ZodiAq: An Isotropic Flagella-Inspired Soft Underwater Drone for Safe Marine Exploration

TL;DR

This work introduces ZodiAq, a soft underwater drone with a dodecahedral shell and 12 flagella-inspired actuators for isotropic, safe navigation in cluttered marine environments. A digital twin built in SoRoSim using the Geometric Variable Strain Cosserat rod model enables system analysis and control design for a 90-DOF platform, while a simplified model-based controller achieves depth and yaw regulation in hardware. Four demonstrations—design redundancy, embodied intelligence, crawling gait, and coral-reef exploration—showcase increased reliability, environmental compatibility, and versatile locomotion, including interaction-enabled motion. The study highlights the potential of soft robotics for fault-tolerant, environmentally aware underwater exploration and outlines avenues for improved planar feedback and fault-tolerant control to advance real-world deployment.

Abstract

The inherent challenges of robotic underwater exploration, such as hydrodynamic effects, the complexity of dynamic coupling, and the necessity for sensitive interaction with marine life, call for the adoption of soft robotic approaches in marine exploration. To address this, we present a novel prototype, ZodiAq, a soft underwater drone inspired by prokaryotic bacterial flagella. ZodiAq's unique dodecahedral structure, equipped with 12 flagella-like arms, ensures design redundancy and compliance, ideal for navigating complex underwater terrains. The prototype features a central unit based on a Raspberry Pi, connected to a sensory system for inertial, depth, and vision detection, and an acoustic modem for communication. Combined with the implemented control law, it renders ZodiAq an intelligent system. This paper details the design and fabrication process of ZodiAq, highlighting design choices and prototype capabilities. Based on the strain-based modeling of Cosserat rods, we have developed a digital twin of the prototype within a simulation toolbox to ease analysis and control. To optimize its operation in dynamic aquatic conditions, a simplified model-based controller has been developed and implemented, facilitating intelligent and adaptive movement in the hydrodynamic environment. Extensive experimental demonstrations highlight the drone's potential, showcasing its design redundancy, embodied intelligence, crawling gait, and practical applications in diverse underwater settings. This research contributes significantly to the field of underwater soft robotics, offering a promising new avenue for safe, efficient, and environmentally conscious underwater exploration.

Figures (9)

• Figure 1: Prototype Design: (A) CAD model of the prototype (including an exploded view of one face of the prototype), with external components marked in green and internal components in yellow. Components are listed in Table \ref{['tab::ZodiAq Components']}, (B) Electrical connection between components, (C) Numbering scheme used for the faces and motors, (C) Fully assembled prototype floating in the water, (E) a Demonstration of passive mechanical stabilization due to neutral and stable buoyancy. A force ($f_a$) is applied to tilt and push the Zodiaq down. The resulting moment ($m_b$) due to the arrangement of CB above the CG corrects the tilt as the robot sinks deeper. The force of buoyancy ($f_b$) restores the height.
• Figure 2: (A) Digital twin of the robot, created using SoRoSim toolbox. GC is the Geometric Centre, CM is the Centre of Mass, and $\bm{g}_f$ is the transformation matrix from the GC to a motor shaft (M7 in the diagram). (B) A simplified flowchart showing the processes in SoRoSim. (C) Superimposed images of the robot at different time steps during a dynamic simulation. An inset shows a top view (xy-plane) of the motion
• Figure 3: Simulated results of the closed-loop system : (A) Schematic illustrating the control strategy implemented in the closed-loop system. The control law aims to simultaneously control the 3D position ($x,y,z$) and orientation ($\psi$). The angular speed of the motors, denoted as $\bm{\omega}$, serves as the system's control input. The output $\bm{q}=[\phi,\theta, \psi, x, y, z]^{T}$ represents the generalized coordinates of the system, while $\bm{\nu}$ represents the output of proportional-derivative (PD) controller. $\bm{\mathcal{F}}_{G}^{*}$ denotes the desired resultant forces and moments applied to the CM, and $\bm{\Omega}$ is the fictitious input that renders the simplified model differentially flat. For a detailed explanation of the simplified model and the proposed control law, readers can refer to the supplementary material. (B) Comparison between reference trajectories and the actual positions of the angular and linear coordinates. (C) 3D representation of the simulation.
• Figure 4: Validation of Height and Orientation Control: (A) The sequence of video snapshots illustrates the active depth control by controlling the motors using depth feedback. (B) Process of orientation stabilization using IMU feedback. The direction of the ZodiAq’s rotation is shown by green arrows, while the green dot on a face assists in visualizing the orientation throughout the maneuver. (C) Measured angle and depth and their desired values showing controller in action during various experiment instances: pushing down, counterclockwise (CCW) rotation, clockwise (CW) rotation, and pulling up. (D) Controlled motor speed ($\omega/\omega_{max}$) vs time. The color of the band represents the value of angular velocity.
• Figure 5: Square Trajectory in Open-loop: (A) Superimposed images of the drone attempting to follow a square trajectory in open-loop control. (B) Robot depth measurement obtained from the depth sensor. (C) Orientation about the vertical axis.