In the design of microrobots, a helical geometry is pivotal to overcome the time-reversal constraints of the scallop theorem. The helical geometry enables the microrobots to propel themselves forward in viscous fluids with a corkscrew like motion when they are allowed to rotate. It is physically advantageous for microrobots to swim with near-zero angle of attack much like buoyant microorganisms, allowing high thrust for forward propulsion. This type of propulsion is not possible as the non-buoyant microrobot drifts downward due to gravity. Here, we analyze the stability problem of controlling magnetically driven helical microrobots to achieve bounded straight runs without drift in a low-Reynolds-number regime. We demonstrate periodic active suspension solutions, that facilitate helical propulsion with minimal angle of attack and zero drift. We theoretically predict unique control inputs, for a given helical microrobot geometry and magnetic composition (i.e., 62% Ni and 24% Au Wt%), which can be generated with rotating field and field-gradient pulling. Using microrobots fabricated of denser-than-water soft-magnetic body (4870 kg•m−3), we find that the microrobot is allowed to swim with near-zero angle of attack of 8.3° ±5.2° (mean ±s.d.), outperforming conventional gravity compensation methods.

Until now, the potential of untethered magnetic robots (UMRs), propelled by external time-periodic magnetic fields, has been hindered by the limitations of wireless manipulation systems or noninvasive imaging techniques combined. The need for simultaneous actuation and noninvasive localization imposes a strict constraint on both functionalities. This study addresses this challenge by substantiating the feasibility through experimental validation, showcasing the direct teleoperation of UMRs within a fluid-filled lumen. This teleoperation capability is facilitated by a scalable X-ray-guided robotic platform, extendable to match the dimensions required for in vivo applications, marking a noteworthy advancement. Our methodology is demonstrated by teleoperating a 12-mm-long screw-shaped UMR (5 mm in diameter) within a bifurcated lumen, filled with blood. This navigation is achieved using controlled rotating magnetic fields, guided by real-time X-ray Fluoroscopy images. Incorporating a two-degree-of-freedom control system, we demonstrate the operator’s capability to use X-ray Fluoroscopy images to keep the UMR coupled with the external field during wireless teleoperations, resulting in a success rate of 76.6% when moving along the intended pathways, with a mean absolute position error of 1.6 ± 2.1 mm.

This paper explores the application of X-ray-guided magnetic fields for the wireless control of untethered magnetic robots (UMRs) within cerebral vascular phantoms. With a focus on addressing challenges associated with strokes and brain aneurysms, the study aims to enhance neurosurgical procedures by improving precision and maneuverability. Experimental findings showcase the feasibility and effectiveness of this innovative approach in navigating UMRs, characterized by a screw-shaped body and a ferromagnetic core, through complex vascular structures. Cone-beam computed tomography is employed to determine the tomography and provide various reference trajectories for the UMR inside the cerebral vascular phantom. Our motion control experiments show that the X-ray-guided magnetic fields enable the UMR to move along any intended path with an average success rate of 89%, allowing the UMR to move between the left and right common carotid artery to the left and right internal and external carotid artery.

To date, all previous research in the wireless magnetic actuation of untethered helical devices has achieved motion stability using feedback control in vitro. However, feedback control systems are likely to be affected by the increased sensory uncertainty during in vivo trials. In this study we investigate the input-output boundedness of an interconnection between a helical device and a single rotating magnet actuator in low-Reynolds-number regime. Using the resistive-force theory, the interconnection is expressed in terms of all possible input-output pairs. Inputs representing the actuation frequency, pitch angle, lateral speed, and field strength are analyzed numerically and experimentally. We demonstrate input-output boundedness of the states of the helical device during circular and straight runs in open-loop, and we demonstrate bounded input-output propulsion without orienting the angle of attack (the often used input to swim horizontally without vertical drift) of the helical device to counteract gravity. Our results are important for a number of minimally invasive applications and tasks requiring improved control authority for stable runs of helical devices without drift due to gravity and without feedback control and restricted configuration imposed on the helical device's motion.

