Andrew J. Petruska

Soft micromachines with programmable motility and morphology

Nature provides a wide range of inspiration for building mobile micromachines that can navigate through confined heterogenous environments and perform minimally invasive environmental and biomedical operations. For example, microstructures fabricated in the form of bacterial or eukaryotic flagella can act as artificial microswimmers. Due to limitations in their design and material properties, these simple micromachines lack multifunctionality, effective addressability and manoeuvrability in complex environments. Here we develop an origami-inspired rapid prototyping process for building self-folding, magnetically powered micromachines with complex body plans, reconfigurable shape and controllable motility. Selective reprogramming of the mechanical design and magnetic anisotropy of body parts dynamically modulates the swimming characteristics of the micromachines. We find that tail and body morphologies together determine swimming efficiency and, unlike for rigid swimmers, the choice of magnetic field can subtly change the motility of soft microswimmers.

Optimal Permanent-Magnet Geometries for Dipole Field Approximation

The dipole approximation for magnetic fields has become a common simplifying assumption in magnetic-manipulation research when dealing with permanent magnets because the approximation provides convenient analytical properties that are a good fit at large distances. What is meant by “good fit at large distances” is generally not quantified in the literature. By using a parameterized multipole expansion and collaborating finite-element analysis (FEA) simulations to represent the magnets field, we quantify the error associated with the dipole approximation as a function of distance from the permanent magnet. Using this expression, we find cylindrical, washer, and rectangular-cross-section bar permanent-magnet aspect ratios that minimize the error of the dipole approximation. For cylinders and rectangular-cross-section bars, these aspect ratios are a diameter-to-length ratio of √{4/3} and a cube, respectively.

3D Printed Microtransporters: Compound Micromachines for Spatiotemporally Controlled Delivery of Therapeutic Agents

Functional compound micromachines are fabricated by a design methodology using 3D direct laser writing and selective physical vapor deposition of magnetic materials. Microtransporters with a wirelessly controlled Archimedes screw pumping mechanism are engineered. Spatiotemporally controlled collection, transport, and delivery of micro particles, as well as magnetic nanohelices inside microfluidic channels are demonstrated.

Minimum Bounds on the Number of Electromagnets Required for Remote Magnetic Manipulation

Numerous magnetic-manipulation systems have been developed to control objects in relatively large workspaces. These systems vary in their number of electromagnets, their configuration, and their limitations. To date, no attempt has been made to rigorously quantify how many electromagnets are required to perform a given magnetic manipulation task. For some tasks, such as controlling the field at a point, the answer is clear: the same number as dimension of control. For tasks that apply magnetic forces on an object, the answer is less clear, and some systems, which have more control magnets than kinematic degrees of freedom (DOFs), have demonstrated unexpected singularities that only arise at specific object orientations. This paper provides a general analysis for static electromagnetic systems rooted in the governing magnetic equations and proves an unintuitive result. That is, if only magnetic fields and forces are used to control an unconstrained magnetic object, four magnetic sources are required for 3-DOF force control and eight magnetic sources are required for orientation-independent 5-DOF force and heading control.

Omnimagnet: An Omnidirectional Electromagnet for Controlled Dipole-Field Generation

An Omnimagnet is an omnidirectional electromagnet comprising a spherical ferromagnetic core inside of three orthogonal nested solenoids. It generates a magnetic dipole field with both a variable dipole-moment magnitude and orientation with no moving parts. The magnetic and physical properties (e.g., dipole moment, weight, resistance, and inductance) of any Omnimagnet are derived. These general relationships are used to design an optimal Omnimagnet subject to the constraints that it has the same dipole-moment per applied current in any direction, each solenoid has no quadrupole contribution to the magnetic field, and the spherical core size maximizes the strength of the resulting dipole field. This optimal design is analyzed using FEA tools and is verified to be dipole-like in nature. Finally, the optimal design is constructed and its utility is demonstrated by driving a helical capsule-endoscope mockup through a transparent lumen.

Remote Manipulation With a Stationary Computer-Controlled Magnetic Dipole Source

In this paper, we examine several magnetic control methods that utilize the fully controllable dipole field generated by the single stationary dipole source. Since the magnetic field generated by a dipole source is nonuniform, it applies both forces and torques to magnetic objects and can be used to manipulate magnetic tools. Recently, the Omnimagnet, a computer-controlled magnetic dipole source capable of varying both its dipole-moment direction and magnitude, was developed to perform magnetic manipulation. The equations and methods are developed generally; therefore, they can be applied to any omnidirectional dipole source, but their effectiveness is demonstrated using the Omnimagnet.

Factors affecting the design of untethered magnetic haptic interfaces

This paper presents an analysis of the factors affecting the performance, workspace, and stability of untethered magnetic haptic interfaces, with the goal of informing the design of future devices. We differentiate untethered magnetic interfaces, which use a stylus with an embedded permanent magnet to interact with magnetic fields projected into space by electromagnets, from the more well-known Lorentz-force magnetic interfaces, which work on different principles. We show that even though untethered magnetic interfaces have little to no damping, they still exhibit inherent stability properties as part of a sampled-data system. Although a ferromagnetic core often enables increased forces to be rendered at distances farther from the electromagnet, we show that there are cases in which larger forces can be rendered and cases in which stiffer virtual walls can be rendered by removing the ferromagnetic core.

Non-drifting limb angle measurement relative to the gravitational vector during dynamic motions using accelerometers and rate gyros

A method for estimating limb orientation, during static, quasi-static, and dynamic motions, by using a combination of gyroscopes and accelerometers is presented. The method uses two tri-axis accelerometers and one single axis rate gyro to calculate an estimate of angle relative to the gravitational vector independently from the rotational accelerations. This unbiased inclination estimate is blended with the angular velocity and acceleration measurements using a Kalman filter to obtain the final estimated orientation. Initially developed for implementation in a feedback control loop for control of sit-to-stand transitions in felines during direct electrical stimulation of the sciatic nerve, the method can be directly applied to other limb angle measurement tasks such as human gait analysis. The algorithm and sensor is tested on a rotational linkage with a predefined trajectory and compared to an encoder measurement with good agreement.

Magnetic control of continuum devices

In this paper we apply Cosserat rod theory to catheters with permanent magnetic components that are subject to spatially varying magnetic fields. The resulting model formulation captures the magnetically coupled catheter behavior and provides numerical solutions for rod equilibrium configurations in real-time. The model is general, covering cases with different catheter geometries, multiple magnetic components, and various boundary constraints. The necessary Jacobians for quasi-static, closed-loop control using an electromagnetic coil system and a motorized advancer are derived and incorporated into a visual-feedback controller. We address the issue of solution bifurcations caused by the magnetic field by proposing an additional, stabilizing control method that makes use of system redundancies. We demonstrate the effectiveness of the model by performing 3D tip-position trajectories with root-mean-square distance errors of 2.7 mm in open-loop, 0.30 mm in closed-loop, and 0.42 mm in stabilizing closed-loop modes. The stabilizing controller achieved on average a factor of 1.6 increase in the restoring wrenches for the least stable direction.

Model-Based Calibration for Magnetic Manipulation

Model-based calibration of a magnetic workspace not only provides a smooth representation of the field and its gradient matrix, but also uses physical constraints to smooth the calibration measurements. This paper presents the first model-based technique to calibrate a magnetic manipulation system by using nonlinear least squares to solve for a scalar potential for each source. The performance of the method is verified by comparison to numerical finite element simulation and a case study calibration of a real system, where it is able to achieve an