ModCube: Modular, Self-Assembling Cubic Underwater Robot

TL;DR

The paper introduces ModCube, a low-cost, modular underwater robot platform designed for swarm coordination and self-assembly, with RS-ModCubes formed by docking multiple ModCube units. It develops a Lagrangian-based dynamic model, a model-based PD controller, a drag lookup table via Monte Carlo methods, and a thrust allocation framework to enable omnidirectional motion and reconfigurable morphologies. A novel morphological characterization using Willmore and Dirichlet energies, along with a convex optimization of the reachable wrench space and maximum inscribed ellipsoid metrics, provides quantitative guidance for configuration selection. Experimental validation in two water tanks demonstrates robust single- and multi-module docking, spiral trajectory tracking, and RS-ModCubes planning, while open-source code and designs facilitate future scaling and broader adoption. Overall, the work shows that reconfigurable modular robotics can offer adaptable, energy-efficient solutions for underwater tasks and pave the way for scalable swarm operations in real environments.

Abstract

This paper presents a low-cost, centralized modular underwater robot platform, ModCube, which can be used to study swarm coordination for a wide range of tasks in underwater environments. A ModCube structure consists of multiple ModCube robots. Each robot can move in six DoF with eight thrusters and can be rigidly connected to other ModCube robots with an electromagnet controlled by onboard computer. In this paper, we present a novel method for characterizing and visualizing dynamic behavior, along with four benchmarks to evaluate the morphological performance of the robot. Analysis shows that our ModCube design is desirable for omnidirectional tasks, compared with the configurations widely used by commercial underwater robots. We run real robot experiments in two water tanks to demonstrate the robust control and self-assemble of the proposed system, We also open-source the design and code to facilitate future research.

Figures (8)

• Figure 1: ModCube's design (top left) features 8 thrusters allowing omnidirectional motion and docking mechanism for assemble and reconfiguration. Two ModCube modules can assemble into RS-ModCubes autonomously. With RS-ModCubes, we show the capability of lifting a metal pipe from the bottom of the water tank, passing through a narrow pipe, and disassembling for reconfiguration.
• Figure 2: System components and architecture. (A) Interior view of ModCube's cabin. (B) Exterior view of ModCube with the cabin highlighted in orange, and MDS layout in the top. (C) Electronic system architecture. (D) Control and planning framework.
• Figure 3: The top row (I to III) illustrates different RS-ModCubes configurations: single, line, and box. The middle row (i to iii) depicts the corresponding approximated drag force space $\boldsymbol{D}_{lut}$ . The body frame $\{ \mathcal{B} \}$ is shown in I, with an arbitrary projection plane highlighted in yellow. The random index $p_{i} \in P_{d}$ is indicated by a red star. The bottom row shows the comparison between approximated drag force values by the proposed method and CFD simulation result, reaching a low RMSE of 6.71 N.
• Figure 4: Comparison of measured force data between an individual ModCube and a two-module RS-ModCubes during target force trajectory tracking (left). A polynomial regression fit for the measured forces (right).
• Figure 5: Benchmark comparison of three differemt RS-ModCubes configurations (A--C) and four commercial underwater robots (D--G). The evaluation includes the power consumption space ($\Omega_{P}$) and the reachable wrench space ($\Omega_{W}$) in the body force frame ($\{\mathcal{B}_f\}$) and body torque frame ($\{\mathcal{B}_{\tau}\}$), respectively. Additionally, the thruster thrust distribution is analyzed using violin plots of variance metrics ($\sigma_{T,P}^2$ and $\sigma_{T,W}^2$), which quantify the thrust effort distribution across force and torque components. X-axis of violin plots represents the thruster index, while the Y-axis indicates the distributions of thrust forces. Detailed evaluations values are provided in Table \ref{['tab:space_metrics_comparison']}.