One approach to the wireless actuation and gravity compensation of untethered helical magnetic devices (UHMD) is through swimming with a non-zero angle of attack (AoA). This configuration allows us to counteract gravity, so that for a given desired path, we can move the UHMD controllably without drifting downward under its own weight. This study seeks to investigate the use a reduced-order model of the complex 6-degrees-of-freedom model of UHMDs in low Reynolds-number regime. A one-dimensional model representing the relative position of the UHMD with respect to an actuator rotating permanent magnet is used to predict a gap which yields bounded behavior of the open-loop system. Using geometric representation of the reduced-order model, the local bounded behavior of the UHMD with near-zero AoA is attributed to periodic active magnetic suspension, which dominates near-zero AoA. Our numerical results are verified experimentally and bounded behavior of the UHMD demonstrates the capability to swim with near-zero AoA (6.3° ± 2.2°) without drifting downward. With this actuation strategy, it is unlikely that the orientation of the UHMD will be needed during noninvasive localization, making the control system dependent on only its position with respect to a prescribed trajectory. This strategy will also provide a computational advantage in adjusting the gap between the UHMD and a robotically controlled rotating permanent magnet actuator.

Magnetic nanoparticles can be electrostatically assembled around sperm cells to form biohybrid micro robots. These biohybrid microrobots possess sufficient magnetic material to potentially allow for pulse-echo localization and wireless actuation. Alternatively, magnetic excitation of these nanoparticles can be used for localization based on Faraday's law of induction using a detection coil. Here, we investigate the influence of the electrostatic attraction between positively charged nanoparticles and negatively charged sperm cells on the activation of the nanoparticles during nonlinear differential magnetometry and wireless magnetic actuation. Activation of clusters of free nanoparticles and nanoparticles bound to the body of sperm cells is achieved by a combination of a high- frequency alternating field and a pulsating static field. The nonlinear response in both cases indicates that constraining the nanoparticles is likely to yield significant decreases in the magnetometry sensitivity. While the attachment of particles to the cells enables wireless actuation (rolling locomotion), the rate of change of the magnetization of the nanoparticles decreases one order of magnitude compared to free nanoparticles.

Control of tetherless magnetically actuated helical robots using rotating dipole fields has a wide variety of medical applications. The most promising technique in manipulation of these robots involves a rotating permanent magnet controlled by a robotic manipulator. In this work, we study the open-loop response of helical robots (in viscous fluids characterized by low Reynolds numbers) in the presence of position constraints on the actuating rotating permanent magnet. We first derive a mapping between the space of the manipulator’s joints, the produced magnetic fields in three-dimensional space, and the translational and rotational velocities of the helical robot. Then, we constrain the 3D position of the rotating dipole field and predict the response of the helical robot by controlling its angular velocity using the constrained mapping. We demonstrate open-loop control and gravity compensation of the robot using the angular velocities of the actuating permanent magnet while enforcing constraints on the end-effector position.

Magnetically-driven screws operating in soft-tissue environments could be used to deploy localized therapy or achieve minimally invasive interventions. In this work, we characterize the closed-loop behavior of magnetic screws in an agar gel tissue phantom using a permanent magnet-based robotic system with an open-configuration. Our closed-loop control strategy capitalizes on an analytical calculation of the swimming speed of the screw in viscoelastic fluids and the magnetic point-dipole approximation of magnetic fields. The analytical solution is based on the Stokes/Oldroyd-B equations and its predictions are compared to experimental results at different actuation frequencies of the screw. Our measurements matches the theoretical prediction of the analytical model before the step-out frequency of the screw owing to the linearity of the analytical model. We demonstrate open-loop control in two-dimensional space, and point-to-point closed-loop motion control of the screw (length and diameter of 6 mm and 2 mm, respectively) with maximum positioning error of 1.8 mm.

