Design and Control of Modular Magnetic Millirobots for Multimodal Locomotion and Shape Reconfiguration

TL;DR

A versatile modular robotic platform capable of multimodal behavior and robust control is established, suggesting a promising pathway toward scalable and adaptive task execution in confined environments.

Abstract

Modular small-scale robots offer the potential for on-demand assembly and disassembly, enabling task-specific adaptation in dynamic and constrained environments. However, existing modular magnetic platforms often depend on workspace collisions for reconfiguration, employ bulky three-dimensional electromagnetic systems, and lack robust single-module control, which limits their applicability in biomedical settings. In this work, we present a modular magnetic millirobotic platform comprising three cube-shaped modules with embedded permanent magnets, each designed for a distinct functional role: a free module that supports self-assembly and reconfiguration, a fixed module that enables flip-and-walk locomotion, and a gripper module for cargo manipulation. Locomotion and reconfiguration are actuated by programmable combinations of time-varying two-dimensional uniform and gradient magnetic field inputs. Experiments demonstrate closed-loop navigation using real-time vision feedback and A* path planning, establishing robust single-module control capabilities. Beyond locomotion, the system achieves self-assembly, multimodal transformations, and disassembly at low field strengths. Chain-to-gripper transformations succeeded in 90% of trials, while chain-to-square transformations were less consistent, underscoring the role of module geometry in reconfiguration reliability. These results establish a versatile modular robotic platform capable of multimodal behavior and robust control, suggesting a promising pathway toward scalable and adaptive task execution in confined environments.

Figures (6)

• Figure 1: Conceptual overview of the modular magnetic millirobot platform. (a) Geometry and key dimensions of the three cube-shaped modules (free, fixed, and gripper), each incorporating an embedded permanent magnet with module-specific orientation. (b) Multimodal, field-programmable behaviors enabled by magnetic actuation: individual locomotion and navigation, self-assembly into chains, reconfiguration for cargo grasping/manipulation, and on-demand disassembly.
• Figure 2: Actuation mechanisms. (a) Single-module locomotion of the free module driven by uniform fields. (b) Single-module locomotion of the fixed module driven by combined uniform and gradient fields. (c) Cuboid modules exhibit field-programmable self-organization: (i) In the absence of an external field, the dipoles align along the $z$-axis and the modules remain separated ("liquid" state). (ii) When brought into close proximity ($<7$ mm), dipole-dipole attraction dominates and modules self-assemble into chains. (iii) Superimposing a strong external field perpendicular to the chain direction aligns the dipoles with the applied field, suppressing chaining and maintaining separation. (iv) Appropriate field modulation yields stable "square" assemblies. (v) A chain composed of two gripper modules and one free module forms through dipole–dipole attraction, creating a linear three-module assembly. (vi) Upon application of a sufficiently strong and rapid uniform-field pulse, the weakest dipole bond in the chain is selectively broken, enabling perpendicular realignment and reattachment of the modules into a functional gripper configuration.
• Figure 3: Experimental and control setup. (a) Two-dimensional electromagnetic actuation system combining Helmholtz (uniform) and Maxwell (gradient) coil pairs. (b) Planar workspace used for locomotion and assembly experiments. (c) Maze workspace for constrained navigation trials. (d) Photograph of the full experimental apparatus. (e) Real-time vision pipeline and live output windows; the software supports live camera processing and recording, single-image inference, and batch analysis of datasets.
• Figure 4: Single-module translation and closed-loop navigation. (a) Mean displacement per direction (Euclidean, Manhattan, $x$, and $y$) with standard deviation after 10 actuation cycles, averaged over five trials per cardinal direction (80 trials total across four directions and four field conditions). (b) Representative trajectories for an "UP" command produced by the free (top) and fixed (bottom) modules under uniform fields only (left) and uniform fields with superimposed gradient fields (right). Both modules move in the commanded direction in all cases, while added gradient fields yield more repeatable straight-line motion. (c) Live goal-setting interface showing the occupancy grid (top) and workspace mask (bottom). (d) Closed-loop trajectory of the fixed module during autonomous navigation.
• Figure 5: Field-programmable self-assembly, reconfiguration, and cargo transport. Top row: (Self-assembly) Discrete modules transition from a separated "liquid" state to a chain configuration under controlled magnetic fields. (Disassembly) Reversal of the field conditions separates the assembled chain into individual modules. Second row: (Reconfiguration: 3 liquid modules into gripper) Three initially separated modules are sequentially assembled and reoriented to form a functional gripper through programmed field modulation. Third row: (Reconfiguration: two 2-module chains into square) Two independent chains merge and rearrange into a stable square assembly. Bottom row: (Open-loop cargo transport) A reconfigured assembly manipulates and transports cargo along a prescribed path under open-loop magnetic control. Timestamps indicate elapsed time, and scale bars denote 3 mm or 6 mm as labeled.