这篇文章发表在soft robotics上，作为robotics领域唯一的双一区journal（2018 中科院一区+JCR一区），现在是robotics领域中科院二区，中科院一区是Science Robotics和T-RO，非常有价值。本文提出了一种新的驱动方式和详细的设计介绍。让胶囊机器人有多种运动能力。

用于细针活检的磁驱动软体胶囊机器人
Magnetically actuated soft capsule robot for fine-needle biopsy [1]
Paper Link
Authors: Donghoon Son, etc.
2019, Soft robotics

目录 outline

摘要 abstract
1. 定位和驱动系统的设计和制造 design and fabrication of localizaiton and actuation system
2. 机器人控制运动 robot controlled motions
3. 磁场生成 magnetic field generation
4. 控制理论 control methods
- 4.1 开环朝向控制器 open-loop orientation controller
- 4.2 闭环 PI 控制器 Closed-loop PI controller
- 4.3 瘤锚定控制器 tumor anchoring controller
- 4.4 坍塌控制器 collapsing controller

摘要 abstract

为了改进用于粘膜下肿瘤/疾病的诊断准确度，我们提出一个磁驱动的软体机器胶囊机器人，它使用细针活检技术取得活检样本在一个胃的一块深度组织中。我们展示用于细针活检胶囊机器人的设计，控制和人机交互理论。
To improve their diagnostic accuracy for submucosal tumors / diseases, we propose a magnetically actuated soft robotic capsule robot, which takes biopsy samples in a deep tissue of a stomach using the fine-needle biopsy technique. We present the design, control and human-machine interfacing methods for the fine-needle biopsy capsule robot.

1. 定位和驱动系统的设计和制造 design and fabrication of localizaiton and actuation system

一个自定义的磁驱动和定位系统被设计并建立来表现运动为了机器人。系统的主要要求是有足够的工作空间（10厘米直径和5厘米深度），用于朝向控制的足够的力矩（10毫牛米），和用于坍塌运动的足够的力（0.6牛）。驱动系统有九个电磁线圈。驱动系统的配置与之前报告的磁驱动系统不同来容纳大的工作空间。配置被优化来最小化在定位系统的磁场并且产生一个强的磁场梯度指向线圈的一般方向。系统利用磁场的不均一性，在磁场中磁势能阱被简单地创造在工作区域中为了控制目的。
A custom magnetic actuation and localization system is designed and built to perform the motions for the robot. The main requirement of the system is to have enough working space (10 cm diameter and 5 cm depth), enough torque for the orientation control (10 mN⋅\cdot⋅M), and enough force for the collapsing motion (0.6N). The actuation system has 9 electromagnetic coils. The configuration of the actuation system is different from previously reported magnetic driving systems to accommodate the large working space. The configuration is optimized to minimize the magnetic field on the localization system and to generate a strong magnetic field gradient torwards the general direction of the coils. The system exploits nonuniformity of the magnetic field where the magnetic potential energy wells are easily created in the working space for the control purpose.