A rotating two-tailed soft microrobot induces a frequency dependent flow-field in low Reynolds number fluids. We use this flow-field to achieve noncontact manipulation of nonmagnetic microbeads with average diameter of 30 μm in 2-D space. Our noncontact manipulation strategy capitalizes on exerting a rotational magnetic torque on the magnetic dipole of the microrobot. The induced flow-field enables microbeads in the surrounding fluid to orbit the microrobot along a sprocketlike trajectory due to a periodic and asymmetric flow-field caused by the two tails. A hydrodynamic model of the two-tailed microrobot and the orbiting microbeads is developed based on the method of regularized Stokeslets for computing Stokes flows. The relations between the angular velocity of the orbiting microbeads and the rotation frequency of the microrobot, their proximity (p), and tail length ratio of the microrobots are studied theoretically and experimentally. Our simulations and experimental results show that the angular velocity of the orbiting microbeads decreases nearly as | p |-2with the distance to the microrobot and its tail length ratio. We also demonstrate closed-loop control of the microbeads toward target positions along sprocketlike trajectories with an average position error of 23.1 ± 9.1 μm (n = 10), and show the ability to swim away without affecting the positioning accuracy after manipulation.

Mid-Air haptic devices have become an active area of research because of their potential impact to augmented/virtual reality. In this work, we develop an electromagnetic-based haptic interface to provide controlled magnetic forces on a wearable orthopedic finger splint with a single magnetic dipole. We model the electromagnetic forces exerted on the finger splint, optimize the design of the electromagnetic coils, and develop an impedance-type haptic rendering algorithm using position feedback. This rendering algorithm capitalizes on minimizing the error between the exerted magnetic force and the desired constraint force of a virtual three-dimensional (3D)object based on the position of the finger splint. In order to investigate the influence of incorporating position feedback, we conduct a comparative study for the same group of participants with (Case I)and without (Case II)position feedback. Our experimental results show that position feedback enables participants to achieve success rate of 66.87 ± 15.0% (n=160) in distinguishing between the geometry of four 3D virtual objects. This rate is decreased to 55.15±15.8% (n=160) in the absence of position feedback. Our analysis shows statistical evidence to conclude that the mean success rate for Case I is greater than that of Case II, at α = 0.1 and 90% confidence level.

Magnetotactic bacteria have the potential to controllably reach stagnant fluids inside the human body and achieve targeted drug delivery. In this application, motion of the magnetotactic bacteria is influenced by the near-surface effects such as the background flows and surface interactions. Here, we provide a hydrodynamic model of bipolarly-flagellated magnetotactic bacteria (Magnetospirillum gryphiswaldense strain MSR-1) based on the resistive-force theory to resemble the helical body and the two flagella bundles, and investigate their swimming characteristics in two environments, i.e., free-space and near flat walls. The free-space is studied using capillary tubes with depth of 200 μm, whereas the effect of the flat walls is investigated using microfluidic chips with depth of 5 μm. We find that the linear speeds of bacteria near- and far-surface are 36±16.4 μm/s (mean±s.d.) and 46±6.8 μm/s, respectively, whereas their respective angular velocities are 12.5±5.7 rad/s and 13.5±5.0 rad/s.

In this study, we develop an electromagnetic-based haptic interface to provide controlled magnetic forces to the operator through a wearable haptic device (an orthopedic finger splint with single dipole moment) without position feedback. First, we model the electromagnetic forces exerted on a single magnetic dipole attached to the wearable haptic device, and derive magnetic force-current mapping for the dipole moment. Second, this mapping is used as basis for parameter selection of the electromagnetic coils of the haptic interface, dipole moment of the wearable haptic device, and the operating workspace of the system. The electromagnetic-based haptic interface enables three-dimensional (3D) virtual object rendering in mid-air within a workspace of 150 mm × 150 mm × 20 mm, using magnetic forces in excess of 50 mN. Participants experimentally demonstrate a 61% success rate in distinguishing the geometry of 4 representative 3D virtual objects. However, our statistical analysis shows that the ability of the participants to distinguish between geometries is not statistically significant, for 95% confidence level.

