### I. Introduction

### II. Microrobot with Wireless Power Transfer-based Propulsion

*μ*

*,*

_{p}*μ*

*, and*

_{m}*r*

*are the relative permeability of the magnetic material, relative permeability of the media, and radius of the magnetic particle, respectively. Several studies have been conducted using this magnetic force as a propulsion force for microrobots [18–20]. Considering that WPT systems are based on a time-varying magnetic field, which is essential for generating induced voltage, the time-varying magnetic field and magnetic material can be used as a source of magnetic force. As a result, the magnetic force on magnetic material, especially a sphere-shaped magnetic particle, when exposed to a time-varying magnetic field, can be obtained as in Eq. (2) [21]:*

_{p}*ω*is the angular frequency of the incident magnetic field of current flows on the transmitting coil. In this research, the medium in which the microrobot will be inserted is a nonmagnetic material fluid. Therefore, the

*μ*

*is 1. Moreover, the magnetic material has a high relative permeability compared to the fluid, so the*

_{m}*μ*

*(*

_{m}*μ*

*−*

_{p}*μ*

*)/(*

_{m}*μ*

*+ 2*

_{m}*μ*

*) term in Eq. (2) converges to 1. According to Eq. (2), the magnetic force depends on the magnitude, relative permeability, and gradient of the incident magnetic field. To achieve a higher magnetic force, a bar-type magnetic material is applied, which introduces a higher magnetic field gradient. By applying this structure, the receiving coil can be wound along the magnetic material. This concentrates the magnetic field compared to a nonmagnetic material and subsequently achieves higher power transfer efficiency.*

_{m}*d*), Eq. (2) can be modified into Eq. (3):

*v*is the volume of magnetic material,

*I*is the magnitude of current flows in the transmitting coil,

*L*is a half-length of rectangular transmitting coil, and

*d*is the distance between the transmitting coil and the receiving coil or microrobot. According to Eq. (3), as the magnetic force on the microrobot is free from the powering frequency, there is no limitation when determining the power frequency. Considering that the magnetic force on a magnetic material at a certain distance (

*d*) is determined by time-varying currents when the required force of the microrobot is given, it is able to determine the current on the transmitting coil.

### III. Propulsion of Microrobot in a Tube

*F*

*) as in the following equation, which is applied to an external flow or free stream condition.*

_{D}*ρ*,

*v*,

*C*

*,*

_{D}*A*are the density of the fluid, the velocity of the microrobot, the drag coefficient, and the cross-sectional area of the fluid, respectively.

### IV. Experimental Verification

### 1. Experiment Setup

### 2. Derivation of Force Required to Move a Microrobot

^{3}and the volume of the capsule is 577 mm

^{3}, the buoyance of the microrobot can be calculated as 5.104 mN, which is 90 μN lower than gravity. Thus, it will require more than 90 μN to move the microrobot upward.