Approximately half of previous small-scale, flexible magnetic robots demonstrated cargo transportation capabilities (see Table S1), including impressive reports of robots capable of transporting cargos 20 times the robot body weight and three times the robot volume \cite{Wu2022a}, and more than 100 times robot body weight \cite{Lu2018}. However, only five identified robots \cite{Ze2022,Joyee2019a,Wu2022a,Hu2018,Ze_2022} included an internal compartment. Advantages of a compartment include easier integration and protection in harsh environments.
The MR-LF central compartment has an internal volume of 300 mm3 (length: 7.8 mm, diameter: 7 mm) which comprises 17% of the robot’s volume (1725 mm3). In comparison, most of the prior robots with compartments have smaller compartment-to-robot volume ratios (Table S1). While some previous works have demonstrated a similar order of compartment-to-robot ratio, these demonstrations are limited to the millimeter length scale that is not compatible with the goal of ingestible electronics. For example, a millimeter-scale multigait magnetic robot \cite{Hu2018} has a compartment volume of 2.5 x 10-2 mm3, which is 120,000 times smaller than the compartment in MR-LF. Another example leverages a magnetically-actuated cylindrical compartment \cite{Wu2022a} with a compartment-to-robot ratio of ~36% but with a ~500 times smaller volume than MR-LF. In another example, a recent ingestible magnetic origami crawler \cite{Ze2022} demonstrated a compartment for a cargo volume that is 12.5x smaller than MR-LF ( 24 mm3, ~7% of robot volume) that is not centralized (3.5% on each robot end) and requires fixed-free mounting to preserve actuation. In summary, in contrast to previous works, MR-LF localized flexibility endows the device with a large (300 mm3) centralized compartment that can be integrated with functional modules (e.g., electronics) within an ingestible form factor (Table S1).
We remark that as the robot gets smaller, the separation distance between the magnets in the robot decreases. A smaller separation distance can decrease the effectiveness of locomotion as it increases interactions between robot magnets and affects the phase shift between the rotation of the robot feet, which enables locomotion in a deterministic direction. While the actuation method is anticipated to remain effective, several design variables of the magnetic and structural design, including the strength of the actuator and robot magnets, material stiffness, and offset distance, would need to be modulated accordingly to maintain dynamic similarity for miniaturization in future studies.
2.3. Effect of geometry on speed
To investigate the effect of localizing flexibility on locomotion speed, experiments were performed using an MR-DF and an MR-LF with an equal mass (2.55 g). In each experiment, the robot was placed in a confined channel and actuated by a rotating actuator magnet at x = 0, y = ya (Figure \ref{709773}D). The rotation of the actuator magnet about the -z axis induced locomotion in the +x direction due to the phase shift in time-varying torque on the robot feet \cite{Pham2020}. A range of ya values was studied because existing literature reported a relationship between ya and locomotion \cite{Pham2020}.
Results show that the average initial speed (average speed for the first ten steps of locomotion) of MR-LF was faster than the MR-DF control at every ya offset (Figure \ref{709773}F). At ya = 11 cm, the robots had the closest speeds (difference of 3%) and exhibited their fastest average initial speed (MR-DF: 6.61 mm/rev, MR-LF: 6.82 mm/rev). The largest difference (299%) and slowest average initial speed for both designs were at ya = 15 cm (MR-DF: 0.34 mm/rev, MR-LF: 1.37 mm/rev). As anticipated, the closeness in robot speeds is likely due to the comparable foot flexion between the designs (0% difference in minimum, 10% difference in maximum foot flexion). The superior performance of MR-LF, which had an average initial speed of 0.21 to 2.27 mm/rev faster than MR-DF across all ya, may be due to an expected difference in mass distribution between the robots or from the 10% reduction in maximum foot flexion. The closeness in locomotion performance between the MR-DF and MR-LF designs, and the superiority of MR-LF across all ya is exciting because it demonstrates that localizing flexibility yielded a 3-299% increase in speed while also freeing up space for an internal compartment (300 mm3) for functional integration.
In the experiments, the robot’s locomotion away from the actuator magnet was consistent with prior literature \cite{Steiner2021} to demonstrate the feasibility of locomotion against the attraction forces between the robot and actuator. In practice, robot speed and endurance can be improved by having the robot travel toward the actuator magnet and actively modulating the separation between the actuator and robot.
2.4. Effect of robot mass on speed
To investigate how the increased mass of functional components and payloads within the compartment affects locomotion speed, experiments were performed using MR-LF with varying mass (2.55, 2.87, 3.5, 4.43 g). Comparison between plots shows that, in general, increasing MR-LF mass increases the initial speed at smaller ya values and lowers the initial speed at larger ya values within the studied ya range (Figure \ref{402200}A). At the smallest offset (ya = 9 cm), the heaviest MR-LF (4.43 g) exhibited the fastest average initial speed (9.01 mm/rev), while the other MR-LFs were unable to exhibit effective locomotion (discussed in the next section). Conversely, at the largest offset (ya = 15 cm), the heaviest MR-LF (4.43 g) exhibited a low average speed (0.02 mm/rev), while the 2.55 g and 2.87 g MR-LFs had average speeds greater than 1.0 mm/rev. The difference in speeds is due to the mass of the robots, as robots with higher mass can resist a higher lift force that is generated by a higher magnetic field strength, which we discuss in detail in Section 2.5.
Our results have also demonstrated that MR-LF achieved locomotion even with a mass greater than existing capsule endoscopy devices (PillCam™ SB 3: 3.0 g \cite{medtronic}, PillCam™ Colon 2: 2.9 g \cite{medtronica}). Indeed, the heaviest robot in our experiments exhibited the fastest average initial speed (9.01 mm/rev), and results show that increasing robot mass can improve locomotion speed and change the ya for the fastest locomotion. To further investigate this mechanism, we study the effect of magnetic field strength on locomotion as described in the next section.