In travelling towards the oviducts, sperm cells undergo transitions between planar to helical flagellar propulsion by a beating tail based on the viscosity of the environment. In this work, we aim to model and mimic this behaviour in low Reynolds number fluids using externally actuated soft robotic sperms. We numerically investigate the effects of transition between planar to helical flagellar propulsion on the swimming characteristics of the robotic sperm using a model based on resistive-force theory to study the role of viscous forces on its flexible tail. Experimental results are obtained using robots that contain magnetic particles within the polymer matrix of its head and an ultra-thin flexible tail. The planar and helical flagellar propulsion are achieved using in-plane and out-of-plane uniform fields with sinusoidally varying components, respectively. We experimentally show that the swimming speed of the robotic sperm increases by a factor of 1.4 (fluid viscosity 5 Pa.s) when it undergoes a controlled transition between planar to helical flagellar propulsion, at relatively low actuation frequencies.

We use electrospinning to fabricate sperm-shaped magnetic microrobots with a range of diameters from 50 μm to 500 μm. The variables of the electrospinning operation (voltage, concentration of the solution, dynamic viscosity, and distance between the syringe needle and collector) to achieve beading effect are determined. This beading effect allows us to fabricate microrobots with similar morphology to that of sperm cells. The bead and the ultra-fine fiber resemble the morphology of the head and tail of the sperm cell, respectively. We incorporate iron oxide nanoparticles to the head of the sperm-shaped microrobot to provide a magnetic dipole moment. This dipole enables directional control under the influence of external magnetic fields. We also apply weak (less than 2 mT) oscillating magnetic fields to exert a magnetic torque on the magnetic head, and generate planar flagellar waves and flagellated swim. The average speed of the sperm-shaped microrobot is calculated to be 0.5 body lengths per second and 1 body lengths per second at frequencies of 5 Hz and 10 Hz, respectively. We also develop a model of the microrobot using elastohydrodynamics approach and Timoshenko-Rayleigh beam theory, and find good agreement with the experimental results.

Magnetotactic bacteria have the potential to controllably reach deep-seated regions of the body via vessels and achieve targeted drug delivery. In this application, motion of the magnetotactic bacteria is influenced by the strength of the external magnetic field. Here, we investigate the swimming characteristics of magnetotactic bacteria (Magnetospirillum gryphiswaldense strain MSR-1) under the influence of uniform and adaptive magnetic fields inside microfluidic chip with depth of 5 µm. This depth enables tracking of single bacterium and comparison of uniform and adaptive magnetic field on the positioning accuracy. We find that under the influence of magnetic field reversal with approximately twice the field strength, the diameter of the U-turn trajectories taken by the magnetotactic bacteria is decreased by 63%. In addition, the adaptive magnetic field decreases the size of region-of-convergence of the controlled bacteria within the vicinity of the reference position by 65.5%, compared to control using uniform magnetic field. The comparisons between motion control using uniform and adaptive magnetic fields are done on the same culture of magnetotactic bacteria and using the same cell in each motion control trial.

In targeted therapy, clusters of drug carriers (nanoparticles and microparticles) could be in contact with a surface such as the lumen of blood vessels and the interior of the gastrointestinal tract. We study the motion characteristics of clusters of microparticles when they slide on a surface under the influence of weak oscillating magnetic fields (less than 11 mT). The oscillating magnetic fields exert a magnetic torque on the microparticles and allow them to oscillate, and hence overcome the static friction and slide on a surface. We characterize the frequency response of clusters of microparticles by applying oscillating magnetic fields with a frequency range of 0 Hz to 55 Hz, in the presence of a constant magnetic field gradient (0.9 T/m). Clusters of 3 to 4 and 5 to 9 microparticles achieve maximum sliding speeds of 1100 µm/s and 1150 µm/s, at oscillating magnetic fields of 30 Hz. In addition, we experimentally demonstrate closed-loop motion control of the clusters with maximum position error of 20 µm. Furthermore, we show that the magnetic field gradient required to drive a cluster of microparticles (with 3 to 4 microparticles) decreases by 75% in the presence of oscillating magnetic fields from 5 Hz to 50 Hz.

