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

1. Problem Statement

Soft underwater robotics faces significant challenges in modeling and control due to the complex fluid-structure interaction (FSI) between the robot's compliant body and the surrounding fluid.

• Computational Cost: High-fidelity methods like Computational Fluid Dynamics (CFD) are too computationally expensive for real-time control or Reinforcement Learning (RL) training.
• Generalization Issues: Black-box neural networks require vast amounts of data and lack interpretability, while classical analytical models (e.g., Elongated Body Theory) often fail to generalize to unseen actuation frequencies or complex control scenarios.
• The Gap: There is a need for a simulation environment that is computationally efficient (real-time or faster), physically accurate enough to match real-world behavior, and capable of serving as a "digital twin" for training control policies.

2. Methodology

A. Hardware Platform

The authors developed a tendon-driven robotic fish with the following characteristics:

• Structure: A passive front-end (acrylic/3D-printed) housing a single waterproof motor, and an active, compliant tail made of four Nitinol rods.
• Actuation: A single motor drives two fishing-wire tendons via a crank-slider mechanism, creating an antagonistic S-bend motion.
• Sensing: 11 markers (on the head, 5 spine segments, and tail fin) are tracked via top-down video (GoPro) to extract ground truth trajectories.
• Environment: Tested in a 2m × 3m pool as a surface swimmer (buoyant foam).

B. Simulation Environment (MuJoCo)

The authors implemented a stateless, simplified hydrodynamics model within the MuJoCo physics engine.

• Discretization: The continuous flexible tail is modeled as an articulated rigid body with 5 hinge joints.
• Fluid Model: Based on a simplified model previously used for fruit flies [11], the fluid forces are calculated directly from the robot's state (velocity, angular velocity) without solving for the fluid field (no CFD). The model includes five force components:
  1. Blunt Drag
  2. Slender Drag
  3. Angular Drag
  4. Kutta Lift
  5. Magnus Lift
  6. (Plus Viscous Drag and Added Mass terms).
• Performance: The simulation runs at ~15x real-time on a standard CPU, enabling rapid training for RL.

C. System Identification (Sim-to-Real)

To bridge the gap between simulation and reality, the authors performed a multi-stage parameter identification process using only two real-world swimming trajectories (at 0.60 Hz and 1.19 Hz):

1. Tail Stiffness: Identified by matching the natural oscillation frequency (3.5 Hz) of the tail in both simulation and reality.
2. Actuation Matching: Optimized motor arm length, angular velocity, and phase offset to match tail kinematics in air (minimizing marker distance error).
3. Fluid Coefficients: Used Bayesian Optimization combined with Nelder-Mead to tune the five fluid coefficients (blunt drag, slender drag, angular drag, Kutta lift, Magnus lift) to match the forward swimming velocity and trajectory in water.

3. Key Contributions

1. Efficient Simulation Environment: Creation of a MuJoCo-based digital twin for tendon-driven underwater robots that runs significantly faster than real-time.
2. Data-Efficient Parameter Identification: Demonstration that a stateless fluid model can be accurately matched to physical reality using only two trajectories, generalizing across a wide range of actuation frequencies.
3. Superiority over Analytical Baselines: The proposed model outperforms the classical Elongated Body Theory (EBT). While EBT struggles to generalize to new frequencies without re-tuning, the proposed model maintains accuracy across unseen actuation frequencies.
4. RL Integration: Successful deployment of the digital twin for downstream Reinforcement Learning tasks, specifically target tracking.

4. Results

A. Sim-to-Real Generalization

• Velocity Accuracy: When tested on 8 new frequencies (0.4 Hz to 1.6 Hz) not used in training, the model achieved a mean velocity error of 0.019 m/s.
• Comparison: The EBT baseline showed a significantly higher error of 0.134 m/s on the same test set, highlighting the limitations of classical analytical models for complex, variable-frequency control.
• Trajectory Matching: The simulation accurately replicated the forward swimming trajectory and tail kinematics of the real robot.

B. Reinforcement Learning (Target Tracking)

• Algorithm: A Soft-Actor-Critic (SAC) agent was trained in the simulation to track random target locations.
• Performance: The agent achieved a 93% success rate in reaching targets within a 4m × 4m area.
• Waypoint Tracking: When tasked with following a circular path, the agent achieved an average tracking error of 0.009 m (0.9 cm), demonstrating that simple velocity control inputs can generate complex turning and acceleration behaviors.

5. Significance and Future Work

• Scalability: The paper proves that simple, stateless models, when carefully calibrated, are sufficient for creating effective digital twins for soft underwater robots. This opens the door for scalable learning in aquatic environments without the prohibitive cost of CFD.
• Accessibility: The open-source simulation environment allows the broader robotics community to apply standard RL pipelines to soft underwater systems.
• Limitations & Future Directions:
  • Current model assumes surface swimming; future work aims to extend to full 3D underwater navigation (requiring pitch/buoyancy control).
  • The stateless model cannot capture complex shape changes or wake interactions; future iterations may involve segment-specific fluid coefficients or more advanced extensions of EBT.
  • The current focus is on constant cruising; future work will address dynamic turning and acceleration/deceleration behaviors.

In conclusion, this work establishes a practical framework for learning-based control of soft underwater robots, demonstrating that high-fidelity simulation is not strictly necessary if the model is efficiently matched to physical data, thereby enabling rapid prototyping and deployment of biomimetic aquatic systems.