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

Chenrui Zhang, Yiyuan Zhang, Yunfei Ye, Junkai Chen, Haozhe Wang, Cecilia Laschi

Abstract

Underwater robots are widely deployed for ocean exploration and manipulation. Underactuated mechanisms are particularly advantageous in aquatic environments, as reducing actuator count lowers the risk of motor leakage while introducing inherent mechanical compliance. However, accurate modeling of underwater underactuated and soft robotic systems remains challenging because it requires identifying a high-dimensional set of internal structural and external 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 internal elastic, damping, and distributed hydrodynamic parameters through trajectory-level matching between simulation and experimental motion. This enables high-fidelity reproduction of both underactuated mechanisms and compliant soft robotic systems in underwater environments. We first validate the framework on a link-by-link underactuated multibody mechanism, demonstrating accurate identification of distributed hydrodynamic coefficients, with a normalized end effector position error below 5% across multiple trajectories, varying initial conditions, and both active-passive and fully passive configurations. The identified modeling strategy is then transferred to a single octopus-inspired soft arm, showing strong real-to-sim consistency without manual retuning. Finally, eight identified arms are assembled into a swimming octopus robot, where the unified parameter set enables realistic whole body behavior without additional parameter calibration. These results demonstrate the scalability and transferability of the proposed structural-hydrodynamic modeling framework across underwater underactuated and soft robotic systems.

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

Abstract

Underwater robots are widely deployed for ocean exploration and manipulation. Underactuated mechanisms are particularly advantageous in aquatic environments, as reducing actuator count lowers the risk of motor leakage while introducing inherent mechanical compliance. However, accurate modeling of underwater underactuated and soft robotic systems remains challenging because it requires identifying a high-dimensional set of internal structural and external 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 internal elastic, damping, and distributed hydrodynamic parameters through trajectory-level matching between simulation and experimental motion. This enables high-fidelity reproduction of both underactuated mechanisms and compliant soft robotic systems in underwater environments. We first validate the framework on a link-by-link underactuated multibody mechanism, demonstrating accurate identification of distributed hydrodynamic coefficients, with a normalized end effector position error below 5% across multiple trajectories, varying initial conditions, and both active-passive and fully passive configurations. The identified modeling strategy is then transferred to a single octopus-inspired soft arm, showing strong real-to-sim consistency without manual retuning. Finally, eight identified arms are assembled into a swimming octopus robot, where the unified parameter set enables realistic whole body behavior without additional parameter calibration. These results demonstrate the scalability and transferability of the proposed structural-hydrodynamic modeling framework across underwater underactuated and soft robotic systems.
Paper Structure (14 sections, 5 equations, 12 figures, 1 table, 2 algorithms)

This paper contains 14 sections, 5 equations, 12 figures, 1 table, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. METHODS
  3. Underactuated Mechanism Experimental Platforms
  4. Real-world Trajectory Extraction
  5. CMA-ES Based Fluid Coefficient Identification
  6. Parameter Modeling
  7. Loss Function and Optimization Objective
  8. CMA-ES-Based Optimization
  9. Optimized Output
  10. Real-to-Sim Underactuated Mechanism Experiments
  11. Soft Robot Component Experiment
  12. Soft Robot Experiment
  13. CONCLUSIONS
  14. ACKNOWLEDGMENT

Figures (12)

  • Figure 1: Trajectory-driven CMA-ES framework for simultaneous identification of distributed hydrodynamic coefficients, validated from a three-link mechanism to an octopus-inspired arm and an eight-arm robot. (a) Real-world data collection: Underwater trajectories are recorded using an active–passive coupled three-link mechanism and a purely passive mechanism. (b) Data extraction: SAM2-based segmentation and centerline extraction are used to obtain key trajectory points from experimental videos. (c) Fluid coefficient identification: Real trajectories are matched with MuJoCo simulations, and CMA-ES iteratively optimizes hydrodynamic parameters to minimize trajectory error. (d) Optimized output: The identified hydrodynamic coefficient set $c_0$-$c_4$ calibrates the underwater dynamics model. (e) Soft robot component: The identified parameters are applied to a single octopus-inspired arm to evaluate parameter transferability. (f) Soft robot: Multiple identified arms are arranged in a circular configuration to construct an octopus-inspired robot, demonstrating scalability.
  • Figure 2: Three-link mechanism setup
  • Figure 3: Vision-based trajectory extraction for the three-link mechanism
  • Figure 4: Horizontal three-link trajectories: extracted vs. real data
  • Figure 5: Right-angle three-link trajectories: extracted vs. real data
  • ...and 7 more figures