In contact micromanipulation, the adhesive forces between manipulators and microobjects decrease the chances of achieving successful releases at the desired positions. We study a non-contact micromanipulation technique of microbeads (300 μm in average diameter) using clusters of paramagnetic microparticles (100 μm in average diameter). This non-contact micromanipulation is done using the hydrodynamic forces instead of the interaction forces in contact manipulation, and hence eliminates the adhesive forces that decrease the chances of achieving successful releases. Motion of the cluster of microparticles results in a pressure gradient (within the vicinity of the microbead in a fluid) that derives and steers the microbeads without contact. The microparticles are moved under the influence of controlled magnetic field gradient to push or pull the microbeads towards reference positions. We achieve non-contact manipulation via pushing and pulling at average speeds of 219 μm/s and 258 μm/s for the microbead, respectively (using cluster of 10 microparticles). The noncontact pushing and pulling localize the microbeads within the vicinity of reference positions with average steady-state errors of 177 μm and 100 μm, respectively. Moreover, we experimentally demonstrate non-contact microassembly of 3 microbeads into an L-shape at a task completion time of 25 seconds.

We control the motion of helical microrobots with average diameter of 500 μm in two-dimensional (2D) and three-dimensional (3D) spaces using two synchronized rotating dipole fields. The utilization of the two synchronized dipole fields not only increases the magnetic torque exerted on the magnetic dipole of the helical microrobot but also eliminates the magnetic field gradients along its lateral directions. Our finite element simulations and experimental results show that the utilization of two rotating dipole fields increases the magnetic field by 100%, as opposed to single rotating magnetic field. In addition, we show that the magnetic field gradient within the workspace of the microrobot is eliminated. Therefore, the lateral oscillations of the helical microrobot are mitigated within the center of two rotating dipole fields, and hence the motion of the microrobot is stabilized inside tubes with relatively large inner diameters, as opposed to the diameter of the helical microrobot. This strategy allows the microrobot to compensate for gravity and swim in 3D space inside water reservoirs at an average speed of 0.25 body lengths per second. In addition, closed-loop motion control of the helical microrobot is achieved in 2D space at an average speed of 2 mm/s and maximum steady-state error of 100 μm.

Controlling the motion of microrobots based on feedback provided using an imaging modality is essential to make them clinically viable. In this study, we demonstrate the wireless magnetic-based motion control of paramagnetic microparticles using ultrasound feedback. This control is accomplished by pulling the microparticles using the magnetic field gradients towards the reference position through feedback provided by an ultrasound system. First, position of the microparticles is determined using the ultrasound images. Second, calibration of the ultrasound-based tracking of microparticles is achieved and verified using a calibrated microscopic system. Third, the feedback provided by the ultrasound system is used in the implementation of a proportional-derivative magnetic-based control system. This control system allows us to achieve point-to-point control of microparticles with an average position tracking error of 48±59 μm, whereas a control system based on a microscopic system achieves an average position tracking error of 21±26 μm. The positioning accuracy accomplished using our ultrasound magnetic-based control system demonstrates the ability to control microrobotic systems in situations where visual feedback cannot be provided via microscopic systems.

Paramagnetic microparticles moving through fluids have the potential to be used in many applications, including microassembly, micromanipulation, and highly localized delivery of therapeutic agents inside the human body. Paramagnetic microparticles with diameters of approximately 100 μm can be wirelessly controlled by externally applying magnetic field gradients using electromagnets. In this paper, we introduce a motion planner to guide a spherical paramagnetic microparticle to a target while avoiding obstacles. The motion planner explicitly considers uncertainty in the microparticle's motion and maximizes the probability that the microparticle avoids obstacle collisions and reaches the target. To enable effective consideration of uncertainty, we use an Expectation Maximization (EM) algorithm to learn a stochastic model of the uncertainty in microparticle motion and state sensing from experiments conducted in a 3D 8-electromagnet microparticle testbed. We apply the motion planner in a simulated 3D environment with static obstacles and demonstrate that the computed plans are more likely to result in task success than plans based on traditional metrics such as shortest path or maximum clearance.

