Microrobots are a promising method in biological and medical applications for a number of purposes, such as drug delivery, biopsy, marking, cell manipulation, micro particle transport, etc., with minimal damage to the desired site [1
]. One of the most common application areas of microrobots is microfluidic systems [7
]. In a microfluidic environment, flow characteristics and environmental effects, related with acting forces on a microrobot, change with decreasing dimensions. For example, decrease in Reynolds number causes a microfluidic environment to present laminar flow behavior. In the laminar flow environment, transfer and movement of micro-objects gets harder, since microfluidic system presents high viscous medium character [8
]. In such laminar flow environment, different kinds of approaches can be used to transfer and move the micro-objects instead of using microrobots. These approaches can be counted as optical tweezers, thermal gradients, electrostatic forces, dielectrophoresis forces, and chemical concentration differences [9
]. However, the use of the microrobots in such applications has more advantages over other applications when considering the spatial effects, the manipulation force to be applied, and the precision of micro/robot-object motion [2
In biomedical applications such as single cell analysis, nanometer resolution is required to move and transfer some micro-objects [7
]. Although microrobots have advantages when compared to other methods, there are still ongoing studies to develop microrobot’s precise movement capability. Viscosity of the medium in microfluidic chip and friction forces between microrobot and microfluidic substrate are the main challenges restricting precise motion and force output of the microrobot during manipulation [12
]. For example, Bradley Nelson et al. were inspired by the artificial bacterial flagella (ABF) in the fabrication of their microrobot. This ferromagnetic microrobot has helical structure, and it can move by the action of rotating magnetic fields. In such a structure, rotational motion of tail allows high efficient motion with low magnetic fields [13
]. In this type of microrobot design, helical structure appears to be a restriction, limiting the design of different robot geometries where there is a need for different microrobot designs in various microfluidic applications. Additionally, the microrobot does not conserve its position when the applied magnetic force is paused and the suspension of the microrobot is lost. Arai et al. have also been working on microrobot control with magnetic field effect using permanent magnets on the microrobot body, focusing on force output and position sensitivity of microrobot in their work [2
]. Design of microrobots was modified in order to decrease friction force, leading to an improvement in accuracy of motion [3
]. But there was still contact between substrate and microrobot as a limiting factor. Thus, ultrasonic vibrations were also introduced to microfluidic chips, in order to reduce surface friction forces [14
]. All the effort was on reducing surface contact and having high force output to provide precise manipulation and effective cell manipulation. Ultrasonic vibrations were, however, also a factor that reveals a new problem that is the main reason of micro-objects’ vibrations and movement.
Recent studies by Metin Sitti and Arai show the use of magnetic levitation and acoustic levitation to provide precise positioning and high force output, respectively. The design of Metin Sitti’s study offers unstable motion control due to nonlinear distribution of electromagnetic field [15
]. Unfortunately, it is hard to obtain time effective motion control. In their other work, a robot with 5 degrees of freedom (DOF) can be moved at higher speeds (>20 mm/s) by 8 electromagnets, although the orientation of the microrobot can be made with high positioning error of 2.83 mm [16
]. In the study of Arai et al. ultrasonic external forces, which are applied for levitating microrobots, appeared once again as a restricting factor. The existence of the ultrasonic waves is still present in the liquid environment [17
]. Also, Lucarini et al. investigated teleoperated and autonomous controls of a microrobot in a liquid environment. Even though they developed a robust control algorithm with high reproducibility to manipulate it at low speed of 2 mm/s, the mean error is as high as 250–300 µm. In addition, the effect of the control response was not mentioned in higher speeds [18
]. Those efforts have shown that microrobot levitation studies had increasing demand to maintain better positioning accuracy and force output, whereas all those studies required constant energy consumption to drive piezo vibrator or run bulky electromagnets, in order to provide continuous suspension of the microrobot.
At this point, the diamagnetic levitation emerges as a powerful method for precise positioning of a microrobot with a suspension mechanism. With the aid of a permanent magnet embedded in the microrobot, which is positioned above a diamagnetic material, the microrobot can be levitated without an active control mechanism. In the studies on diamagnetic levitation, it is seen that, the dipole–dipole [19
] interaction could be used by dividing the bismuth [20
] and the permanent magnet into two halves, respectively. Unlike Pigot’s set-up, which works on a magnetic array, our system is in liquid, which is more suitable for lab-on-chip systems, and has higher control accuracy [20
]. According to Profijt and his team, the levitation height is much lower than our proposed method [19
]. To the best of our knowledge, the first diamagnetically floating microrobot application was developed by Ron Pelrine et al. [21
]. In their work, impressive motion repeatability and speed results are demonstrated on the trajectory designed by the microrobot printed circuit board (PCB). However, in the proposed method, it is necessary to regulate the PCB and the 4-pole magnet for levitating the microrobot. Also, how to control the levitation height on the z
-axis has not been specified. Despite the existence of a microrobot levitation technique, which moves horizontally very fast, there is no theoretical calculation, also minimum and maximum levitation ranges are not specified. In addition, the proposed levitation system is not in the liquid medium, so the potential for lab-on-a-chip applications have not been discussed. The current on the PCB affects the positioning accuracy of the passing path. In our case, the positioning resolution of the linear stage shows the same effect. The greater the PCB path width and the wider the path spacing, the lower the sensitivity is, because the uniformity of the distribution of the generated magnetic field is impaired.