2. 机器人控制运动 robot controlled motions

机器人在胃中导航，使用滚动运动并控制朝向。对于活检来说，机器人锚定于一个SMT的顶点并且插入活检针在SMT组织中，使用多次坍塌动作。机器人的朝向被施加的一个特定磁场和它的梯度控制。通过设定在机器人上的侧边力为0并且最小化在2D上机器人周围的磁力的改变，作用于机器人的磁力的影响被最小化了。这使得机器人控制鲁棒对于2D侧边定位误差和机器人位置的快速改变。滚动运动是朝向控制的一个拓展。通过滚动胶囊期望朝向，机器人在胃的表面滚动并移动到其他的地方。机器人能容易地滑下瘤当一个下落力，比如重力，被施加。这是因为磁力矩不能被施加沿着磁矩的轴；因此，机器人会绕轴旋转并滑下瘤。这个问题能被处理通过在瘤的中心的2D侧位置创造一个相对强的磁能量。机器人执行这个动作（坍塌）在瘤锚定动作之后。
The robot navigates inside the stomach using rolling locomotion and controls the orientation. For biopsy, the robot anchors on top of a SMT and inserts the biopsy needle inside the SMT tissue using the collapsing motion several times. The robot’s orientation is controlled by applying a specific magnetic field and its gradient. By setting the lateral force on the robot as 0 and minimizing the change of magnetic force around the robot in 2D, the effect of the magnetic force on robot is minimized. This makes the robot control robust to the 2D lateral localization error and fast change of the position of the robot. The rolling locomotion is an extension of the orientation control. By rolling the desired orientation of the capsule, the robot rolls on the surface of the stomach and translates to another location. The robot can easily roll off the tumor when a downward force, such as the gravity, is applied. This is because the magnetic torque can not be applied along the axis of the magnetic moment; therefore, the robot can rotate about this axis and roll off the tumor. This problem is handled by creating a relatively strong magnetic energy well in 2D lateral position at the center of the tumor. The robot performs this motion (collapse) after the tumor anchoring motion.

3. 磁场生成 magnetic field generation

磁场和它的梯度通过单独线圈的贡献的叠加被生成。每个电磁铁的磁场被建模为一个磁极子。通过叠加磁场和梯度，我们能找到用于磁场，梯度和力的映射。磁场能被表达为：
The magnetic field and its gradient are generated by the superposition of individual coils’ contribution. The magnetic field of each electromagnet is modeled as a magnetic dipole. By superimposing the magnetic field and the gradient, we can find maps for magnetic field, gradient and force. The magnetic field could be expressed as:

b=B(r)I\textbf{b}=\mathbb{B}(\mathbf{r})\mathbf{I}b=B(r)I

磁场梯度能被描述为：
The magnetic field gradient is described as:

h=G(r)I\textbf{h}=\mathbb{G}(\mathbf{r})\mathbf{I}h=G(r)I

与其他映射相似，磁力能被表达为：
Same as the other mappings, the magnetic force is expressed as:

f=F(r,n^)I\textbf{f}=\mathbb{F}(\mathbf{r,\hat{n}})\mathbf{I}f=F(r,n^)I

I\mathbf{I}I是流荡在每个线圈上的电流。B\mathbb{B}B是磁场映射矩阵。G\mathbb{G}G是磁场导数映射。F\mathbb{F}F是力映射矩阵。n^\mathbf{\hat{n}}n^是朝向向量，它表示胶囊的头朝向。

4. 控制理论 control methods

胶囊机器人通过非均匀磁场被控制。线圈的被测稳定时间（有一个磁芯的存在）是0.1s。相对地，机器人的系统动态是快速的因为低质量和低惯性矩。因此，我们好好使用磁能量用于控制机器人，它展现了开环的稳定的行为。
有三种不同的控制器基于在robot controlled motions章节中展示的不同的运动。一个高等级比例积分控制器被使用通过反馈来闭上开环控制器。
The capsule robot is controlled by the non-uniform magnetic field. The measured settling time of the coil ( with the presence of a magnetic core ) was 0.1s. Relatively, the system dynamics of the robot is fast due to the low mass and low moment of inertia.Thus, we utilized the magnetic energy well for controlling the robot, which showed open-loop stable behaviors.
There are three different controllers based on the different motions presented in the robot controlled motions section above. A high-level PI controller is used to close the open-loop controllers with feedback.

4.1 开环朝向控制器 open-loop orientation controller

我们将控制分离为两个部分：用于重力消除的磁场和用于朝向控制的磁场。
We seperate the control in two parts: the magnetic field for gravity cancellation and the magnetic field for the orientation control.

