Simple Models, Real Swimming: Digital Twins for Tendon-Driven Underwater Robots

Mike Y. Michelis; Nana Obayashi; Josie Hughes; Robert K. Katzschmann

cs.ROFeb 26, 2026

Simple Models, Real Swimming: Digital Twins for Tendon-Driven Underwater Robots

Authors: Mike Y. Michelis, Nana Obayashi, Josie Hughes, Robert K. Katzschmann

Organizations: Soft Robotics Lab and ETH AI Center, ETH Zurich, Switzerland · Prema Lab, New York University, USA · CREATE Lab, EPFL, Switzerland

Abstract

Mimicking the graceful motion of swimming animals remains a core challenge in soft robotics due to the complexity of fluid-structure interaction and the difficulty of controlling soft, biomimetic bodies. Existing modeling approaches are often computationally expensive and impractical for complex control or reinforcement learning needed for realistic motions to emerge in robotic systems. In this work, we present a tendon-driven fish robot modeled in an efficient underwater swimmer environment using a simplified, stateless hydrodynamics formulation implemented in the widespread robotics framework MuJoCo. With just two real-world swimming trajectories, we identify five fluid parameters that allow a matching to experimental behavior and generalize across a range of actuation frequencies. We show that this stateless fluid model can generalize to unseen actuation and outperform classical analytical models such as the elongated body theory. This simulation environment runs faster than real-time and can easily enable downstream learning algorithms such as reinforcement learning for target tracking, reaching a 93% success rate. Due to the simplicity and ease of use of the model and our open-source simulation environment, our results show that even simple, stateless models -- when carefully matched to physical data -- can serve as effective digital twins for soft underwater robots, opening up new directions for scalable learning and control in aquatic environments.

Figures & tables

Fig. 1 : Overview of the simulated and real swimmer robots. A) Robot swimming in the pool captured from a top-down view, images overlaid are $3\text{\,}\mathrm{s}$ apart. B) The 11 markers are tracked and extracted from the video. C) Side-view of the hardware with a single motor actuating the tendon-driven tail. D) Simulated robot with markers indicated by small orange spheres. Center of mass is located at the large orange sphere in the head. E) Simulated trajectory after matching fluid model to real experiment.

Fig. 2 : Overview of the main mechanisms for the swimmer simulation environment. We simplify the deformable spine with multiple hinge joints as an articulated rigid body, we use stiff elastic tendons for the tendon-driven actuation, a velocity-controlled motor that pulls the tendons, and a simplified fluid model to mimic real-world swimming behavior.

Fig. 3 : Natural frequency in both time and frequency domain of the fish tail measured on the real robot tail (left) and of the simulated system after matching the main amplitude frequency with reality (right). The different colors in the left plot indicate the 5 spine segments that are tracked during the oscillation.

Fig. 4 : System identification of motor angular frequency and phase offset to minimize the distance between simulated and real markers, with a minimal distance of

0.026\text{\,}\mathrm{m}

for the

0.60\text{\,}\mathrm{Hz}

swimming shown on the left.

Fig. 5 : Optimized results of sim-to-real in-water experiment for

1.19\text{\,}\mathrm{Hz}

data. We show the tail fin marker position (left) and forward swimming position (right) to validate the thrust generated by the hydrodynamics model. The average distance error on all markers is computed to be

0.016\text{\,}\mathrm{m}

Fig. 6 : Sim-to-real generalization across frequencies of our optimized fluid coefficient model,

0.019\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}

error, and the EBT model,

0.134\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}

. Velocity direction is defined in the local fish frame.

Fig. 7 : A) SAC agent trained to track random target locations (green) with a $93\%$ success rate. Robot states are overlaid $1\text{\,}\mathrm{s}$ apart. B) SAC agent tracking waypoints along the green circle trajectory with an average target error of $0.009\text{\,}\mathrm{m}$ . C) We demonstrate the ability to simulate a large number of swimmers in real-time.

	Observations
Motor Joint	$\cos(\alpha)$ , $\sin(\alpha)$ , $\dot{\alpha}$
Head Frame	$\dot{\theta}_{x},\dot{\theta}_{y},\dot{\theta}_{z}$
Tail Joint $i$	$\phi_{i},\dot{\phi}_{i}$
Target Vector	$\\|\vec{d}_{t}\\|$ , $\vec{d}_{t}$ , $\dot{\vec{d}}_{t}$
Prev Action	$u_{old}$

TABLE I : The observations used for training the SAC agent for target tracking. All observations are defined relative to the robot frame.

Panel of Figure 9 — Fig. 8 : (Left) Tracking random waypoints in $20$ evaluation environments. The red points are the randomized target locations, while the blue curves are the trajectories of the swimmer. (Right) Tracking waypoints along circle with an average distance error of $0.009\text{\,}\mathrm{m}$ . The green and red points indicate start and end positions respectively.

Underwater Robotics

Underwater robotics develops autonomous and remotely operated machines for navigation, inspection, manipulation, and exploration in aquatic environments.

