在提出对于旋转胶囊的旋转驱动方式之后，对于某一个位置上的胶囊，由无数种驱动器姿态可以驱动胶囊前进，也就是在胶囊所在的位置和期望前进方向产生一个与期望前进方向垂直的旋转磁场，这是没问题的。本文提出了一种优化驱动器位姿的方式，使胶囊能更好的更有效率的被驱动，文章考虑了在胶囊轴向和径向所受到的磁力和磁力矩的作用大小，建立和相关的模型，并定制为一个优化函数，利用遗传算法解出最优解，即为驱动器最优化位姿。
发现用于磁驱动胶囊内窥镜的基于遗传算法的优化驱动配置
Finding Optimal Actuation Configuration for Magnetically Driven Capsule Endoscopy Based on Genetic Algorithm [1]
Paper Link
Authors: Katayoun Madani, etc.
2016, Journal of Medical and Biological Engineering
把一个旋转磁铁考虑为一个磁场生成器，磁力和磁力矩能被用来同时推进。最优驱动磁铁位移在这篇文章中被讨论来管理磁吸力贡献在期望的移动方向，它缩短胶囊的移动时间。这问题被定制为一个优化问题并且一个基于磁力和磁力矩的拟合函数被展示。一个二进制遗传算法被使用来解出这个优化问题并且相对于外部永磁铁的胶囊的优化相对位置被找到。
Considering a rotating magnet as a magnetic field generator, magnetic force and torque can be used for propulsion at the same time. The optimal actuator magnet placement is discussed in this paper to manage the attractive magnetic force contribution along the desired movement direction, which shortens the capsule’s trave time. The problem is formulated as an optimization problem and a fitness function based on magnetic force and torque is presented. A binary genetic algorithm is used to solve the optimization problem and the optimal relative position of the capsule with respect to the external permanent magnet is found.
p = [ − p x ; 0 ; − p z ] \textbf{p}=[-p_{x};0;-p_{z}] p=[−px;0;−pz]
因此，有一个最优位置，导致在胶囊推进中吸引磁力和磁力矩的有效贡献。而且，注意 ∣ ∣ p z ∣ ∣ ||p_{z}|| ∣∣pz∣∣增加，轴向和径向力和力矩的大小减少，它是有利的当胶囊失去控制或者丢失与EPM同步的时候因为由大量的磁力引起的一个突然的大改变不会发生。通过选择确保一个安全驱动流程的 ∣ ∣ p z ∣ ∣ ||p_{z}|| ∣∣pz∣∣的一个恰当值， ∣ ∣ p x ∣ ∣ ||p_{x}|| ∣∣px∣∣的一个最优值能被发现，它导致了在胶囊移动在期望路径上的磁力和磁力矩的有效合作。
Therefore, there is an optimal position that leads to the effective contribution of the attractive magnetic force and torque in the capsule propulsion. Also, it is noted that as ∣ ∣ p z ∣ ∣ ||p_{z}|| ∣∣pz∣∣ increases, the magnitudes of axial and radial forces and torques decrease, which is beneficial when the capsule gets out of control or loses synchronization with the EPM because a sudden large change caused by a large mount of magentic force cannot happen. By choosing an appropriate value for ∣ ∣ p z ∣ ∣ || p_{z}|| ∣∣pz∣∣ that guarantees a safe actuation procedure, an optimal value for ∣ ∣ p x ∣ ∣ ||p_{x}|| ∣∣px∣∣ can be found that leads to effective coopration of magentic force and torque in capsule movement in its desired path.
优化问题可以被定制为基于磁力和磁力矩的径向和轴向分量。拟合函数能被定义为如下式子：
The optimization problem can be formulated basd on the radial and axial compoments of magnetic force and torque. The fitness function can be defined as follows:
f i t n e s s _ f u n c t i o n = α a x ⋅ f a x + α r a ⋅ ∣ ∣ f r a ∣ ∣ + β a x ⋅ τ a x + β r a ⋅ ∣ ∣ τ r a ∣ ∣ fitness\_function=\alpha_{ax}\cdot f_{ax}+\alpha_{ra}\cdot||f_{ra}||+\beta_{ax}\cdot\tau_{ax}+\beta_{ra}\cdot||\tau_{ra}|| fitness_function=αax⋅fax+αra⋅∣∣fra∣∣+βax⋅τax+βra⋅∣∣τra∣∣
f a x f_{ax} fax和 τ a x \tau_{ax} τax， f r a f_{ra} fra和 τ r a \tau_{ra} τra分是磁力和磁力矩的轴向分量，径向分量。 α a x \alpha_{ax} αax, α r a \alpha_{ra} αra, β a x \beta_{ax} βax和 β r a \beta_{ra} βra是四个不变协参数，它们分别决定轴向和径向磁力和轴向和径向最大磁力矩的影响。这些协参数被选择基于分量的重要性和它们对移动方向的影响。当轴向分量平行于期望运动方向时，它们对推进有一个直接正向影响，但是径向分量不能有任何正向印象，因此应该有小的值。
where f a x f_{ax} fax and τ a x \tau_{ax} τax are the axial components and f r a f_{ra} fra and τ r a \tau_{ra} τra are the radial components of magnetic force and torque, respectively. α a x \alpha_{ax} αax, α r a \alpha_{ra} αra, β a x \beta_{ax} βax and β r a \beta_{ra} βra are four constant coefficients that respectively determine the impacts of axial and radial magnetic force and axial and raidal maximum magnetic torque. These coefficients are selected based on the importance of components and their effect on movement direction. When the axial components are parallel to the desired movement direction, they have a direct positive impact on propulsion, but the radial components do not have any positive effect, and thus should have small values.
α a x \alpha_{ax} αax和 β a x \beta_{ax} βax被设定为2。 α r a \alpha_{ra} αra和 β r a \beta_{ra} βra被设定为-1。
α a x \alpha_{ax} αax and β a x \beta_{ax} βax are set to 2. α r a \alpha_{ra} αra and β r a \beta_{ra} βra are set to -1.
[1]: Madani, Katayoun, Sohrab Khanmohammadi, and Vahid Azimirad. “Finding Optimal Actuation Configuration for Magnetically Driven Capsule Endoscopy Based on Genetic Algorithm.” Journal of Medical and Biological Engineering 36.6 (2016): 776-787.