Magnetic modular millibots, capable of deterministic self-assembly and reconfiguration under wireless magnetic fields, offer a promising route toward mesoscale manipulation in structured and confined environments. This work presents a modular chain millibot composed of cubic units with free-to-spin internal magnets that align under external fields. While individual cubes cannot propel independently, their assembly into chains enables controlled locomotion through sliding and tumbling modes. We first demonstrate open-loop operation in confined workspaces, including chain formation, navigation, controlled disassembly, and wall climbing, supported by a dynamic model and parametric analysis that identify the actuation and geometric conditions required for successful climbing. Building on this foundation, we introduce a closed-loop control framework that integrates vision-based feedback. As the millibot’s movement speed increases with chain length, the order of assembly strongly affects task completion time; we therefore formulate the sequence-planning problem as a harmonic traveling salesman problem (HTSP) and solve it to compute deterministic cube-collection sequences that minimize the effective travel cost. The controller applies sliding and tumbling dynamics to realize obstacle-aware navigation and reliable self-assembly. Experiments validate autonomous assembly of four cubes with a two-cube chain into a six-cube chain in free space and collection of three cubes with wall climbing in a confined workspace, both with 100% success. The measured mean unit travel times were 0.67 s/mm in free space and 0.89 s/mm in confined environments. Collectively, these results establish a robust automation framework for reversible mesoscale self-assembly, programmable navigation, and lab-on-chip applications.

Reconfigurable modular robots, which can actively assemble and disassemble on command, offer the possibility of mesoscale (milliscale and microscale) manufacturing with robustness and controllability. In this study, we present a design of a scalable modular subunit with embedded permanent magnets in a 3-D printed cubic body. The subunit can be wirelessly controlled by an external uniform magnetic field. We also present controlled assembly–disassembly techniques for these subunits. Our modular robotic platform is highly reconfigurable and can create programmable, predetermined patterns based on open-loop control. The 2-D motion planner computes all reachable polyomino shapes from an arbitrary initial configuration and provides the shortest movement sequences to form each shape. Experimental results match computational modeling, demonstrating robust and reproducible behavior of the modular robotic platform that is promising for mesoscale manufacturing applications. Two cube sizes were tested: 10-mm edge lengths and 2.8-mm edge lengths.

This paper presents an adaptive backstepping controller for the reference tracking of an alginate artificial cell. An adaptive controller was implemented to precisely manipulate a magnetic artificial cell actuated by rotating magnetic fields. The rolling motion of a small-scale robot in a fluidic environment is challenging, especially when the fluid imparts an unknown response at low Reynolds number. In order to compensate for this uncertainty, an unknown tuning parameter encapsulating these effects was added to the governing equations of motion. A controller with an update law was then designed to estimate the unknown parameter and force the artificial cell to produce the desired response. The stability of the proposed controller was established by a candidate Lyapunov function. Real-time experiments were conducted to demonstrate the effectiveness of the designed controller at guiding an artificial cell to an arbitrary target position. Alginate cells were guided through a maze using the controller and was later combined with wall constraints to allow multiple alginate cells to reach the same target location. This controller can be applied to both surface motion and swimming-based small-scale robots in future applications for micro-assembly and targeted drug delivery.

This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The magnets are positioned so that each face has either magnetic south or north pole outward. Moreover, we require that the net magnetic moment of the cube passes through the center of opposing faces. These magnetic arrangements enable coupling when cube faces with opposite polarity are brought in close proximity and enable moving the cubes by controlling the orientation of a global magnetic field. This paper investigates the 2D and 3D shapes that can be constructed by magnetic modular cubes, and describes all possible magnet arrangements that obey these rules. We select ten magnetic arrangements and assign a "color" to each of them for ease of visualization and reference. We provide a method to enumerate the number of unique polyominoes and polycubes that can be constructed from a given set of colored cubes. We use this method to enumerate all arrangements for up to 20 modules in 2D and 16 modules in 3D. We provide a motion planner for 2D assembly and through simulations compare which arrangements require fewer movements to generate and which arrangements are more common. Hardware demonstrations explore the self-assembly and disassembly of these modules in 2D and 3D.

This paper presents scalable designs and fabrication, actuation, and manipulation techniques for soft millirobots under uniform magnetic field control. The millirobots were fabricated through an economic and robust moulding technique using polydimethylsiloxane (PDMS), acrylonitrile butadiene styrene (ABS) filaments, and 3D printed polylactic acid (PLA) rings. The soft millirobots were simple hollow rod-like structures with different configurations of embedded permanent magnets inside of their soft-body or at their ends. The soft-robots were actuated using six different motion modes including: pivot walking, rolling, tumbling, side-tapping, wiggling, and wavy-motion under an external uniform magnetic field control system. The velocities of the millirobots under different motion modes were analyzed under varying magnetic flux densities (B). Moreover, deformation of the soft-robotic body in response to the magnetic field strength was measured and a deflection curve showing bending angle (φ) was produced. Soft millirobots were navigated through a maze using a combination of the available motion modes. Different arrangements of the embedded permanent magnets enabled individual soft millirobots to respond heterogeneously under the same magnetic field inputs towards performing assembly and disassembly operation as modular subunits. Overall, this soft millirobot platform shows enormous potential for minimally invasive in vivo applications.

The modular assembly and actuation of 3D printed milliscale cuboid robots using a globally applied magnetic field is presented. Cuboids are composed of a rectangular resin shell embedded with two spherical permanent magnets that can independently align with any applied magnetic field. Placing cuboids within short distances of each other allows for modular assembly and disassembly by changing magnetic field direction. Assembled cuboids are demonstrated to stably self-propel under sequential field inputs allowing for both rolling and pivot walking motion modes. Swarms of cuboids could be actuated within the working space and exhibit near identical behavior. Specialized `trap robots' were developed to capture objects, transport them within the working space, and subsequently release the payload in a new location. Cuboids with male and female connectors were developed to exhibit the selective mating between cuboids. The results show that cuboids are a diverse and adaptable platform that has the potential to be scaled down to the sub-millimeter regime for use in medical or small-scale assembly applications.

This paper presents 2D feedback control and open loop 3D trajectories of heterogeneous chemically catalyzing Janus particles. Self-actuated particles have enormous implications for both in vivo and in vitro environments, which make them a diverse resource for a variety of medical and assembly applications. Janus particles, consisting of cobalt and platinum hemispheres, can self-propel in hydrogen peroxide solutions due to platinum's catalyzation properties. These particles are directionally controlled using static magnetic fields produced from a triaxial approximate Helmholtz coil system. Since the magnetization direction of Janus particles is often heterogeneous, and thereby not consistent with the propulsion direction, this creates a unique opportunity to explore the motion effects of these particles under 2D feedback control and open loop 3D control. Using a modified closed loop controller, Janus particles with magnetization both closely aligned and greatly misaligned to the propulsion vectors, were instructed to perform complex trajectories. These trajectories were then compared between trials to measure both consistency and accuracy. The effects of increasing offset between the magnetization and propulsion vectors were also analyzed. The effects this heterogeneity had on 3D motion is also briefly discussed. It is our hope going forward to develop a 3D closed loop control system that can retroactively account for variations in the magnetization vector.