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Sep 29, 2026

All You Need Is Low Fidelity: Zero-Shot Sim-to-Real of Learned Robotic Fish Control

Complex tasks for underwater robots remain limited by the capabilities of their controllers. Learning a better one for a soft, underactuated robotic fish trades simulator cost against fidelity. We show that an intentionally low-fidelity simulator is enough: a stateless, quasi-steady fluid model with no wake and no added-mass history suffices to learn a general, closed-loop controller that transfers to hardware without tuning. Our platform is a soft, single-motor, tendon-driven fish whose policy observes only what the hardware can measure. A staged pipeline grounds the simulator in two independent identifications, fixing the tail dynamics and a stateless fluid model; the policy then acts through a band-limited rhythmic trajectory generator rather than commanding the tail directly. Deployed unchanged in an outdoor pool, a single policy performs closed-loop target reaching, disturbance rejection, and out-of-distribution target acquisition and tracking. The transfer rests on the constraint rather than the fidelity: the generator cannot leave the band over which the fluid was identified. This raises the question of how much of the physics can reside in the controller rather than in the simulator.

Liam Maloney, Simon Ramchandani, Mike Y. Michelis +2

Soft Robotics Lab, ETH Zurich, Switzerland · ETH AI Center, ETH Zurich, Switzerland

Robotic Control Robotics Simulation Sim-to-Real Transfer Underwater Robotics Soft Robotics

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Mar 9, 2026

Unified Structural-Hydrodynamic Modeling of Underwater Underactuated Mechanisms and Soft Robots

Underwater robots are widely deployed for ocean exploration and manipulation. Underactuated mechanisms are advantageous in aquatic environments because reducing actuator count lowers motor-leakage risk while introducing inherent mechanical compliance. However, accurate modeling of underwater underactuated and soft robotic systems remains challenging, as it requires identifying high-dimensional structural and hydrodynamic parameters. In this work, we propose a trajectory-driven global optimization framework for unified structural-hydrodynamic modeling of underwater multibody systems. Inspired by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the proposed approach simultaneously identifies coupled elastic, damping, and distributed hydrodynamic parameters through trajectory-level matching between simulated and experimental motion. This enables high-fidelity reproduction of underactuated mechanisms and compliant soft robotic systems in underwater environments, using as little as a single video recording. We first validate the framework on a link-by-link underactuated multibody mechanism, demonstrating accurate identification of distributed hydrodynamic coefficients, with normalized end-effector position error below 5% across multiple trajectories, initial conditions, and both active-passive and fully passive configurations. The modeling strategy is further validated on an asymmetric octopus-inspired soft arm, confirming its effectiveness for compliant soft robotic systems. Finally, eight identified arms are assembled into a swimming octopus robot, where the unified parameter set enables realistic whole-body behavior without additional retuning. These results demonstrate the scalability and transferability of the proposed structural-hydrodynamic modeling framework across underwater underactuated and soft robotic systems.

Chenrui Zhang, Yiyuan Zhang, Yunfei Ye +3

Department of Mechanical Engineering and Advanced Robotics Centre, National University of Singapore, Singapore. · Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore.

Robot System Identification Underwater Robotics System Identification Soft Robotics

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Jun 9, 2026

Model-based Optimization of Anguilliform Swimming Gaits for Soft Robotic Applications

In this paper, we introduce the Soft Lamprey-Inspired Dual Environment Robot (SLIDER) and a proper modeling and optimization procedure employed to design the robot. We represent the primary fluid environment actions - inertial effects, vortex forces, and viscous dissipation - using Lighthill's theory for large-amplitude elongated bodies. For structural design parameters such as internal pressure, tail size, and body stiffness, a fast, geometrically and materially nonlinear model is developed and validated. The fluid-structure interaction equations are solved implicitly with an efficient second-order box method. A pneumatic manifold robotic system is employed to actuate SLIDER in a quiescent water tank environment, allowing cross-comparison of computational and experimental results. We find that low-frequency swimming is dominated by resistant environmental forces, whereas higher-frequency swimming is primarily affected by inertial fluid forces. Using our efficient model alongside a genetic algorithm, we co-optimize a swimming control pattern and caudal fin design (subject to SLIDER's climbing morphology) to achieve a tethered swimming speed of 21.7 +/- 0.4 cm/s (0.59 Bl/s). Furthermore, we investigate the optimization procedure for a multimodal robot performing both swimming and climbing tasks.

Brian Van Stratum, James Gallentine, Caleb Rucker +3

FAMU/FSU College of Engineering, Tallahassee, FL 323109 · Mechanical Engineering, Vanderbilt University, Nashville Tennessee 37235 · Mechanical Engineering, The University of Tennessee, Knoxville, Tennessee 37996

Robot Locomotion Underwater Robotics Fluid-Structure Interaction Soft Robotics Physics-Based Simulation

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Abstract

Underwater Robotics

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