# Analysis and Comparison of Electromagnetic Microrobotic Platforms for Biomedical Applications
## 3 The Electromagnetic Microrobotic Systems
### Analysis  
From the various developed electromagnetic microrobotic setups, the uniform magnetic field can be generated by the Helmholtz coils pair and the uniform saddle coils pair, while the uniform gradient can be produced by the Maxwell coils pair and the gradient saddle coils pair with the different settings, respectively. Such electromagnetic coils form the EMA system with different desired functions. The four stationary coils pairs, such as two pairs of Helmholtz coils and two pairs of Maxwell coils, can control a magnetic microrobot in 2D workspace. The same function of control is also achieved by the four pairs of saddle coils or combination of four coils pairs with the correct configuration. Meanwhile, only two rotating coils pairs can control the 2D motion of microrobots. The one rotating Helmholtz and one rotating Maxwell coils pairs can contribute a 2D position and an orientation control. Similarly, the two rotating saddle coils pairs also can provide the same control with a suitable setting. Thus, all these platforms designed for a 2D workspace allow up to a three DOFs (two translations and one rotation). When the workspace is expanded to the 3D, at least six stationary independent electromagnetic coils are required. If the coils pair is able to be rotated, the number of coils pair could be reduced. For instance, two pairs of the Helmholtz coils and two pairs of the Maxwell coils can actuate a 3D locomotion of the microrobot where one Helmholtz coils pair and one Maxwell coils pair can rotate along a same axis for rotating a 2D manipulation plane over a 3D workspace. When an electromagnetic coil is used to generate both magnetic field and gradient by adjusting the current, the number of stationary coils pairs can be further reduced to three pairs. In addition, the number and type of coils also depend on the manipulated microrobot. The motion of the microswimmer only requires three pairs of coils that generate the uniform magnetic field throughout the 3D workspace. With the exception of the 3 DH and 9E platforms, the others allow up to the 5 DOF (3 translations and 2 rotations). The independent manipulation of multiple microrobots has been also investigated [72; 92; 95; 97]. It requires either complicated control strategy or special design of the microrobots. Such as, the eight independent electromagnetic coils are responsible for generating the common magnetic gradient to propel the multiple microrobots in the workspace. With the unique viscous drag due to the specific microrobots, their responses are independent to obtain their control. Basically, the electromagnetic actuation system is useful for various manipulation tasks with different configurations of electromagnetic coils under adjustable current inputs and efficient control strategies. Table 2 summarizes the comparison of the different EMA setups. More comparative and mathematical analyses regarding different configurations of EMA systems have been presented in the previous study [81]. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**EMA** & **Coils and Workspace** & **Advantages** & **Limitations** \\ \hline \multirow{4}{*}{HMr [49]} & \multirow{4}{*}{4 coils, 2D} & Use few coils with simple structure; 2 DOFs of translation and 1 DOF of rotation; Manipulation of the orthotropic body. & Low magnetic gradient over larger areas; Rotating coils limit medical applications. \\ \hline \multirow{4}{*}{2C [70]} & \multirow{4}{*}{4 coils, 2D} & Less number of coils, 18\% smaller volume and 26.7\% less power & Non-uniform magnetic field at the edge of the workspace. \\  & & consumption to the same magnetic actuation. & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of the EMA systems.