We experimentally demonstrate that using oscillating weak magnetic fields a sperm-shaped microrobot (which we refer to as MagnetoSperm) can swim using flagellar propulsion and slide on a surface under water. The sperm morphology allows the MagnetoSperm to mimic the locomotion mechanism of a living sperm cell. The MagnetoSperm is designed and developed with a magnetic head and a flexible tail to provide a magnetic dipole moment and propulsion, respectively. The head oscillates under the influence of controlled oscillating weak magnetic fields (~5 mT). This oscillation generates a thrust force in the flexible tail, and hence allows the MagnetoSperm to overcome the drag and friction forces during swimming and sliding on a surface, respectively. Point-to-point open- and closed-loop control of the MagnetoSperm are accomplished using an electromagnetic system under microscopic guidance. This motion control is done in two cases, i.e., swimming in water and sliding on a surface. At oscillating magnetic field of 5 Hz and 45 Hz, the MagnetoSperm swims at an average swimming speed of 32 μm/s (0.1 body lengths per second) and 158 μm/s (0.5 body lengths per second), respectively. At the same frequencies, the MagnetoSperm slides on the bottom of a petri-dish at an average speed of 21 μm/s (0.07 body lengths per second) and 6 μm/s (0.02 body lengths per second), respectively.

We demonstrate the closed-loop motion control of self-propelled microjets inside a fluidic microchannel. The motion control of the microjets is achieved in hydrogen peroxide solution with time-varying flow rates, under the influence of the controlled magnetic fields and the self-propulsion force. Magnetic dipole moment of the microjets is characterized using the U-turn and the rotating field techniques. The characterized magnetic dipole moment has an average of$\hbox{1.4}\times \hbox{10}^{-13}$A.m$^{2}$at magnetic field, linear velocity, and boundary frequency of 2 mT, 100$\mu$m/s, and 25 rad/s, respectively. We implement a closed-loop control system that is based on the characterized magnetic dipole moment of the microjets. This closed-loop control system positions the microjets by directing the magnetic field lines toward the reference position. Experiments are done using a magnetic system and a fluidic microchannel with a width of 500$\mu$m. In the absence of a fluid flow, our control system positions the microjets at an average velocity and within an average region-of-convergence (ROC) of 119$\mu$m/s and 390$\mu$m, respectively. As a representative case, we observe that our control system positions the microjets at an average velocity and within an average ROC of 90$\mu$m/s and 600$\mu$m and 120$\mu$m/s and 600$\mu$m when a flow rate of 2.5$\mu$l/min is applied against and along the direction of the microjets, respectively. Furthermore, the average velocity and ROC are determined throughout the flow range (0 to 7.5$\mu$l/min) to characterize the motion of the microjets inside the microchannel.

We use a cluster of paramagnetic microparticles to carry out a wireless two-dimensional microassembly operation. A magnetic-based manipulation system is used to control the motion of the cluster under the influence of the applied magnetic fields. Wireless motion control of the cluster is implemented at an average velocity and maximum position tracking error of 144 μm/s and 50 μm, respectively. This control is used to achieve point-to-point positioning of the cluster, manipulation of microobjects, and assembly of microobjects into a microstructure. The control system achieves stable positioning of the cluster, while simultaneously compensating for the planar drag forces on the cluster and the microobject. The presented magnetic-based microassembly technique allows for the selective pushing and pulling of microobjects with specific geometries towards their destinations inside a microstructure in an execution time of 18 s, within a workspace of 1.8 mm × 2.4 mm.

We demonstrate the closed-loop control of a magnetotactic bacterium (MTB), i.e., Magnetospirillum magnetotacticum, within a micro-fabricated maze using a magnetic-based manipulation system. The effect of the channel wall on the motion of the MTB is experimentally analyzed. This analysis is done by comparing the characteristics of the transient- and steady-states of the controlled MTB inside and outside a micro-fabricated maze. In this analysis, the magnetic dipole moment of our MTB is characterized using a motile technique (the u-turn technique), then used in the realization of a closed-loop control system. This control system allows the MTB to reach reference positions within a micro-fabricated maze with a channel width of 10 μm, at a velocity of 8 μm/s. Further, the control system positions the MTB within a region-of-convergence of 10 μm in diameter. Due to the effect of the channel wall, we observe that the velocity and the positioning accuracy of the MTB are decreased and increased by 71% and 44%, respectively.

