## 4 Experiments and Results  
### System Implementation  
Based on the coil set layout model proposed in Section 2, the Rect3D (see Figure 7) has been established. The electromagnet cores are made of H125, which is an FeNi alloy produced by Hengdian Group DMEGC Magnetics CO.,LTD (Dongyang city, Zhejiang province, China).Its saturation magnetization is on the order of 1500 mT, and the initial permeability is 125 H/m. Each core has a length of 30 mm, width of 30 mm and height of 30 mm. Each coil is assembled with ten cores. Figure 7: Rectangular electromagnetic coil set actuation platform. (**a**) System setup. The power supply for the system is \(\Pi\)6942A produced by ITECHELECTRONIC CO., LTD and its response time is 100 ms. This power supply drive system can simultaneously operate eight electromagnetic coils with a full load of 15A. (**b**) Schematic diagram of the placement of the workspace. The size of the workspace is 37\(\times\)37\(\times\)25 mm\({}^{3}\). (**c**) The overall shape of the microrobot is a cone with a radius of 1.25 mm and a height of 2 mm, and is designed with threads embedded in the cone. Such a structure makes it possible to advance forward and wear the obstruction in front of the movement when it is rotated about its central axis. A cylindrical hole with a diameter of 1 mm and a height of 1 mm at the bottom of the cone is used for assembling the magnetic carrier. Microrobots are made by aluminum 3D printing. This makes the microrobot body not subject to any torque and force under the magnetic field and has a low mass to facilitate driving. The magnetic carrier can realize movements such as translation and rotation under the action of an external magnetic field to provide power for the microrobot. (**d**) Assembly relationship between microrobot and magnetic carrier. (**e**) The magnetic carrier is a cylinder having a diameter of 1 mm and a height of 1 mm and is made of neodymium iron boron and a density of 7500 kg/m\({}^{3}\). (**f**) Mounting position of the side camera. (**g**) Assembly diagram of the coil module. (**h**) FeNi alloy. The uppercase yellow English letters in the figure show the same thing. The power control unit is composed of a host PC and eight DC programmable power supplies, respectively, connected to the corresponding coils on the electromagnetic actuation platform. The host computer and the DC programable power supply are connected through the USB serial port, and the I/O interface control of the program control instrument is realized by using the VISA function library developed by the NI company. SCPI (Standard Commands for Programmable Instruments) command format is used to realize remote communication between the host computer and the DC power supply. The camera has a resolution of 640 \(\times\) 480. Its visual standard protocol supports the Directshow protocol and Twain protocol. The camera lens uses a large multiple continuous zoom lens with an optical magnification of 0.13 \(\sim\) 2 times and a working distance of 65 \(\sim\) 700 mm. The software part of the milli/microrobot magnetic actuation system includes the magnetic actuation algorithm, the power driver, the milli/microrobot real-time recognition program, and the implementation of a UI control interface. In part of the mathematical model of the spatial magnetic field distribution, the spatial magnetic field model of the rectangular electromagnetic coil combination is built by C ++ on the Qt Creator platform and is packaged into a class, which mainly includes the magnetic field solving method of the rectangular electromagnetic coil under the local coordinate system and the absolute coordinate system. The magnetic field model is used to obtain the magnetic field at the point of the absolute coordinate system of the rectangular electromagnetic coil. Combined with the milli/microrobot magnetic actuation algorithm, the mapping relationship between the magnetic field torque and the force to the input current is established.