Swimming dynamics of screw-shaped untethered magnetic robots in confined spaces

In confined environments, the propulsion speed of torque-driven helical untethered magnetic robots (UMRs) depends on vessel diameter and helical pitch. This phenomenon likely affects the swimming speed of these robots when navigating in vivo within blood vessels. Achieving a consistent swimming speed across a range of vessel diameters is therefore essential for precise control of UMRs. With this goal, we investigate how vessel diameter and helical pitch influence UMR propulsion to identify optimal robot designs. UMRs from two groups-fixed length (FL) and fixed wave (FW)-were analyzed. In the FW group, longer robots achieved higher speeds in larger vessels due to better vessel guidance, whereas shorter robots performed best in medium-sized vessels. The FL group showed peak speeds at intermediate normalized wavenumbers ( $\nu \approx 1$ to 1.8), significantly influenced by robot geometry and vessel confinement. Normalized wavenumber affected swimming speed and stability, with maximum efficiency at $\nu \approx 1$ and stability increasing with higher wavenumbers. Swimming performance was modeled using Stokeslets method and additional effects were considered by correction factors to improve agreement of experimental and modeling results. Ex vivo tests under physiological conditions demonstrated clear performance differences between robust (FL-9 ( $\nu =2.3$ ), FW-5 ( $\nu =2$ )) and unstable swimmers, with robust designs showing consistent correlation between phantom and ex vivo trials. Unstable designs exhibited unpredictable behavior, emphasizing the importance of specific design parameters for stability and maneuverability. These findings highlight critical design factors-such as the normalized wavenumber, body length, and degree of vessel confinement-that are essential for enhancing UMR propulsion efficiency and control consistency, which are fundamental for successful navigation in targeted vascular biomedical applications.

The online version contains supplementary material available at 10.1007/s11071-025-11646-7.