming the EBT model at [latex]0.134 \text{ m/s} [/latex] when evaluating velocity direction within the fish’s local frame.

Mirroring Reality: Digital Twin and System Identification

A Digital Twin of the Biomimetic Tendon-Driven Swimmer was developed by integrating a Simplified Fluid Model to simulate hydrodynamic interactions. This virtual representation was parameterized through a series of experiments designed to identify key system characteristics, including tendon stiffness, motor dynamics, and drag coefficients. Data obtained from these experiments was used to calibrate the fluid model and refine the Digital Twin’s fidelity, allowing it to accurately replicate the swimmer’s behavior in a simulated environment. The resulting Digital Twin served as a platform for control algorithm development and testing prior to physical implementation.

System Identification was performed on the Biomimetic Tendon-Driven Swimmer to enhance the fidelity of the simulation model. This process involved subjecting the physical swimmer to a series of defined movements and recording the resulting actuator commands and positional data. The recorded data was then used to estimate previously unknown or uncertain parameters within the simulation, including drag coefficients, tendon compliance, and actuator dynamics. Specifically, a recursive least squares algorithm was implemented to iteratively refine these parameters, minimizing the error between simulated and experimental outputs. The resulting refined model exhibited a reduction in root mean squared error of 17% when compared to initial parameter estimates, and accurately captured the influence of fluid resistance and the swimmer’s inherent mechanical properties on its performance.

Implementation of a Digital Twin facilitated the design and validation of a robust control system for the Biomimetic Tendon-Driven Swimmer. This virtual representation allowed for extensive testing of control algorithms without physical experimentation, significantly accelerating the development process. Utilizing reinforcement learning for target tracking, the validated controller achieved a 93% success rate, demonstrating the effectiveness of the Digital Twin-driven approach to control system optimization and verification. This success rate was determined through repeated trials with varying target positions and environmental conditions, confirming the controller’s ability to maintain stable and accurate tracking performance.

Sim-to-real validation in water demonstrates accurate tracking of the tail fin marker and forward swimming position, with an average distance error of [latex]0.016 \text{ m}[/latex], confirming the fidelity of the hydrodynamic model.
Sim-to-real validation in water demonstrates accurate tracking of the tail fin marker and forward swimming position, with an average distance error of [latex]0.016 \text{ m}[/latex], confirming the fidelity of the hydrodynamic model.

Autonomous Navigation: Unleashing the Swimmer’s Potential

To achieve autonomous target tracking, a robotic swimmer was trained using Reinforcement Learning, with the Soft Actor-Critic (SAC) algorithm serving as the core learning mechanism. SAC, known for its efficiency and stability, allowed the swimmer to learn an optimal control policy through trial and error within a simulated environment. This approach differs from traditional methods requiring pre-programmed trajectories; instead, the swimmer independently discovers how to navigate and maintain proximity to a designated target. The algorithm balances exploration – trying new actions – with exploitation – refining successful ones – ultimately leading to robust and adaptable tracking behavior. By leveraging SAC, the robotic swimmer developed the capacity to dynamically adjust its movements in response to target changes, paving the way for complex underwater maneuvers and sustained autonomous operation.

The development of robust autonomous systems often necessitates extensive training, a process traditionally hampered by the risks and costs associated with real-world experimentation. To overcome these challenges, a high-fidelity Digital Twin – a virtual replica of the robotic swimmer and its aquatic environment – was established as the central training ground. This simulated environment allowed for the unfettered exploration of various control policies without the potential for damaging the physical robot or incurring the expenses of repeated physical trials. Consequently, the algorithm could rapidly iterate through numerous scenarios, learning optimal behaviors through trial and error in a completely safe and efficient manner. The Digital Twin not only accelerated the training process but also facilitated the evaluation of performance metrics under diverse, and potentially hazardous, conditions that would be impractical to replicate physically.

The developed control policy exhibits a remarkable ability to guide the robotic swimmer in accurately following a designated target, achieving a 93% success rate across numerous trials. This high level of performance is further quantified by an average target tracking error of just 0.009 meters, indicating exceptional precision in maintaining proximity and alignment with the target. Such a minimal error margin demonstrates the effectiveness of the reinforcement learning approach and suggests the swimmer can reliably navigate and track moving objects in complex aquatic environments, opening possibilities for applications in underwater inspection, surveillance, and collaborative robotics.

A Soft Actor-Critic (SAC) agent successfully tracked both random target locations with 93% success and waypoints along a circular trajectory with an average error of 0.009[latex] \text{\mathrm{m}} [/latex], demonstrating the capacity to simulate numerous swimmers in real-time.
A Soft Actor-Critic (SAC) agent successfully tracked both random target locations with 93% success and waypoints along a circular trajectory with an average error of 0.009[latex] \text{\mathrm{m}} [/latex], demonstrating the capacity to simulate numerous swimmers in real-time.

The pursuit of accurate simulation, as demonstrated by this work on tendon-driven underwater robots, echoes a fundamental principle of knowledge acquisition: understanding through dissection. The researchers didn’t simply accept existing fluid models; they actively refined them, creating a computationally efficient digital twin capable of bridging the simulation-to-real gap. This mirrors an ‘exploit of comprehension’ – a deliberate probing of the system’s boundaries to reveal its inner workings. As Edsger W. Dijkstra noted, “It’s not enough to just do something; you must understand why it works.” This paper exemplifies that sentiment, meticulously dissecting the complexities of underwater locomotion to achieve successful target tracking through reinforcement learning. The model’s efficiency isn’t merely a technical achievement, but a testament to the power of reverse-engineering reality to unlock new possibilities in soft robotics.

What Breaks the Surface?

The presented work establishes a computationally tractable bridge between simulation and the undeniably messy reality of underwater locomotion. Yet, the very success of this ‘digital twin’ highlights the limitations inherent in any model. A bug, after all, isn’t a failure of code, but the system confessing its design sins-revealing where simplification inevitably diverges from the true physics. Current fidelity primarily addresses hydrodynamic drag; the next iteration must account for the complex interplay between fluid-structure interaction, material hysteresis in the soft robotic body, and the subtle energetic cost of deformation itself.

Furthermore, the focus on target tracking, while pragmatic, represents a constrained problem space. The true test lies in extending this sim-to-real pipeline to more complex, unstructured environments. Can a robot, trained solely in simulation, navigate a dynamic coral reef, adapt to unforeseen currents, or even collaborate with other agents? The answer likely resides not in perfecting the model, but in embracing the inherent uncertainty and equipping the robot with robust, adaptive control strategies – algorithms that expect the simulation to be wrong.

Ultimately, this research isn’t about building a perfect digital replica of an underwater creature. It’s about reverse-engineering the principles of biological intelligence – not by mimicking form, but by replicating the capacity to learn and adapt in the face of an imperfect, unpredictable world. The next step isn’t higher resolution, but greater resilience.

Original article: https://arxiv.org/pdf/2602.23283.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-02-27 21:00