被施加到倒立摆的重力通过一个静态磁场被消除。
The gravity applied to the inverted pendulum is cancelled by a static magentic field.

n^L×mg+Mn^×bc=0→bc=−mgM\mathbf{\hat{n}} L \times m \mathbf{g} + M \mathbf{\hat{n}} \times \mathbf{b}_{c} = 0 \rightarrow \mathbf{b}_{c} = -\frac{m \mathbf{g}}{M}n^L×mg+Mn^×bc=0→bc=−Mmg

L是从枢纽点到质量中心的距离。通过分离重力的影响，调节机器人朝向的磁场，就简单是与所需方向相同方向的B场。用于朝向调整的B场是：
By seperating the effect of the gravity, the magnetic field, which regulates the orientation of the robot, is simply the B-field at the same direction as the desired orientation. The B-field for the orientation regulation is:

b0=cn^d\mathbf{b}_{0} = c \mathbf{\hat{n}_{d}}b0=cn^d

在胃的横向方向上的力被设置为零来稳定当前位置的机器人。磁能阱的深度应设置为最小，因为创建强磁能阱总是会试图将机器人吸引到当前点并干扰向另一个方向的移动。
The force at the lateral direction of the stomach is set to zero to stabilize at the current position of the robot. The depth of the magnetic energy well is set to be the minimum, as creating a strong magnetic energy well always try to attract the robot to the current point and disturbs moving toward the other direction.

以上准测被列为一个在线优化问题：
Above criteria are formulated as an online optimization problem as：

arg⁡min⁡Iα∣I∣+βΣsubjecttob=bc+bo,fx,y=0.\begin{aligned} \arg\min_{\mathbf{I}} \ \ \ \ &\alpha |\mathbf{I}| + \beta \Sigma \\ subject\ to\ \ \ \ &\mathbf{b}=\mathbf{b}_{c}+\mathbf{b}_{o},\\ &\mathbf{f}_{x,y}=0. \\ \end{aligned}argImin subject to α∣I∣+βΣb=bc+bo,fx,y=0.

Σ\SigmaΣ是磁能陷阱的最大绝对曲率。这个值被计算为：
Σ\SigmaΣ is the maximum absolute curvature of the magnetic energy well. This value is calculated as:

Σ=max(svd(H(Em)))\Sigma=max(svd(H(E_{m})))Σ=max(svd(H(Em)))

Em=−Mn^⋅bE_{m}=-M \mathbf{\hat{n}} \cdot \mathbf{b}Em=−Mn^⋅b是磁标量势能。
where Em=−Mn^⋅bE_{m}=-M \mathbf{\hat{n}} \cdot \mathbf{b}Em=−Mn^⋅b is the magnetic scalar potential energy.

4.2 闭环 PI 控制器 Closed-loop PI controller

以上讨论的开环控制器被高阶PI控制器闭环。控制器生成输出，它是开环控制器的控制输入。在参考朝向n^ref\mathbf{\hat{n}_{ref}}n^ref和当前朝向n^\mathbf{\hat{n}}n^之间的误差被定义为一个叉乘：

e=n^×n^ref\mathbf{e}=\mathbf{\hat{n}} \times \mathbf{\hat{n}_{ref}}e=n^×n^ref

这暗示了从当前状态到参考状态我们错过了多少旋转，作为一个角轴法表示。然后，PI控制器输入能被线性定义为：

upi=Kpe+Ki∫edt\mathbf{u}_{pi} = K_{p}\mathbf{e} + K_{i} \int \mathbf{e} dtupi=Kpe+Ki∫edt

upi\mathbf{u}_{pi}upi能被转化为3D旋转 RRR。然后，最终控制输入在高等级控制器形如：

n^d=Rn^ref\mathbf{\hat{n}_{d}} = R\ \mathbf{\hat{n}_{ref}}n^d=R n^ref

值n^d\mathbf{\hat{n}_{d}}n^d被连接到低等级控制器。
This value n^d\mathbf{\hat{n}_{d}}n^d would be connectted with the low-level controller.

