Magnetically actuated soft capsule endoscope for fine-needle aspiration biopsy

这篇文章发表在ICRA会议上，之后该工作的完整版本发表在Soft Robotics上。本文提出了一种特殊的胶囊机器人设计和一种新的磁驱动系统，以及它们的详细的设计介绍。本文也利用了OctoMag framework的设计框架，很有意义。

用于细针穿刺活检的磁驱动软体胶囊内窥镜
Magnetically actuated soft capsule endoscope for fine-needle aspiration biopsy [1]
Paper Link
Authors: Donghoon Son, etc.
2017, IEEE International Conference on Robotics and Automation (ICRA)

1. 应用场景 Application scenario

(1) B-MASCE被冰包裹，并被吞咽。
(2) 在冰融化之后，B-MASCE能移动到胃中并且诊断。
(3) 如果一个病灶被发现，B-MASCE通过滚动运动移动到病灶的位置，并进行细针穿刺取样。
(4) 在完成所有工作之后，B-MASCE被一个细绳拉回。
(1) B-MASCE is capsuled by ice, and swallowed.
(2) After the ice melts, B-MASCE can move inside the stomach and diagnose.
(3) If a lesion is found, B-MASCE moves to the site of the lesion by rolling locomotion, and performs the fine-needle aspiration biopsy.
(4) After completing all the tasks, B-MASCE is retracted by a thin tether.

2. B-MASCE的操纵 Manipulation of B-MASCE

2.1 驱动系统描述 Actuation system description

B-MASCE被外部磁场操纵，所以控制磁场和磁场导数的一个精确方式是重要的。
B-MASCE is manipulated by the external magnetic field, so an accurate means of controlling the B-field and the gradient of the B-field is essential.

电磁铁被指定放在底部而传感器阵列被指定放在顶部。它们被分开足够的距离来防止磁传感器饱和。电磁铁的配置被优化来产生一个强的z方向的磁梯度，并且线圈被定在一个平面上来保证它们离传感器系统尽量远。来自OctoMag系统的设计框架被用于磁驱动系统的优化。但是，我们增加一个额外的线圈来产生一个更强的磁场和场梯度，并也允许冗余的使用为了最小化浪费的能量。在设计框架的应用中，我们已经改变了投射到非均匀磁场的磁映射和它的梯度映射，因为系统使用磁场的非均匀性。
The electromagnets are positioned at the bottom and the sensor arrays are positioned at the top. They are seperated by enough distance to prevent saturation of the magnetic sensors. The configuration of the electromagnet is optimized to generate a stronger z-directional magnetic gradient, and coils are located in a plane to keep them far enough away from the sensor system. A design framework from OctoMag system is used for the optimization of the magnetic actuation system. However, we added one additional coil to generate a stronger magnetic field an field gradient, and also to allow the use of redundancy for minimization of the wasted power. In the application of the design framework, we have changed the magnetic mapping into non-uniform magnetic fields and its gradient mapping, as the system uses the non-uniformity of the magnetic field.

2.2 控制理论 Control methods

由于每个线圈的磁场的叠加决定作用在B-MASCE的永磁铁上的净合力和力矩。互相靠近的多个铁芯产生耦合磁场。这是因为来自于一个电磁铁的磁场在其他核心中产生磁化场，在它自己线圈产生的原始磁化场之外。这些耦合影响应该要被考虑在我们的设置中。一个多核心系统的磁场和力映射在这儿被使用。
The superposition of the magnetic field due to each coil determines the net resultant force and torque on B-MASCE’s permanent magnet. The multiple ferrous cores that are close to each other generate coupled magnetic fields. This is because a magnetic field from an electromagnet becomes additional H-field in the other cores, besides the original H-field from its own coil. These coupling effects should be considered in our setup. The magnetic field and force map of a multiple-core system is used here.

