We demonstrate five-degree-of-freedom (5-DOF) wireless magnetic control of a fully untethered microrobot (3-DOF position and 2-DOF pointing orientation). The microrobot can move through a large workspace and is completely unrestrained in the rotation DOF. We accomplish this level of wireless control with an electromagnetic system that we call OctoMag. OctoMag's unique abilities are due to its utilization of complex nonuniform magnetic fields, which capitalizes on a linear representation of the coupled field contributions of multiple soft-magnetic-core electromagnets acting in concert. OctoMag was primarily designed to control intraocular microrobots for delicate retinal procedures, but it also has potential uses in other medical applications or micromanipulation under an optical microscope.

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OctoMag: An Electromagnetic System for 5-DOF Wireless Micromanipulation

We demonstrate five-degree-of-freedom (5-DOF) wireless magnetic control of a fully untethered microrobot with a magnetic steering system we call OctoMag. Although only occupying a single hemisphere, this system is capable of isotropically applying forces on the order of 1–40 µN with unrestricted control of the 2 orienting DOF. These capabilities are enabled through the use of soft-magnetic-cores which provide an increase of approximately 20× that of air cores in magnetic-field strength, but comes at the cost of more complicated interactions between coils. We propose a modeling mechanism that assumes the field contributions of the individual currents superimpose linearly when using cores with large linear regions and negligible hysteresis. When designing the system, the locations and quantity of electromagnets were optimized with regards to the force generation in the worst-case direction predicted by the model. The resultant system is capable of both open and closed-loop operation over a workspace of 4 cm3. OctoMag was primarily designed for the control of intraocular microrobots for delicate retinal procedures, but also has potential uses in other medical applications or micromanipulation under an optical microscope.

/pdf/octomag-an-electromagnetic-system-for-5-dof-wireless-3nyhufftcq.pdf

OctoMag: An electromagnetic system for 5-DOF wireless micromanipulation

In any optical system, distortions to a propagating wavefront reduce the spatial coherence of a light field, making it increasingly difficult to obtain the theoretical diffraction-limited spot size. Such aberrations are severely detrimental to optimal performance in imaging, nanosurgery, nanofabrication and micromanipulation, as well as other techniques within modern microscopy. We present a generic method based on complex modulation for true in situ wavefront correction that allows compensation of all aberrations along the entire optical train. The power of the method is demonstrated for the field of micromanipulation, which is very sensitive to wavefront distortions. We present direct trapping with optimally focused laser light carrying power of a fraction of a milliwatt as well as the first trapping through highly turbid and diffusive media. This opens up new perspectives for optical micromanipulation in colloidal and biological physics and may be useful for various forms of advanced imaging.

In situ wavefront correction and its application to micromanipulation

Optical microscopy has for centuries been a key tool to study living cells with minimum invasiveness The advent of single molecule techniques over the past two decades has revolutionized the field of cell biology by providing a more quantitative picture of the complex and highly dynamic organization of living systems Amongst these techniques, single particle tracking (SPT) has emerged as a powerful approach to study a variety of dynamic processes in life sciences SPT provides access to single molecule behavior in the natural context of living cells, thereby allowing a complete statistical characterization of the system under study In this review we describe the foundations of SPT together with novel optical implementations that nowadays allow the investigation of single molecule dynamic events with increasingly high spatiotemporal resolution using molecular densities closer to physiological expression levels We outline some of the algorithms for the faithful reconstruction of SPT trajectories as well as data analysis, and highlight biological examples where the technique has provided novel insights into the role of diffusion regulating cellular function The last part of the review concentrates on different theoretical models that describe anomalous transport behavior and ergodicity breaking observed from SPT studies in living cells

https://iopscience.iop.org/article/10.1088/0034-4885/78/12/124601/pdf

A review of progress in single particle tracking: from methods to biophysical insights.

The phenomenon of light's momentum was first observed in the laboratory at the beginning of the twentieth century, and its potential for manipulating microscopic particles was demonstrated by Ashkin some 70 years later. Since that initial demonstration, and the seminal 1986 paper where a single-beam gradient-force trap was realized, optical trapping has been exploited as both a rich example of physical phenomena and a powerful tool for sensitive measurement. This review outlines the underlying theory of optical traps, and explores many of the physical observations that have been made in such systems. These phenomena include 'optical binding', where trapped objects interact with one another through the trapping light field. We also discuss a number of the applications of 'optical tweezers' across the physical and life sciences, as well as covering some of the issues involved in constructing and using such a tool.

