First Demonstration of a modular and reconfigurable magnetic manipulation system

这篇文章主要提出了基于多个电磁铁的模块化的，可实时重新配置的磁操作系统。所有的电磁铁模块采用球型铁芯和三轴正交螺线圈。这样的模块可实时重新配置的原因是因为，施加在球形电磁铁上的磁场等价于施加在球形电磁铁球心的磁场，所以在计算一个磁芯的偶极磁矩时，考虑其他磁物体对它的磁化比较简单。这对采用什么电磁驱动模块有重要的指导意义。

一种模块化，可重配置的磁操作系统的第一个演示
First Demonstration of a modular and reconfigurable magnetic manipulation system [1]
Paper Link
Authors: J. J. Abbott, etc.
2015, ICRA IEEE International Conference on Robotics and Automation

1. 摘要 Abstract

这个系统包含多个全磁铁，每个包含三个正交螺线管和一个球形铁磁芯，能够灵活地操纵一个磁工具。
This system - which includes multiple Omnimagnets, each comprising three orthogonal solenoids and a spherical ferromagnetic core, - is capable of dexterous manipulation of a magnetic tool.
球形铁磁芯任意排列的磁化耦合问题被解决，从而为磁力和转矩提供了解析解决方案。
The magnetization coupling of an arbitrary arrangment of spherical ferromagnetic cores is solved, enabling an analytical solution for the magnetic forces and torques.
因此，该系统不需要大量的现场图或原位现场表征。 如果感应到全方位磁铁的位置和方向，则可以在操纵过程中主动重排列全方位磁铁，同时保持对工具的控制。
Thus, this system does not require extensive field maps or in situ field characterization. If the positions and orientations of the Omnimagnets are sensed, the Omnimagnets can be actively rearranged during the manipulation while maintaining control of the tool.

2. 理论 Methods

球型铁磁物有一个独特的几何性质：施加在球体上的平均磁场总是与施加在球心的磁场相等。
Spherical ferromagnetic objects have a property which is unique to their geometry: the average magnetic field applied over the volume of a sphere is always equal to the magnetic field applied at the center of the sphere.
我们将展示的是，这个性质的结果是，任意数量和排列的全磁铁的耦合磁场能被精确的代数计算，而不是用之前要求的场映射理论。
We will show that a consequence of this property is that the coupled magnetic field of an arbitrary number and arrangement of Omnimagnets can be accurately calculated algebraically, rather than with the field-map method required previously.
这意味着全磁铁的一个系统不仅仅表示第一个真的模块化和可重配置的磁操作系统，而且他们能被实时重配置，全磁铁被移动，增加，和从系统中移除，而不需要任何额外的标定步骤。
This means that a system of Omnimagnets not only represents the first truly modular and reconfigurable magnetic manipulation system, but they are capable of being reconfigured in real-time, with Omnimagnets being moved, added, and removed from the system without any additional calibration step.
全磁铁的偶极磁矩与电流呈线性关系，假设核心运行在它的线性区域，磁矩能被写成：
The dipole moment of an Omnimagnet is linear with current, assuming the core operates in its linear region, and can be written as:
$${\text{m}}_0={\text{M}}_0{\text{I}}_0$$
附带磁芯磁化的扰动偶极磁矩为：
The perturbed dipole moment with the additional core magnetization is:
$${\text{m}}_0={\text{M}}_0{\text{I}}_0+\frac{4\pi }{{\mu }_0}{R}^3{\text{B}}_{ext}$$
在第i个全磁铁铁芯中心的总外部磁场为:
The total external magnetic field at the center of the i-th Omnimagnet’s core is:
$${\text{B}}_{ext,i}=\frac{{\mu }_0}{4\pi }(\sum _{k=1}^{L}P\cdot {\text{m}}_{tk}+\sum _{j=1}^{N}P\cdot {\text{m}}_{oj})$$
${\text{m}}_{tk}$指的是永磁体tool的磁矩，${\text{m}}_{oj}$指的是其他电磁铁的生成磁矩。

[1]: Petruska, Andrew J. , J. B. Brink , and J. J. Abbott . “First demonstration of a modular and reconfigurable magnetic-manipulation system.” Proceedings - IEEE International Conference on Robotics and Automation 2015(2015):149-155.