多个电磁场的磁场和力的叠加被表达为如下矩阵形式：
The superposition of multiple electromagnets’ magnetic fields and forces are expressed in a matrix form as:

$$\left[\begin{array}{c}\mathbf{B}\\ \mathbf{F}\end{array}\right]=\mathbb{A}{\mathbb{D}}^{-1}\mathbb{M}\mathbf{I}$$

$\mathbb{A}=\frac{\mu }{4\pi }\left[\begin{array}{cc}\mathbb{I}& \mathbb{O}\\ \mathbb{O}& 3\mathbb{I}\end{array}\right]\left[\begin{array}{ccc}{\mathbb{P}}_1& \cdots & {\mathbb{P}}_9\\ {\mathbb{F}}_1& \cdots & {\mathbb{F}}_9\end{array}\right]$是驱动映射，将电磁铁的合磁矩投射到磁场合磁力上。
$\mathbb{A}=\frac{\mu }{4\pi }\left[\begin{array}{cc}\mathbb{I}& \mathbb{O}\\ \mathbb{O}& 3\mathbb{I}\end{array}\right]\left[\begin{array}{ccc}{\mathbb{P}}_1& \cdots & {\mathbb{P}}_9\\ {\mathbb{F}}_1& \cdots & {\mathbb{F}}_9\end{array}\right]$ is the actuation map which maps from the resultant magnetic moments of the electromagnets to the B field and magnetic force.

$\mathbb{D}=\left[\begin{array}{cccc}\mathbb{I}& -\frac{V_1}{4\pi }{\mathbb{N}}_1{\mathbb{P}}_{12}& -\frac{V_1}{4\pi }{\mathbb{N}}_1{\mathbb{P}}_{13}& \cdots \\ -\frac{V_2}{4\pi }{\mathbb{N}}_2{\mathbb{P}}_{21}& \mathbb{I}& -\frac{V_2}{4\pi }{\mathbb{N}}_2{\mathbb{P}}_{23}& \cdots \\ -\frac{V_3}{4\pi }{\mathbb{N}}_3{\mathbb{P}}_{31}& -\frac{V_3}{4\pi }{\mathbb{N}}_3{\mathbb{P}}_{32}& \mathbb{I}& \cdots \\ ⋮& ⋮& ⋮& \ddots \end{array}\right]$是磁耦合映射，将核心间的耦合效应编码，$V_i$是第i个核心的体积，${\mathbb{N}}_i$是第i个核心的3*3外易感性矩阵，${\mathbb{P}}_{ij}$是距离矩阵，$\mathbb{M}$是每个电磁铁的磁矩值。
$\mathbb{D}=\left[\begin{array}{cccc}\mathbb{I}& -\frac{V_1}{4\pi }{\mathbb{N}}_1{\mathbb{P}}_{12}& -\frac{V_1}{4\pi }{\mathbb{N}}_1{\mathbb{P}}_{13}& \cdots \\ -\frac{V_2}{4\pi }{\mathbb{N}}_2{\mathbb{P}}_{21}& \mathbb{I}& -\frac{V_2}{4\pi }{\mathbb{N}}_2{\mathbb{P}}_{23}& \cdots \\ -\frac{V_3}{4\pi }{\mathbb{N}}_3{\mathbb{P}}_{31}& -\frac{V_3}{4\pi }{\mathbb{N}}_3{\mathbb{P}}_{32}& \mathbb{I}& \cdots \\ ⋮& ⋮& ⋮& \ddots \end{array}\right]$ is the magnetic coupling map, which encodes the coupling effects among the cores, $V_i$ is the volume of the i-th core, ${\mathbb{N}}_i$ is the 3x3 external suspectibility matrix of the i-th core, ${\mathbb{P}}_{ij}$ is the distance matrix, $\mathbb{M}$ is about the magnetic moments of each electromagnets.

所需要的在每个线圈中的电流被获得通过使用伪逆：
The required current in each coil is achieved using pseudo-inverse:

$$\mathbf{I}=(\mathbb{A}{\mathbb{D}}^{-1}\mathbb{M}{)}^{†}\left[\begin{array}{c}\mathbf{B}\\ \mathbf{F}\end{array}\right]$$

我们应用和胶囊的期望朝向一样方向的磁场7mT，和0.015N力在机器人和基质之间给足够的牵引力用于滚动运动。
We applied $B=7mT$ with the same direction as the desired orientation of the capsule, and $F=0.015N$ to give enough traction between the robot and the substrate for rolling locomotion.

[1]: Son, Donghoon, Mustafa Doga Dogan, and Metin Sitti. “Magnetically actuated soft capsule endoscope for fine-needle aspiration biopsy.” 2017 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2017.