Magneto-oscillatory localization for small-scale robots

TL;DR

The SMOL device uses the temporal oscillation of a mechanically resonant cantilever with a magnetic dipole to break the rotational symmetry, and exploits the frequency-response to achieve a high signal-to-noise ratio with sub-millimeter accuracy over a large distance and quasi-continuous refresh rates up to 200 Hz.

Abstract

Magnetism is widely used for the wireless localization and actuation of robots and devices for medical procedures. However, current static magnetic localization methods suffer from large required magnets and are limited to only five degrees of freedom due to a fundamental constraint of the rotational symmetry around the magnetic axis. We present the small-scale magneto-oscillatory localization (SMOL) method, which is capable of wirelessly localizing a millimeter-scale tracker with full six degrees of freedom in deep biological tissues. The SMOL device uses the temporal oscillation of a mechanically resonant cantilever with a magnetic dipole to break the rotational symmetry, and exploits the frequency-response to achieve a high signal-to-noise ratio with sub-millimeter accuracy over a large distance of up to 12 centimeters and quasi-continuous refresh rates up to 200 Hz. Integration into real-time closed-loop controlled robots and minimally-invasive surgical tools are demonstrated to reveal the vast potential of the SMOL method.

Figures (14)

• Figure 1: Overview of the SMOL method. (A) Schematic of a SMOL system with an excitation coil, an embedded SMOL device and a sensing array. (B) Oscillating cantilever model. The magnetic moment $\mathbf{m}$ at position $\mathbf{r}$ oscillates in time on a circular path upon excitation by an external B-field $\mathbf{B}_\mathrm{ext}$. The deflection angle $\uptheta$ is limited by the housing. (C) High-speed optical analysis of the magnets center point (orange) and orientation (red) at two times during the oscillation. (D) Schematic illustration of the excitation and signal phase. During the excitation phase, a current $I_\mathrm{coil}$ is applied to the excitation coil. The resulting B-field leads to a continuous increase of the deflection angle $\uptheta$ and to the saturation of the sensor signals $B_1$ to $B_i$. After $I_\mathrm{coil}$ is shut down, $\uptheta$ slowly decays in an underdamped harmonic oscillation and the sensors measure the signal emitted from the SMOL device. (E) Raw signal measured at 80 mm distance with a resonance frequency $f_\mathrm{res} = 103.5$ Hz. (F) Resulting signal after filtering. (G) Full oscillation period. The corresponding cantilever deflection is illustrated below. The fully sampled data (orange) is down-sampled to 5 points per half-period (blue) for insertion into the optimization model. The fitting result (red) for the physical model yields an excellent fit with R² = 0.99.
• Figure 2: Characterization of the 6 DoF accuracy and localization rate. (A--B) Translational accuracy in $x$- and $z$-direction for the speed mode (number of evaluated half periods $N = 2$) and precision mode ($N = 20$) as inset, respectively. Experiments (blue) and simulations (red) accurately represent the ground truths, as the data points span on the 45° line in the graphs. (C) Rotational accuracy around the $z$-axis, which is the missing rotational DoF for a static magnet (see Fig. 1B). (D) Summary table for the accuracies in presented ranges. The translation axes correspond to the systems extrinsic axes with respect to the sensor array (Fig. 1A), while the rotation axes are the intrinsic axes of the SMOL device according to Fig. 1B. (E) Maximum localization distance $z_\mathrm{max}$ versus magnet size $a$ of an equivalent cube. (F) Standard deviation $\sigma_{x,y,z}$ and localization rate $f_\mathrm{loc}$ versus $N$. (G) $\sigma_{x,y,z}$ versus damping coefficient $\eta$ (Eq. S4) for both modes with linear trend lines. A larger $\eta$ indicates a faster decay of the signal. (H) Superfast localization demonstration with 51.7 Hz refresh rate for a linear stepping motion. The original signal is segmented into $N_\mathrm{seg} = 4$ half period segments.
• Figure 3: Integration of SMOL and actuation in millirobots. (A) R-shaped actuation path of a millirobot in viscous fluid determined by optical tracking (orange) and SMOL tracking (red). The robot is controlled in a closed-loop by a magnetic gradient setup (Figs. S8A and B) and localized using SMOL at an average refresh rate of 3.5 Hz. Note that optical tracking was not used as feedback and is only presented for reference. (B) S-shaped actuation path of a helical millirobot in viscoelastic gel. Red arrows indicate the main axis of the robot determined by SMOL. An external rotating magnet (see Figs. S8C and D) induces a torque $\tau$ along the main axis of the robot due to the perpendicular alignment between the cantilever (green) and the magnet (blue-red).
• Figure 4: Integration of SMOL for biomedical applications. (A) Schematic illustration of the urinary tract. (B) Navigation of a flexible endoscope with an attached SMOL device in an in vitro kidney organ phantom. The localization results of the endoscopic tip by SMOL are shown as red dots, and yellow arrows indicate the movement of the endoscope. An average localization rate of 4.2 Hz was achieved (see Movie S4). (C) Implantation of a SMOL device into an ex vivo pig brain. (D) Ultrasound (US) image of the implanted SMOL device. A distinction of the tracker to the background is difficult due to biological inhomogeneity. (E) The overlay of the SMOL result on the enlarged US image. The position and orientation (red) are precisely determined by SMOL.
• Figure S1: SMOL system components. (A) Main components of the SMOL system. The SMOL device (circled in red) is attached to a rod for visibility. (B) Block-diagram of the SMOL system with its four subsystems for software control and data analysis, data acquisition, excitation and the embedded system, which is the SMOL tracker.