Magnetic drug carriers such as microrobots and paramagnetic microparticles have the potential to increase the therapeutic indices by selectively targeting the diseased tissue. These magnetic microobjects can be controlled using magnetic-based manipulation systems. In this study, we analyze a minimum input motion control to minimize the currents at each of the electromagnets of a magnetic system. This minimum input control allows us to achieve point-to-point closed-loop motion control of microparticles in the three-dimensional space, at an average speed of 198 μm/s, and maximum root mean square position tracking error of 104 μm. The minimum input control system is further evaluated by comparing norm-2 of its resulting current vector to the current vector of a proportional-integral (PI) control system. This comparison shows that the minimum input control achieves 11% decrease in the current input, as opposed to the PI control system. However, the PI control system achieves 43% and 285% higher average speed and positioning accuracy, respectively, as opposed to the minimum input controller. The magnetic-based minimum input control can be used to perform closed-loop control of magnetic microrobots while decreasing the current input.

We provide a comparative study between two self-propelled microrobots, i.e., magnetotactic bacteria and microjets. This study includes characterization of their fluidic properties (linear and rotational drag coefficients) based on their morphologies and characterization of their magnetic properties using the rotating-field technique. Further, the control characteristics of our microrobots are evaluated in the transient- and steady-states. The average boundary frequencies of our magnetotactic bacteria and microjets are 2.2 rad/s and 25.1 rad/s, respectively. The characterized fluidic properties and boundary frequencies are used in the characterization of the magnetic properties of our microrobots. The average magnetic dipole moments of our magnetotactic bacteria and microjets are 1.4×10-17A.m2and 1.5×10-13A.m2at magnetic field of 2 mT and linear velocities of 32 μm/s (approximately 6 body lengths per second) and 119 μm/s (approximately 2 body lengths per second), respectively. These characterized magnetic dipole moments are utilized in the realization of closed-loop control systems for the magnetotactic bacteria and microjets. Our closed-loop control system positions the magnetotactic bacteria and the microjets within the vicinity of reference positions with average diameters of 23 μm (approximately 4 body lengths) and 417 μm (approximately 8 body lengths), respectively.

This work investigates the utilization of microparticles for the wireless sensing of interaction forces in magnetic-based manipulation systems. The proposed force estimation approach allows for using microparticles in sensing the interaction forces at hard-to-reach regions to avoid the mechanical and electronic complexities associated with physical force sensors. Based on the velocity of the microparticle and the applied currents at each of the electromagnets of the magnetic system, an interaction force observer is designed to estimate the contact forces between the microparticle and a soft-tissue simulant with different elasticities. Experimentally, a magnetic system is utilized to steer a microparticle towards a soft-tissue simulant to carry out force sensing. The experimental results show that forces in the range of nano-Newton can be estimated without nano-force sensors. The estimated interaction forces due to this contact can be used either in sensing and diagnosis applications, or in the realization of a force control system.

This work presents an energy-based state estimation formalism for a class of dynamical systems with inaccessible/unknown outputs, and systems at which sensor utilization is impractical, or when measurements can not be taken. The power-conserving physical interconnections among most of the dynamical subsystems allow for power exchange through their power ports. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. This information is used in the design of an energy-based state observer. Convergence stability of the estimation error for the proposed state observer is proved for systems with linear dynamics. Furthermore, robustness of the convergence stability is analyzed over a range of parameter deviation and model uncertainties. Experiments are conducted on a dynamical system with a single input and multiple inaccessible outputs (Fig. 1) to demonstrate the validity of the proposed energy-based state estimation formalism.

This paper presents an algorithm for parameters and positions estimation of lumped flexible systems. As soon as the parameters and the positions are estimated they can be used to design virtual sensors that can be moved along the system to estimate the position of any lumped mass keeping the system free from any attached sensors. The virtual sensors are nothing but a chain of estimators that are connected at the end of each other, starting with two actuator's measurements and ending up with system parameters and all the system lumped positions. An estimation based PID controller is presented based on the feedback of the virtual sensor's estimates instead of the actual measurement.