4.3 瘤锚定控制器 tumor anchoring controller

瘤锚定控制器与朝向控制器相似。然而，它需要一个条件，机器人不应该滚下凹形几何体。这能被防止通过创建一个相对较强的磁陷在瘤的位置，在这个位置上磁力尝试来推机器人到瘤上同时磁力不足够来压塌机器人。
The tumor anchoring controller is similar to the orientation controller. However, it needs a condition that the robot should not roll off a concave geometry. This could be prevented by creating a relatively strong magnetic well at the location of the tumor, where the magnetic force tries to push the robot toward the tumor while the magnetic force is not enough to collapse the robot.

这样的控制被列为一个在线优化问题：
This control is formulated as an online optimization problem:

arg⁡min⁡Imin(eig(H(−Em)))subjecttob=bc+bo,fx,y,{L}=0,fz,{L}>fmin.\begin{aligned} \arg\min_{\mathbf{I}} \ \ \ \ &min(eig(H(-E_{m}))) \\ subject\ to\ \ \ \ &\mathbf{b}=\mathbf{b}_{c}+\mathbf{b}_{o},\\ &\mathbf{f}_{x,y,\{L\}}=0,\\ &\mathbf{f}_{z,\{L\}}>f_{min}. \\ \end{aligned}argImin subject to min(eig(H(−Em)))b=bc+bo,fx,y,{L}=0,fz,{L}>fmin.

min(eig(H(−Em)))min(eig(H(-E_{m})))min(eig(H(−Em)))是磁能陷阱的最小曲率，fx,y,{L}\mathbf{f}_{x,y,\{L\}}fx,y,{L}是在本地坐标系下的磁力，有个z轴对齐机器人的长轴，fz,{L}\mathbf{f}_{z,\{L\}}fz,{L}是z轴方向的磁力，同时fminf_{min}fmin是不压塌机器人的向下最小力（-0.4N）。

4.4 坍塌控制器 collapsing controller

坍塌运动以一种不同的方式被控制而不是上面这些其他的控制器。这是因为一个强磁力需要被施加到机器人上为了坍塌和针渗透。同时，一个强稳定磁力矩应该被施加到机器人来防止由强力引发的不稳定。没有稳定力矩的话，机器人能滑落到一边，不会导致机器人的坍塌。强力力和力矩的生成需要一个强力磁场和梯度。为了压塌机器人需要产生足够的力（-0.6N）。
The collapsing motion is controlled in a different manner than the other controllers above. This is because a strong magnetic force needs to be applied to the robot for collapse and needle penetration. Concurrently, a strong stabilizing magnetic torque should be applied to the robot to prevent the instability caused by the strong force. Without the stabilizing torque, the robot can fall down to the side, not resulting in the collapse of the robot. The generation of the strong force and torque requires a strong magnetic field and gradient. To generate enough force (-0.6 N) to collapse the robot.

这被列为另一个优化问题：
Thisis formulated as another optimization problem:

arg⁡min⁡Iγfz,{L}−δ(min(H(−Em)))subjecttobx,y,{L}=0,bz,{L}>bth,fmax>fz,{L}>fmin.\begin{aligned} \arg\min_{\mathbf{I}} \ \ \ \ &\gamma\ \mathbf{f}_{z,\{L\}} - \delta(min(H(-E_{m}))) \\ subject\ to\ \ \ \ &\mathbf{b}_{x,y,\{L\}}=0,\\ &\mathbf{b}_{z,\{L\}}>b_{th},\\ &f_{max}>\mathbf{f}_{z,\{L\}}>f_{min}. \\ \end{aligned}argImin subject to γ fz,{L}−δ(min(H(−Em)))bx,y,{L}=0,bz,{L}>bth,fmax>fz,{L}>fmin.

这儿γ\gammaγ和δ\deltaδ是可微调的在磁力和磁能井曲率之间增益。
where γ\gammaγ and δ\deltaδ are tunable gains between the magnetic force and the curvature of the magnetic energy well.

[1]: Son, Donghoon, Hunter Gilbert, and Metin Sitti. “Magnetically Actuated Soft Capsule Endoscope for Fine-Needle Biopsy.” Soft robotics (2019).

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Magnetically actuated soft capsule robot for fine-needle biopsy