Microrobot collectives with reconfigurable morphologies, behaviors, and functions

The study addresses how to realize microrobotic collectives that can robustly reconfigure their morphology and behavior on demand to perform multiple functions in complex environments at small scales. The context is inspired by natural collectives that adapt via reconfiguration. Prior microscale artificial systems often exhibit only single modes or lack tunable control over the relative strengths of inter-particle and particle-environment interactions. The research goal is to develop a system that uses both global magnetic field inputs and mutual particle interactions to switch among multiple, tunable modes—including a transition from globally driven behavior to a self-propelling, active-like state—thereby enabling navigation, manipulation, and exploration at the air-water interface.

Prior work has demonstrated reconfigurable macro-scale robot collectives (e.g., Kilobots forming patterns and reconfiguring for object manipulation under global inputs) and environment-mediated coupling enabling shape and function changes. At the fluid-air interface, early magnetically actuated disk systems (Grzybowski et al.) formed hexatic patterns under rotating magnetic fields via hydrodynamic interactions. Patterned micro-disks with edge corrugations have used capillary interactions to self-organize into square lattices and rotating collectives. Other microrobotic swarms and colloidal systems have shown ribbon, chain, or vortex formations, locomotion, and manipulation, including systems that exhibit multiple emergent modes but often require a solid substrate for symmetry breaking, lack clear tunability of interaction strengths, or cannot switch robustly between modes. There remains a need for systems where an external, easily tunable parameter (e.g., magnetic field frequency relationship) can program the dominance among capillary, hydrodynamic, and magnetic interactions to achieve multiple controlled modes and their transitions, and ideally connect globally driven and active (self-propelling) regimes.

System and actuation: Collectives of magnetic micro-disks operate at the air-water interface and are driven by two orthogonal, time-varying, uniform magnetic fields with independently set oscillation frequencies along x and y, Ωx and Ωy. The magnetic field is B(t) = [Bx0 cos(2πΩx t) + Bx1, By0 sin(2πΩy t) + By1], with Bx0 = By0 = 10 mT. Constant offsets are zero except for X-chain cases ((Bx1, By1) = (0,10) mT). Using two independent axes enables a rich set of Lissajous-like field traces, tuning the time dependence of the field orientation θ and its angular rate θ̇. Microrobots: Each micro-disk is circular with six cosinusoidal edge corrugations (six-fold symmetry) to enable orientation-dependent capillary interactions (attractive when corrugations align, repulsive when misaligned above ~8°). A 500 nm cobalt ferromagnetic film (with 60 nm Au) provides magnetic dipole interactions. Hydrodynamic interactions depend on instantaneous spin speed; faster spins increase hydrodynamic repulsion and generate stronger azimuthal flows. Experimental setup: Characterizations largely used ~120 micro-disks in a 12 mm square arena. Frequency ranges were chosen above aggregation (>10 Hz) and below step-out (~65–75 Hz). Static-mode tests were up to ~60 Hz before step-out; chain modes were generated by setting one axis frequency to zero (or low) to create alignment along x or y. Magnetic field gradients (e.g., 0.7 Gauss/mm) were applied for locomotion and navigation tests. Object manipulation used polystyrene beads (1 mm) and ring/rod/star-shaped passive structures. Fabrication used two-photon polymerization microprinting followed by sputtering. Imaging used a Leica Z16 APO microscope and Basler camera; tracking by Python (OpenCV) with MATLAB analysis. Simulation model: A numerical model (adapted from prior work) includes pairwise capillary forces/torques (embedding six-fold symmetry), magnetic dipole-dipole forces/torques, hydrodynamic interactions (including lubrication corrections below ~1.1R separation), wall repulsion, and the prescribed time-varying B(t). Simulations used initial hexagonal-lattice placements, RK45 integration (dt = 1 ms) for 10 s. For GaSPP, an additional stochastic term in orientation dynamics (Gaussian white noise) was introduced to capture symmetry-breaking and pair formation under 1D oscillating fields. Simulations did not include hydrodynamic drag from arena boundaries and assumed a flat interface.

