A Framework of Designing Multi-Coil Electromagnetic System for 6-DOF Manipulation of Magnetic Miniature Robot

Precise and programmable magnetic field control is essential for the reliable actuation of magnetic miniature robots in biomedical applications. However, the workspace of existing systems often relies on empirical designs and lacks a clear framework to define an entire workspace with independently controllable magnetic field strength, as well as precisely specified volume, shape, and position. Here, we present a rational design framework that systematically elucidates the fundamental principles governing the generation of uniform and gradient magnetic fields using spherically distributed magnetic coil arrays (SDMCAs). We first identify the eight independent parameters that fully define the magnetic field. Using both analytical and numerical methods, we demonstrate that the control of the magnetic field strength and gradient can be decoupled. This concept is then extended to three dimensions through the development of a finite element analysis (FEA) model, which accurately simulates the spatial magnetic field distribution of complex coil geometries. The simulation results are validated experimentally, showing excellent agreement. Finally, we propose a step-by-step SDMCA design workflow that enables precise control over the magnetic field parameters within a target workspace. This framework provides a practical and scalable approach for the development of high-performance magnetic actuation systems for miniature robots.