https://iopscience.iop.org/article/10.1088/0034-4885/76/2/026401/pdf

Optical trapping and binding

A three-dimensional (3D) particle tracking algorithm based on microscope off-focus images is presented in this paper. Subnanometer resolution in all three axes at 400 Hz sampling rate is achieved using a complementary metal-oxide-semiconductor (CMOS) camera. At each sampling, the lateral position of the spherical particle is first estimated by the centroid method. The axial position is then estimated by comparing the radius vector, which is converted from the off-focus two-dimensional image of the particle with no information loss, with an object-specific model, calibrated automatically prior to each experiment. Estimation bias and variance of the 3D tracking algorithm are characterized through analytical analysis. It leads to an analytical model, enabling prediction of the measurement performance based on calibration data. Finally, experimental results are presented to illustrate the performance of the measurement method in terms of precision and range. The validity of the theoretical analysis is also experimentally confirmed.

Three-dimensional particle tracking with subnanometer resolution using off-focus images

This paper presents the development of a compact six-axis magnetic levitation stage, including the design and implementation of magnetic actuators, laser interferometer motion sensors, and motion controllers. The designed travel volume of the stage is 2times2times2 mm in translation and 4degtimes4degtimes4deg in rotation. A two-axis linear actuator, based on the magnetic Lorentz force law, was designed, and three two-axis actuators, equivalent to six single -axis actuators, were implemented to achieve six-axis actuation. A high-resolution laser interferometer measurement system was implemented and employed to measure the six-axis motion of the stage, facilitating real-time feedback control. Feedback linearization, based on rigid-body dynamics of the levitated stage, and force distribution were implemented in a computer-controlled architecture so as to establish a decoupled dynamics between the six computed inputs and the resulting six-axis motions. Constant gain controllers were then designed and implemented, according to the concept of loop shaping, for each of the six axes, and high positioning stability, 1.1 nm root mean square (RMS) for x and 0.74 nm RMS for y, has been achieved. Experimental results are presented to illustrate positioning stability, system linearity, dynamic response invariance, nano stepping, multiaxis contouring, and large rotational motion

Six-Axis Magnetic Levitation and Motion Control

This paper presents the design, implementation, and force modeling of quadrupole magnetic tweezers, which are capable of exerting magnetic forces in arbitrary 2-D directions on magnetic particles in the workspace. A lumped-parameter model based on magnetic monopole approximation is employed to describe the magnetic field generated by the quadrupole magnetic tweezers in the workspace. In this model, the magnetic field generated by each magnetic pole is approximated by the field of a point magnetic charge associated with the magnetic pole, and the total magnetic field produced by the system is obtained by applying the principle of superposition. An analytical force model considering the interaction between a magnetic particle and the magnetic field is then developed. The derived force model accurately characterizes the nonlinearity of the magnetic force exerting on the magnetic particle with respect to the applied currents to the coils and the position dependency of the magnetic force in the workspace. The directionality as well as the force generation anisotropy of the designed system is then explored using the force model. The model also facilitates the implementation of a feedback control law to stabilize and control the motion of a magnetic particle. Experimental results in terms of the magnetic force in relation to stable motion control of a magnetic particle are used to validate the force model.

Design, Implementation, and Force Modeling of Quadrupole Magnetic Tweezers

This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe's Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 microm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe's Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.

Minimum-variance Brownian motion control of an optically trapped probe

This paper presents the development of a visual servo control system that is capable of trapping and steering a microscopic magnetic bead in a 3-D workspace using a hexapole magnetic actuator. The magnetic actuator employs six sharp-tipped magnetic poles, arranged in a hexagonal configuration, and six actuating coils to achieve 3-D magnetic actuation. Real-time 3-D visual tracking is realized through processing video images acquired by a complementary metal-oxide semiconductor (CMOS) camera to achieve nanometer-scale resolution for particle tracking. A model-based nonlinear control law is developed to achieve two objectives: 1) to stabilize the magnetically propelled microscopic bead and control its Brownian motion and 2) to rapidly steer the microscopic bead within the 3-D workspace. Specifically, 3-D visual servo control of a 2.8-μm magnetic bead is employed to validate the capability of the developed control system. The control performances in terms of variance minimization, 100 nm stepping, and large range steering are experimentally demonstrated.

Zhipeng Zhang

Papers

Three-dimensional particle tracking with subnanometer resolution using off-focus images

Six-Axis Magnetic Levitation and Motion Control

Design, Implementation, and Force Modeling of Quadrupole Magnetic Tweezers

Minimum-variance Brownian motion control of an optically trapped probe

Three-Dimensional Visual Servo Control of a Magnetically Propelled Microscopic Bead