- The collective exhibits six major, reconfigurable modes controlled by linear relationships between Ωx and Ωy: (1) Rotation (Ωx = Ωy): rotating field causes each disk to spin, generating an azimuthal flow; collective forms a rotating cluster whose radius increases with frequency, decreasing orbital speed and local hexatic order; step-out occurs at ~65–75 Hz. (2) Static (Ωx ≈ 2Ωy): disks oscillate about their own axes while centers of mass remain stationary; hydrodynamic effects cancel, yielding a static cluster with high hexatic order and tunable neighbor spacing that increases with frequency up to step-out. (3) Oscillation (Ωx = Ωy − 1): collective exhibits net rotation over short windows with periodic reversals in angular speed; neighbor spacing increases with frequency; hexatic order is intermediate between static and rotation; average angular speed lower than rotation. (4) Chains: one axis frequency set while the other is zero (e.g., X chains: Ωx≠0, Ωy=0; Y chains: Ωy≠0, Ωx=0) aligns disks along the driven axis. At low frequencies (Ω < 50 Hz), attractive capillary/magnetic forces dominate and disks attach along corrugations, forming connected chains; at Ω < 10 Hz, chains oscillate about the center (oscillating chains). At high frequencies (Ω > 50 Hz), hydrodynamic repulsion separates neighbors, yielding spaced chains with increased neighbor distances. (5) GaSPP (gas-like self-propelling pairs): a 1D oscillating field (e.g., B = [10 cos(40 t); 0]) breaks the cluster into many pairs of disks spinning in opposite directions; each pair translates perpendicular to the inter-disk axis; mean pair speed increases with frequency up to ~50 Hz and then decreases due to more frequent wall collisions; pairs exchange partners upon collision. - Transitions: The system transitions on demand among modes (e.g., rotation → static → oscillation → Y chains → X chains → oscillating chains → GaSPP → rotation → static), validated by experiments and simulations with qualitative agreement. Discrepancies at high frequencies arise from neglected boundary drag and slight meniscus concavity in experiments. - Navigation and manipulation: Under magnetic field gradients, chains aligned with the gradient move fastest among modes; collectives trace prescribed paths (e.g., spelling letters) and navigate mazes by switching chain orientation. Contact-based pushing is achieved by reconfiguring into Y chains to push a 1 mm bead, while X chains enable fast approach without displacing the bead. Flow-induced locomotion occurs when rotating near boundaries, producing counterintuitive motion due to symmetry breaking. - Flow-based manipulation: Azimuthal flows around spinning disks advect dye and drive contact-free transport of 1 mm beads along designed trajectories. Collectives inside a ring rotate the ring in the same direction; collectives outside rotate rings in the opposite direction. Angular speeds of rings decrease with increasing magnetic frequency; varying disk number, ring size, and rotation speed tunes torque. Noncircular objects (rod, star) can be rotated via encapsulated collectives. Adjacent rings show coupled rotation: with collectives in both, they co-rotate about a common center due to capillary torque; with a collective in only one ring, gear-like opposite rotation occurs via torque transfer. - Dispersion and splitting: Rotating collectives can expand uniformly and rotate enclosing structures; GaSPP disperses faster and nonuniformly without rotating the boundary. Collectives can be split temporarily or persistently using chains, rotation, and GaSPP, and recombined via gradient-assisted chain locomotion through narrow openings. - Quantitative highlights: Magnetic field amplitude 10 mT; step-out ~65–75 Hz; chain and oscillation thresholds (connected vs separated chains around 50 Hz; oscillating chains below ~10 Hz); gradient magnitude 0.7 Gauss/mm; ring angular speed decreases with frequency; GaSPP speed peaks near ~50 Hz.

The results demonstrate a versatile, reconfigurable microrobot collective where a single global control scheme (biaxial oscillating magnetic fields) tunes the balance among capillary, hydrodynamic, and magnetic interactions to realize multiple distinct modes and robust transitions. Crucially, the system connects globally driven collective behaviors with an active-matter-like, self-propelling GaSPP mode, enabling dispersion and exploration with tunable pair speeds. This versatility allows navigation in constrained environments, contact and contact-free manipulation using generated flows, and torque transfer resembling mesoscale mechanical coupling. Simulations incorporating key pairwise interactions qualitatively reproduce observed behaviors, supporting the mechanistic understanding. The ability to exploit environmental features (boundaries, object geometry) further enhances functional robustness, highlighting relevance to micromanipulation, soft-matter studies, and active matter research bridging driven and self-propelled regimes.

This work introduces a microrobot collective capable of six reconfigurable behaviors—rotation, static, oscillation, chains, oscillating chains, and a novel gas-like self-propelling pairs mode—controlled by the frequency relationship of two orthogonal oscillating magnetic fields. The system offers tunable collective size, neighbor spacing, angular velocity, and locomotion speed, with robust mode transitions demonstrated experimentally and in simulations. Using these modes, the collectives navigate complex environments, perform contact-based and contact-free transport, rotate and orient diverse objects, disperse rapidly, and split/merge as needed. Two behaviors—the static collective of dynamic disks and GaSPP—are unique to this system, and transitions between globally driven and self-propelled behaviors are demonstrated for the first time in such collectives. Future work includes expanding the control space (varying phase differences and field intensities), enhancing force-bearing capacity (larger swarms or stronger gradients), elucidating the origin of noise in GaSPP modeling, and developing real-time optimal control for targeted manipulation, with potential extensions toward 3D and biomedical/environmental applications.

- Force-bearing capacity is limited, constraining the size/weight of objects that chains can push; mitigation may require larger collectives or stronger magnetic gradients. - Parameter space was only partially explored; phase differences and field intensities were held constant and may reveal additional behaviors if varied. - Simulations omit hydrodynamic drag from arena boundaries and assume a flat interface; experimental meniscus concavity and boundary effects introduce discrepancies at high frequencies and in chain formations. - The GaSPP simulation model includes an ad hoc noise term whose physical origin requires further study. - Behaviors are demonstrated at the air-water interface (quasi-2D); translation to fully 3D environments may require additional mechanisms.