Wang et al. (2020) demonstrated a 96 mg, electromagnetically driven, tailless flapping-wing micro robot that lifts off along a guide rail and independently modulates roll, pitch, and yaw torques in open loop. The open problem posed by that work is the transition to stable controlled flight: developing more detailed models of flapping-wing aerodynamics and the robot's multibody dynamics, implementing robust feedback flight control initially based on an external motion-capture system, and, ultimately, achieving untethered operation through integrated micro power sources, miniature onboard sensors, and improved flight efficiency via wing and transmission optimization. That core remains open for the electromagnetic actuation class: every closed-loop and untethered flight milestone at insect scale — motion-capture-based hover (2013), untethered open-loop flight (2019), LQR and adaptive control of 95–150 mg robots (2025–2026), and flight with onboard sensing and computation (2026) — was achieved on piezoelectric or dielectric-elastomer platforms, while electromagnetic insect-scale flapping robots remain at bench-top lift/torque characterization and guided liftoff.

Background

Flapping-wing micro aerial vehicles (FWMAVs) are flying robots of roughly insect size — here, total mass below about 100 mg and wingspan of a few centimeters — that hover and steer by reciprocating wing strokes like flies and bees. At this scale the aerodynamics differ fundamentally from conventional aircraft: the wings operate at low Reynolds number, where lift is dominated by unsteady mechanisms such as the leading-edge vortex (a stable vortex that stays attached to the wing edge during each stroke), so compact quasi-steady or stroke-averaged models (forces and torques averaged over one wingbeat cycle and used as the plant model for control design) are only approximate. Two actuation technologies dominate the field. Piezoelectric bending actuators, used on the Harvard RoboBee lineage, provide high force density but require driving voltages of hundreds of volts. Electromagnetic actuators — a miniature coil and a permanent magnet whose magnetic interaction produces the reciprocating force — run at a few volts, which simplifies drive electronics and favors miniaturization, but have lower force density. In 2013 the 80 mg piezoelectric RoboBee demonstrated the first closed-loop controlled flight of an insect-scale robot, with attitude feedback from an external motion-capture system (Ma et al., Science 340:603–607, 2013). In 2019 a solar-powered version, RoboBee X-Wing, achieved untethered flight but without attitude control, only short open-loop climbs (Jafferis et al., Nature 570:491–495, 2019). Against this backdrop, Wang et al. presented in 2020 a tailless robot of 96 mg total mass and 3.5 cm wingspan driven by two optimized electromagnetic actuators placed back to back, each driving one wing through a spherical four-bar transmission (a lightweight linkage converting the actuator's reciprocation into wing stroke), so that the kinematics of the two wings can be controlled independently. Bench measurements confirmed that the mean lift is proportional to the square of the drive-voltage amplitude and exceeds the robot's weight above about 1.3 V, that the robot lifts off along a vertical guide rail, and that the three steering torques are modulated independently and approximately linearly: roll torque by the amplitude difference of the two wing drive voltages, pitch torque by a DC offset that shifts the flapping plane relative to the center of mass, and yaw torque by a split factor that makes upstroke and downstroke durations asymmetric within a cycle. This established electromagnetic actuation as a viable drive for sub-100 mg flapping robots with full three-axis control authority in principle — but everything was demonstrated open-loop on test fixtures. The robot has flown no free flight: no feedback controller regulates its state, the drive current arrives through power wires whose tension is itself a flight disturbance at this scale, and no onboard power source or sensors exist. The paper's conclusion therefore states an explicit research program: more detailed flapping aerodynamics and multibody system-dynamics modeling, robust feedback control based on external motion capture, and, toward untethered flight, micro power sources, micro sensors, and wing/transmission efficiency optimization.

Problem Statement

Achieve stable, closed-loop controlled flight — and ultimately untethered flight — of an electromagnetically actuated insect-scale flapping-wing micro robot of the sub-100 mg platform class introduced by Wang et al. (2020). Concretely, as stated by the source: (1) develop more detailed models of the flapping-wing aerodynamics and of the robot's multibody system dynamics than the simplified quasi-steady lift/torque model validated on the bench, sufficient for flight-controller design; (2) design and implement a robust feedback flight-control algorithm, initially using an external motion-capture system for state estimation, so that the robot hovers and regulates its attitude and position in free flight rather than lifting off along a guide rail; and (3) progress to untethered operation by integrating micro power sources and miniature onboard sensors and improving flight efficiency through wing and transmission optimization, removing the external power tether. These tiers form one staged objective — the path to autonomous electromagnetic insect-scale flight. A solution must reach tier (2), the near-term sub-objective: the answer is the tier-(1) dynamics/aerodynamics model together with a tier-(2) feedback controller that stabilizes the robot's attitude and position in free flight under external motion-capture state estimation, validated in closed-loop simulation of that model, so a physical flight demonstration is not required and a tier-(2) solution resolves the task. Tier (3), untethered operation, is the longer-term objective of the source's program and is not a condition for resolving this task. The problem is open for the electromagnetic actuation class specifically: no electromagnetically driven insect-scale flapping robot has yet flown under closed-loop control.

References

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