Feng Ling and his team performed passive diamagnetic levitation using 4-pole magnets. However, the orbits can be 1 mm at most, and no motion sensitivities or control strategies are mentioned in their work [23
]. Besides, in our method, the levitation height is controlled by one external ring-shaped permanent magnet, because we utilized pyrolytic graphite (PG) as a balancing force instead of a microrobot. Our robot is formed by SU8 and permanent magnet combination. Also, according to the position of the lifter magnet, microrobot 3D orientation can be provided. In our previous studies, the maximum and minimum microrobot operating points are also indicated by controlling the levitation height on the microrobot z
]. In those studies, we also show how to find optimum parameters in order to setup a diamagnetically levitated microrobot manipulation system.
In this work, our proposed system provides a solution for three-dimensional motion control in liquid environments using single carrier magnet and lifter magnet. It does not require current control and can eliminate unwanted physical effects, such as heat and noise that can occur in other methods. According to similar approaches, size can be reduced by 1/4, and complex permanent magnet fusion methods are not needed. In the future, it will allow the construction of different polymer microrobots in which the buoyancy force can be used effectively. This study shows the analytical approach which includes theoretical, numerical, and experimental elements, including positioning accuracy, phase differences, and motion reaction, such as head tilting. The theoretically presented equations are solved numerically by FEM analysis. Design steps of microrobot levitation are demonstrated by multi-coupled physics analysis prior to the experimental stage. The proposed approach is experimentally confirmed. In addition, it is shown that complex trajectories can be tracked with submicron error. In this way, a high precision untethered microrobot manipulation technique has been developed without using bulky electromagnetic installations or extra sensory attachments to increase manipulation accuracy.
5. Discussion and Conclusions
In this system, which we designed with our team, we offer an innovative micro-UFO working mechanism suspended by diamagnetic levitation, unlike other studies. In the system we designed, the micro-UFO was able to successfully track the maximum range of motion of the linear stage at 500 nm through the lifter magnet after it was suspended at certain heights. With the use of nano-positioner with higher motion sensitivity, it is obvious that higher resolution position capabilities can be achieved successfully. Another innovative feature of the designed micro-UFO, which is different from micro-UFOs providing permanent magnet motion, is that it has a more suitable design for biomedical applications. PDA coated micro-UFO also have the ability to prevent contamination.
5.2. Levitation on z-Axis
It is possible to control the movement of x-y and z-axes within the microfluidic channel of the micro-UFO. By means of finite element analysis in COMSOL, the levitation height limits of the micro-UFO were successfully determined and compared with the experimental results. Magnetic analysis showed that the micro-UFO showed linear surface behavior in the range of 90–280 μm according to surface force graph on z-axis direction. Experimentally, it was determined that the current micro-UFO levitation characteristic has an unstable structure in the range of 0 to 30 microns, and 290 to 333.8 microns, and the stable working range of the system is in the range of 30 to 290 microns. Accordingly, when compared with the experimental results, the analysis results were found to be within the experimental limits. If the analytical findings obtained are used on the system, it has been proved that safe and linear behavior range can be studied.
5.3. Drag Force—Lifter Magnet Effects
The distance between the lifter magnet and the pyrolytic graphite, as well as the range of levitation, are calculated numerically. Compared to the experimental results, it has been shown that the working range of 54–58 mm is common with current experimental setup. Although the micro-UFO can be controlled beyond this range, it has been shown that the linear zone is the better working range. As shown in the experimental results, the numerical analysis result showed that the micro-UFO in the determined range has more stable characteristics. The result of the drag force analysis shows that the viscous effect of the water is not much higher than micro-UFO. It is calculated that the maximum value of drag force is about 5% of the force required to levitate the robot. If micro-stages’ operating speed range is set to ±2 (mm/s), it is estimated that the drag force will be less than 0.75%. Thus, we can say that the drag force can be neglected, and the system can be linearized by neglecting the drag force effect. For future studies, a linear control technique can be potentially utilized in this application.
5.4. Center Alignment
Precise position control is also provided on the x- and y-axes of the micro-UFO in the direction of the experimental data. The mobility of the micro-UFO has been tested in motion trajectories that may be encountered in different scenarios and work areas. The micro-UFO has successfully followed the sinusoidal and circular orbits, in addition to the linear motion. As you can see in COMSOL analysis, when 0.1 mm phase difference occurs between lifter-carrier magnets’ center, it is calculated that forces generated in x- and y-axes are about 1/103 of the force in z-axis. Therefore, predominant z-axis force cannot be affected by x- and y-axes forces dramatically, and levitation height does not change during motion of the micro-UFO. Furthermore, it is always centralized with lifter magnet poles that provide stable trajectory tracking.
5.5. Phase Difference
According to levitation characteristics with the help of motorized micro-stage motions, the phase difference during the movements is seen as a factor that will force us to do real-time position control. On the other hand, for many biomedical applications, nanometric speeds are being used. In this case, the phase difference was found to be negligible as a result of our experimental studies. According to the analysis and experimental results regarding the phase difference, the torque and force values applied on the robot were not affected. The micro-stage is moving at a maximum speed of 2 mm/s. In this case, an offset of 0.6 mm is calculated and shown in Figure 15
. It can be seen that the calculated phase difference is very small (1/66) compared to the lifter magnet size. Thus, it is observed that there will be no effect on the magnetic force and torque produced. In addition, when the phase difference is high, the head-tilting reaction observed at high speed levels is likewise observed to be negligible within the operating speed requirements of the applications. However, the possibility of giving capillary damage to the surface boundaries of the head-tilt reaction cannot be overlooked, especially in low run-up working conditions. In this regard, in future studies, closed loop control-based studies will be carried out to prevent the head-tilt reaction.